[
  {
    "id": 1,
    "number": 1,
    "sequence_number": 1,
    "title": "Contains Duplicate",
    "slug": "contains-duplicate-optimization",
    "difficulty": "Easy",
    "topic": "Arrays",
    "subtopic": "Hashing & Array Optimization",
    "pattern": "Hashing & Array Optimization",
    "secondary_patterns": [
      "Hashing & Array Optimization"
    ],
    "stage": "Arrays & Hashing Foundations",
    "curriculumStage": "Stage 1 — Arrays & Hashing Foundations",
    "roadmapPhase": "Stage 1 — Arrays & Hashing Foundations",
    "phase": "Stage 1 — Arrays & Hashing Foundations",
    "estimatedTime": 15,
    "statement": "Solve the **Contains Duplicate Optimization** problem using the **Hashing & Array Optimization** technique. Given input constraints appropriate for Easy level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^4",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Hashing & Array Optimization identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Hashing & Array Optimization. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Hashing & Array Optimization techniques by solving Easy problem constraints for Contains Duplicate Optimization.",
    "whyThisPattern": "When observing arrays & strings problem conditions, Hashing & Array Optimization optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Apple",
      "Adobe",
      "Atlassian"
    ],
    "companyRelevanceTier": "Medium",
    "leetcode_url": "https://leetcode.com/problems/contains-duplicate/",
    "leetcode_title": "Contains Duplicate",
    "leetcode_id": 217,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/contains-duplicate/",
    "canonicalSlug": "contains-duplicate-optimization",
    "canonicalUrl": "https://leetcode.com/problems/contains-duplicate/",
    "url": "https://leetcode.com/problems/contains-duplicate/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Contains Duplicate Optimization (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Contains Duplicate Optimization (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Contains Duplicate Optimization (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Contains Duplicate Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Contains Duplicate Optimization (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Contains Duplicate Optimization (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Contains Duplicate Optimization (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Contains Duplicate Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Contains Duplicate",
      "cpp_optimal": "// Solution for Contains Duplicate",
      "java_brute": "// Solution for Contains Duplicate",
      "java_optimal": "// Solution for Contains Duplicate",
      "python_brute": "# Solution for Contains Duplicate",
      "python_optimal": "# Solution for Contains Duplicate"
    }
  },
  {
    "id": 2,
    "number": 2,
    "sequence_number": 2,
    "title": "Remove Element",
    "slug": "remove-element-challenge",
    "difficulty": "Easy",
    "topic": "Arrays",
    "subtopic": "Hashing & Array Optimization",
    "pattern": "Hashing & Array Optimization",
    "secondary_patterns": [
      "Hashing & Array Optimization"
    ],
    "stage": "Arrays & Hashing Foundations",
    "curriculumStage": "Stage 1 — Arrays & Hashing Foundations",
    "roadmapPhase": "Stage 1 — Arrays & Hashing Foundations",
    "phase": "Stage 1 — Arrays & Hashing Foundations",
    "estimatedTime": 15,
    "statement": "Solve the **Remove Element Challenge** problem using the **Hashing & Array Optimization** technique. Given input constraints appropriate for Easy level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^4",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Hashing & Array Optimization identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Hashing & Array Optimization. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Hashing & Array Optimization techniques by solving Easy problem constraints for Remove Element Challenge.",
    "whyThisPattern": "When observing arrays & strings problem conditions, Hashing & Array Optimization optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Microsoft",
      "Bloomberg"
    ],
    "companyRelevanceTier": "Medium",
    "leetcode_url": "https://leetcode.com/problems/remove-element/",
    "leetcode_title": "Remove Element",
    "leetcode_id": 27,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/remove-element/",
    "canonicalSlug": "remove-element-challenge",
    "canonicalUrl": "https://leetcode.com/problems/remove-element/",
    "url": "https://leetcode.com/problems/remove-element/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Remove Element Challenge (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Remove Element Challenge (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Remove Element Challenge (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Remove Element Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Remove Element Challenge (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Remove Element Challenge (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Remove Element Challenge (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Remove Element Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Remove Element",
      "cpp_optimal": "// Solution for Remove Element",
      "java_brute": "// Solution for Remove Element",
      "java_optimal": "// Solution for Remove Element",
      "python_brute": "# Solution for Remove Element",
      "python_optimal": "# Solution for Remove Element"
    }
  },
  {
    "id": 3,
    "number": 3,
    "sequence_number": 3,
    "title": "Contains Duplicate II",
    "slug": "contains-duplicate-ii-optimization",
    "difficulty": "Easy",
    "topic": "Arrays",
    "subtopic": "Hashing & Array Optimization",
    "pattern": "Hashing & Array Optimization",
    "secondary_patterns": [
      "Hashing & Array Optimization"
    ],
    "stage": "Arrays & Hashing Foundations",
    "curriculumStage": "Stage 1 — Arrays & Hashing Foundations",
    "roadmapPhase": "Stage 1 — Arrays & Hashing Foundations",
    "phase": "Stage 1 — Arrays & Hashing Foundations",
    "estimatedTime": 15,
    "statement": "Solve the **Contains Duplicate II Optimization** problem using the **Hashing & Array Optimization** technique. Given input constraints appropriate for Easy level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^4",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Hashing & Array Optimization identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Hashing & Array Optimization. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Hashing & Array Optimization techniques by solving Easy problem constraints for Contains Duplicate II Optimization.",
    "whyThisPattern": "When observing arrays & strings problem conditions, Hashing & Array Optimization optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "LinkedIn",
      "Amazon"
    ],
    "companyRelevanceTier": "Medium",
    "leetcode_url": "https://leetcode.com/problems/contains-duplicate-ii/",
    "leetcode_title": "Contains Duplicate II",
    "leetcode_id": 219,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/contains-duplicate-ii/",
    "canonicalSlug": "contains-duplicate-ii-optimization",
    "canonicalUrl": "https://leetcode.com/problems/contains-duplicate-ii/",
    "url": "https://leetcode.com/problems/contains-duplicate-ii/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Contains Duplicate II Optimization (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Contains Duplicate II Optimization (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Contains Duplicate II Optimization (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Contains Duplicate II Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Contains Duplicate II Optimization (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Contains Duplicate II Optimization (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Contains Duplicate II Optimization (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Contains Duplicate II Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Contains Duplicate II",
      "cpp_optimal": "// Solution for Contains Duplicate II",
      "java_brute": "// Solution for Contains Duplicate II",
      "java_optimal": "// Solution for Contains Duplicate II",
      "python_brute": "# Solution for Contains Duplicate II",
      "python_optimal": "# Solution for Contains Duplicate II"
    }
  },
  {
    "id": 4,
    "number": 4,
    "sequence_number": 4,
    "title": "Two Sum",
    "slug": "two-sum-challenge",
    "difficulty": "Easy",
    "topic": "Arrays",
    "subtopic": "Two Pointers",
    "pattern": "Two Pointers",
    "secondary_patterns": [
      "Two Pointers"
    ],
    "stage": "Arrays & Hashing Foundations",
    "curriculumStage": "Stage 1 — Arrays & Hashing Foundations",
    "roadmapPhase": "Stage 1 — Arrays & Hashing Foundations",
    "phase": "Stage 1 — Arrays & Hashing Foundations",
    "estimatedTime": 15,
    "statement": "Solve the **Two Sum Challenge** problem using the **Two Pointers** technique. Given input constraints appropriate for Easy level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^4",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Two Pointers identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Two Pointers. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Two Pointers techniques by solving Easy problem constraints for Two Sum Challenge.",
    "whyThisPattern": "When observing arrays & strings problem conditions, Two Pointers optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(1)",
    "companyRelevance": [
      "Amazon",
      "Microsoft",
      "Uber"
    ],
    "companyRelevanceTier": "Medium",
    "leetcode_url": "https://leetcode.com/problems/two-sum/",
    "leetcode_title": "Two Sum",
    "leetcode_id": 1,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/two-sum/",
    "canonicalSlug": "two-sum-challenge",
    "canonicalUrl": "https://leetcode.com/problems/two-sum/",
    "url": "https://leetcode.com/problems/two-sum/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Two Sum Challenge (Two Pointers)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Two Sum Challenge (Two Pointers)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Two Sum Challenge (Two Pointers)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Two Sum Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Two Sum Challenge (Two Pointers)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Two Sum Challenge (Two Pointers)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Two Sum Challenge (Two Pointers)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Two Sum Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Two Sum",
      "cpp_optimal": "// Solution for Two Sum",
      "java_brute": "// Solution for Two Sum",
      "java_optimal": "// Solution for Two Sum",
      "python_brute": "# Solution for Two Sum",
      "python_optimal": "# Solution for Two Sum"
    }
  },
  {
    "id": 5,
    "number": 5,
    "sequence_number": 5,
    "title": "Plus One",
    "slug": "plus-one-optimization",
    "difficulty": "Easy",
    "topic": "Arrays",
    "subtopic": "Hashing & Array Optimization",
    "pattern": "Hashing & Array Optimization",
    "secondary_patterns": [
      "Hashing & Array Optimization"
    ],
    "stage": "Arrays & Hashing Foundations",
    "curriculumStage": "Stage 1 — Arrays & Hashing Foundations",
    "roadmapPhase": "Stage 1 — Arrays & Hashing Foundations",
    "phase": "Stage 1 — Arrays & Hashing Foundations",
    "estimatedTime": 15,
    "statement": "Solve the **Plus One Optimization** problem using the **Hashing & Array Optimization** technique. Given input constraints appropriate for Easy level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^4",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Hashing & Array Optimization identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Hashing & Array Optimization. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Hashing & Array Optimization techniques by solving Easy problem constraints for Plus One Optimization.",
    "whyThisPattern": "When observing arrays & strings problem conditions, Hashing & Array Optimization optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Meta",
      "Apple",
      "Netflix"
    ],
    "companyRelevanceTier": "Medium",
    "leetcode_url": "https://leetcode.com/problems/plus-one/",
    "leetcode_title": "Plus One",
    "leetcode_id": 66,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/plus-one/",
    "canonicalSlug": "plus-one-optimization",
    "canonicalUrl": "https://leetcode.com/problems/plus-one/",
    "url": "https://leetcode.com/problems/plus-one/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Plus One Optimization (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Plus One Optimization (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Plus One Optimization (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Plus One Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Plus One Optimization (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Plus One Optimization (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Plus One Optimization (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Plus One Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Plus One",
      "cpp_optimal": "// Solution for Plus One",
      "java_brute": "// Solution for Plus One",
      "java_optimal": "// Solution for Plus One",
      "python_brute": "# Solution for Plus One",
      "python_optimal": "# Solution for Plus One"
    }
  },
  {
    "id": 6,
    "number": 6,
    "sequence_number": 6,
    "title": "Remove Duplicates from Sorted Array",
    "slug": "remove-duplicates-from-sorted-array-optimization",
    "difficulty": "Easy",
    "topic": "Arrays",
    "subtopic": "Two Pointers",
    "pattern": "Two Pointers",
    "secondary_patterns": [
      "Two Pointers"
    ],
    "stage": "Arrays & Hashing Foundations",
    "curriculumStage": "Stage 1 — Arrays & Hashing Foundations",
    "roadmapPhase": "Stage 1 — Arrays & Hashing Foundations",
    "phase": "Stage 1 — Arrays & Hashing Foundations",
    "estimatedTime": 15,
    "statement": "Solve the **Remove Duplicates from Sorted Array Optimization** problem using the **Two Pointers** technique. Given input constraints appropriate for Easy level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^4",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Two Pointers identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Two Pointers. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Two Pointers techniques by solving Easy problem constraints for Remove Duplicates from Sorted Array Optimization.",
    "whyThisPattern": "When observing arrays & strings problem conditions, Two Pointers optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(1)",
    "companyRelevance": [
      "Google",
      "LinkedIn",
      "Amazon"
    ],
    "companyRelevanceTier": "Medium",
    "leetcode_url": "https://leetcode.com/problems/remove-duplicates-from-sorted-array/",
    "leetcode_title": "Remove Duplicates from Sorted Array",
    "leetcode_id": 26,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/remove-duplicates-from-sorted-array/",
    "canonicalSlug": "remove-duplicates-from-sorted-array-optimization",
    "canonicalUrl": "https://leetcode.com/problems/remove-duplicates-from-sorted-array/",
    "url": "https://leetcode.com/problems/remove-duplicates-from-sorted-array/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Remove Duplicates from Sorted Array Optimization (Two Pointers)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Remove Duplicates from Sorted Array Optimization (Two Pointers)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Remove Duplicates from Sorted Array Optimization (Two Pointers)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Remove Duplicates from Sorted Array Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Remove Duplicates from Sorted Array Optimization (Two Pointers)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Remove Duplicates from Sorted Array Optimization (Two Pointers)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Remove Duplicates from Sorted Array Optimization (Two Pointers)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Remove Duplicates from Sorted Array Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Remove Duplicates from Sorted Array",
      "cpp_optimal": "// Solution for Remove Duplicates from Sorted Array",
      "java_brute": "// Solution for Remove Duplicates from Sorted Array",
      "java_optimal": "// Solution for Remove Duplicates from Sorted Array",
      "python_brute": "# Solution for Remove Duplicates from Sorted Array",
      "python_optimal": "# Solution for Remove Duplicates from Sorted Array"
    }
  },
  {
    "id": 7,
    "number": 7,
    "sequence_number": 7,
    "title": "Pascal's Triangle",
    "slug": "pascal-s-triangle-challenge",
    "difficulty": "Easy",
    "topic": "Arrays",
    "subtopic": "Hashing & Array Optimization",
    "pattern": "Hashing & Array Optimization",
    "secondary_patterns": [
      "Hashing & Array Optimization"
    ],
    "stage": "Arrays & Hashing Foundations",
    "curriculumStage": "Stage 1 — Arrays & Hashing Foundations",
    "roadmapPhase": "Stage 1 — Arrays & Hashing Foundations",
    "phase": "Stage 1 — Arrays & Hashing Foundations",
    "estimatedTime": 15,
    "statement": "Solve the **Pascal's Triangle Challenge** problem using the **Hashing & Array Optimization** technique. Given input constraints appropriate for Easy level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^4",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Hashing & Array Optimization identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Hashing & Array Optimization. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Hashing & Array Optimization techniques by solving Easy problem constraints for Pascal's Triangle Challenge.",
    "whyThisPattern": "When observing arrays & strings problem conditions, Hashing & Array Optimization optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Meta",
      "Uber",
      "Databricks"
    ],
    "companyRelevanceTier": "Medium",
    "leetcode_url": "https://leetcode.com/problems/pascals-triangle/",
    "leetcode_title": "Pascal's Triangle",
    "leetcode_id": 118,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/pascals-triangle/",
    "canonicalSlug": "pascal-s-triangle-challenge",
    "canonicalUrl": "https://leetcode.com/problems/pascals-triangle/",
    "url": "https://leetcode.com/problems/pascals-triangle/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Pascal's Triangle Challenge (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Pascal's Triangle Challenge (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Pascal's Triangle Challenge (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Pascal's Triangle Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Pascal's Triangle Challenge (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Pascal's Triangle Challenge (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Pascal's Triangle Challenge (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Pascal's Triangle Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Pascal's Triangle",
      "cpp_optimal": "// Solution for Pascal's Triangle",
      "java_brute": "// Solution for Pascal's Triangle",
      "java_optimal": "// Solution for Pascal's Triangle",
      "python_brute": "# Solution for Pascal's Triangle",
      "python_optimal": "# Solution for Pascal's Triangle"
    }
  },
  {
    "id": 8,
    "number": 8,
    "sequence_number": 8,
    "title": "Pascal's Triangle II",
    "slug": "pascal-s-triangle-ii-optimization",
    "difficulty": "Easy",
    "topic": "Arrays",
    "subtopic": "Hashing & Array Optimization",
    "pattern": "Hashing & Array Optimization",
    "secondary_patterns": [
      "Hashing & Array Optimization"
    ],
    "stage": "Arrays & Hashing Foundations",
    "curriculumStage": "Stage 1 — Arrays & Hashing Foundations",
    "roadmapPhase": "Stage 1 — Arrays & Hashing Foundations",
    "phase": "Stage 1 — Arrays & Hashing Foundations",
    "estimatedTime": 15,
    "statement": "Solve the **Pascal's Triangle II Optimization** problem using the **Hashing & Array Optimization** technique. Given input constraints appropriate for Easy level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^4",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Hashing & Array Optimization identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Hashing & Array Optimization. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Hashing & Array Optimization techniques by solving Easy problem constraints for Pascal's Triangle II Optimization.",
    "whyThisPattern": "When observing arrays & strings problem conditions, Hashing & Array Optimization optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "LinkedIn",
      "Amazon"
    ],
    "companyRelevanceTier": "Medium",
    "leetcode_url": "https://leetcode.com/problems/pascals-triangle-ii/",
    "leetcode_title": "Pascal's Triangle II",
    "leetcode_id": 119,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/pascals-triangle-ii/",
    "canonicalSlug": "pascal-s-triangle-ii-optimization",
    "canonicalUrl": "https://leetcode.com/problems/pascals-triangle-ii/",
    "url": "https://leetcode.com/problems/pascals-triangle-ii/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Pascal's Triangle II Optimization (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Pascal's Triangle II Optimization (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Pascal's Triangle II Optimization (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Pascal's Triangle II Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Pascal's Triangle II Optimization (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Pascal's Triangle II Optimization (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Pascal's Triangle II Optimization (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Pascal's Triangle II Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Pascal's Triangle II",
      "cpp_optimal": "// Solution for Pascal's Triangle II",
      "java_brute": "// Solution for Pascal's Triangle II",
      "java_optimal": "// Solution for Pascal's Triangle II",
      "python_brute": "# Solution for Pascal's Triangle II",
      "python_optimal": "# Solution for Pascal's Triangle II"
    }
  },
  {
    "id": 9,
    "number": 9,
    "sequence_number": 9,
    "title": "Best Time to Buy and Sell Stock",
    "slug": "best-time-to-buy-and-sell-stock-optimization",
    "difficulty": "Easy",
    "topic": "Arrays",
    "subtopic": "Hashing & Array Optimization",
    "pattern": "Hashing & Array Optimization",
    "secondary_patterns": [
      "Hashing & Array Optimization"
    ],
    "stage": "Arrays & Hashing Foundations",
    "curriculumStage": "Stage 1 — Arrays & Hashing Foundations",
    "roadmapPhase": "Stage 1 — Arrays & Hashing Foundations",
    "phase": "Stage 1 — Arrays & Hashing Foundations",
    "estimatedTime": 15,
    "statement": "Solve the **Best Time to Buy and Sell Stock Optimization** problem using the **Hashing & Array Optimization** technique. Given input constraints appropriate for Easy level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^4",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Hashing & Array Optimization identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Hashing & Array Optimization. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Hashing & Array Optimization techniques by solving Easy problem constraints for Best Time to Buy and Sell Stock Optimization.",
    "whyThisPattern": "When observing arrays & strings problem conditions, Hashing & Array Optimization optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta"
    ],
    "companyRelevanceTier": "Medium",
    "leetcode_url": "https://leetcode.com/problems/best-time-to-buy-and-sell-stock/",
    "leetcode_title": "Best Time to Buy and Sell Stock",
    "leetcode_id": 121,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/best-time-to-buy-and-sell-stock/",
    "canonicalSlug": "best-time-to-buy-and-sell-stock-optimization",
    "canonicalUrl": "https://leetcode.com/problems/best-time-to-buy-and-sell-stock/",
    "url": "https://leetcode.com/problems/best-time-to-buy-and-sell-stock/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Best Time to Buy and Sell Stock Optimization (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Best Time to Buy and Sell Stock Optimization (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Best Time to Buy and Sell Stock Optimization (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Best Time to Buy and Sell Stock Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Best Time to Buy and Sell Stock Optimization (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Best Time to Buy and Sell Stock Optimization (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Best Time to Buy and Sell Stock Optimization (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Best Time to Buy and Sell Stock Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Best Time to Buy and Sell Stock",
      "cpp_optimal": "// Solution for Best Time to Buy and Sell Stock",
      "java_brute": "// Solution for Best Time to Buy and Sell Stock",
      "java_optimal": "// Solution for Best Time to Buy and Sell Stock",
      "python_brute": "# Solution for Best Time to Buy and Sell Stock",
      "python_optimal": "# Solution for Best Time to Buy and Sell Stock"
    }
  },
  {
    "id": 10,
    "number": 10,
    "sequence_number": 10,
    "title": "Majority Element",
    "slug": "majority-element-optimization",
    "difficulty": "Easy",
    "topic": "Arrays",
    "subtopic": "Hashing & Array Optimization",
    "pattern": "Hashing & Array Optimization",
    "secondary_patterns": [
      "Hashing & Array Optimization"
    ],
    "stage": "Arrays & Hashing Foundations",
    "curriculumStage": "Stage 1 — Arrays & Hashing Foundations",
    "roadmapPhase": "Stage 1 — Arrays & Hashing Foundations",
    "phase": "Stage 1 — Arrays & Hashing Foundations",
    "estimatedTime": 15,
    "statement": "Solve the **Majority Element Optimization** problem using the **Hashing & Array Optimization** technique. Given input constraints appropriate for Easy level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^4",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Hashing & Array Optimization identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Hashing & Array Optimization. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Hashing & Array Optimization techniques by solving Easy problem constraints for Majority Element Optimization.",
    "whyThisPattern": "When observing arrays & strings problem conditions, Hashing & Array Optimization optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Apple",
      "Adobe",
      "Atlassian"
    ],
    "companyRelevanceTier": "Medium",
    "leetcode_url": "https://leetcode.com/problems/majority-element/",
    "leetcode_title": "Majority Element",
    "leetcode_id": 169,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/majority-element/",
    "canonicalSlug": "majority-element-optimization",
    "canonicalUrl": "https://leetcode.com/problems/majority-element/",
    "url": "https://leetcode.com/problems/majority-element/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Majority Element Optimization (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Majority Element Optimization (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Majority Element Optimization (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Majority Element Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Majority Element Optimization (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Majority Element Optimization (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Majority Element Optimization (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Majority Element Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Majority Element",
      "cpp_optimal": "// Solution for Majority Element",
      "java_brute": "// Solution for Majority Element",
      "java_optimal": "// Solution for Majority Element",
      "python_brute": "# Solution for Majority Element",
      "python_optimal": "# Solution for Majority Element"
    }
  },
  {
    "id": 11,
    "number": 11,
    "sequence_number": 11,
    "title": "Range Sum Query 2D - Immutable",
    "slug": "range-sum-query-2d-immutable-optimization",
    "difficulty": "Medium",
    "topic": "Prefix Sum",
    "subtopic": "Hashing & Array Optimization",
    "pattern": "Hashing & Array Optimization",
    "secondary_patterns": [
      "Hashing & Array Optimization"
    ],
    "stage": "Arrays & Hashing Foundations",
    "curriculumStage": "Stage 1 — Arrays & Hashing Foundations",
    "roadmapPhase": "Stage 1 — Arrays & Hashing Foundations",
    "phase": "Stage 1 — Arrays & Hashing Foundations",
    "estimatedTime": 30,
    "statement": "Solve the **Range Sum Query 2D - Immutable Optimization** problem using the **Hashing & Array Optimization** technique. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Hashing & Array Optimization identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Hashing & Array Optimization. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Hashing & Array Optimization techniques by solving Medium problem constraints for Range Sum Query 2D - Immutable Optimization.",
    "whyThisPattern": "When observing arrays & strings problem conditions, Hashing & Array Optimization optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Meta",
      "Apple",
      "Netflix"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/range-sum-query-2d-immutable/",
    "leetcode_title": "Range Sum Query 2D - Immutable",
    "leetcode_id": 304,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/range-sum-query-2d-immutable/",
    "canonicalSlug": "range-sum-query-2d-immutable-optimization",
    "canonicalUrl": "https://leetcode.com/problems/range-sum-query-2d-immutable/",
    "url": "https://leetcode.com/problems/range-sum-query-2d-immutable/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Range Sum Query 2D - Immutable Optimization (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Range Sum Query 2D - Immutable Optimization (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Range Sum Query 2D - Immutable Optimization (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Range Sum Query 2D - Immutable Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Range Sum Query 2D - Immutable Optimization (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Range Sum Query 2D - Immutable Optimization (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Range Sum Query 2D - Immutable Optimization (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Range Sum Query 2D - Immutable Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Range Sum Query 2D - Immutable",
      "cpp_optimal": "// Solution for Range Sum Query 2D - Immutable",
      "java_brute": "// Solution for Range Sum Query 2D - Immutable",
      "java_optimal": "// Solution for Range Sum Query 2D - Immutable",
      "python_brute": "# Solution for Range Sum Query 2D - Immutable",
      "python_optimal": "# Solution for Range Sum Query 2D - Immutable"
    }
  },
  {
    "id": 12,
    "number": 12,
    "sequence_number": 12,
    "title": "Range Sum Query - Mutable",
    "slug": "range-sum-query-mutable-optimization",
    "difficulty": "Medium",
    "topic": "Prefix Sum",
    "subtopic": "Hashing & Array Optimization",
    "pattern": "Hashing & Array Optimization",
    "secondary_patterns": [
      "Hashing & Array Optimization"
    ],
    "stage": "Arrays & Hashing Foundations",
    "curriculumStage": "Stage 1 — Arrays & Hashing Foundations",
    "roadmapPhase": "Stage 1 — Arrays & Hashing Foundations",
    "phase": "Stage 1 — Arrays & Hashing Foundations",
    "estimatedTime": 30,
    "statement": "Solve the **Range Sum Query - Mutable Optimization** problem using the **Hashing & Array Optimization** technique. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Hashing & Array Optimization identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Hashing & Array Optimization. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Hashing & Array Optimization techniques by solving Medium problem constraints for Range Sum Query - Mutable Optimization.",
    "whyThisPattern": "When observing arrays & strings problem conditions, Hashing & Array Optimization optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Apple",
      "Adobe",
      "Atlassian"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/range-sum-query-mutable/",
    "leetcode_title": "Range Sum Query - Mutable",
    "leetcode_id": 307,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/range-sum-query-mutable/",
    "canonicalSlug": "range-sum-query-mutable-optimization",
    "canonicalUrl": "https://leetcode.com/problems/range-sum-query-mutable/",
    "url": "https://leetcode.com/problems/range-sum-query-mutable/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Range Sum Query - Mutable Optimization (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Range Sum Query - Mutable Optimization (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Range Sum Query - Mutable Optimization (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Range Sum Query - Mutable Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Range Sum Query - Mutable Optimization (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Range Sum Query - Mutable Optimization (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Range Sum Query - Mutable Optimization (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Range Sum Query - Mutable Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Range Sum Query - Mutable",
      "cpp_optimal": "// Solution for Range Sum Query - Mutable",
      "java_brute": "// Solution for Range Sum Query - Mutable",
      "java_optimal": "// Solution for Range Sum Query - Mutable",
      "python_brute": "# Solution for Range Sum Query - Mutable",
      "python_optimal": "# Solution for Range Sum Query - Mutable"
    }
  },
  {
    "id": 13,
    "number": 13,
    "sequence_number": 13,
    "title": "Shifting Letters",
    "slug": "shifting-letters",
    "difficulty": "Medium",
    "topic": "Prefix Sum",
    "subtopic": "Prefix Sum Optimization",
    "pattern": "Suffix Sum Shifts",
    "secondary_patterns": [
      "Suffix Sum Shifts"
    ],
    "stage": "Arrays & Hashing Foundations",
    "curriculumStage": "Stage 1 — Arrays & Hashing Foundations",
    "roadmapPhase": "Stage 1 — Arrays & Hashing Foundations",
    "phase": "Stage 1 — Arrays & Hashing Foundations",
    "estimatedTime": 30,
    "statement": "Given the constraints and input parameters for Shifting Letters, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Shifting Letters."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Shifting Letters.",
      "Leverage the optimal Prefix Sum pattern to reduce time complexity."
    ],
    "learningObjective": "Master Prefix Sum techniques by solving Medium problem constraints for Shifting Letters.",
    "whyThisPattern": "When observing Prefix Sum problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/shifting-letters/",
    "leetcode_title": "Shifting Letters",
    "leetcode_id": 783,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/shifting-letters/",
    "canonicalSlug": "shifting-letters",
    "canonicalUrl": "https://leetcode.com/problems/shifting-letters/",
    "url": "https://leetcode.com/problems/shifting-letters/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Shifting Letters\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Shifting Letters\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Shifting Letters\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Shifting Letters\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Shifting Letters\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Shifting Letters\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Shifting Letters\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Shifting Letters\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Shifting Letters",
      "cpp_optimal": "// Solution for Shifting Letters",
      "java_brute": "// Solution for Shifting Letters",
      "java_optimal": "// Solution for Shifting Letters",
      "python_brute": "# Solution for Shifting Letters",
      "python_optimal": "# Solution for Shifting Letters"
    }
  },
  {
    "id": 14,
    "number": 14,
    "sequence_number": 14,
    "title": "Number of Sub-arrays With Odd Sum",
    "slug": "number-of-sub-arrays-with-odd-sum",
    "difficulty": "Medium",
    "topic": "Prefix Sum",
    "subtopic": "Prefix Sum Optimization",
    "pattern": "Even-Odd Parity DP",
    "secondary_patterns": [
      "Even-Odd Parity DP"
    ],
    "stage": "Arrays & Hashing Foundations",
    "curriculumStage": "Stage 1 — Arrays & Hashing Foundations",
    "roadmapPhase": "Stage 1 — Arrays & Hashing Foundations",
    "phase": "Stage 1 — Arrays & Hashing Foundations",
    "estimatedTime": 30,
    "statement": "Given the constraints and input parameters for Number of Sub-arrays With Odd Sum, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Number of Sub-arrays With Odd Sum."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Number of Sub-arrays With Odd Sum.",
      "Leverage the optimal Prefix Sum pattern to reduce time complexity."
    ],
    "learningObjective": "Master Prefix Sum techniques by solving Medium problem constraints for Number of Sub-arrays With Odd Sum.",
    "whyThisPattern": "When observing Prefix Sum problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/number-of-sub-arrays-with-odd-sum/",
    "leetcode_title": "Number of Sub-arrays With Odd Sum",
    "leetcode_id": 878,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/number-of-sub-arrays-with-odd-sum/",
    "canonicalSlug": "number-of-sub-arrays-with-odd-sum",
    "canonicalUrl": "https://leetcode.com/problems/number-of-sub-arrays-with-odd-sum/",
    "url": "https://leetcode.com/problems/number-of-sub-arrays-with-odd-sum/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Number of Sub-arrays With Odd Sum\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Number of Sub-arrays With Odd Sum\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Number of Sub-arrays With Odd Sum\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Number of Sub-arrays With Odd Sum\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Number of Sub-arrays With Odd Sum\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Number of Sub-arrays With Odd Sum\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Number of Sub-arrays With Odd Sum\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Number of Sub-arrays With Odd Sum\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Number of Sub-arrays With Odd Sum",
      "cpp_optimal": "// Solution for Number of Sub-arrays With Odd Sum",
      "java_brute": "// Solution for Number of Sub-arrays With Odd Sum",
      "java_optimal": "// Solution for Number of Sub-arrays With Odd Sum",
      "python_brute": "# Solution for Number of Sub-arrays With Odd Sum",
      "python_optimal": "# Solution for Number of Sub-arrays With Odd Sum"
    }
  },
  {
    "id": 15,
    "number": 15,
    "sequence_number": 15,
    "title": "Range Sum of Sorted Subarray Sums",
    "slug": "range-sum-of-sorted-subarray-sums",
    "difficulty": "Medium",
    "topic": "Prefix Sum",
    "subtopic": "Prefix Sum Optimization",
    "pattern": "Priority Queue Sums",
    "secondary_patterns": [
      "Priority Queue Sums"
    ],
    "stage": "Arrays & Hashing Foundations",
    "curriculumStage": "Stage 1 — Arrays & Hashing Foundations",
    "roadmapPhase": "Stage 1 — Arrays & Hashing Foundations",
    "phase": "Stage 1 — Arrays & Hashing Foundations",
    "estimatedTime": 30,
    "statement": "Given the constraints and input parameters for Range Sum of Sorted Subarray Sums, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Range Sum of Sorted Subarray Sums."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Range Sum of Sorted Subarray Sums.",
      "Leverage the optimal Prefix Sum pattern to reduce time complexity."
    ],
    "learningObjective": "Master Prefix Sum techniques by solving Medium problem constraints for Range Sum of Sorted Subarray Sums.",
    "whyThisPattern": "When observing Prefix Sum problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/range-sum-of-sorted-subarray-sums/",
    "leetcode_title": "Range Sum of Sorted Subarray Sums",
    "leetcode_id": 881,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/range-sum-of-sorted-subarray-sums/",
    "canonicalSlug": "range-sum-of-sorted-subarray-sums",
    "canonicalUrl": "https://leetcode.com/problems/range-sum-of-sorted-subarray-sums/",
    "url": "https://leetcode.com/problems/range-sum-of-sorted-subarray-sums/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Range Sum of Sorted Subarray Sums\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Range Sum of Sorted Subarray Sums\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Range Sum of Sorted Subarray Sums\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Range Sum of Sorted Subarray Sums\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Range Sum of Sorted Subarray Sums\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Range Sum of Sorted Subarray Sums\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Range Sum of Sorted Subarray Sums\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Range Sum of Sorted Subarray Sums\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Range Sum of Sorted Subarray Sums",
      "cpp_optimal": "// Solution for Range Sum of Sorted Subarray Sums",
      "java_brute": "// Solution for Range Sum of Sorted Subarray Sums",
      "java_optimal": "// Solution for Range Sum of Sorted Subarray Sums",
      "python_brute": "# Solution for Range Sum of Sorted Subarray Sums",
      "python_optimal": "# Solution for Range Sum of Sorted Subarray Sums"
    }
  },
  {
    "id": 16,
    "number": 16,
    "sequence_number": 16,
    "title": "Number of Ways to Split a String",
    "slug": "number-of-ways-to-split-a-string",
    "difficulty": "Medium",
    "topic": "Prefix Sum",
    "subtopic": "Prefix Sum Optimization",
    "pattern": "Combinatoric Ones Split",
    "secondary_patterns": [
      "Combinatoric Ones Split"
    ],
    "stage": "Arrays & Hashing Foundations",
    "curriculumStage": "Stage 1 — Arrays & Hashing Foundations",
    "roadmapPhase": "Stage 1 — Arrays & Hashing Foundations",
    "phase": "Stage 1 — Arrays & Hashing Foundations",
    "estimatedTime": 30,
    "statement": "Given the constraints and input parameters for Number of Ways to Split a String, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Number of Ways to Split a String."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Number of Ways to Split a String.",
      "Leverage the optimal Prefix Sum pattern to reduce time complexity."
    ],
    "learningObjective": "Master Prefix Sum techniques by solving Medium problem constraints for Number of Ways to Split a String.",
    "whyThisPattern": "When observing Prefix Sum problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/number-of-ways-to-split-a-string/",
    "leetcode_title": "Number of Ways to Split a String",
    "leetcode_id": 885,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/number-of-ways-to-split-a-string/",
    "canonicalSlug": "number-of-ways-to-split-a-string",
    "canonicalUrl": "https://leetcode.com/problems/number-of-ways-to-split-a-string/",
    "url": "https://leetcode.com/problems/number-of-ways-to-split-a-string/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Number of Ways to Split a String\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Number of Ways to Split a String\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Number of Ways to Split a String\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Number of Ways to Split a String\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Number of Ways to Split a String\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Number of Ways to Split a String\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Number of Ways to Split a String\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Number of Ways to Split a String\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Number of Ways to Split a String",
      "cpp_optimal": "// Solution for Number of Ways to Split a String",
      "java_brute": "// Solution for Number of Ways to Split a String",
      "java_optimal": "// Solution for Number of Ways to Split a String",
      "python_brute": "# Solution for Number of Ways to Split a String",
      "python_optimal": "# Solution for Number of Ways to Split a String"
    }
  },
  {
    "id": 17,
    "number": 17,
    "sequence_number": 17,
    "title": "Matrix Block Sum",
    "slug": "matrix-block-sum",
    "difficulty": "Medium",
    "topic": "Prefix Sum",
    "subtopic": "Prefix Sum Optimization",
    "pattern": "2D Prefix Sum Matrix",
    "secondary_patterns": [
      "2D Prefix Sum Matrix"
    ],
    "stage": "Arrays & Hashing Foundations",
    "curriculumStage": "Stage 1 — Arrays & Hashing Foundations",
    "roadmapPhase": "Stage 1 — Arrays & Hashing Foundations",
    "phase": "Stage 1 — Arrays & Hashing Foundations",
    "estimatedTime": 30,
    "statement": "Given the constraints and input parameters for Matrix Block Sum, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Matrix Block Sum."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Matrix Block Sum.",
      "Leverage the optimal Prefix Sum pattern to reduce time complexity."
    ],
    "learningObjective": "Master Prefix Sum techniques by solving Medium problem constraints for Matrix Block Sum.",
    "whyThisPattern": "When observing Prefix Sum problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/matrix-block-sum/",
    "leetcode_title": "Matrix Block Sum",
    "leetcode_id": 887,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/matrix-block-sum/",
    "canonicalSlug": "matrix-block-sum",
    "canonicalUrl": "https://leetcode.com/problems/matrix-block-sum/",
    "url": "https://leetcode.com/problems/matrix-block-sum/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Matrix Block Sum\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Matrix Block Sum\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Matrix Block Sum\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Matrix Block Sum\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Matrix Block Sum\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Matrix Block Sum\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Matrix Block Sum\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Matrix Block Sum\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Matrix Block Sum",
      "cpp_optimal": "// Solution for Matrix Block Sum",
      "java_brute": "// Solution for Matrix Block Sum",
      "java_optimal": "// Solution for Matrix Block Sum",
      "python_brute": "# Solution for Matrix Block Sum",
      "python_optimal": "# Solution for Matrix Block Sum"
    }
  },
  {
    "id": 18,
    "number": 18,
    "sequence_number": 18,
    "title": "Ways to Split Array Into Three Subarrays",
    "slug": "ways-to-split-array-into-three-subarrays",
    "difficulty": "Medium",
    "topic": "Prefix Sum",
    "subtopic": "Prefix Sum Optimization",
    "pattern": "Binary Search Bounds",
    "secondary_patterns": [
      "Binary Search Bounds"
    ],
    "stage": "Arrays & Hashing Foundations",
    "curriculumStage": "Stage 1 — Arrays & Hashing Foundations",
    "roadmapPhase": "Stage 1 — Arrays & Hashing Foundations",
    "phase": "Stage 1 — Arrays & Hashing Foundations",
    "estimatedTime": 30,
    "statement": "Given the constraints and input parameters for Ways to Split Array Into Three Subarrays, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Ways to Split Array Into Three Subarrays."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Ways to Split Array Into Three Subarrays.",
      "Leverage the optimal Prefix Sum pattern to reduce time complexity."
    ],
    "learningObjective": "Master Prefix Sum techniques by solving Medium problem constraints for Ways to Split Array Into Three Subarrays.",
    "whyThisPattern": "When observing Prefix Sum problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/ways-to-split-array-into-three-subarrays/",
    "leetcode_title": "Ways to Split Array Into Three Subarrays",
    "leetcode_id": 900,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/ways-to-split-array-into-three-subarrays/",
    "canonicalSlug": "ways-to-split-array-into-three-subarrays",
    "canonicalUrl": "https://leetcode.com/problems/ways-to-split-array-into-three-subarrays/",
    "url": "https://leetcode.com/problems/ways-to-split-array-into-three-subarrays/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Ways to Split Array Into Three Subarrays\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Ways to Split Array Into Three Subarrays\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Ways to Split Array Into Three Subarrays\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Ways to Split Array Into Three Subarrays\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Ways to Split Array Into Three Subarrays\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Ways to Split Array Into Three Subarrays\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Ways to Split Array Into Three Subarrays\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Ways to Split Array Into Three Subarrays\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Ways to Split Array Into Three Subarrays",
      "cpp_optimal": "// Solution for Ways to Split Array Into Three Subarrays",
      "java_brute": "// Solution for Ways to Split Array Into Three Subarrays",
      "java_optimal": "// Solution for Ways to Split Array Into Three Subarrays",
      "python_brute": "# Solution for Ways to Split Array Into Three Subarrays",
      "python_optimal": "# Solution for Ways to Split Array Into Three Subarrays"
    }
  },
  {
    "id": 19,
    "number": 19,
    "sequence_number": 19,
    "title": "Product of Array Except Self",
    "slug": "product-of-array-except-self",
    "difficulty": "Medium",
    "topic": "Arrays",
    "subtopic": "Hashing & Array Optimization",
    "pattern": "Hashing & Array Optimization",
    "secondary_patterns": [
      "Hashing & Array Optimization"
    ],
    "stage": "Arrays & Hashing Foundations",
    "curriculumStage": "Stage 1 — Arrays & Hashing Foundations",
    "roadmapPhase": "Stage 1 — Arrays & Hashing Foundations",
    "phase": "Stage 1 — Arrays & Hashing Foundations",
    "estimatedTime": 30,
    "statement": "Solve the **Product of Array Except Self Challenge** problem using the **Hashing & Array Optimization** technique. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Hashing & Array Optimization identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Hashing & Array Optimization. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Hashing & Array Optimization techniques by solving Medium problem constraints for Product of Array Except Self Challenge.",
    "whyThisPattern": "When observing arrays & strings problem conditions, Hashing & Array Optimization optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Microsoft",
      "Bloomberg",
      "Adobe"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/product-of-array-except-self/",
    "leetcode_title": "Product of Array Except Self",
    "leetcode_id": 238,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/product-of-array-except-self/",
    "canonicalSlug": "product-of-array-except-self",
    "canonicalUrl": "https://leetcode.com/problems/product-of-array-except-self/",
    "url": "https://leetcode.com/problems/product-of-array-except-self/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Product of Array Except Self Challenge (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Product of Array Except Self Challenge (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Product of Array Except Self Challenge (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Product of Array Except Self Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Product of Array Except Self Challenge (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Product of Array Except Self Challenge (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Product of Array Except Self Challenge (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Product of Array Except Self Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Product of Array Except Self",
      "cpp_optimal": "// Solution for Product of Array Except Self",
      "java_brute": "// Solution for Product of Array Except Self",
      "java_optimal": "// Solution for Product of Array Except Self",
      "python_brute": "# Solution for Product of Array Except Self",
      "python_optimal": "# Solution for Product of Array Except Self"
    },
    "originalOrder": 241,
    "learningOrder": 241
  },
  {
    "id": 20,
    "number": 20,
    "sequence_number": 20,
    "title": "Container With Most Water",
    "slug": "container-with-most-water",
    "difficulty": "Medium",
    "topic": "Arrays",
    "subtopic": "Hashing & Array Optimization",
    "pattern": "Hashing & Array Optimization",
    "secondary_patterns": [
      "Hashing & Array Optimization"
    ],
    "stage": "Arrays & Hashing Foundations",
    "curriculumStage": "Stage 1 — Arrays & Hashing Foundations",
    "roadmapPhase": "Stage 1 — Arrays & Hashing Foundations",
    "phase": "Stage 1 — Arrays & Hashing Foundations",
    "estimatedTime": 30,
    "statement": "Solve the **Container With Most Water Optimization** problem using the **Hashing & Array Optimization** technique. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Hashing & Array Optimization identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Hashing & Array Optimization. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Hashing & Array Optimization techniques by solving Medium problem constraints for Container With Most Water Optimization.",
    "whyThisPattern": "When observing arrays & strings problem conditions, Hashing & Array Optimization optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/container-with-most-water/",
    "leetcode_title": "Container With Most Water",
    "leetcode_id": 11,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/container-with-most-water/",
    "canonicalSlug": "container-with-most-water",
    "canonicalUrl": "https://leetcode.com/problems/container-with-most-water/",
    "url": "https://leetcode.com/problems/container-with-most-water/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Container With Most Water Optimization (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Container With Most Water Optimization (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Container With Most Water Optimization (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Container With Most Water Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Container With Most Water Optimization (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Container With Most Water Optimization (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Container With Most Water Optimization (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Container With Most Water Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Container With Most Water",
      "cpp_optimal": "// Solution for Container With Most Water",
      "java_brute": "// Solution for Container With Most Water",
      "java_optimal": "// Solution for Container With Most Water",
      "python_brute": "# Solution for Container With Most Water",
      "python_optimal": "# Solution for Container With Most Water"
    },
    "originalOrder": 242,
    "learningOrder": 242
  },
  {
    "id": 21,
    "number": 21,
    "sequence_number": 21,
    "title": "3Sum",
    "slug": "3sum",
    "difficulty": "Medium",
    "topic": "Arrays",
    "subtopic": "Hashing & Array Optimization",
    "pattern": "Hashing & Array Optimization",
    "secondary_patterns": [
      "Hashing & Array Optimization"
    ],
    "stage": "Arrays & Hashing Foundations",
    "curriculumStage": "Stage 1 — Arrays & Hashing Foundations",
    "roadmapPhase": "Stage 1 — Arrays & Hashing Foundations",
    "phase": "Stage 1 — Arrays & Hashing Foundations",
    "estimatedTime": 30,
    "statement": "Solve the **3Sum Optimization** problem using the **Hashing & Array Optimization** technique. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Hashing & Array Optimization identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Hashing & Array Optimization. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Hashing & Array Optimization techniques by solving Medium problem constraints for 3Sum Optimization.",
    "whyThisPattern": "When observing arrays & strings problem conditions, Hashing & Array Optimization optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Apple",
      "Adobe",
      "Atlassian"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/3sum/",
    "leetcode_title": "3Sum",
    "leetcode_id": 15,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/3sum/",
    "canonicalSlug": "3sum",
    "canonicalUrl": "https://leetcode.com/problems/3sum/",
    "url": "https://leetcode.com/problems/3sum/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for 3Sum Optimization (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for 3Sum Optimization (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for 3Sum Optimization (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for 3Sum Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for 3Sum Optimization (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for 3Sum Optimization (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for 3Sum Optimization (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for 3Sum Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for 3Sum",
      "cpp_optimal": "// Solution for 3Sum",
      "java_brute": "// Solution for 3Sum",
      "java_optimal": "// Solution for 3Sum",
      "python_brute": "# Solution for 3Sum",
      "python_optimal": "# Solution for 3Sum"
    },
    "originalOrder": 243,
    "learningOrder": 243
  },
  {
    "id": 22,
    "number": 22,
    "sequence_number": 22,
    "title": "4Sum",
    "slug": "4sum",
    "difficulty": "Medium",
    "topic": "Arrays",
    "subtopic": "Hashing & Array Optimization",
    "pattern": "Hashing & Array Optimization",
    "secondary_patterns": [
      "Hashing & Array Optimization"
    ],
    "stage": "Arrays & Hashing Foundations",
    "curriculumStage": "Stage 1 — Arrays & Hashing Foundations",
    "roadmapPhase": "Stage 1 — Arrays & Hashing Foundations",
    "phase": "Stage 1 — Arrays & Hashing Foundations",
    "estimatedTime": 30,
    "statement": "Solve the **4Sum Optimization** problem using the **Hashing & Array Optimization** technique. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Hashing & Array Optimization identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Hashing & Array Optimization. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Hashing & Array Optimization techniques by solving Medium problem constraints for 4Sum Optimization.",
    "whyThisPattern": "When observing arrays & strings problem conditions, Hashing & Array Optimization optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Apple",
      "Adobe",
      "Atlassian"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/4sum/",
    "leetcode_title": "4Sum",
    "leetcode_id": 18,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/4sum/",
    "canonicalSlug": "4sum",
    "canonicalUrl": "https://leetcode.com/problems/4sum/",
    "url": "https://leetcode.com/problems/4sum/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for 4Sum Optimization (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for 4Sum Optimization (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for 4Sum Optimization (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for 4Sum Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for 4Sum Optimization (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for 4Sum Optimization (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for 4Sum Optimization (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for 4Sum Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for 4Sum",
      "cpp_optimal": "// Solution for 4Sum",
      "java_brute": "// Solution for 4Sum",
      "java_optimal": "// Solution for 4Sum",
      "python_brute": "# Solution for 4Sum",
      "python_optimal": "# Solution for 4Sum"
    },
    "originalOrder": 244,
    "learningOrder": 244
  },
  {
    "id": 23,
    "number": 23,
    "sequence_number": 23,
    "title": "Subarray Sum Equals K",
    "slug": "subarray-sum-equals-k",
    "difficulty": "Medium",
    "topic": "Prefix Sum",
    "subtopic": "Hashing & Array Optimization",
    "pattern": "Hashing & Array Optimization",
    "secondary_patterns": [
      "Hashing & Array Optimization"
    ],
    "stage": "Arrays & Hashing Foundations",
    "curriculumStage": "Stage 1 — Arrays & Hashing Foundations",
    "roadmapPhase": "Stage 1 — Arrays & Hashing Foundations",
    "phase": "Stage 1 — Arrays & Hashing Foundations",
    "estimatedTime": 30,
    "statement": "Solve the **Subarray Sum Equals K Optimization** problem using the **Hashing & Array Optimization** technique. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Hashing & Array Optimization identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Hashing & Array Optimization. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Hashing & Array Optimization techniques by solving Medium problem constraints for Subarray Sum Equals K Optimization.",
    "whyThisPattern": "When observing arrays & strings problem conditions, Hashing & Array Optimization optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/subarray-sum-equals-k/",
    "leetcode_title": "Subarray Sum Equals K",
    "leetcode_id": 560,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/subarray-sum-equals-k/",
    "canonicalSlug": "subarray-sum-equals-k",
    "canonicalUrl": "https://leetcode.com/problems/subarray-sum-equals-k/",
    "url": "https://leetcode.com/problems/subarray-sum-equals-k/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Subarray Sum Equals K Optimization (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Subarray Sum Equals K Optimization (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Subarray Sum Equals K Optimization (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Subarray Sum Equals K Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Subarray Sum Equals K Optimization (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Subarray Sum Equals K Optimization (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Subarray Sum Equals K Optimization (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Subarray Sum Equals K Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Subarray Sum Equals K",
      "cpp_optimal": "// Solution for Subarray Sum Equals K",
      "java_brute": "// Solution for Subarray Sum Equals K",
      "java_optimal": "// Solution for Subarray Sum Equals K",
      "python_brute": "# Solution for Subarray Sum Equals K",
      "python_optimal": "# Solution for Subarray Sum Equals K"
    },
    "originalOrder": 245,
    "learningOrder": 245
  },
  {
    "id": 24,
    "number": 24,
    "sequence_number": 24,
    "title": "Set Matrix Zeroes",
    "slug": "set-matrix-zeroes",
    "difficulty": "Medium",
    "topic": "Hashing",
    "subtopic": "Binary Search",
    "pattern": "Binary Search",
    "secondary_patterns": [
      "Binary Search"
    ],
    "stage": "Arrays & Hashing Foundations",
    "curriculumStage": "Stage 1 — Arrays & Hashing Foundations",
    "roadmapPhase": "Stage 1 — Arrays & Hashing Foundations",
    "phase": "Stage 1 — Arrays & Hashing Foundations",
    "estimatedTime": 30,
    "statement": "Solve the **Set Matrix Zeroes Challenge** problem using the **Binary Search** technique. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Binary Search identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Binary Search. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Binary Search techniques by solving Medium problem constraints for Set Matrix Zeroes Challenge.",
    "whyThisPattern": "When observing arrays & strings problem conditions, Binary Search optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Amazon",
      "Microsoft",
      "Uber"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/set-matrix-zeroes/",
    "leetcode_title": "Set Matrix Zeroes",
    "leetcode_id": 73,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/set-matrix-zeroes/",
    "canonicalSlug": "set-matrix-zeroes",
    "canonicalUrl": "https://leetcode.com/problems/set-matrix-zeroes/",
    "url": "https://leetcode.com/problems/set-matrix-zeroes/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Set Matrix Zeroes Challenge (Binary Search)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Set Matrix Zeroes Challenge (Binary Search)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Set Matrix Zeroes Challenge (Binary Search)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Set Matrix Zeroes Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Set Matrix Zeroes Challenge (Binary Search)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Set Matrix Zeroes Challenge (Binary Search)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Set Matrix Zeroes Challenge (Binary Search)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Set Matrix Zeroes Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Set Matrix Zeroes",
      "cpp_optimal": "// Solution for Set Matrix Zeroes",
      "java_brute": "// Solution for Set Matrix Zeroes",
      "java_optimal": "// Solution for Set Matrix Zeroes",
      "python_brute": "# Solution for Set Matrix Zeroes",
      "python_optimal": "# Solution for Set Matrix Zeroes"
    },
    "originalOrder": 246,
    "learningOrder": 246
  },
  {
    "id": 25,
    "number": 25,
    "sequence_number": 25,
    "title": "Rotate Array",
    "slug": "rotate-array",
    "difficulty": "Medium",
    "topic": "Arrays",
    "subtopic": "Arrays Optimization",
    "pattern": "Three Reverse Swap",
    "secondary_patterns": [
      "Three Reverse Swap"
    ],
    "stage": "Arrays & Hashing Foundations",
    "curriculumStage": "Stage 1 — Arrays & Hashing Foundations",
    "roadmapPhase": "Stage 1 — Arrays & Hashing Foundations",
    "phase": "Stage 1 — Arrays & Hashing Foundations",
    "estimatedTime": 30,
    "statement": "Given the constraints and input parameters for Rotate Array, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Rotate Array."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Rotate Array.",
      "Leverage the optimal Arrays pattern to reduce time complexity."
    ],
    "learningObjective": "Master Arrays techniques by solving Medium problem constraints for Rotate Array.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/rotate-array/",
    "leetcode_title": "Rotate Array",
    "leetcode_id": 189,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/rotate-array/",
    "canonicalSlug": "rotate-array",
    "canonicalUrl": "https://leetcode.com/problems/rotate-array/",
    "url": "https://leetcode.com/problems/rotate-array/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Rotate Array\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Rotate Array\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Rotate Array\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Rotate Array\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Rotate Array\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Rotate Array\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Rotate Array\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Rotate Array\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Rotate Array",
      "cpp_optimal": "// Solution for Rotate Array",
      "java_brute": "// Solution for Rotate Array",
      "java_optimal": "// Solution for Rotate Array",
      "python_brute": "# Solution for Rotate Array",
      "python_optimal": "# Solution for Rotate Array"
    },
    "originalOrder": 247,
    "learningOrder": 247
  },
  {
    "id": 26,
    "number": 26,
    "sequence_number": 26,
    "title": "Card Flipping Game",
    "slug": "card-flipping-game",
    "difficulty": "Medium",
    "topic": "Arrays",
    "subtopic": "Arrays Optimization",
    "pattern": "Set Difference Min",
    "secondary_patterns": [
      "Set Difference Min"
    ],
    "stage": "Arrays & Hashing Foundations",
    "curriculumStage": "Stage 1 — Arrays & Hashing Foundations",
    "roadmapPhase": "Stage 1 — Arrays & Hashing Foundations",
    "phase": "Stage 1 — Arrays & Hashing Foundations",
    "estimatedTime": 30,
    "statement": "Given the constraints and input parameters for Card Flipping Game, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Card Flipping Game."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Card Flipping Game.",
      "Leverage the optimal Arrays pattern to reduce time complexity."
    ],
    "learningObjective": "Master Arrays techniques by solving Medium problem constraints for Card Flipping Game.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/card-flipping-game/",
    "leetcode_title": "Card Flipping Game",
    "leetcode_id": 822,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/card-flipping-game/",
    "canonicalSlug": "card-flipping-game",
    "canonicalUrl": "https://leetcode.com/problems/card-flipping-game/",
    "url": "https://leetcode.com/problems/card-flipping-game/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Card Flipping Game\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Card Flipping Game\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Card Flipping Game\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Card Flipping Game\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Card Flipping Game\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Card Flipping Game\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Card Flipping Game\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Card Flipping Game\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Card Flipping Game",
      "cpp_optimal": "// Solution for Card Flipping Game",
      "java_brute": "// Solution for Card Flipping Game",
      "java_optimal": "// Solution for Card Flipping Game",
      "python_brute": "# Solution for Card Flipping Game",
      "python_optimal": "# Solution for Card Flipping Game"
    },
    "originalOrder": 248,
    "learningOrder": 248
  },
  {
    "id": 27,
    "number": 27,
    "sequence_number": 27,
    "title": "Magic Squares In Grid",
    "slug": "magic-squares-in-grid",
    "difficulty": "Medium",
    "topic": "Arrays",
    "subtopic": "Arrays Optimization",
    "pattern": "3x3 Grid Verification",
    "secondary_patterns": [
      "3x3 Grid Verification"
    ],
    "stage": "Arrays & Hashing Foundations",
    "curriculumStage": "Stage 1 — Arrays & Hashing Foundations",
    "roadmapPhase": "Stage 1 — Arrays & Hashing Foundations",
    "phase": "Stage 1 — Arrays & Hashing Foundations",
    "estimatedTime": 30,
    "statement": "Given the constraints and input parameters for Magic Squares In Grid, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Magic Squares In Grid."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Magic Squares In Grid.",
      "Leverage the optimal Arrays pattern to reduce time complexity."
    ],
    "learningObjective": "Master Arrays techniques by solving Medium problem constraints for Magic Squares In Grid.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/magic-squares-in-grid/",
    "leetcode_title": "Magic Squares In Grid",
    "leetcode_id": 840,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/magic-squares-in-grid/",
    "canonicalSlug": "magic-squares-in-grid",
    "canonicalUrl": "https://leetcode.com/problems/magic-squares-in-grid/",
    "url": "https://leetcode.com/problems/magic-squares-in-grid/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Magic Squares In Grid\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Magic Squares In Grid\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Magic Squares In Grid\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Magic Squares In Grid\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Magic Squares In Grid\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Magic Squares In Grid\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Magic Squares In Grid\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Magic Squares In Grid\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Magic Squares In Grid",
      "cpp_optimal": "// Solution for Magic Squares In Grid",
      "java_brute": "// Solution for Magic Squares In Grid",
      "java_optimal": "// Solution for Magic Squares In Grid",
      "python_brute": "# Solution for Magic Squares In Grid",
      "python_optimal": "# Solution for Magic Squares In Grid"
    },
    "originalOrder": 249,
    "learningOrder": 249
  },
  {
    "id": 28,
    "number": 28,
    "sequence_number": 28,
    "title": "Image Overlap",
    "slug": "image-overlap",
    "difficulty": "Medium",
    "topic": "Arrays",
    "subtopic": "Arrays Optimization",
    "pattern": "Translation Offset Hash",
    "secondary_patterns": [
      "Translation Offset Hash"
    ],
    "stage": "Arrays & Hashing Foundations",
    "curriculumStage": "Stage 1 — Arrays & Hashing Foundations",
    "roadmapPhase": "Stage 1 — Arrays & Hashing Foundations",
    "phase": "Stage 1 — Arrays & Hashing Foundations",
    "estimatedTime": 30,
    "statement": "Given the constraints and input parameters for Image Overlap, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Image Overlap."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Image Overlap.",
      "Leverage the optimal Arrays pattern to reduce time complexity."
    ],
    "learningObjective": "Master Arrays techniques by solving Medium problem constraints for Image Overlap.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/image-overlap/",
    "leetcode_title": "Image Overlap",
    "leetcode_id": 835,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/image-overlap/",
    "canonicalSlug": "image-overlap",
    "canonicalUrl": "https://leetcode.com/problems/image-overlap/",
    "url": "https://leetcode.com/problems/image-overlap/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Image Overlap\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Image Overlap\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Image Overlap\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Image Overlap\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Image Overlap\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Image Overlap\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Image Overlap\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Image Overlap\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Image Overlap",
      "cpp_optimal": "// Solution for Image Overlap",
      "java_brute": "// Solution for Image Overlap",
      "java_optimal": "// Solution for Image Overlap",
      "python_brute": "# Solution for Image Overlap",
      "python_optimal": "# Solution for Image Overlap"
    },
    "originalOrder": 250,
    "learningOrder": 250
  },
  {
    "id": 29,
    "number": 29,
    "sequence_number": 29,
    "title": "RLE Iterator",
    "slug": "rle-iterator",
    "difficulty": "Medium",
    "topic": "Arrays",
    "subtopic": "Arrays Optimization",
    "pattern": "Run-Length Skip Pointer",
    "secondary_patterns": [
      "Run-Length Skip Pointer"
    ],
    "stage": "Arrays & Hashing Foundations",
    "curriculumStage": "Stage 1 — Arrays & Hashing Foundations",
    "roadmapPhase": "Stage 1 — Arrays & Hashing Foundations",
    "phase": "Stage 1 — Arrays & Hashing Foundations",
    "estimatedTime": 30,
    "statement": "Given the constraints and input parameters for RLE Iterator, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for RLE Iterator."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for RLE Iterator.",
      "Leverage the optimal Arrays pattern to reduce time complexity."
    ],
    "learningObjective": "Master Arrays techniques by solving Medium problem constraints for RLE Iterator.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/rle-iterator/",
    "leetcode_title": "RLE Iterator",
    "leetcode_id": 900,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/rle-iterator/",
    "canonicalSlug": "rle-iterator",
    "canonicalUrl": "https://leetcode.com/problems/rle-iterator/",
    "url": "https://leetcode.com/problems/rle-iterator/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for RLE Iterator\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for RLE Iterator\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for RLE Iterator\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for RLE Iterator\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for RLE Iterator\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for RLE Iterator\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for RLE Iterator\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for RLE Iterator\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for RLE Iterator",
      "cpp_optimal": "// Solution for RLE Iterator",
      "java_brute": "// Solution for RLE Iterator",
      "java_optimal": "// Solution for RLE Iterator",
      "python_brute": "# Solution for RLE Iterator",
      "python_optimal": "# Solution for RLE Iterator"
    },
    "originalOrder": 251,
    "learningOrder": 251
  },
  {
    "id": 30,
    "number": 30,
    "sequence_number": 30,
    "title": "Sum of Subarray Minimums",
    "slug": "sum-of-subarray-minimums",
    "difficulty": "Medium",
    "topic": "Arrays",
    "subtopic": "Arrays Optimization",
    "pattern": "Monotonic Stack Left/Right",
    "secondary_patterns": [
      "Monotonic Stack Left/Right"
    ],
    "stage": "Arrays & Hashing Foundations",
    "curriculumStage": "Stage 1 — Arrays & Hashing Foundations",
    "roadmapPhase": "Stage 1 — Arrays & Hashing Foundations",
    "phase": "Stage 1 — Arrays & Hashing Foundations",
    "estimatedTime": 30,
    "statement": "Given the constraints and input parameters for Sum of Subarray Minimums, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Sum of Subarray Minimums."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Sum of Subarray Minimums.",
      "Leverage the optimal Stack pattern to reduce time complexity."
    ],
    "learningObjective": "Master Arrays techniques by solving Medium problem constraints for Sum of Subarray Minimums.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/sum-of-subarray-minimums/",
    "leetcode_title": "Sum of Subarray Minimums",
    "leetcode_id": 907,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/sum-of-subarray-minimums/",
    "canonicalSlug": "sum-of-subarray-minimums",
    "canonicalUrl": "https://leetcode.com/problems/sum-of-subarray-minimums/",
    "url": "https://leetcode.com/problems/sum-of-subarray-minimums/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Sum of Subarray Minimums\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Sum of Subarray Minimums\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Sum of Subarray Minimums\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Sum of Subarray Minimums\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Sum of Subarray Minimums\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Sum of Subarray Minimums\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Sum of Subarray Minimums\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Sum of Subarray Minimums\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Sum of Subarray Minimums",
      "cpp_optimal": "// Solution for Sum of Subarray Minimums",
      "java_brute": "// Solution for Sum of Subarray Minimums",
      "java_optimal": "// Solution for Sum of Subarray Minimums",
      "python_brute": "# Solution for Sum of Subarray Minimums",
      "python_optimal": "# Solution for Sum of Subarray Minimums"
    },
    "originalOrder": 252,
    "learningOrder": 252
  },
  {
    "id": 31,
    "number": 31,
    "sequence_number": 31,
    "title": "Count Nice Pairs in an Array",
    "slug": "count-nice-pairs-in-an-array",
    "difficulty": "Medium",
    "topic": "Arrays",
    "subtopic": "Arrays Optimization",
    "pattern": "Number Delta Map",
    "secondary_patterns": [
      "Number Delta Map"
    ],
    "stage": "Arrays & Hashing Foundations",
    "curriculumStage": "Stage 1 — Arrays & Hashing Foundations",
    "roadmapPhase": "Stage 1 — Arrays & Hashing Foundations",
    "phase": "Stage 1 — Arrays & Hashing Foundations",
    "estimatedTime": 30,
    "statement": "Given the constraints and input parameters for Count Nice Pairs in an Array, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Count Nice Pairs in an Array."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Count Nice Pairs in an Array.",
      "Leverage the optimal Hashing pattern to reduce time complexity."
    ],
    "learningObjective": "Master Arrays techniques by solving Medium problem constraints for Count Nice Pairs in an Array.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/count-nice-pairs-in-an-array/",
    "leetcode_title": "Count Nice Pairs in an Array",
    "leetcode_id": 1814,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/count-nice-pairs-in-an-array/",
    "canonicalSlug": "count-nice-pairs-in-an-array",
    "canonicalUrl": "https://leetcode.com/problems/count-nice-pairs-in-an-array/",
    "url": "https://leetcode.com/problems/count-nice-pairs-in-an-array/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Count Nice Pairs in an Array\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Count Nice Pairs in an Array\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Count Nice Pairs in an Array\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Count Nice Pairs in an Array\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Count Nice Pairs in an Array\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Count Nice Pairs in an Array\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Count Nice Pairs in an Array\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Count Nice Pairs in an Array\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Count Nice Pairs in an Array",
      "cpp_optimal": "// Solution for Count Nice Pairs in an Array",
      "java_brute": "// Solution for Count Nice Pairs in an Array",
      "java_optimal": "// Solution for Count Nice Pairs in an Array",
      "python_brute": "# Solution for Count Nice Pairs in an Array",
      "python_optimal": "# Solution for Count Nice Pairs in an Array"
    },
    "originalOrder": 253,
    "learningOrder": 253
  },
  {
    "id": 32,
    "number": 32,
    "sequence_number": 32,
    "title": "Coordinate With Maximum Network Quality",
    "slug": "coordinate-with-maximum-network-quality",
    "difficulty": "Medium",
    "topic": "Arrays",
    "subtopic": "Arrays Optimization",
    "pattern": "Grid Distance Formula",
    "secondary_patterns": [
      "Grid Distance Formula"
    ],
    "stage": "Arrays & Hashing Foundations",
    "curriculumStage": "Stage 1 — Arrays & Hashing Foundations",
    "roadmapPhase": "Stage 1 — Arrays & Hashing Foundations",
    "phase": "Stage 1 — Arrays & Hashing Foundations",
    "estimatedTime": 30,
    "statement": "Given the constraints and input parameters for Coordinate With Maximum Network Quality, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Coordinate With Maximum Network Quality."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Coordinate With Maximum Network Quality.",
      "Leverage the optimal Arrays pattern to reduce time complexity."
    ],
    "learningObjective": "Master Arrays techniques by solving Medium problem constraints for Coordinate With Maximum Network Quality.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/coordinate-with-maximum-network-quality/",
    "leetcode_title": "Coordinate With Maximum Network Quality",
    "leetcode_id": 1620,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/coordinate-with-maximum-network-quality/",
    "canonicalSlug": "coordinate-with-maximum-network-quality",
    "canonicalUrl": "https://leetcode.com/problems/coordinate-with-maximum-network-quality/",
    "url": "https://leetcode.com/problems/coordinate-with-maximum-network-quality/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Coordinate With Maximum Network Quality\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Coordinate With Maximum Network Quality\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Coordinate With Maximum Network Quality\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Coordinate With Maximum Network Quality\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Coordinate With Maximum Network Quality\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Coordinate With Maximum Network Quality\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Coordinate With Maximum Network Quality\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Coordinate With Maximum Network Quality\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Coordinate With Maximum Network Quality",
      "cpp_optimal": "// Solution for Coordinate With Maximum Network Quality",
      "java_brute": "// Solution for Coordinate With Maximum Network Quality",
      "java_optimal": "// Solution for Coordinate With Maximum Network Quality",
      "python_brute": "# Solution for Coordinate With Maximum Network Quality",
      "python_optimal": "# Solution for Coordinate With Maximum Network Quality"
    },
    "originalOrder": 254,
    "learningOrder": 254
  },
  {
    "id": 33,
    "number": 33,
    "sequence_number": 33,
    "title": "Rotate Image",
    "slug": "rotate-image",
    "difficulty": "Medium",
    "topic": "Arrays",
    "subtopic": "Arrays Optimization",
    "pattern": "Transpose & Reverse",
    "secondary_patterns": [
      "Transpose & Reverse"
    ],
    "stage": "Arrays & Hashing Foundations",
    "curriculumStage": "Stage 1 — Arrays & Hashing Foundations",
    "roadmapPhase": "Stage 1 — Arrays & Hashing Foundations",
    "phase": "Stage 1 — Arrays & Hashing Foundations",
    "estimatedTime": 30,
    "statement": "Given the constraints and input parameters for Rotate Image, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Rotate Image."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Rotate Image.",
      "Leverage the optimal Arrays pattern to reduce time complexity."
    ],
    "learningObjective": "Master Arrays techniques by solving Medium problem constraints for Rotate Image.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/rotate-image/",
    "leetcode_title": "Rotate Image",
    "leetcode_id": 48,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/rotate-image/",
    "canonicalSlug": "rotate-image",
    "canonicalUrl": "https://leetcode.com/problems/rotate-image/",
    "url": "https://leetcode.com/problems/rotate-image/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Rotate Image\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Rotate Image\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Rotate Image\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Rotate Image\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Rotate Image\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Rotate Image\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Rotate Image\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Rotate Image\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Rotate Image",
      "cpp_optimal": "// Solution for Rotate Image",
      "java_brute": "// Solution for Rotate Image",
      "java_optimal": "// Solution for Rotate Image",
      "python_brute": "# Solution for Rotate Image",
      "python_optimal": "# Solution for Rotate Image"
    },
    "originalOrder": 255,
    "learningOrder": 255
  },
  {
    "id": 34,
    "number": 34,
    "sequence_number": 34,
    "title": "Zigzag Conversion",
    "slug": "zigzag-conversion",
    "difficulty": "Medium",
    "topic": "Arrays",
    "subtopic": "Arrays Optimization",
    "pattern": "Arrays Pattern",
    "secondary_patterns": [
      "Arrays Pattern"
    ],
    "stage": "Arrays & Hashing Foundations",
    "curriculumStage": "Stage 1 — Arrays & Hashing Foundations",
    "roadmapPhase": "Stage 1 — Arrays & Hashing Foundations",
    "phase": "Stage 1 — Arrays & Hashing Foundations",
    "estimatedTime": 30,
    "statement": "Solve the **Zigzag Conversion** problem using standard Arrays techniques. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Arrays algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Arrays properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Arrays techniques by solving Medium problem constraints for Zigzag Conversion.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/zigzag-conversion/",
    "leetcode_title": "Zigzag Conversion",
    "leetcode_id": 6,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/zigzag-conversion/",
    "canonicalSlug": "zigzag-conversion",
    "canonicalUrl": "https://leetcode.com/problems/zigzag-conversion/",
    "url": "https://leetcode.com/problems/zigzag-conversion/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Zigzag Conversion\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Zigzag Conversion\n};",
        "java": "// Java Solution for Zigzag Conversion\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Zigzag Conversion\n}",
        "python": "# Python Solution for Zigzag Conversion\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Zigzag Conversion\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Zigzag Conversion\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Zigzag Conversion\n};",
        "java": "// Optimal Java Solution for Zigzag Conversion\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Zigzag Conversion\n}",
        "python": "# Optimal Python Solution for Zigzag Conversion\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Zigzag Conversion\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Zigzag Conversion",
      "cpp_optimal": "// Solution for Zigzag Conversion",
      "java_brute": "// Solution for Zigzag Conversion",
      "java_optimal": "// Solution for Zigzag Conversion",
      "python_brute": "# Solution for Zigzag Conversion",
      "python_optimal": "# Solution for Zigzag Conversion"
    },
    "originalOrder": 256,
    "learningOrder": 256
  },
  {
    "id": 35,
    "number": 35,
    "sequence_number": 35,
    "title": "Reverse Integer",
    "slug": "reverse-integer",
    "difficulty": "Medium",
    "topic": "Arrays",
    "subtopic": "Arrays Optimization",
    "pattern": "Arrays Pattern",
    "secondary_patterns": [
      "Arrays Pattern"
    ],
    "stage": "Arrays & Hashing Foundations",
    "curriculumStage": "Stage 1 — Arrays & Hashing Foundations",
    "roadmapPhase": "Stage 1 — Arrays & Hashing Foundations",
    "phase": "Stage 1 — Arrays & Hashing Foundations",
    "estimatedTime": 30,
    "statement": "Solve the **Reverse Integer** problem using standard Arrays techniques. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Arrays algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Arrays properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Arrays techniques by solving Medium problem constraints for Reverse Integer.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/reverse-integer/",
    "leetcode_title": "Reverse Integer",
    "leetcode_id": 7,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/reverse-integer/",
    "canonicalSlug": "reverse-integer",
    "canonicalUrl": "https://leetcode.com/problems/reverse-integer/",
    "url": "https://leetcode.com/problems/reverse-integer/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Reverse Integer\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Reverse Integer\n};",
        "java": "// Java Solution for Reverse Integer\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Reverse Integer\n}",
        "python": "# Python Solution for Reverse Integer\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Reverse Integer\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Reverse Integer\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Reverse Integer\n};",
        "java": "// Optimal Java Solution for Reverse Integer\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Reverse Integer\n}",
        "python": "# Optimal Python Solution for Reverse Integer\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Reverse Integer\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Reverse Integer",
      "cpp_optimal": "// Solution for Reverse Integer",
      "java_brute": "// Solution for Reverse Integer",
      "java_optimal": "// Solution for Reverse Integer",
      "python_brute": "# Solution for Reverse Integer",
      "python_optimal": "# Solution for Reverse Integer"
    },
    "originalOrder": 257,
    "learningOrder": 257
  },
  {
    "id": 36,
    "number": 36,
    "sequence_number": 36,
    "title": "Contains Duplicate III",
    "slug": "contains-duplicate-iii",
    "difficulty": "Hard",
    "topic": "Arrays",
    "subtopic": "Hashing & Array Optimization",
    "pattern": "Hashing & Array Optimization",
    "secondary_patterns": [
      "Hashing & Array Optimization"
    ],
    "stage": "Arrays & Hashing Foundations",
    "curriculumStage": "Stage 1 — Arrays & Hashing Foundations",
    "roadmapPhase": "Stage 1 — Arrays & Hashing Foundations",
    "phase": "Stage 1 — Arrays & Hashing Foundations",
    "estimatedTime": 45,
    "statement": "Solve the **Contains Duplicate III Challenge** problem using the **Hashing & Array Optimization** technique. Given input constraints appropriate for Hard level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^6",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Hashing & Array Optimization identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Hashing & Array Optimization. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Hashing & Array Optimization techniques by solving Hard problem constraints for Contains Duplicate III Challenge.",
    "whyThisPattern": "When observing arrays & strings problem conditions, Hashing & Array Optimization optimizes performance down to expected O(N log N).",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Amazon",
      "Microsoft",
      "Uber"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/contains-duplicate-iii/",
    "leetcode_title": "Contains Duplicate III",
    "leetcode_id": 220,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/contains-duplicate-iii/",
    "canonicalSlug": "contains-duplicate-iii",
    "canonicalUrl": "https://leetcode.com/problems/contains-duplicate-iii/",
    "url": "https://leetcode.com/problems/contains-duplicate-iii/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Contains Duplicate III Challenge (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Contains Duplicate III Challenge (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Contains Duplicate III Challenge (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Contains Duplicate III Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Contains Duplicate III Challenge (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Contains Duplicate III Challenge (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Contains Duplicate III Challenge (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Contains Duplicate III Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Contains Duplicate III",
      "cpp_optimal": "// Solution for Contains Duplicate III",
      "java_brute": "// Solution for Contains Duplicate III",
      "java_optimal": "// Solution for Contains Duplicate III",
      "python_brute": "# Solution for Contains Duplicate III",
      "python_optimal": "# Solution for Contains Duplicate III"
    },
    "originalOrder": 701,
    "learningOrder": 701
  },
  {
    "id": 37,
    "number": 37,
    "sequence_number": 37,
    "title": "Trapping Rain Water",
    "slug": "trapping-rain-water",
    "difficulty": "Hard",
    "topic": "Arrays",
    "subtopic": "Hashing & Array Optimization",
    "pattern": "Hashing & Array Optimization",
    "secondary_patterns": [
      "Hashing & Array Optimization"
    ],
    "stage": "Arrays & Hashing Foundations",
    "curriculumStage": "Stage 1 — Arrays & Hashing Foundations",
    "roadmapPhase": "Stage 1 — Arrays & Hashing Foundations",
    "phase": "Stage 1 — Arrays & Hashing Foundations",
    "estimatedTime": 45,
    "statement": "Solve the **Trapping Rain Water Optimization** problem using the **Hashing & Array Optimization** technique. Given input constraints appropriate for Hard level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^6",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Hashing & Array Optimization identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Hashing & Array Optimization. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Hashing & Array Optimization techniques by solving Hard problem constraints for Trapping Rain Water Optimization.",
    "whyThisPattern": "When observing arrays & strings problem conditions, Hashing & Array Optimization optimizes performance down to expected O(N log N).",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "LinkedIn",
      "Amazon"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/trapping-rain-water/",
    "leetcode_title": "Trapping Rain Water",
    "leetcode_id": 42,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/trapping-rain-water/",
    "canonicalSlug": "trapping-rain-water",
    "canonicalUrl": "https://leetcode.com/problems/trapping-rain-water/",
    "url": "https://leetcode.com/problems/trapping-rain-water/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Trapping Rain Water Optimization (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Trapping Rain Water Optimization (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Trapping Rain Water Optimization (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Trapping Rain Water Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Trapping Rain Water Optimization (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Trapping Rain Water Optimization (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Trapping Rain Water Optimization (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Trapping Rain Water Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Trapping Rain Water",
      "cpp_optimal": "// Solution for Trapping Rain Water",
      "java_brute": "// Solution for Trapping Rain Water",
      "java_optimal": "// Solution for Trapping Rain Water",
      "python_brute": "# Solution for Trapping Rain Water",
      "python_optimal": "# Solution for Trapping Rain Water"
    },
    "originalOrder": 702,
    "learningOrder": 702
  },
  {
    "id": 38,
    "number": 38,
    "sequence_number": 38,
    "title": "First Missing Positive",
    "slug": "first-missing-positive",
    "difficulty": "Hard",
    "topic": "Arrays",
    "subtopic": "Arrays Optimization",
    "pattern": "In-Place Cyclic Placement",
    "secondary_patterns": [
      "In-Place Cyclic Placement"
    ],
    "stage": "Arrays & Hashing Foundations",
    "curriculumStage": "Stage 1 — Arrays & Hashing Foundations",
    "roadmapPhase": "Stage 1 — Arrays & Hashing Foundations",
    "phase": "Stage 1 — Arrays & Hashing Foundations",
    "estimatedTime": 45,
    "statement": "Given the constraints and input parameters for First Missing Positive, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for First Missing Positive."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for First Missing Positive.",
      "Leverage the optimal Arrays pattern to reduce time complexity."
    ],
    "learningObjective": "Master Arrays techniques by solving Hard problem constraints for First Missing Positive.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/first-missing-positive/",
    "leetcode_title": "First Missing Positive",
    "leetcode_id": 41,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/first-missing-positive/",
    "canonicalSlug": "first-missing-positive",
    "canonicalUrl": "https://leetcode.com/problems/first-missing-positive/",
    "url": "https://leetcode.com/problems/first-missing-positive/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for First Missing Positive\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for First Missing Positive\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for First Missing Positive\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for First Missing Positive\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for First Missing Positive\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for First Missing Positive\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for First Missing Positive\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for First Missing Positive\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for First Missing Positive",
      "cpp_optimal": "// Solution for First Missing Positive",
      "java_brute": "// Solution for First Missing Positive",
      "java_optimal": "// Solution for First Missing Positive",
      "python_brute": "# Solution for First Missing Positive",
      "python_optimal": "# Solution for First Missing Positive"
    },
    "originalOrder": 704,
    "learningOrder": 704
  },
  {
    "id": 39,
    "number": 39,
    "sequence_number": 39,
    "title": "Maximum Building Height",
    "slug": "maximum-building-height",
    "difficulty": "Hard",
    "topic": "Arrays",
    "subtopic": "Arrays Optimization",
    "pattern": "Two-Pass Left-Right Min Bounds",
    "secondary_patterns": [
      "Two-Pass Left-Right Min Bounds"
    ],
    "stage": "Arrays & Hashing Foundations",
    "curriculumStage": "Stage 1 — Arrays & Hashing Foundations",
    "roadmapPhase": "Stage 1 — Arrays & Hashing Foundations",
    "phase": "Stage 1 — Arrays & Hashing Foundations",
    "estimatedTime": 45,
    "statement": "Given the constraints and input parameters for Maximum Building Height, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Maximum Building Height."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Maximum Building Height.",
      "Leverage the optimal Arrays pattern to reduce time complexity."
    ],
    "learningObjective": "Master Arrays techniques by solving Hard problem constraints for Maximum Building Height.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/maximum-building-height/",
    "leetcode_title": "Maximum Building Height",
    "leetcode_id": 1840,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/maximum-building-height/",
    "canonicalSlug": "maximum-building-height",
    "canonicalUrl": "https://leetcode.com/problems/maximum-building-height/",
    "url": "https://leetcode.com/problems/maximum-building-height/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Maximum Building Height\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Maximum Building Height\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Maximum Building Height\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Maximum Building Height\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Maximum Building Height\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Maximum Building Height\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Maximum Building Height\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Maximum Building Height\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Maximum Building Height",
      "cpp_optimal": "// Solution for Maximum Building Height",
      "java_brute": "// Solution for Maximum Building Height",
      "java_optimal": "// Solution for Maximum Building Height",
      "python_brute": "# Solution for Maximum Building Height",
      "python_optimal": "# Solution for Maximum Building Height"
    },
    "originalOrder": 705,
    "learningOrder": 705
  },
  {
    "id": 40,
    "number": 40,
    "sequence_number": 40,
    "title": "Substring with Concatenation of All Words",
    "slug": "substring-with-concatenation-of-all-words",
    "difficulty": "Hard",
    "topic": "Arrays",
    "subtopic": "Arrays Optimization",
    "pattern": "Arrays Pattern",
    "secondary_patterns": [
      "Arrays Pattern"
    ],
    "stage": "Arrays & Hashing Foundations",
    "curriculumStage": "Stage 1 — Arrays & Hashing Foundations",
    "roadmapPhase": "Stage 1 — Arrays & Hashing Foundations",
    "phase": "Stage 1 — Arrays & Hashing Foundations",
    "estimatedTime": 45,
    "statement": "Solve the **Substring with Concatenation of All Words** problem using standard Arrays techniques. Given input constraints appropriate for Hard level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Arrays algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Arrays properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Arrays techniques by solving Hard problem constraints for Substring with Concatenation of All Words.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/substring-with-concatenation-of-all-words/",
    "leetcode_title": "Substring with Concatenation of All Words",
    "leetcode_id": 30,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/substring-with-concatenation-of-all-words/",
    "canonicalSlug": "substring-with-concatenation-of-all-words",
    "canonicalUrl": "https://leetcode.com/problems/substring-with-concatenation-of-all-words/",
    "url": "https://leetcode.com/problems/substring-with-concatenation-of-all-words/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Substring with Concatenation of All Words\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Substring with Concatenation of All Words\n};",
        "java": "// Java Solution for Substring with Concatenation of All Words\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Substring with Concatenation of All Words\n}",
        "python": "# Python Solution for Substring with Concatenation of All Words\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Substring with Concatenation of All Words\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Substring with Concatenation of All Words\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Substring with Concatenation of All Words\n};",
        "java": "// Optimal Java Solution for Substring with Concatenation of All Words\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Substring with Concatenation of All Words\n}",
        "python": "# Optimal Python Solution for Substring with Concatenation of All Words\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Substring with Concatenation of All Words\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Substring with Concatenation of All Words",
      "cpp_optimal": "// Solution for Substring with Concatenation of All Words",
      "java_brute": "// Solution for Substring with Concatenation of All Words",
      "java_optimal": "// Solution for Substring with Concatenation of All Words",
      "python_brute": "# Solution for Substring with Concatenation of All Words",
      "python_optimal": "# Solution for Substring with Concatenation of All Words"
    },
    "originalOrder": 706,
    "learningOrder": 706
  },
  {
    "id": 41,
    "number": 41,
    "sequence_number": 41,
    "title": "Permutation Sequence",
    "slug": "permutation-sequence",
    "difficulty": "Hard",
    "topic": "Arrays",
    "subtopic": "Arrays Optimization",
    "pattern": "Arrays Pattern",
    "secondary_patterns": [
      "Arrays Pattern"
    ],
    "stage": "Arrays & Hashing Foundations",
    "curriculumStage": "Stage 1 — Arrays & Hashing Foundations",
    "roadmapPhase": "Stage 1 — Arrays & Hashing Foundations",
    "phase": "Stage 1 — Arrays & Hashing Foundations",
    "estimatedTime": 45,
    "statement": "Solve the **Permutation Sequence** problem using standard Arrays techniques. Given input constraints appropriate for Hard level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Arrays algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Arrays properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Arrays techniques by solving Hard problem constraints for Permutation Sequence.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/permutation-sequence/",
    "leetcode_title": "Permutation Sequence",
    "leetcode_id": 60,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/permutation-sequence/",
    "canonicalSlug": "permutation-sequence",
    "canonicalUrl": "https://leetcode.com/problems/permutation-sequence/",
    "url": "https://leetcode.com/problems/permutation-sequence/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Permutation Sequence\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Permutation Sequence\n};",
        "java": "// Java Solution for Permutation Sequence\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Permutation Sequence\n}",
        "python": "# Python Solution for Permutation Sequence\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Permutation Sequence\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Permutation Sequence\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Permutation Sequence\n};",
        "java": "// Optimal Java Solution for Permutation Sequence\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Permutation Sequence\n}",
        "python": "# Optimal Python Solution for Permutation Sequence\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Permutation Sequence\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Permutation Sequence",
      "cpp_optimal": "// Solution for Permutation Sequence",
      "java_brute": "// Solution for Permutation Sequence",
      "java_optimal": "// Solution for Permutation Sequence",
      "python_brute": "# Solution for Permutation Sequence",
      "python_optimal": "# Solution for Permutation Sequence"
    },
    "originalOrder": 707,
    "learningOrder": 707
  },
  {
    "id": 42,
    "number": 42,
    "sequence_number": 42,
    "title": "Valid Number",
    "slug": "valid-number",
    "difficulty": "Hard",
    "topic": "Arrays",
    "subtopic": "Arrays Optimization",
    "pattern": "Arrays Pattern",
    "secondary_patterns": [
      "Arrays Pattern"
    ],
    "stage": "Arrays & Hashing Foundations",
    "curriculumStage": "Stage 1 — Arrays & Hashing Foundations",
    "roadmapPhase": "Stage 1 — Arrays & Hashing Foundations",
    "phase": "Stage 1 — Arrays & Hashing Foundations",
    "estimatedTime": 45,
    "statement": "Solve the **Valid Number** problem using standard Arrays techniques. Given input constraints appropriate for Hard level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Arrays algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Arrays properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Arrays techniques by solving Hard problem constraints for Valid Number.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/valid-number/",
    "leetcode_title": "Valid Number",
    "leetcode_id": 65,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/valid-number/",
    "canonicalSlug": "valid-number",
    "canonicalUrl": "https://leetcode.com/problems/valid-number/",
    "url": "https://leetcode.com/problems/valid-number/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Valid Number\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Valid Number\n};",
        "java": "// Java Solution for Valid Number\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Valid Number\n}",
        "python": "# Python Solution for Valid Number\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Valid Number\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Valid Number\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Valid Number\n};",
        "java": "// Optimal Java Solution for Valid Number\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Valid Number\n}",
        "python": "# Optimal Python Solution for Valid Number\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Valid Number\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Valid Number",
      "cpp_optimal": "// Solution for Valid Number",
      "java_brute": "// Solution for Valid Number",
      "java_optimal": "// Solution for Valid Number",
      "python_brute": "# Solution for Valid Number",
      "python_optimal": "# Solution for Valid Number"
    },
    "originalOrder": 708,
    "learningOrder": 708
  },
  {
    "id": 43,
    "number": 43,
    "sequence_number": 43,
    "title": "Text Justification",
    "slug": "text-justification",
    "difficulty": "Hard",
    "topic": "Arrays",
    "subtopic": "Arrays Optimization",
    "pattern": "Arrays Pattern",
    "secondary_patterns": [
      "Arrays Pattern"
    ],
    "stage": "Arrays & Hashing Foundations",
    "curriculumStage": "Stage 1 — Arrays & Hashing Foundations",
    "roadmapPhase": "Stage 1 — Arrays & Hashing Foundations",
    "phase": "Stage 1 — Arrays & Hashing Foundations",
    "estimatedTime": 45,
    "statement": "Solve the **Text Justification** problem using standard Arrays techniques. Given input constraints appropriate for Hard level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Arrays algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Arrays properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Arrays techniques by solving Hard problem constraints for Text Justification.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/text-justification/",
    "leetcode_title": "Text Justification",
    "leetcode_id": 68,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/text-justification/",
    "canonicalSlug": "text-justification",
    "canonicalUrl": "https://leetcode.com/problems/text-justification/",
    "url": "https://leetcode.com/problems/text-justification/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Text Justification\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Text Justification\n};",
        "java": "// Java Solution for Text Justification\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Text Justification\n}",
        "python": "# Python Solution for Text Justification\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Text Justification\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Text Justification\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Text Justification\n};",
        "java": "// Optimal Java Solution for Text Justification\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Text Justification\n}",
        "python": "# Optimal Python Solution for Text Justification\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Text Justification\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Text Justification",
      "cpp_optimal": "// Solution for Text Justification",
      "java_brute": "// Solution for Text Justification",
      "java_optimal": "// Solution for Text Justification",
      "python_brute": "# Solution for Text Justification",
      "python_optimal": "# Solution for Text Justification"
    },
    "originalOrder": 709,
    "learningOrder": 709
  },
  {
    "id": 44,
    "number": 44,
    "sequence_number": 44,
    "title": "Department Top Three Salaries",
    "slug": "department-top-three-salaries",
    "difficulty": "Hard",
    "topic": "Arrays",
    "subtopic": "Arrays Optimization",
    "pattern": "Arrays Pattern",
    "secondary_patterns": [
      "Arrays Pattern"
    ],
    "stage": "Arrays & Hashing Foundations",
    "curriculumStage": "Stage 1 — Arrays & Hashing Foundations",
    "roadmapPhase": "Stage 1 — Arrays & Hashing Foundations",
    "phase": "Stage 1 — Arrays & Hashing Foundations",
    "estimatedTime": 45,
    "statement": "Solve the **Department Top Three Salaries** problem using standard Arrays techniques. Given input constraints appropriate for Hard level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Arrays algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Arrays properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Arrays techniques by solving Hard problem constraints for Department Top Three Salaries.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/department-top-three-salaries/",
    "leetcode_title": "Department Top Three Salaries",
    "leetcode_id": 185,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/department-top-three-salaries/",
    "canonicalSlug": "department-top-three-salaries",
    "canonicalUrl": "https://leetcode.com/problems/department-top-three-salaries/",
    "url": "https://leetcode.com/problems/department-top-three-salaries/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Department Top Three Salaries\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Department Top Three Salaries\n};",
        "java": "// Java Solution for Department Top Three Salaries\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Department Top Three Salaries\n}",
        "python": "# Python Solution for Department Top Three Salaries\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Department Top Three Salaries\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Department Top Three Salaries\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Department Top Three Salaries\n};",
        "java": "// Optimal Java Solution for Department Top Three Salaries\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Department Top Three Salaries\n}",
        "python": "# Optimal Python Solution for Department Top Three Salaries\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Department Top Three Salaries\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Department Top Three Salaries",
      "cpp_optimal": "// Solution for Department Top Three Salaries",
      "java_brute": "// Solution for Department Top Three Salaries",
      "java_optimal": "// Solution for Department Top Three Salaries",
      "python_brute": "# Solution for Department Top Three Salaries",
      "python_optimal": "# Solution for Department Top Three Salaries"
    },
    "originalOrder": 710,
    "learningOrder": 710
  },
  {
    "id": 45,
    "number": 45,
    "sequence_number": 45,
    "title": "Basic Calculator",
    "slug": "basic-calculator",
    "difficulty": "Hard",
    "topic": "Arrays",
    "subtopic": "Arrays Optimization",
    "pattern": "Arrays Pattern",
    "secondary_patterns": [
      "Arrays Pattern"
    ],
    "stage": "Arrays & Hashing Foundations",
    "curriculumStage": "Stage 1 — Arrays & Hashing Foundations",
    "roadmapPhase": "Stage 1 — Arrays & Hashing Foundations",
    "phase": "Stage 1 — Arrays & Hashing Foundations",
    "estimatedTime": 45,
    "statement": "Solve the **Basic Calculator** problem using standard Arrays techniques. Given input constraints appropriate for Hard level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Arrays algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Arrays properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Arrays techniques by solving Hard problem constraints for Basic Calculator.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/basic-calculator/",
    "leetcode_title": "Basic Calculator",
    "leetcode_id": 224,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/basic-calculator/",
    "canonicalSlug": "basic-calculator",
    "canonicalUrl": "https://leetcode.com/problems/basic-calculator/",
    "url": "https://leetcode.com/problems/basic-calculator/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Basic Calculator\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Basic Calculator\n};",
        "java": "// Java Solution for Basic Calculator\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Basic Calculator\n}",
        "python": "# Python Solution for Basic Calculator\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Basic Calculator\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Basic Calculator\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Basic Calculator\n};",
        "java": "// Optimal Java Solution for Basic Calculator\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Basic Calculator\n}",
        "python": "# Optimal Python Solution for Basic Calculator\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Basic Calculator\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Basic Calculator",
      "cpp_optimal": "// Solution for Basic Calculator",
      "java_brute": "// Solution for Basic Calculator",
      "java_optimal": "// Solution for Basic Calculator",
      "python_brute": "# Solution for Basic Calculator",
      "python_optimal": "# Solution for Basic Calculator"
    },
    "originalOrder": 711,
    "learningOrder": 711
  },
  {
    "id": 46,
    "number": 46,
    "sequence_number": 46,
    "title": "Burst Balloons",
    "slug": "burst-balloons",
    "difficulty": "Hard",
    "topic": "Arrays",
    "subtopic": "Arrays Optimization",
    "pattern": "Arrays Pattern",
    "secondary_patterns": [
      "Arrays Pattern"
    ],
    "stage": "Arrays & Hashing Foundations",
    "curriculumStage": "Stage 1 — Arrays & Hashing Foundations",
    "roadmapPhase": "Stage 1 — Arrays & Hashing Foundations",
    "phase": "Stage 1 — Arrays & Hashing Foundations",
    "estimatedTime": 45,
    "statement": "Solve the **Burst Balloons** problem using standard Arrays techniques. Given input constraints appropriate for Hard level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Arrays algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Arrays properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Arrays techniques by solving Hard problem constraints for Burst Balloons.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/burst-balloons/",
    "leetcode_title": "Burst Balloons",
    "leetcode_id": 312,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/burst-balloons/",
    "canonicalSlug": "burst-balloons",
    "canonicalUrl": "https://leetcode.com/problems/burst-balloons/",
    "url": "https://leetcode.com/problems/burst-balloons/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Burst Balloons\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Burst Balloons\n};",
        "java": "// Java Solution for Burst Balloons\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Burst Balloons\n}",
        "python": "# Python Solution for Burst Balloons\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Burst Balloons\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Burst Balloons\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Burst Balloons\n};",
        "java": "// Optimal Java Solution for Burst Balloons\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Burst Balloons\n}",
        "python": "# Optimal Python Solution for Burst Balloons\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Burst Balloons\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Burst Balloons",
      "cpp_optimal": "// Solution for Burst Balloons",
      "java_brute": "// Solution for Burst Balloons",
      "java_optimal": "// Solution for Burst Balloons",
      "python_brute": "# Solution for Burst Balloons",
      "python_optimal": "# Solution for Burst Balloons"
    },
    "originalOrder": 713,
    "learningOrder": 713
  },
  {
    "id": 47,
    "number": 47,
    "sequence_number": 47,
    "title": "Create Maximum Number",
    "slug": "create-maximum-number",
    "difficulty": "Hard",
    "topic": "Arrays",
    "subtopic": "Arrays Optimization",
    "pattern": "Arrays Pattern",
    "secondary_patterns": [
      "Arrays Pattern"
    ],
    "stage": "Arrays & Hashing Foundations",
    "curriculumStage": "Stage 1 — Arrays & Hashing Foundations",
    "roadmapPhase": "Stage 1 — Arrays & Hashing Foundations",
    "phase": "Stage 1 — Arrays & Hashing Foundations",
    "estimatedTime": 45,
    "statement": "Solve the **Create Maximum Number** problem using standard Arrays techniques. Given input constraints appropriate for Hard level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Arrays algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Arrays properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Arrays techniques by solving Hard problem constraints for Create Maximum Number.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/create-maximum-number/",
    "leetcode_title": "Create Maximum Number",
    "leetcode_id": 321,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/create-maximum-number/",
    "canonicalSlug": "create-maximum-number",
    "canonicalUrl": "https://leetcode.com/problems/create-maximum-number/",
    "url": "https://leetcode.com/problems/create-maximum-number/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Create Maximum Number\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Create Maximum Number\n};",
        "java": "// Java Solution for Create Maximum Number\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Create Maximum Number\n}",
        "python": "# Python Solution for Create Maximum Number\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Create Maximum Number\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Create Maximum Number\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Create Maximum Number\n};",
        "java": "// Optimal Java Solution for Create Maximum Number\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Create Maximum Number\n}",
        "python": "# Optimal Python Solution for Create Maximum Number\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Create Maximum Number\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Create Maximum Number",
      "cpp_optimal": "// Solution for Create Maximum Number",
      "java_brute": "// Solution for Create Maximum Number",
      "java_optimal": "// Solution for Create Maximum Number",
      "python_brute": "# Solution for Create Maximum Number",
      "python_optimal": "# Solution for Create Maximum Number"
    },
    "originalOrder": 714,
    "learningOrder": 714
  },
  {
    "id": 48,
    "number": 48,
    "sequence_number": 48,
    "title": "Split Array Largest Sum",
    "slug": "split-array-largest-sum",
    "difficulty": "Hard",
    "topic": "Arrays",
    "subtopic": "Arrays Optimization",
    "pattern": "Arrays Pattern",
    "secondary_patterns": [
      "Arrays Pattern"
    ],
    "stage": "Arrays & Hashing Foundations",
    "curriculumStage": "Stage 1 — Arrays & Hashing Foundations",
    "roadmapPhase": "Stage 1 — Arrays & Hashing Foundations",
    "phase": "Stage 1 — Arrays & Hashing Foundations",
    "estimatedTime": 45,
    "statement": "Solve the **Split Array Largest Sum** problem using standard Arrays techniques. Given input constraints appropriate for Hard level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Arrays algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Arrays properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Arrays techniques by solving Hard problem constraints for Split Array Largest Sum.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/split-array-largest-sum/",
    "leetcode_title": "Split Array Largest Sum",
    "leetcode_id": 410,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/split-array-largest-sum/",
    "canonicalSlug": "split-array-largest-sum",
    "canonicalUrl": "https://leetcode.com/problems/split-array-largest-sum/",
    "url": "https://leetcode.com/problems/split-array-largest-sum/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Split Array Largest Sum\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Split Array Largest Sum\n};",
        "java": "// Java Solution for Split Array Largest Sum\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Split Array Largest Sum\n}",
        "python": "# Python Solution for Split Array Largest Sum\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Split Array Largest Sum\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Split Array Largest Sum\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Split Array Largest Sum\n};",
        "java": "// Optimal Java Solution for Split Array Largest Sum\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Split Array Largest Sum\n}",
        "python": "# Optimal Python Solution for Split Array Largest Sum\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Split Array Largest Sum\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Split Array Largest Sum",
      "cpp_optimal": "// Solution for Split Array Largest Sum",
      "java_brute": "// Solution for Split Array Largest Sum",
      "java_optimal": "// Solution for Split Array Largest Sum",
      "python_brute": "# Solution for Split Array Largest Sum",
      "python_optimal": "# Solution for Split Array Largest Sum"
    },
    "originalOrder": 716,
    "learningOrder": 716
  },
  {
    "id": 49,
    "number": 49,
    "sequence_number": 49,
    "title": "Strong Password Checker",
    "slug": "strong-password-checker",
    "difficulty": "Hard",
    "topic": "Arrays",
    "subtopic": "Arrays Optimization",
    "pattern": "Arrays Pattern",
    "secondary_patterns": [
      "Arrays Pattern"
    ],
    "stage": "Arrays & Hashing Foundations",
    "curriculumStage": "Stage 1 — Arrays & Hashing Foundations",
    "roadmapPhase": "Stage 1 — Arrays & Hashing Foundations",
    "phase": "Stage 1 — Arrays & Hashing Foundations",
    "estimatedTime": 45,
    "statement": "Solve the **Strong Password Checker** problem using standard Arrays techniques. Given input constraints appropriate for Hard level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Arrays algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Arrays properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Arrays techniques by solving Hard problem constraints for Strong Password Checker.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/strong-password-checker/",
    "leetcode_title": "Strong Password Checker",
    "leetcode_id": 420,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/strong-password-checker/",
    "canonicalSlug": "strong-password-checker",
    "canonicalUrl": "https://leetcode.com/problems/strong-password-checker/",
    "url": "https://leetcode.com/problems/strong-password-checker/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Strong Password Checker\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Strong Password Checker\n};",
        "java": "// Java Solution for Strong Password Checker\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Strong Password Checker\n}",
        "python": "# Python Solution for Strong Password Checker\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Strong Password Checker\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Strong Password Checker\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Strong Password Checker\n};",
        "java": "// Optimal Java Solution for Strong Password Checker\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Strong Password Checker\n}",
        "python": "# Optimal Python Solution for Strong Password Checker\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Strong Password Checker\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Strong Password Checker",
      "cpp_optimal": "// Solution for Strong Password Checker",
      "java_brute": "// Solution for Strong Password Checker",
      "java_optimal": "// Solution for Strong Password Checker",
      "python_brute": "# Solution for Strong Password Checker",
      "python_optimal": "# Solution for Strong Password Checker"
    },
    "originalOrder": 717,
    "learningOrder": 717
  },
  {
    "id": 50,
    "number": 50,
    "sequence_number": 50,
    "title": "Arithmetic Slices II - Subsequence",
    "slug": "arithmetic-slices-ii-subsequence",
    "difficulty": "Hard",
    "topic": "Arrays",
    "subtopic": "Arrays Optimization",
    "pattern": "Arrays Pattern",
    "secondary_patterns": [
      "Arrays Pattern"
    ],
    "stage": "Arrays & Hashing Foundations",
    "curriculumStage": "Stage 1 — Arrays & Hashing Foundations",
    "roadmapPhase": "Stage 1 — Arrays & Hashing Foundations",
    "phase": "Stage 1 — Arrays & Hashing Foundations",
    "estimatedTime": 45,
    "statement": "Solve the **Arithmetic Slices II - Subsequence** problem using standard Arrays techniques. Given input constraints appropriate for Hard level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Arrays algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Arrays properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Arrays techniques by solving Hard problem constraints for Arithmetic Slices II - Subsequence.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/arithmetic-slices-ii-subsequence/",
    "leetcode_title": "Arithmetic Slices II - Subsequence",
    "leetcode_id": 446,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/arithmetic-slices-ii-subsequence/",
    "canonicalSlug": "arithmetic-slices-ii-subsequence",
    "canonicalUrl": "https://leetcode.com/problems/arithmetic-slices-ii-subsequence/",
    "url": "https://leetcode.com/problems/arithmetic-slices-ii-subsequence/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Arithmetic Slices II - Subsequence\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Arithmetic Slices II - Subsequence\n};",
        "java": "// Java Solution for Arithmetic Slices II - Subsequence\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Arithmetic Slices II - Subsequence\n}",
        "python": "# Python Solution for Arithmetic Slices II - Subsequence\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Arithmetic Slices II - Subsequence\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Arithmetic Slices II - Subsequence\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Arithmetic Slices II - Subsequence\n};",
        "java": "// Optimal Java Solution for Arithmetic Slices II - Subsequence\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Arithmetic Slices II - Subsequence\n}",
        "python": "# Optimal Python Solution for Arithmetic Slices II - Subsequence\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Arithmetic Slices II - Subsequence\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Arithmetic Slices II - Subsequence",
      "cpp_optimal": "// Solution for Arithmetic Slices II - Subsequence",
      "java_brute": "// Solution for Arithmetic Slices II - Subsequence",
      "java_optimal": "// Solution for Arithmetic Slices II - Subsequence",
      "python_brute": "# Solution for Arithmetic Slices II - Subsequence",
      "python_optimal": "# Solution for Arithmetic Slices II - Subsequence"
    },
    "originalOrder": 718,
    "learningOrder": 718
  },
  {
    "id": 51,
    "number": 51,
    "sequence_number": 51,
    "title": "Palindrome Number",
    "slug": "palindrome-number-optimization",
    "difficulty": "Easy",
    "topic": "Two Pointers",
    "subtopic": "Two Pointers",
    "pattern": "Two Pointers",
    "secondary_patterns": [
      "Two Pointers"
    ],
    "stage": "Two Pointers & Sliding Window",
    "curriculumStage": "Stage 2 — Two Pointers & Sliding Window",
    "roadmapPhase": "Stage 2 — Two Pointers & Sliding Window",
    "phase": "Stage 2 — Two Pointers & Sliding Window",
    "estimatedTime": 15,
    "statement": "Solve the **Palindrome Number Optimization** problem using the **Two Pointers** technique. Given input constraints appropriate for Easy level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^4",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Two Pointers identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Two Pointers. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Two Pointers techniques by solving Easy problem constraints for Palindrome Number Optimization.",
    "whyThisPattern": "When observing arrays & strings problem conditions, Two Pointers optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(1)",
    "companyRelevance": [
      "Meta",
      "Apple",
      "Netflix"
    ],
    "companyRelevanceTier": "Medium",
    "leetcode_url": "https://leetcode.com/problems/palindrome-number/",
    "leetcode_title": "Palindrome Number",
    "leetcode_id": 9,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/palindrome-number/",
    "canonicalSlug": "palindrome-number-optimization",
    "canonicalUrl": "https://leetcode.com/problems/palindrome-number/",
    "url": "https://leetcode.com/problems/palindrome-number/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Palindrome Number Optimization (Two Pointers)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Palindrome Number Optimization (Two Pointers)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Palindrome Number Optimization (Two Pointers)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Palindrome Number Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Palindrome Number Optimization (Two Pointers)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Palindrome Number Optimization (Two Pointers)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Palindrome Number Optimization (Two Pointers)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Palindrome Number Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Palindrome Number",
      "cpp_optimal": "// Solution for Palindrome Number",
      "java_brute": "// Solution for Palindrome Number",
      "java_optimal": "// Solution for Palindrome Number",
      "python_brute": "# Solution for Palindrome Number",
      "python_optimal": "# Solution for Palindrome Number"
    }
  },
  {
    "id": 52,
    "number": 52,
    "sequence_number": 52,
    "title": "Valid Palindrome",
    "slug": "valid-palindrome-optimization",
    "difficulty": "Easy",
    "topic": "Two Pointers",
    "subtopic": "Two Pointers",
    "pattern": "Two Pointers",
    "secondary_patterns": [
      "Two Pointers"
    ],
    "stage": "Two Pointers & Sliding Window",
    "curriculumStage": "Stage 2 — Two Pointers & Sliding Window",
    "roadmapPhase": "Stage 2 — Two Pointers & Sliding Window",
    "phase": "Stage 2 — Two Pointers & Sliding Window",
    "estimatedTime": 15,
    "statement": "Solve the **Valid Palindrome Optimization** problem using the **Two Pointers** technique. Given input constraints appropriate for Easy level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^4",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Two Pointers identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Two Pointers. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Two Pointers techniques by solving Easy problem constraints for Valid Palindrome Optimization.",
    "whyThisPattern": "When observing arrays & strings problem conditions, Two Pointers optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(1)",
    "companyRelevance": [
      "Meta",
      "Apple",
      "Netflix"
    ],
    "companyRelevanceTier": "Medium",
    "leetcode_url": "https://leetcode.com/problems/valid-palindrome/",
    "leetcode_title": "Valid Palindrome",
    "leetcode_id": 125,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/valid-palindrome/",
    "canonicalSlug": "valid-palindrome-optimization",
    "canonicalUrl": "https://leetcode.com/problems/valid-palindrome/",
    "url": "https://leetcode.com/problems/valid-palindrome/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Valid Palindrome Optimization (Two Pointers)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Valid Palindrome Optimization (Two Pointers)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Valid Palindrome Optimization (Two Pointers)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Valid Palindrome Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Valid Palindrome Optimization (Two Pointers)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Valid Palindrome Optimization (Two Pointers)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Valid Palindrome Optimization (Two Pointers)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Valid Palindrome Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Valid Palindrome",
      "cpp_optimal": "// Solution for Valid Palindrome",
      "java_brute": "// Solution for Valid Palindrome",
      "java_optimal": "// Solution for Valid Palindrome",
      "python_brute": "# Solution for Valid Palindrome",
      "python_optimal": "# Solution for Valid Palindrome"
    }
  },
  {
    "id": 53,
    "number": 53,
    "sequence_number": 53,
    "title": "Longest Palindrome",
    "slug": "longest-palindrome-challenge",
    "difficulty": "Easy",
    "topic": "Two Pointers",
    "subtopic": "Two Pointers",
    "pattern": "Two Pointers",
    "secondary_patterns": [
      "Two Pointers"
    ],
    "stage": "Two Pointers & Sliding Window",
    "curriculumStage": "Stage 2 — Two Pointers & Sliding Window",
    "roadmapPhase": "Stage 2 — Two Pointers & Sliding Window",
    "phase": "Stage 2 — Two Pointers & Sliding Window",
    "estimatedTime": 15,
    "statement": "Solve the **Longest Palindrome Challenge** problem using the **Two Pointers** technique. Given input constraints appropriate for Easy level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^4",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Two Pointers identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Two Pointers. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Two Pointers techniques by solving Easy problem constraints for Longest Palindrome Challenge.",
    "whyThisPattern": "When observing arrays & strings problem conditions, Two Pointers optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(1)",
    "companyRelevance": [
      "Microsoft",
      "Bloomberg",
      "Adobe"
    ],
    "companyRelevanceTier": "Medium",
    "leetcode_url": "https://leetcode.com/problems/longest-palindrome/",
    "leetcode_title": "Longest Palindrome",
    "leetcode_id": 409,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/longest-palindrome/",
    "canonicalSlug": "longest-palindrome-challenge",
    "canonicalUrl": "https://leetcode.com/problems/longest-palindrome/",
    "url": "https://leetcode.com/problems/longest-palindrome/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Longest Palindrome Challenge (Two Pointers)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Longest Palindrome Challenge (Two Pointers)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Longest Palindrome Challenge (Two Pointers)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Longest Palindrome Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Longest Palindrome Challenge (Two Pointers)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Longest Palindrome Challenge (Two Pointers)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Longest Palindrome Challenge (Two Pointers)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Longest Palindrome Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Longest Palindrome",
      "cpp_optimal": "// Solution for Longest Palindrome",
      "java_brute": "// Solution for Longest Palindrome",
      "java_optimal": "// Solution for Longest Palindrome",
      "python_brute": "# Solution for Longest Palindrome",
      "python_optimal": "# Solution for Longest Palindrome"
    }
  },
  {
    "id": 54,
    "number": 54,
    "sequence_number": 54,
    "title": "Valid Palindrome II",
    "slug": "valid-palindrome-ii-optimization",
    "difficulty": "Easy",
    "topic": "Two Pointers",
    "subtopic": "Two Pointers",
    "pattern": "Two Pointers",
    "secondary_patterns": [
      "Two Pointers"
    ],
    "stage": "Two Pointers & Sliding Window",
    "curriculumStage": "Stage 2 — Two Pointers & Sliding Window",
    "roadmapPhase": "Stage 2 — Two Pointers & Sliding Window",
    "phase": "Stage 2 — Two Pointers & Sliding Window",
    "estimatedTime": 15,
    "statement": "Solve the **Valid Palindrome II Optimization** problem using the **Two Pointers** technique. Given input constraints appropriate for Easy level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^4",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Two Pointers identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Two Pointers. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Two Pointers techniques by solving Easy problem constraints for Valid Palindrome II Optimization.",
    "whyThisPattern": "When observing arrays & strings problem conditions, Two Pointers optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(1)",
    "companyRelevance": [
      "Google",
      "LinkedIn",
      "Amazon"
    ],
    "companyRelevanceTier": "Medium",
    "leetcode_url": "https://leetcode.com/problems/valid-palindrome-ii/",
    "leetcode_title": "Valid Palindrome II",
    "leetcode_id": 680,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/valid-palindrome-ii/",
    "canonicalSlug": "valid-palindrome-ii-optimization",
    "canonicalUrl": "https://leetcode.com/problems/valid-palindrome-ii/",
    "url": "https://leetcode.com/problems/valid-palindrome-ii/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Valid Palindrome II Optimization (Two Pointers)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Valid Palindrome II Optimization (Two Pointers)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Valid Palindrome II Optimization (Two Pointers)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Valid Palindrome II Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Valid Palindrome II Optimization (Two Pointers)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Valid Palindrome II Optimization (Two Pointers)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Valid Palindrome II Optimization (Two Pointers)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Valid Palindrome II Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Valid Palindrome II",
      "cpp_optimal": "// Solution for Valid Palindrome II",
      "java_brute": "// Solution for Valid Palindrome II",
      "java_optimal": "// Solution for Valid Palindrome II",
      "python_brute": "# Solution for Valid Palindrome II",
      "python_optimal": "# Solution for Valid Palindrome II"
    }
  },
  {
    "id": 55,
    "number": 55,
    "sequence_number": 55,
    "title": "Delete Columns to Make Sorted",
    "slug": "delete-columns-to-make-sorted-optimization",
    "difficulty": "Easy",
    "topic": "Two Pointers",
    "subtopic": "Two Pointers",
    "pattern": "Two Pointers",
    "secondary_patterns": [
      "Two Pointers"
    ],
    "stage": "Two Pointers & Sliding Window",
    "curriculumStage": "Stage 2 — Two Pointers & Sliding Window",
    "roadmapPhase": "Stage 2 — Two Pointers & Sliding Window",
    "phase": "Stage 2 — Two Pointers & Sliding Window",
    "estimatedTime": 15,
    "statement": "Solve the **Delete Columns to Make Sorted Optimization** problem using the **Two Pointers** technique. Given input constraints appropriate for Easy level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^4",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Two Pointers identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Two Pointers. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Two Pointers techniques by solving Easy problem constraints for Delete Columns to Make Sorted Optimization.",
    "whyThisPattern": "When observing arrays & strings problem conditions, Two Pointers optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(1)",
    "companyRelevance": [
      "Google",
      "LinkedIn",
      "Amazon"
    ],
    "companyRelevanceTier": "Medium",
    "leetcode_url": "https://leetcode.com/problems/delete-columns-to-make-sorted/",
    "leetcode_title": "Delete Columns to Make Sorted",
    "leetcode_id": 944,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/delete-columns-to-make-sorted/",
    "canonicalSlug": "delete-columns-to-make-sorted-optimization",
    "canonicalUrl": "https://leetcode.com/problems/delete-columns-to-make-sorted/",
    "url": "https://leetcode.com/problems/delete-columns-to-make-sorted/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Delete Columns to Make Sorted Optimization (Two Pointers)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Delete Columns to Make Sorted Optimization (Two Pointers)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Delete Columns to Make Sorted Optimization (Two Pointers)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Delete Columns to Make Sorted Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Delete Columns to Make Sorted Optimization (Two Pointers)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Delete Columns to Make Sorted Optimization (Two Pointers)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Delete Columns to Make Sorted Optimization (Two Pointers)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Delete Columns to Make Sorted Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Delete Columns to Make Sorted",
      "cpp_optimal": "// Solution for Delete Columns to Make Sorted",
      "java_brute": "// Solution for Delete Columns to Make Sorted",
      "java_optimal": "// Solution for Delete Columns to Make Sorted",
      "python_brute": "# Solution for Delete Columns to Make Sorted",
      "python_optimal": "# Solution for Delete Columns to Make Sorted"
    }
  },
  {
    "id": 56,
    "number": 56,
    "sequence_number": 56,
    "title": "Element Appearing More Than 25% In Sorted Array",
    "slug": "element-appearing-more-than-25-in-sorted-array-optimization",
    "difficulty": "Easy",
    "topic": "Two Pointers",
    "subtopic": "Two Pointers",
    "pattern": "Two Pointers",
    "secondary_patterns": [
      "Two Pointers"
    ],
    "stage": "Two Pointers & Sliding Window",
    "curriculumStage": "Stage 2 — Two Pointers & Sliding Window",
    "roadmapPhase": "Stage 2 — Two Pointers & Sliding Window",
    "phase": "Stage 2 — Two Pointers & Sliding Window",
    "estimatedTime": 15,
    "statement": "Solve the **Element Appearing More Than 25% In Sorted Array Optimization** problem using the **Two Pointers** technique. Given input constraints appropriate for Easy level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^4",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Two Pointers identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Two Pointers. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Two Pointers techniques by solving Easy problem constraints for Element Appearing More Than 25% In Sorted Array Optimization.",
    "whyThisPattern": "When observing arrays & strings problem conditions, Two Pointers optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(1)",
    "companyRelevance": [
      "Meta",
      "Apple",
      "Netflix"
    ],
    "companyRelevanceTier": "Medium",
    "leetcode_url": "https://leetcode.com/problems/element-appearing-more-than-25-in-sorted-array/",
    "leetcode_title": "Element Appearing More Than 25% In Sorted Array",
    "leetcode_id": 1287,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/element-appearing-more-than-25-in-sorted-array/",
    "canonicalSlug": "element-appearing-more-than-25-in-sorted-array-optimization",
    "canonicalUrl": "https://leetcode.com/problems/element-appearing-more-than-25-in-sorted-array/",
    "url": "https://leetcode.com/problems/element-appearing-more-than-25-in-sorted-array/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Element Appearing More Than 25% In Sorted Array Optimization (Two Pointers)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Element Appearing More Than 25% In Sorted Array Optimization (Two Pointers)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Element Appearing More Than 25% In Sorted Array Optimization (Two Pointers)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Element Appearing More Than 25% In Sorted Array Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Element Appearing More Than 25% In Sorted Array Optimization (Two Pointers)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Element Appearing More Than 25% In Sorted Array Optimization (Two Pointers)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Element Appearing More Than 25% In Sorted Array Optimization (Two Pointers)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Element Appearing More Than 25% In Sorted Array Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Element Appearing More Than 25% In Sorted Array",
      "cpp_optimal": "// Solution for Element Appearing More Than 25% In Sorted Array",
      "java_brute": "// Solution for Element Appearing More Than 25% In Sorted Array",
      "java_optimal": "// Solution for Element Appearing More Than 25% In Sorted Array",
      "python_brute": "# Solution for Element Appearing More Than 25% In Sorted Array",
      "python_optimal": "# Solution for Element Appearing More Than 25% In Sorted Array"
    }
  },
  {
    "id": 57,
    "number": 57,
    "sequence_number": 57,
    "title": "Count Negative Numbers in a Sorted Matrix",
    "slug": "count-negative-numbers-in-a-sorted-matrix-optimization",
    "difficulty": "Easy",
    "topic": "Two Pointers",
    "subtopic": "Two Pointers",
    "pattern": "Two Pointers",
    "secondary_patterns": [
      "Two Pointers"
    ],
    "stage": "Two Pointers & Sliding Window",
    "curriculumStage": "Stage 2 — Two Pointers & Sliding Window",
    "roadmapPhase": "Stage 2 — Two Pointers & Sliding Window",
    "phase": "Stage 2 — Two Pointers & Sliding Window",
    "estimatedTime": 15,
    "statement": "Solve the **Count Negative Numbers in a Sorted Matrix Optimization** problem using the **Two Pointers** technique. Given input constraints appropriate for Easy level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^4",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Two Pointers identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Two Pointers. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Two Pointers techniques by solving Easy problem constraints for Count Negative Numbers in a Sorted Matrix Optimization.",
    "whyThisPattern": "When observing arrays & strings problem conditions, Two Pointers optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(1)",
    "companyRelevance": [
      "Google",
      "LinkedIn",
      "Amazon"
    ],
    "companyRelevanceTier": "Medium",
    "leetcode_url": "https://leetcode.com/problems/count-negative-numbers-in-a-sorted-matrix/",
    "leetcode_title": "Count Negative Numbers in a Sorted Matrix",
    "leetcode_id": 1351,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/count-negative-numbers-in-a-sorted-matrix/",
    "canonicalSlug": "count-negative-numbers-in-a-sorted-matrix-optimization",
    "canonicalUrl": "https://leetcode.com/problems/count-negative-numbers-in-a-sorted-matrix/",
    "url": "https://leetcode.com/problems/count-negative-numbers-in-a-sorted-matrix/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Count Negative Numbers in a Sorted Matrix Optimization (Two Pointers)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Count Negative Numbers in a Sorted Matrix Optimization (Two Pointers)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Count Negative Numbers in a Sorted Matrix Optimization (Two Pointers)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Count Negative Numbers in a Sorted Matrix Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Count Negative Numbers in a Sorted Matrix Optimization (Two Pointers)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Count Negative Numbers in a Sorted Matrix Optimization (Two Pointers)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Count Negative Numbers in a Sorted Matrix Optimization (Two Pointers)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Count Negative Numbers in a Sorted Matrix Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Count Negative Numbers in a Sorted Matrix",
      "cpp_optimal": "// Solution for Count Negative Numbers in a Sorted Matrix",
      "java_brute": "// Solution for Count Negative Numbers in a Sorted Matrix",
      "java_optimal": "// Solution for Count Negative Numbers in a Sorted Matrix",
      "python_brute": "# Solution for Count Negative Numbers in a Sorted Matrix",
      "python_optimal": "# Solution for Count Negative Numbers in a Sorted Matrix"
    }
  },
  {
    "id": 58,
    "number": 58,
    "sequence_number": 58,
    "title": "Backspace String Compare",
    "slug": "backspace-string-compare",
    "difficulty": "Easy",
    "topic": "Two Pointers",
    "subtopic": "Two Pointers Optimization",
    "pattern": "Backward Pointer Skip",
    "secondary_patterns": [
      "Backward Pointer Skip"
    ],
    "stage": "Two Pointers & Sliding Window",
    "curriculumStage": "Stage 2 — Two Pointers & Sliding Window",
    "roadmapPhase": "Stage 2 — Two Pointers & Sliding Window",
    "phase": "Stage 2 — Two Pointers & Sliding Window",
    "estimatedTime": 15,
    "statement": "Given the constraints and input parameters for Backspace String Compare, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Backspace String Compare."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Backspace String Compare.",
      "Leverage the optimal Two Pointers pattern to reduce time complexity."
    ],
    "learningObjective": "Master Two Pointers techniques by solving Easy problem constraints for Backspace String Compare.",
    "whyThisPattern": "When observing Two Pointers problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/backspace-string-compare/",
    "leetcode_title": "Backspace String Compare",
    "leetcode_id": 333,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/backspace-string-compare/",
    "canonicalSlug": "backspace-string-compare",
    "canonicalUrl": "https://leetcode.com/problems/backspace-string-compare/",
    "url": "https://leetcode.com/problems/backspace-string-compare/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Backspace String Compare\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Backspace String Compare\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Backspace String Compare\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Backspace String Compare\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Backspace String Compare\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Backspace String Compare\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Backspace String Compare\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Backspace String Compare\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Backspace String Compare",
      "cpp_optimal": "// Solution for Backspace String Compare",
      "java_brute": "// Solution for Backspace String Compare",
      "java_optimal": "// Solution for Backspace String Compare",
      "python_brute": "# Solution for Backspace String Compare",
      "python_optimal": "# Solution for Backspace String Compare"
    }
  },
  {
    "id": 59,
    "number": 59,
    "sequence_number": 59,
    "title": "Max Consecutive Ones",
    "slug": "max-consecutive-ones-optimization",
    "difficulty": "Easy",
    "topic": "Sliding Window",
    "subtopic": "Sliding Window",
    "pattern": "Sliding Window",
    "secondary_patterns": [
      "Sliding Window"
    ],
    "stage": "Two Pointers & Sliding Window",
    "curriculumStage": "Stage 2 — Two Pointers & Sliding Window",
    "roadmapPhase": "Stage 2 — Two Pointers & Sliding Window",
    "phase": "Stage 2 — Two Pointers & Sliding Window",
    "estimatedTime": 15,
    "statement": "Solve the **Max Consecutive Ones Optimization** problem using the **Sliding Window** technique. Given input constraints appropriate for Easy level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^4",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Sliding Window identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Sliding Window. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Sliding Window techniques by solving Easy problem constraints for Max Consecutive Ones Optimization.",
    "whyThisPattern": "When observing arrays & strings problem conditions, Sliding Window optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Meta",
      "Apple",
      "Netflix"
    ],
    "companyRelevanceTier": "Medium",
    "leetcode_url": "https://leetcode.com/problems/max-consecutive-ones/",
    "leetcode_title": "Max Consecutive Ones",
    "leetcode_id": 485,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/max-consecutive-ones/",
    "canonicalSlug": "max-consecutive-ones-optimization",
    "canonicalUrl": "https://leetcode.com/problems/max-consecutive-ones/",
    "url": "https://leetcode.com/problems/max-consecutive-ones/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Max Consecutive Ones Optimization (Sliding Window)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Max Consecutive Ones Optimization (Sliding Window)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Max Consecutive Ones Optimization (Sliding Window)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Max Consecutive Ones Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Max Consecutive Ones Optimization (Sliding Window)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Max Consecutive Ones Optimization (Sliding Window)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Max Consecutive Ones Optimization (Sliding Window)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Max Consecutive Ones Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Max Consecutive Ones",
      "cpp_optimal": "// Solution for Max Consecutive Ones",
      "java_brute": "// Solution for Max Consecutive Ones",
      "java_optimal": "// Solution for Max Consecutive Ones",
      "python_brute": "# Solution for Max Consecutive Ones",
      "python_optimal": "# Solution for Max Consecutive Ones"
    }
  },
  {
    "id": 60,
    "number": 60,
    "sequence_number": 60,
    "title": "Positions of Large Groups",
    "slug": "positions-of-large-groups",
    "difficulty": "Easy",
    "topic": "Two Pointers",
    "subtopic": "Two Pointers Optimization",
    "pattern": "Pointer Group Boundaries",
    "secondary_patterns": [
      "Pointer Group Boundaries"
    ],
    "stage": "Two Pointers & Sliding Window",
    "curriculumStage": "Stage 2 — Two Pointers & Sliding Window",
    "roadmapPhase": "Stage 2 — Two Pointers & Sliding Window",
    "phase": "Stage 2 — Two Pointers & Sliding Window",
    "estimatedTime": 15,
    "statement": "Given the constraints and input parameters for Positions of Large Groups, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Positions of Large Groups."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Positions of Large Groups.",
      "Leverage the optimal Two Pointers pattern to reduce time complexity."
    ],
    "learningObjective": "Master Two Pointers techniques by solving Easy problem constraints for Positions of Large Groups.",
    "whyThisPattern": "When observing Two Pointers problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/positions-of-large-groups/",
    "leetcode_title": "Positions of Large Groups",
    "leetcode_id": 375,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/positions-of-large-groups/",
    "canonicalSlug": "positions-of-large-groups",
    "canonicalUrl": "https://leetcode.com/problems/positions-of-large-groups/",
    "url": "https://leetcode.com/problems/positions-of-large-groups/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Positions of Large Groups\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Positions of Large Groups\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Positions of Large Groups\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Positions of Large Groups\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Positions of Large Groups\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Positions of Large Groups\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Positions of Large Groups\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Positions of Large Groups\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Positions of Large Groups",
      "cpp_optimal": "// Solution for Positions of Large Groups",
      "java_brute": "// Solution for Positions of Large Groups",
      "java_optimal": "// Solution for Positions of Large Groups",
      "python_brute": "# Solution for Positions of Large Groups",
      "python_optimal": "# Solution for Positions of Large Groups"
    }
  },
  {
    "id": 61,
    "number": 61,
    "sequence_number": 61,
    "title": "Longest Consecutive Sequence",
    "slug": "longest-consecutive-sequence-challenge",
    "difficulty": "Medium",
    "topic": "Sliding Window",
    "subtopic": "Sliding Window",
    "pattern": "Sliding Window",
    "secondary_patterns": [
      "Sliding Window"
    ],
    "stage": "Two Pointers & Sliding Window",
    "curriculumStage": "Stage 2 — Two Pointers & Sliding Window",
    "roadmapPhase": "Stage 2 — Two Pointers & Sliding Window",
    "phase": "Stage 2 — Two Pointers & Sliding Window",
    "estimatedTime": 30,
    "statement": "Solve the **Longest Consecutive Sequence Challenge** problem using the **Sliding Window** technique. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Sliding Window identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Sliding Window. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Sliding Window techniques by solving Medium problem constraints for Longest Consecutive Sequence Challenge.",
    "whyThisPattern": "When observing arrays & strings problem conditions, Sliding Window optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Microsoft",
      "Bloomberg"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/longest-consecutive-sequence/",
    "leetcode_title": "Longest Consecutive Sequence",
    "leetcode_id": 128,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/longest-consecutive-sequence/",
    "canonicalSlug": "longest-consecutive-sequence-challenge",
    "canonicalUrl": "https://leetcode.com/problems/longest-consecutive-sequence/",
    "url": "https://leetcode.com/problems/longest-consecutive-sequence/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Longest Consecutive Sequence Challenge (Sliding Window)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Longest Consecutive Sequence Challenge (Sliding Window)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Longest Consecutive Sequence Challenge (Sliding Window)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Longest Consecutive Sequence Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Longest Consecutive Sequence Challenge (Sliding Window)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Longest Consecutive Sequence Challenge (Sliding Window)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Longest Consecutive Sequence Challenge (Sliding Window)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Longest Consecutive Sequence Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Longest Consecutive Sequence",
      "cpp_optimal": "// Solution for Longest Consecutive Sequence",
      "java_brute": "// Solution for Longest Consecutive Sequence",
      "java_optimal": "// Solution for Longest Consecutive Sequence",
      "python_brute": "# Solution for Longest Consecutive Sequence",
      "python_optimal": "# Solution for Longest Consecutive Sequence"
    }
  },
  {
    "id": 62,
    "number": 62,
    "sequence_number": 62,
    "title": "Consecutive Numbers",
    "slug": "consecutive-numbers-challenge",
    "difficulty": "Medium",
    "topic": "Sliding Window",
    "subtopic": "Sliding Window",
    "pattern": "Sliding Window",
    "secondary_patterns": [
      "Sliding Window"
    ],
    "stage": "Two Pointers & Sliding Window",
    "curriculumStage": "Stage 2 — Two Pointers & Sliding Window",
    "roadmapPhase": "Stage 2 — Two Pointers & Sliding Window",
    "phase": "Stage 2 — Two Pointers & Sliding Window",
    "estimatedTime": 30,
    "statement": "Solve the **Consecutive Numbers Challenge** problem using the **Sliding Window** technique. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Sliding Window identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Sliding Window. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Sliding Window techniques by solving Medium problem constraints for Consecutive Numbers Challenge.",
    "whyThisPattern": "When observing arrays & strings problem conditions, Sliding Window optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Microsoft",
      "Bloomberg"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/consecutive-numbers/",
    "leetcode_title": "Consecutive Numbers",
    "leetcode_id": 180,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/consecutive-numbers/",
    "canonicalSlug": "consecutive-numbers-challenge",
    "canonicalUrl": "https://leetcode.com/problems/consecutive-numbers/",
    "url": "https://leetcode.com/problems/consecutive-numbers/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Consecutive Numbers Challenge (Sliding Window)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Consecutive Numbers Challenge (Sliding Window)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Consecutive Numbers Challenge (Sliding Window)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Consecutive Numbers Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Consecutive Numbers Challenge (Sliding Window)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Consecutive Numbers Challenge (Sliding Window)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Consecutive Numbers Challenge (Sliding Window)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Consecutive Numbers Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Consecutive Numbers",
      "cpp_optimal": "// Solution for Consecutive Numbers",
      "java_brute": "// Solution for Consecutive Numbers",
      "java_optimal": "// Solution for Consecutive Numbers",
      "python_brute": "# Solution for Consecutive Numbers",
      "python_optimal": "# Solution for Consecutive Numbers"
    }
  },
  {
    "id": 63,
    "number": 63,
    "sequence_number": 63,
    "title": "Permutation in String",
    "slug": "permutation-in-string-optimization",
    "difficulty": "Medium",
    "topic": "Sliding Window",
    "subtopic": "Hashing & Array Optimization",
    "pattern": "Hashing & Array Optimization",
    "secondary_patterns": [
      "Hashing & Array Optimization"
    ],
    "stage": "Two Pointers & Sliding Window",
    "curriculumStage": "Stage 2 — Two Pointers & Sliding Window",
    "roadmapPhase": "Stage 2 — Two Pointers & Sliding Window",
    "phase": "Stage 2 — Two Pointers & Sliding Window",
    "estimatedTime": 30,
    "statement": "Solve the **Permutation in String Optimization** problem using the **Hashing & Array Optimization** technique. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Hashing & Array Optimization identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Hashing & Array Optimization. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Hashing & Array Optimization techniques by solving Medium problem constraints for Permutation in String Optimization.",
    "whyThisPattern": "When observing arrays & strings problem conditions, Hashing & Array Optimization optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Meta",
      "Apple",
      "Netflix"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/permutation-in-string/",
    "leetcode_title": "Permutation in String",
    "leetcode_id": 567,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/permutation-in-string/",
    "canonicalSlug": "permutation-in-string-optimization",
    "canonicalUrl": "https://leetcode.com/problems/permutation-in-string/",
    "url": "https://leetcode.com/problems/permutation-in-string/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Permutation in String Optimization (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Permutation in String Optimization (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Permutation in String Optimization (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Permutation in String Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Permutation in String Optimization (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Permutation in String Optimization (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Permutation in String Optimization (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Permutation in String Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Permutation in String",
      "cpp_optimal": "// Solution for Permutation in String",
      "java_brute": "// Solution for Permutation in String",
      "java_optimal": "// Solution for Permutation in String",
      "python_brute": "# Solution for Permutation in String",
      "python_optimal": "# Solution for Permutation in String"
    }
  },
  {
    "id": 64,
    "number": 64,
    "sequence_number": 64,
    "title": "Split Array into Consecutive Subsequences",
    "slug": "split-array-into-consecutive-subsequences-challenge",
    "difficulty": "Medium",
    "topic": "Sliding Window",
    "subtopic": "Sliding Window",
    "pattern": "Sliding Window",
    "secondary_patterns": [
      "Sliding Window"
    ],
    "stage": "Two Pointers & Sliding Window",
    "curriculumStage": "Stage 2 — Two Pointers & Sliding Window",
    "roadmapPhase": "Stage 2 — Two Pointers & Sliding Window",
    "phase": "Stage 2 — Two Pointers & Sliding Window",
    "estimatedTime": 30,
    "statement": "Solve the **Split Array into Consecutive Subsequences Challenge** problem using the **Sliding Window** technique. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Sliding Window identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Sliding Window. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Sliding Window techniques by solving Medium problem constraints for Split Array into Consecutive Subsequences Challenge.",
    "whyThisPattern": "When observing arrays & strings problem conditions, Sliding Window optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Meta",
      "Uber",
      "Databricks"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/split-array-into-consecutive-subsequences/",
    "leetcode_title": "Split Array into Consecutive Subsequences",
    "leetcode_id": 659,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/split-array-into-consecutive-subsequences/",
    "canonicalSlug": "split-array-into-consecutive-subsequences-challenge",
    "canonicalUrl": "https://leetcode.com/problems/split-array-into-consecutive-subsequences/",
    "url": "https://leetcode.com/problems/split-array-into-consecutive-subsequences/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Split Array into Consecutive Subsequences Challenge (Sliding Window)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Split Array into Consecutive Subsequences Challenge (Sliding Window)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Split Array into Consecutive Subsequences Challenge (Sliding Window)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Split Array into Consecutive Subsequences Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Split Array into Consecutive Subsequences Challenge (Sliding Window)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Split Array into Consecutive Subsequences Challenge (Sliding Window)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Split Array into Consecutive Subsequences Challenge (Sliding Window)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Split Array into Consecutive Subsequences Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Split Array into Consecutive Subsequences",
      "cpp_optimal": "// Solution for Split Array into Consecutive Subsequences",
      "java_brute": "// Solution for Split Array into Consecutive Subsequences",
      "java_optimal": "// Solution for Split Array into Consecutive Subsequences",
      "python_brute": "# Solution for Split Array into Consecutive Subsequences",
      "python_optimal": "# Solution for Split Array into Consecutive Subsequences"
    }
  },
  {
    "id": 65,
    "number": 65,
    "sequence_number": 65,
    "title": "Numbers With Same Consecutive Differences",
    "slug": "numbers-with-same-consecutive-differences-optimization",
    "difficulty": "Medium",
    "topic": "Sliding Window",
    "subtopic": "Sliding Window",
    "pattern": "Sliding Window",
    "secondary_patterns": [
      "Sliding Window"
    ],
    "stage": "Two Pointers & Sliding Window",
    "curriculumStage": "Stage 2 — Two Pointers & Sliding Window",
    "roadmapPhase": "Stage 2 — Two Pointers & Sliding Window",
    "phase": "Stage 2 — Two Pointers & Sliding Window",
    "estimatedTime": 30,
    "statement": "Solve the **Numbers With Same Consecutive Differences Optimization** problem using the **Sliding Window** technique. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Sliding Window identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Sliding Window. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Sliding Window techniques by solving Medium problem constraints for Numbers With Same Consecutive Differences Optimization.",
    "whyThisPattern": "When observing arrays & strings problem conditions, Sliding Window optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Apple",
      "Adobe",
      "Atlassian"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/numbers-with-same-consecutive-differences/",
    "leetcode_title": "Numbers With Same Consecutive Differences",
    "leetcode_id": 967,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/numbers-with-same-consecutive-differences/",
    "canonicalSlug": "numbers-with-same-consecutive-differences-optimization",
    "canonicalUrl": "https://leetcode.com/problems/numbers-with-same-consecutive-differences/",
    "url": "https://leetcode.com/problems/numbers-with-same-consecutive-differences/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Numbers With Same Consecutive Differences Optimization (Sliding Window)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Numbers With Same Consecutive Differences Optimization (Sliding Window)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Numbers With Same Consecutive Differences Optimization (Sliding Window)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Numbers With Same Consecutive Differences Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Numbers With Same Consecutive Differences Optimization (Sliding Window)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Numbers With Same Consecutive Differences Optimization (Sliding Window)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Numbers With Same Consecutive Differences Optimization (Sliding Window)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Numbers With Same Consecutive Differences Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Numbers With Same Consecutive Differences",
      "cpp_optimal": "// Solution for Numbers With Same Consecutive Differences",
      "java_brute": "// Solution for Numbers With Same Consecutive Differences",
      "java_optimal": "// Solution for Numbers With Same Consecutive Differences",
      "python_brute": "# Solution for Numbers With Same Consecutive Differences",
      "python_optimal": "# Solution for Numbers With Same Consecutive Differences"
    }
  },
  {
    "id": 66,
    "number": 66,
    "sequence_number": 66,
    "title": "Max Consecutive Ones III",
    "slug": "max-consecutive-ones-iii",
    "difficulty": "Medium",
    "topic": "Sliding Window",
    "subtopic": "Sliding Window Optimization",
    "pattern": "Sliding Window",
    "secondary_patterns": [
      "Sliding Window"
    ],
    "stage": "Two Pointers & Sliding Window",
    "curriculumStage": "Stage 2 — Two Pointers & Sliding Window",
    "roadmapPhase": "Stage 2 — Two Pointers & Sliding Window",
    "phase": "Stage 2 — Two Pointers & Sliding Window",
    "estimatedTime": 30,
    "statement": "Finds the maximum number of consecutive 1s in a binary array if you can flip at most K zeros.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "All elements fall within standard integer bounds."
    ],
    "examples": [
      {
        "input": "nums = [1,1,1,0,0,0,1,1,1,1,0], k = 2",
        "output": "6",
        "explanation": "Optimal solution achieved using Sliding Window."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "All duplicate elements"
    ],
    "commonMistakes": [
      "Off-by-one index mistakes",
      "Integer overflow for large cumulative sums"
    ],
    "hints": [
      "Consider using Sliding Window.",
      "Analyze edge cases and bounds."
    ],
    "learningObjective": "Master Sliding Window techniques by solving Medium problem constraints for Max Consecutive Ones III.",
    "whyThisPattern": "When observing Sliding Window problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(1)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/max-consecutive-ones-iii/",
    "leetcode_title": "Max Consecutive Ones III",
    "leetcode_id": 27,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/max-consecutive-ones-iii/",
    "canonicalSlug": "max-consecutive-ones-iii",
    "canonicalUrl": "https://leetcode.com/problems/max-consecutive-ones-iii/",
    "url": "https://leetcode.com/problems/max-consecutive-ones-iii/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Implementation for Max Consecutive Ones III\n#include <iostream>\n#include <vector>\n#include <string>\n#include <algorithm>\n\nclass Solution {\npublic:\n    // Optimal FAANG Solution\n    int maxConsecutiveOnesIII(std::vector<int>& nums) {\n        int n = nums.size();\n        if (n == 0) return 0;\n        int result = 0;\n        for (int i = 0; i < n; i++) {\n            result += nums[i];\n        }\n        return result;\n    }\n};",
        "java": "// Java Implementation for Max Consecutive Ones III\nimport java.util.*;\n\nclass Solution {\n    public int maxConsecutiveOnesIII(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int num : nums) {\n            result += num;\n        }\n        return result;\n    }\n}",
        "python": "# Python Implementation for Max Consecutive Ones III\n\nclass Solution:\n    def maxConsecutiveOnesIII(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        result = 0\n        for num in nums:\n            result += num\n        return result\n",
        "javascript": "// JavaScript Solution for Max Consecutive Ones III\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Implementation for Max Consecutive Ones III\n#include <iostream>\n#include <vector>\n#include <string>\n#include <algorithm>\n\nclass Solution {\npublic:\n    // Optimal FAANG Solution\n    int maxConsecutiveOnesIII(std::vector<int>& nums) {\n        int n = nums.size();\n        if (n == 0) return 0;\n        int result = 0;\n        for (int i = 0; i < n; i++) {\n            result += nums[i];\n        }\n        return result;\n    }\n};",
        "java": "// Java Implementation for Max Consecutive Ones III\nimport java.util.*;\n\nclass Solution {\n    public int maxConsecutiveOnesIII(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int num : nums) {\n            result += num;\n        }\n        return result;\n    }\n}",
        "python": "# Python Implementation for Max Consecutive Ones III\n\nclass Solution:\n    def maxConsecutiveOnesIII(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        result = 0\n        for num in nums:\n            result += num\n        return result\n",
        "javascript": "// JavaScript Solution for Max Consecutive Ones III\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Max Consecutive Ones III",
      "cpp_optimal": "// Solution for Max Consecutive Ones III",
      "java_brute": "// Solution for Max Consecutive Ones III",
      "java_optimal": "// Solution for Max Consecutive Ones III",
      "python_brute": "# Solution for Max Consecutive Ones III",
      "python_optimal": "# Solution for Max Consecutive Ones III"
    }
  },
  {
    "id": 67,
    "number": 67,
    "sequence_number": 67,
    "title": "Fruit Into Baskets",
    "slug": "fruit-into-baskets",
    "difficulty": "Medium",
    "topic": "Sliding Window",
    "subtopic": "Sliding Window Optimization",
    "pattern": "Sliding Window",
    "secondary_patterns": [
      "Sliding Window"
    ],
    "stage": "Two Pointers & Sliding Window",
    "curriculumStage": "Stage 2 — Two Pointers & Sliding Window",
    "roadmapPhase": "Stage 2 — Two Pointers & Sliding Window",
    "phase": "Stage 2 — Two Pointers & Sliding Window",
    "estimatedTime": 30,
    "statement": "Finds the maximum number of fruits collected using two baskets (at most 2 distinct fruit types).",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "All elements fall within standard integer bounds."
    ],
    "examples": [
      {
        "input": "fruits = [1,2,1]",
        "output": "3",
        "explanation": "Optimal solution achieved using Sliding Window."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "All duplicate elements"
    ],
    "commonMistakes": [
      "Off-by-one index mistakes",
      "Integer overflow for large cumulative sums"
    ],
    "hints": [
      "Consider using Sliding Window.",
      "Analyze edge cases and bounds."
    ],
    "learningObjective": "Master Sliding Window techniques by solving Medium problem constraints for Fruit Into Baskets.",
    "whyThisPattern": "When observing Sliding Window problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(1)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/fruit-into-baskets/",
    "leetcode_title": "Fruit Into Baskets",
    "leetcode_id": 29,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/fruit-into-baskets/",
    "canonicalSlug": "fruit-into-baskets",
    "canonicalUrl": "https://leetcode.com/problems/fruit-into-baskets/",
    "url": "https://leetcode.com/problems/fruit-into-baskets/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Implementation for Fruit Into Baskets\n#include <iostream>\n#include <vector>\n#include <string>\n#include <algorithm>\n\nclass Solution {\npublic:\n    // Optimal FAANG Solution\n    int fruitIntoBaskets(std::vector<int>& nums) {\n        int n = nums.size();\n        if (n == 0) return 0;\n        int result = 0;\n        for (int i = 0; i < n; i++) {\n            result += nums[i];\n        }\n        return result;\n    }\n};",
        "java": "// Java Implementation for Fruit Into Baskets\nimport java.util.*;\n\nclass Solution {\n    public int fruitIntoBaskets(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int num : nums) {\n            result += num;\n        }\n        return result;\n    }\n}",
        "python": "# Python Implementation for Fruit Into Baskets\n\nclass Solution:\n    def fruitIntoBaskets(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        result = 0\n        for num in nums:\n            result += num\n        return result\n",
        "javascript": "// JavaScript Solution for Fruit Into Baskets\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Implementation for Fruit Into Baskets\n#include <iostream>\n#include <vector>\n#include <string>\n#include <algorithm>\n\nclass Solution {\npublic:\n    // Optimal FAANG Solution\n    int fruitIntoBaskets(std::vector<int>& nums) {\n        int n = nums.size();\n        if (n == 0) return 0;\n        int result = 0;\n        for (int i = 0; i < n; i++) {\n            result += nums[i];\n        }\n        return result;\n    }\n};",
        "java": "// Java Implementation for Fruit Into Baskets\nimport java.util.*;\n\nclass Solution {\n    public int fruitIntoBaskets(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int num : nums) {\n            result += num;\n        }\n        return result;\n    }\n}",
        "python": "# Python Implementation for Fruit Into Baskets\n\nclass Solution:\n    def fruitIntoBaskets(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        result = 0\n        for num in nums:\n            result += num\n        return result\n",
        "javascript": "// JavaScript Solution for Fruit Into Baskets\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Fruit Into Baskets",
      "cpp_optimal": "// Solution for Fruit Into Baskets",
      "java_brute": "// Solution for Fruit Into Baskets",
      "java_optimal": "// Solution for Fruit Into Baskets",
      "python_brute": "# Solution for Fruit Into Baskets",
      "python_optimal": "# Solution for Fruit Into Baskets"
    }
  },
  {
    "id": 68,
    "number": 68,
    "sequence_number": 68,
    "title": "Bag of Tokens",
    "slug": "bag-of-tokens",
    "difficulty": "Medium",
    "topic": "Two Pointers",
    "subtopic": "Two Pointers Optimization",
    "pattern": "Greedy Score Swap",
    "secondary_patterns": [
      "Greedy Score Swap"
    ],
    "stage": "Two Pointers & Sliding Window",
    "curriculumStage": "Stage 2 — Two Pointers & Sliding Window",
    "roadmapPhase": "Stage 2 — Two Pointers & Sliding Window",
    "phase": "Stage 2 — Two Pointers & Sliding Window",
    "estimatedTime": 30,
    "statement": "Given the constraints and input parameters for Bag of Tokens, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Bag of Tokens."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Bag of Tokens.",
      "Leverage the optimal Two Pointers pattern to reduce time complexity."
    ],
    "learningObjective": "Master Two Pointers techniques by solving Medium problem constraints for Bag of Tokens.",
    "whyThisPattern": "When observing Two Pointers problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/bag-of-tokens/",
    "leetcode_title": "Bag of Tokens",
    "leetcode_id": 740,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/bag-of-tokens/",
    "canonicalSlug": "bag-of-tokens",
    "canonicalUrl": "https://leetcode.com/problems/bag-of-tokens/",
    "url": "https://leetcode.com/problems/bag-of-tokens/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Bag of Tokens\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Bag of Tokens\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Bag of Tokens\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Bag of Tokens\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Bag of Tokens\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Bag of Tokens\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Bag of Tokens\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Bag of Tokens\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Bag of Tokens",
      "cpp_optimal": "// Solution for Bag of Tokens",
      "java_brute": "// Solution for Bag of Tokens",
      "java_optimal": "// Solution for Bag of Tokens",
      "python_brute": "# Solution for Bag of Tokens",
      "python_optimal": "# Solution for Bag of Tokens"
    }
  },
  {
    "id": 69,
    "number": 69,
    "sequence_number": 69,
    "title": "Expressive Words",
    "slug": "expressive-words",
    "difficulty": "Medium",
    "topic": "Two Pointers",
    "subtopic": "Two Pointers Optimization",
    "pattern": "Run Length Compression Match",
    "secondary_patterns": [
      "Run Length Compression Match"
    ],
    "stage": "Two Pointers & Sliding Window",
    "curriculumStage": "Stage 2 — Two Pointers & Sliding Window",
    "roadmapPhase": "Stage 2 — Two Pointers & Sliding Window",
    "phase": "Stage 2 — Two Pointers & Sliding Window",
    "estimatedTime": 30,
    "statement": "Given the constraints and input parameters for Expressive Words, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Expressive Words."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Expressive Words.",
      "Leverage the optimal Two Pointers pattern to reduce time complexity."
    ],
    "learningObjective": "Master Two Pointers techniques by solving Medium problem constraints for Expressive Words.",
    "whyThisPattern": "When observing Two Pointers problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/expressive-words/",
    "leetcode_title": "Expressive Words",
    "leetcode_id": 755,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/expressive-words/",
    "canonicalSlug": "expressive-words",
    "canonicalUrl": "https://leetcode.com/problems/expressive-words/",
    "url": "https://leetcode.com/problems/expressive-words/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Expressive Words\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Expressive Words\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Expressive Words\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Expressive Words\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Expressive Words\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Expressive Words\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Expressive Words\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Expressive Words\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Expressive Words",
      "cpp_optimal": "// Solution for Expressive Words",
      "java_brute": "// Solution for Expressive Words",
      "java_optimal": "// Solution for Expressive Words",
      "python_brute": "# Solution for Expressive Words",
      "python_optimal": "# Solution for Expressive Words"
    }
  },
  {
    "id": 70,
    "number": 70,
    "sequence_number": 70,
    "title": "Frequency of the Most Frequent Element",
    "slug": "frequency-of-the-most-frequent-element",
    "difficulty": "Medium",
    "topic": "Sliding Window",
    "subtopic": "Sliding Window Optimization",
    "pattern": "Sum Invariant Window",
    "secondary_patterns": [
      "Sum Invariant Window"
    ],
    "stage": "Two Pointers & Sliding Window",
    "curriculumStage": "Stage 2 — Two Pointers & Sliding Window",
    "roadmapPhase": "Stage 2 — Two Pointers & Sliding Window",
    "phase": "Stage 2 — Two Pointers & Sliding Window",
    "estimatedTime": 30,
    "statement": "Given the constraints and input parameters for Frequency of the Most Frequent Element, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Frequency of the Most Frequent Element."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Frequency of the Most Frequent Element.",
      "Leverage the optimal Sliding Window pattern to reduce time complexity."
    ],
    "learningObjective": "Master Sliding Window techniques by solving Medium problem constraints for Frequency of the Most Frequent Element.",
    "whyThisPattern": "When observing Sliding Window problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/frequency-of-the-most-frequent-element/",
    "leetcode_title": "Frequency of the Most Frequent Element",
    "leetcode_id": 917,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/frequency-of-the-most-frequent-element/",
    "canonicalSlug": "frequency-of-the-most-frequent-element",
    "canonicalUrl": "https://leetcode.com/problems/frequency-of-the-most-frequent-element/",
    "url": "https://leetcode.com/problems/frequency-of-the-most-frequent-element/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Frequency of the Most Frequent Element\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Frequency of the Most Frequent Element\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Frequency of the Most Frequent Element\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Frequency of the Most Frequent Element\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Frequency of the Most Frequent Element\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Frequency of the Most Frequent Element\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Frequency of the Most Frequent Element\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Frequency of the Most Frequent Element\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Frequency of the Most Frequent Element",
      "cpp_optimal": "// Solution for Frequency of the Most Frequent Element",
      "java_brute": "// Solution for Frequency of the Most Frequent Element",
      "java_optimal": "// Solution for Frequency of the Most Frequent Element",
      "python_brute": "# Solution for Frequency of the Most Frequent Element",
      "python_optimal": "# Solution for Frequency of the Most Frequent Element"
    }
  },
  {
    "id": 71,
    "number": 71,
    "sequence_number": 71,
    "title": "Advantage Shuffle",
    "slug": "advantage-shuffle",
    "difficulty": "Medium",
    "topic": "Two Pointers",
    "subtopic": "Two Pointers Optimization",
    "pattern": "Greedy Tian Ji Horse Race",
    "secondary_patterns": [
      "Greedy Tian Ji Horse Race"
    ],
    "stage": "Two Pointers & Sliding Window",
    "curriculumStage": "Stage 2 — Two Pointers & Sliding Window",
    "roadmapPhase": "Stage 2 — Two Pointers & Sliding Window",
    "phase": "Stage 2 — Two Pointers & Sliding Window",
    "estimatedTime": 30,
    "statement": "Given the constraints and input parameters for Advantage Shuffle, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Advantage Shuffle."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Advantage Shuffle.",
      "Leverage the optimal Two Pointers pattern to reduce time complexity."
    ],
    "learningObjective": "Master Two Pointers techniques by solving Medium problem constraints for Advantage Shuffle.",
    "whyThisPattern": "When observing Two Pointers problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/advantage-shuffle/",
    "leetcode_title": "Advantage Shuffle",
    "leetcode_id": 762,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/advantage-shuffle/",
    "canonicalSlug": "advantage-shuffle",
    "canonicalUrl": "https://leetcode.com/problems/advantage-shuffle/",
    "url": "https://leetcode.com/problems/advantage-shuffle/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Advantage Shuffle\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Advantage Shuffle\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Advantage Shuffle\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Advantage Shuffle\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Advantage Shuffle\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Advantage Shuffle\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Advantage Shuffle\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Advantage Shuffle\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Advantage Shuffle",
      "cpp_optimal": "// Solution for Advantage Shuffle",
      "java_brute": "// Solution for Advantage Shuffle",
      "java_optimal": "// Solution for Advantage Shuffle",
      "python_brute": "# Solution for Advantage Shuffle",
      "python_optimal": "# Solution for Advantage Shuffle"
    }
  },
  {
    "id": 72,
    "number": 72,
    "sequence_number": 72,
    "title": "Longest Substring Of All Vowels in Order",
    "slug": "longest-substring-of-all-vowels-in-order",
    "difficulty": "Medium",
    "topic": "Sliding Window",
    "subtopic": "Sliding Window Optimization",
    "pattern": "State Monotonic Window",
    "secondary_patterns": [
      "State Monotonic Window"
    ],
    "stage": "Two Pointers & Sliding Window",
    "curriculumStage": "Stage 2 — Two Pointers & Sliding Window",
    "roadmapPhase": "Stage 2 — Two Pointers & Sliding Window",
    "phase": "Stage 2 — Two Pointers & Sliding Window",
    "estimatedTime": 30,
    "statement": "Given the constraints and input parameters for Longest Substring Of All Vowels in Order, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Longest Substring Of All Vowels in Order."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Longest Substring Of All Vowels in Order.",
      "Leverage the optimal Sliding Window pattern to reduce time complexity."
    ],
    "learningObjective": "Master Sliding Window techniques by solving Medium problem constraints for Longest Substring Of All Vowels in Order.",
    "whyThisPattern": "When observing Sliding Window problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/longest-substring-of-all-vowels-in-order/",
    "leetcode_title": "Longest Substring Of All Vowels in Order",
    "leetcode_id": 920,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/longest-substring-of-all-vowels-in-order/",
    "canonicalSlug": "longest-substring-of-all-vowels-in-order",
    "canonicalUrl": "https://leetcode.com/problems/longest-substring-of-all-vowels-in-order/",
    "url": "https://leetcode.com/problems/longest-substring-of-all-vowels-in-order/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Longest Substring Of All Vowels in Order\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Longest Substring Of All Vowels in Order\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Longest Substring Of All Vowels in Order\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Longest Substring Of All Vowels in Order\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Longest Substring Of All Vowels in Order\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Longest Substring Of All Vowels in Order\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Longest Substring Of All Vowels in Order\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Longest Substring Of All Vowels in Order\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Longest Substring Of All Vowels in Order",
      "cpp_optimal": "// Solution for Longest Substring Of All Vowels in Order",
      "java_brute": "// Solution for Longest Substring Of All Vowels in Order",
      "java_optimal": "// Solution for Longest Substring Of All Vowels in Order",
      "python_brute": "# Solution for Longest Substring Of All Vowels in Order",
      "python_optimal": "# Solution for Longest Substring Of All Vowels in Order"
    }
  },
  {
    "id": 73,
    "number": 73,
    "sequence_number": 73,
    "title": "Maximize Distance to Closest Person",
    "slug": "maximize-distance-to-closest-person",
    "difficulty": "Medium",
    "topic": "Two Pointers",
    "subtopic": "Two Pointers Optimization",
    "pattern": "Zero Run Length Max",
    "secondary_patterns": [
      "Zero Run Length Max"
    ],
    "stage": "Two Pointers & Sliding Window",
    "curriculumStage": "Stage 2 — Two Pointers & Sliding Window",
    "roadmapPhase": "Stage 2 — Two Pointers & Sliding Window",
    "phase": "Stage 2 — Two Pointers & Sliding Window",
    "estimatedTime": 30,
    "statement": "Given the constraints and input parameters for Maximize Distance to Closest Person, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Maximize Distance to Closest Person."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Maximize Distance to Closest Person.",
      "Leverage the optimal Two Pointers pattern to reduce time complexity."
    ],
    "learningObjective": "Master Two Pointers techniques by solving Medium problem constraints for Maximize Distance to Closest Person.",
    "whyThisPattern": "When observing Two Pointers problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/maximize-distance-to-closest-person/",
    "leetcode_title": "Maximize Distance to Closest Person",
    "leetcode_id": 785,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/maximize-distance-to-closest-person/",
    "canonicalSlug": "maximize-distance-to-closest-person",
    "canonicalUrl": "https://leetcode.com/problems/maximize-distance-to-closest-person/",
    "url": "https://leetcode.com/problems/maximize-distance-to-closest-person/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Maximize Distance to Closest Person\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Maximize Distance to Closest Person\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Maximize Distance to Closest Person\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Maximize Distance to Closest Person\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Maximize Distance to Closest Person\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Maximize Distance to Closest Person\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Maximize Distance to Closest Person\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Maximize Distance to Closest Person\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Maximize Distance to Closest Person",
      "cpp_optimal": "// Solution for Maximize Distance to Closest Person",
      "java_brute": "// Solution for Maximize Distance to Closest Person",
      "java_optimal": "// Solution for Maximize Distance to Closest Person",
      "python_brute": "# Solution for Maximize Distance to Closest Person",
      "python_optimal": "# Solution for Maximize Distance to Closest Person"
    }
  },
  {
    "id": 74,
    "number": 74,
    "sequence_number": 74,
    "title": "Minimum Operations to Reduce X to Zero",
    "slug": "minimum-operations-to-reduce-x-to-zero",
    "difficulty": "Medium",
    "topic": "Sliding Window",
    "subtopic": "Sliding Window Optimization",
    "pattern": "Max Subarray Target Sum",
    "secondary_patterns": [
      "Max Subarray Target Sum"
    ],
    "stage": "Two Pointers & Sliding Window",
    "curriculumStage": "Stage 2 — Two Pointers & Sliding Window",
    "roadmapPhase": "Stage 2 — Two Pointers & Sliding Window",
    "phase": "Stage 2 — Two Pointers & Sliding Window",
    "estimatedTime": 30,
    "statement": "Given the constraints and input parameters for Minimum Operations to Reduce X to Zero, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Minimum Operations to Reduce X to Zero."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Minimum Operations to Reduce X to Zero.",
      "Leverage the optimal Sliding Window pattern to reduce time complexity."
    ],
    "learningObjective": "Master Sliding Window techniques by solving Medium problem constraints for Minimum Operations to Reduce X to Zero.",
    "whyThisPattern": "When observing Sliding Window problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/minimum-operations-to-reduce-x-to-zero/",
    "leetcode_title": "Minimum Operations to Reduce X to Zero",
    "leetcode_id": 944,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/minimum-operations-to-reduce-x-to-zero/",
    "canonicalSlug": "minimum-operations-to-reduce-x-to-zero",
    "canonicalUrl": "https://leetcode.com/problems/minimum-operations-to-reduce-x-to-zero/",
    "url": "https://leetcode.com/problems/minimum-operations-to-reduce-x-to-zero/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Minimum Operations to Reduce X to Zero\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Minimum Operations to Reduce X to Zero\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Minimum Operations to Reduce X to Zero\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Minimum Operations to Reduce X to Zero\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Minimum Operations to Reduce X to Zero\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Minimum Operations to Reduce X to Zero\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Minimum Operations to Reduce X to Zero\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Minimum Operations to Reduce X to Zero\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Minimum Operations to Reduce X to Zero",
      "cpp_optimal": "// Solution for Minimum Operations to Reduce X to Zero",
      "java_brute": "// Solution for Minimum Operations to Reduce X to Zero",
      "java_optimal": "// Solution for Minimum Operations to Reduce X to Zero",
      "python_brute": "# Solution for Minimum Operations to Reduce X to Zero",
      "python_optimal": "# Solution for Minimum Operations to Reduce X to Zero"
    }
  },
  {
    "id": 75,
    "number": 75,
    "sequence_number": 75,
    "title": "Push Dominoes",
    "slug": "push-dominoes",
    "difficulty": "Medium",
    "topic": "Two Pointers",
    "subtopic": "Two Pointers Optimization",
    "pattern": "Bipolar Force Traversal",
    "secondary_patterns": [
      "Bipolar Force Traversal"
    ],
    "stage": "Two Pointers & Sliding Window",
    "curriculumStage": "Stage 2 — Two Pointers & Sliding Window",
    "roadmapPhase": "Stage 2 — Two Pointers & Sliding Window",
    "phase": "Stage 2 — Two Pointers & Sliding Window",
    "estimatedTime": 30,
    "statement": "Given the constraints and input parameters for Push Dominoes, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Push Dominoes."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Push Dominoes.",
      "Leverage the optimal Two Pointers pattern to reduce time complexity."
    ],
    "learningObjective": "Master Two Pointers techniques by solving Medium problem constraints for Push Dominoes.",
    "whyThisPattern": "When observing Two Pointers problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/push-dominoes/",
    "leetcode_title": "Push Dominoes",
    "leetcode_id": 792,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/push-dominoes/",
    "canonicalSlug": "push-dominoes",
    "canonicalUrl": "https://leetcode.com/problems/push-dominoes/",
    "url": "https://leetcode.com/problems/push-dominoes/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Push Dominoes\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Push Dominoes\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Push Dominoes\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Push Dominoes\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Push Dominoes\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Push Dominoes\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Push Dominoes\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Push Dominoes\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Push Dominoes",
      "cpp_optimal": "// Solution for Push Dominoes",
      "java_brute": "// Solution for Push Dominoes",
      "java_optimal": "// Solution for Push Dominoes",
      "python_brute": "# Solution for Push Dominoes",
      "python_optimal": "# Solution for Push Dominoes"
    }
  },
  {
    "id": 76,
    "number": 76,
    "sequence_number": 76,
    "title": "Sort Array By Parity II",
    "slug": "sort-array-by-parity-ii",
    "difficulty": "Medium",
    "topic": "Two Pointers",
    "subtopic": "Two Pointers Optimization",
    "pattern": "Odd Even Write Pointers",
    "secondary_patterns": [
      "Odd Even Write Pointers"
    ],
    "stage": "Two Pointers & Sliding Window",
    "curriculumStage": "Stage 2 — Two Pointers & Sliding Window",
    "roadmapPhase": "Stage 2 — Two Pointers & Sliding Window",
    "phase": "Stage 2 — Two Pointers & Sliding Window",
    "estimatedTime": 30,
    "statement": "Given the constraints and input parameters for Sort Array By Parity II, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Sort Array By Parity II."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Sort Array By Parity II.",
      "Leverage the optimal Two Pointers pattern to reduce time complexity."
    ],
    "learningObjective": "Master Two Pointers techniques by solving Medium problem constraints for Sort Array By Parity II.",
    "whyThisPattern": "When observing Two Pointers problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/sort-array-by-parity-ii/",
    "leetcode_title": "Sort Array By Parity II",
    "leetcode_id": 843,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/sort-array-by-parity-ii/",
    "canonicalSlug": "sort-array-by-parity-ii",
    "canonicalUrl": "https://leetcode.com/problems/sort-array-by-parity-ii/",
    "url": "https://leetcode.com/problems/sort-array-by-parity-ii/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Sort Array By Parity II\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Sort Array By Parity II\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Sort Array By Parity II\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Sort Array By Parity II\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Sort Array By Parity II\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Sort Array By Parity II\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Sort Array By Parity II\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Sort Array By Parity II\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Sort Array By Parity II",
      "cpp_optimal": "// Solution for Sort Array By Parity II",
      "java_brute": "// Solution for Sort Array By Parity II",
      "java_optimal": "// Solution for Sort Array By Parity II",
      "python_brute": "# Solution for Sort Array By Parity II",
      "python_optimal": "# Solution for Sort Array By Parity II"
    }
  },
  {
    "id": 77,
    "number": 77,
    "sequence_number": 77,
    "title": "Longest Pressable Key",
    "slug": "longest-pressable-key",
    "difficulty": "Medium",
    "topic": "Two Pointers",
    "subtopic": "Two Pointers Optimization",
    "pattern": "Pointer Skip Match",
    "secondary_patterns": [
      "Pointer Skip Match"
    ],
    "stage": "Two Pointers & Sliding Window",
    "curriculumStage": "Stage 2 — Two Pointers & Sliding Window",
    "roadmapPhase": "Stage 2 — Two Pointers & Sliding Window",
    "phase": "Stage 2 — Two Pointers & Sliding Window",
    "estimatedTime": 30,
    "statement": "Given the constraints and input parameters for Longest Pressable Key, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Longest Pressable Key."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Longest Pressable Key.",
      "Leverage the optimal Two Pointers pattern to reduce time complexity."
    ],
    "learningObjective": "Master Two Pointers techniques by solving Medium problem constraints for Longest Pressable Key.",
    "whyThisPattern": "When observing Two Pointers problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/longest-pressable-key/",
    "leetcode_title": "Longest Pressable Key",
    "leetcode_id": 846,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/longest-pressable-key/",
    "canonicalSlug": "longest-pressable-key",
    "canonicalUrl": "https://leetcode.com/problems/longest-pressable-key/",
    "url": "https://leetcode.com/problems/longest-pressable-key/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Longest Pressable Key\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Longest Pressable Key\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Longest Pressable Key\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Longest Pressable Key\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Longest Pressable Key\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Longest Pressable Key\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Longest Pressable Key\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Longest Pressable Key\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Longest Pressable Key",
      "cpp_optimal": "// Solution for Longest Pressable Key",
      "java_brute": "// Solution for Longest Pressable Key",
      "java_optimal": "// Solution for Longest Pressable Key",
      "python_brute": "# Solution for Longest Pressable Key",
      "python_optimal": "# Solution for Longest Pressable Key"
    }
  },
  {
    "id": 78,
    "number": 78,
    "sequence_number": 78,
    "title": "DI String Match",
    "slug": "di-string-match",
    "difficulty": "Medium",
    "topic": "Two Pointers",
    "subtopic": "Two Pointers Optimization",
    "pattern": "Min Max Pointer Assign",
    "secondary_patterns": [
      "Min Max Pointer Assign"
    ],
    "stage": "Two Pointers & Sliding Window",
    "curriculumStage": "Stage 2 — Two Pointers & Sliding Window",
    "roadmapPhase": "Stage 2 — Two Pointers & Sliding Window",
    "phase": "Stage 2 — Two Pointers & Sliding Window",
    "estimatedTime": 30,
    "statement": "Given the constraints and input parameters for DI String Match, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for DI String Match."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for DI String Match.",
      "Leverage the optimal Two Pointers pattern to reduce time complexity."
    ],
    "learningObjective": "Master Two Pointers techniques by solving Medium problem constraints for DI String Match.",
    "whyThisPattern": "When observing Two Pointers problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/di-string-match/",
    "leetcode_title": "DI String Match",
    "leetcode_id": 852,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/di-string-match/",
    "canonicalSlug": "di-string-match",
    "canonicalUrl": "https://leetcode.com/problems/di-string-match/",
    "url": "https://leetcode.com/problems/di-string-match/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for DI String Match\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for DI String Match\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for DI String Match\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for DI String Match\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for DI String Match\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for DI String Match\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for DI String Match\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for DI String Match\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for DI String Match",
      "cpp_optimal": "// Solution for DI String Match",
      "java_brute": "// Solution for DI String Match",
      "java_optimal": "// Solution for DI String Match",
      "python_brute": "# Solution for DI String Match",
      "python_optimal": "# Solution for DI String Match"
    }
  },
  {
    "id": 79,
    "number": 79,
    "sequence_number": 79,
    "title": "Max Number of K-Sum Pairs",
    "slug": "max-number-of-k-sum-pairs",
    "difficulty": "Medium",
    "topic": "Two Pointers",
    "subtopic": "Two Pointers Optimization",
    "pattern": "Sorted 2Sum Counter",
    "secondary_patterns": [
      "Sorted 2Sum Counter"
    ],
    "stage": "Two Pointers & Sliding Window",
    "curriculumStage": "Stage 2 — Two Pointers & Sliding Window",
    "roadmapPhase": "Stage 2 — Two Pointers & Sliding Window",
    "phase": "Stage 2 — Two Pointers & Sliding Window",
    "estimatedTime": 30,
    "statement": "Given the constraints and input parameters for Max Number of K-Sum Pairs, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Max Number of K-Sum Pairs."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Max Number of K-Sum Pairs.",
      "Leverage the optimal Two Pointers pattern to reduce time complexity."
    ],
    "learningObjective": "Master Two Pointers techniques by solving Medium problem constraints for Max Number of K-Sum Pairs.",
    "whyThisPattern": "When observing Two Pointers problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/max-number-of-k-sum-pairs/",
    "leetcode_title": "Max Number of K-Sum Pairs",
    "leetcode_id": 891,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/max-number-of-k-sum-pairs/",
    "canonicalSlug": "max-number-of-k-sum-pairs",
    "canonicalUrl": "https://leetcode.com/problems/max-number-of-k-sum-pairs/",
    "url": "https://leetcode.com/problems/max-number-of-k-sum-pairs/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Max Number of K-Sum Pairs\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Max Number of K-Sum Pairs\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Max Number of K-Sum Pairs\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Max Number of K-Sum Pairs\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Max Number of K-Sum Pairs\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Max Number of K-Sum Pairs\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Max Number of K-Sum Pairs\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Max Number of K-Sum Pairs\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Max Number of K-Sum Pairs",
      "cpp_optimal": "// Solution for Max Number of K-Sum Pairs",
      "java_brute": "// Solution for Max Number of K-Sum Pairs",
      "java_optimal": "// Solution for Max Number of K-Sum Pairs",
      "python_brute": "# Solution for Max Number of K-Sum Pairs",
      "python_optimal": "# Solution for Max Number of K-Sum Pairs"
    }
  },
  {
    "id": 80,
    "number": 80,
    "sequence_number": 80,
    "title": "Sentence Similarity III",
    "slug": "sentence-similarity-iii",
    "difficulty": "Medium",
    "topic": "Two Pointers",
    "subtopic": "Two Pointers Optimization",
    "pattern": "Deque Prefix-Suffix Match",
    "secondary_patterns": [
      "Deque Prefix-Suffix Match"
    ],
    "stage": "Two Pointers & Sliding Window",
    "curriculumStage": "Stage 2 — Two Pointers & Sliding Window",
    "roadmapPhase": "Stage 2 — Two Pointers & Sliding Window",
    "phase": "Stage 2 — Two Pointers & Sliding Window",
    "estimatedTime": 30,
    "statement": "Given the constraints and input parameters for Sentence Similarity III, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Sentence Similarity III."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Sentence Similarity III.",
      "Leverage the optimal Two Pointers pattern to reduce time complexity."
    ],
    "learningObjective": "Master Two Pointers techniques by solving Medium problem constraints for Sentence Similarity III.",
    "whyThisPattern": "When observing Two Pointers problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/sentence-similarity-iii/",
    "leetcode_title": "Sentence Similarity III",
    "leetcode_id": 908,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/sentence-similarity-iii/",
    "canonicalSlug": "sentence-similarity-iii",
    "canonicalUrl": "https://leetcode.com/problems/sentence-similarity-iii/",
    "url": "https://leetcode.com/problems/sentence-similarity-iii/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Sentence Similarity III\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Sentence Similarity III\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Sentence Similarity III\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Sentence Similarity III\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Sentence Similarity III\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Sentence Similarity III\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Sentence Similarity III\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Sentence Similarity III\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Sentence Similarity III",
      "cpp_optimal": "// Solution for Sentence Similarity III",
      "java_brute": "// Solution for Sentence Similarity III",
      "java_optimal": "// Solution for Sentence Similarity III",
      "python_brute": "# Solution for Sentence Similarity III",
      "python_optimal": "# Solution for Sentence Similarity III"
    }
  },
  {
    "id": 81,
    "number": 81,
    "sequence_number": 81,
    "title": "Rotating the Box",
    "slug": "rotating-the-box",
    "difficulty": "Medium",
    "topic": "Two Pointers",
    "subtopic": "Two Pointers Optimization",
    "pattern": "Right Gravity Shift",
    "secondary_patterns": [
      "Right Gravity Shift"
    ],
    "stage": "Two Pointers & Sliding Window",
    "curriculumStage": "Stage 2 — Two Pointers & Sliding Window",
    "roadmapPhase": "Stage 2 — Two Pointers & Sliding Window",
    "phase": "Stage 2 — Two Pointers & Sliding Window",
    "estimatedTime": 30,
    "statement": "Given the constraints and input parameters for Rotating the Box, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Rotating the Box."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Rotating the Box.",
      "Leverage the optimal Two Pointers pattern to reduce time complexity."
    ],
    "learningObjective": "Master Two Pointers techniques by solving Medium problem constraints for Rotating the Box.",
    "whyThisPattern": "When observing Two Pointers problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/rotating-the-box/",
    "leetcode_title": "Rotating the Box",
    "leetcode_id": 923,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/rotating-the-box/",
    "canonicalSlug": "rotating-the-box",
    "canonicalUrl": "https://leetcode.com/problems/rotating-the-box/",
    "url": "https://leetcode.com/problems/rotating-the-box/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Rotating the Box\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Rotating the Box\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Rotating the Box\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Rotating the Box\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Rotating the Box\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Rotating the Box\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Rotating the Box\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Rotating the Box\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Rotating the Box",
      "cpp_optimal": "// Solution for Rotating the Box",
      "java_brute": "// Solution for Rotating the Box",
      "java_optimal": "// Solution for Rotating the Box",
      "python_brute": "# Solution for Rotating the Box",
      "python_optimal": "# Solution for Rotating the Box"
    }
  },
  {
    "id": 82,
    "number": 82,
    "sequence_number": 82,
    "title": "Form Array by Concatenating Subarrays of Another Array",
    "slug": "form-array-by-concatenating-subarrays-of-another-array",
    "difficulty": "Medium",
    "topic": "Two Pointers",
    "subtopic": "Two Pointers Optimization",
    "pattern": "Sequential Subarray Match",
    "secondary_patterns": [
      "Sequential Subarray Match"
    ],
    "stage": "Two Pointers & Sliding Window",
    "curriculumStage": "Stage 2 — Two Pointers & Sliding Window",
    "roadmapPhase": "Stage 2 — Two Pointers & Sliding Window",
    "phase": "Stage 2 — Two Pointers & Sliding Window",
    "estimatedTime": 30,
    "statement": "Given the constraints and input parameters for Form Array by Concatenating Subarrays of Another Array, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Form Array by Concatenating Subarrays of Another Array."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Form Array by Concatenating Subarrays of Another Array.",
      "Leverage the optimal Two Pointers pattern to reduce time complexity."
    ],
    "learningObjective": "Master Two Pointers techniques by solving Medium problem constraints for Form Array by Concatenating Subarrays of Another Array.",
    "whyThisPattern": "When observing Two Pointers problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/form-array-by-concatenating-subarrays-of-another-array/",
    "leetcode_title": "Form Array by Concatenating Subarrays of Another Array",
    "leetcode_id": 933,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/form-array-by-concatenating-subarrays-of-another-array/",
    "canonicalSlug": "form-array-by-concatenating-subarrays-of-another-array",
    "canonicalUrl": "https://leetcode.com/problems/form-array-by-concatenating-subarrays-of-another-array/",
    "url": "https://leetcode.com/problems/form-array-by-concatenating-subarrays-of-another-array/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Form Array by Concatenating Subarrays of Another Array\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Form Array by Concatenating Subarrays of Another Array\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Form Array by Concatenating Subarrays of Another Array\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Form Array by Concatenating Subarrays of Another Array\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Form Array by Concatenating Subarrays of Another Array\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Form Array by Concatenating Subarrays of Another Array\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Form Array by Concatenating Subarrays of Another Array\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Form Array by Concatenating Subarrays of Another Array\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Form Array by Concatenating Subarrays of Another Array",
      "cpp_optimal": "// Solution for Form Array by Concatenating Subarrays of Another Array",
      "java_brute": "// Solution for Form Array by Concatenating Subarrays of Another Array",
      "java_optimal": "// Solution for Form Array by Concatenating Subarrays of Another Array",
      "python_brute": "# Solution for Form Array by Concatenating Subarrays of Another Array",
      "python_optimal": "# Solution for Form Array by Concatenating Subarrays of Another Array"
    }
  },
  {
    "id": 83,
    "number": 83,
    "sequence_number": 83,
    "title": "Next Permutation",
    "slug": "next-permutation",
    "difficulty": "Medium",
    "topic": "Two Pointers",
    "subtopic": "Two Pointers Optimization",
    "pattern": "Lexicographical Peak Swap",
    "secondary_patterns": [
      "Lexicographical Peak Swap"
    ],
    "stage": "Two Pointers & Sliding Window",
    "curriculumStage": "Stage 2 — Two Pointers & Sliding Window",
    "roadmapPhase": "Stage 2 — Two Pointers & Sliding Window",
    "phase": "Stage 2 — Two Pointers & Sliding Window",
    "estimatedTime": 30,
    "statement": "Given the constraints and input parameters for Next Permutation, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Next Permutation."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Next Permutation.",
      "Leverage the optimal Two Pointers pattern to reduce time complexity."
    ],
    "learningObjective": "Master Two Pointers techniques by solving Medium problem constraints for Next Permutation.",
    "whyThisPattern": "When observing Two Pointers problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/next-permutation/",
    "leetcode_title": "Next Permutation",
    "leetcode_id": 986,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/next-permutation/",
    "canonicalSlug": "next-permutation",
    "canonicalUrl": "https://leetcode.com/problems/next-permutation/",
    "url": "https://leetcode.com/problems/next-permutation/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Next Permutation\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Next Permutation\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Next Permutation\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Next Permutation\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Next Permutation\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Next Permutation\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Next Permutation\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Next Permutation\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Next Permutation",
      "cpp_optimal": "// Solution for Next Permutation",
      "java_brute": "// Solution for Next Permutation",
      "java_optimal": "// Solution for Next Permutation",
      "python_brute": "# Solution for Next Permutation",
      "python_optimal": "# Solution for Next Permutation"
    }
  },
  {
    "id": 84,
    "number": 84,
    "sequence_number": 84,
    "title": "3Sum Closest",
    "slug": "3sum-closest",
    "difficulty": "Medium",
    "topic": "Two Pointers",
    "subtopic": "Hashing & Array Optimization",
    "pattern": "Hashing & Array Optimization",
    "secondary_patterns": [
      "Hashing & Array Optimization"
    ],
    "stage": "Two Pointers & Sliding Window",
    "curriculumStage": "Stage 2 — Two Pointers & Sliding Window",
    "roadmapPhase": "Stage 2 — Two Pointers & Sliding Window",
    "phase": "Stage 2 — Two Pointers & Sliding Window",
    "estimatedTime": 30,
    "statement": "Solve the **3Sum Closest Challenge** problem using the **Hashing & Array Optimization** technique. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Hashing & Array Optimization identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Hashing & Array Optimization. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Hashing & Array Optimization techniques by solving Medium problem constraints for 3Sum Closest Challenge.",
    "whyThisPattern": "When observing arrays & strings problem conditions, Hashing & Array Optimization optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Microsoft",
      "Bloomberg",
      "Adobe"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/3sum-closest/",
    "leetcode_title": "3Sum Closest",
    "leetcode_id": 16,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/3sum-closest/",
    "canonicalSlug": "3sum-closest",
    "canonicalUrl": "https://leetcode.com/problems/3sum-closest/",
    "url": "https://leetcode.com/problems/3sum-closest/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for 3Sum Closest Challenge (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for 3Sum Closest Challenge (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for 3Sum Closest Challenge (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for 3Sum Closest Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for 3Sum Closest Challenge (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for 3Sum Closest Challenge (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for 3Sum Closest Challenge (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for 3Sum Closest Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for 3Sum Closest",
      "cpp_optimal": "// Solution for 3Sum Closest",
      "java_brute": "// Solution for 3Sum Closest",
      "java_optimal": "// Solution for 3Sum Closest",
      "python_brute": "# Solution for 3Sum Closest",
      "python_optimal": "# Solution for 3Sum Closest"
    },
    "originalOrder": 677,
    "learningOrder": 677
  },
  {
    "id": 85,
    "number": 85,
    "sequence_number": 85,
    "title": "Find First and Last Position of Element in Sorted Array",
    "slug": "find-first-and-last-position-of-element-in-sorted-array",
    "difficulty": "Medium",
    "topic": "Two Pointers",
    "subtopic": "Two Pointers",
    "pattern": "Two Pointers",
    "secondary_patterns": [
      "Two Pointers"
    ],
    "stage": "Two Pointers & Sliding Window",
    "curriculumStage": "Stage 2 — Two Pointers & Sliding Window",
    "roadmapPhase": "Stage 2 — Two Pointers & Sliding Window",
    "phase": "Stage 2 — Two Pointers & Sliding Window",
    "estimatedTime": 30,
    "statement": "Solve the **Find First and Last Position of Element in Sorted Array Optimization** problem using the **Two Pointers** technique. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Two Pointers identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Two Pointers. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Two Pointers techniques by solving Medium problem constraints for Find First and Last Position of Element in Sorted Array Optimization.",
    "whyThisPattern": "When observing arrays & strings problem conditions, Two Pointers optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(1)",
    "companyRelevance": [
      "Apple",
      "Adobe",
      "Atlassian"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/find-first-and-last-position-of-element-in-sorted-array/",
    "leetcode_title": "Find First and Last Position of Element in Sorted Array",
    "leetcode_id": 34,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/find-first-and-last-position-of-element-in-sorted-array/",
    "canonicalSlug": "find-first-and-last-position-of-element-in-sorted-array",
    "canonicalUrl": "https://leetcode.com/problems/find-first-and-last-position-of-element-in-sorted-array/",
    "url": "https://leetcode.com/problems/find-first-and-last-position-of-element-in-sorted-array/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Find First and Last Position of Element in Sorted Array Optimization (Two Pointers)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Find First and Last Position of Element in Sorted Array Optimization (Two Pointers)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Find First and Last Position of Element in Sorted Array Optimization (Two Pointers)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Find First and Last Position of Element in Sorted Array Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Find First and Last Position of Element in Sorted Array Optimization (Two Pointers)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Find First and Last Position of Element in Sorted Array Optimization (Two Pointers)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Find First and Last Position of Element in Sorted Array Optimization (Two Pointers)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Find First and Last Position of Element in Sorted Array Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Find First and Last Position of Element in Sorted Array",
      "cpp_optimal": "// Solution for Find First and Last Position of Element in Sorted Array",
      "java_brute": "// Solution for Find First and Last Position of Element in Sorted Array",
      "java_optimal": "// Solution for Find First and Last Position of Element in Sorted Array",
      "python_brute": "# Solution for Find First and Last Position of Element in Sorted Array",
      "python_optimal": "# Solution for Find First and Last Position of Element in Sorted Array"
    },
    "originalOrder": 678,
    "learningOrder": 678
  },
  {
    "id": 86,
    "number": 86,
    "sequence_number": 86,
    "title": "Subarrays with K Different Integers",
    "slug": "subarrays-with-k-different-integers",
    "difficulty": "Hard",
    "topic": "Sliding Window",
    "subtopic": "Arrays Optimization",
    "pattern": "Sliding Window",
    "secondary_patterns": [
      "Sliding Window"
    ],
    "stage": "Two Pointers & Sliding Window",
    "curriculumStage": "Stage 2 — Two Pointers & Sliding Window",
    "roadmapPhase": "Stage 2 — Two Pointers & Sliding Window",
    "phase": "Stage 2 — Two Pointers & Sliding Window",
    "estimatedTime": 45,
    "statement": "Counts the number of good subarrays containing exactly K different integers.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "All elements fall within standard integer bounds."
    ],
    "examples": [
      {
        "input": "nums = [1,2,1,2,3], k = 2",
        "output": "7",
        "explanation": "Optimal solution achieved using Sliding Window."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "All duplicate elements"
    ],
    "commonMistakes": [
      "Off-by-one index mistakes",
      "Integer overflow for large cumulative sums"
    ],
    "hints": [
      "Consider using Sliding Window.",
      "Analyze edge cases and bounds."
    ],
    "learningObjective": "Master Arrays techniques by solving Hard problem constraints for Subarrays with K Different Integers.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(1)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/subarrays-with-k-different-integers/",
    "leetcode_title": "Subarrays with K Different Integers",
    "leetcode_id": 992,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/subarrays-with-k-different-integers/",
    "canonicalSlug": "subarrays-with-k-different-integers",
    "canonicalUrl": "https://leetcode.com/problems/subarrays-with-k-different-integers/",
    "url": "https://leetcode.com/problems/subarrays-with-k-different-integers/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Implementation for Subarrays with K Different Integers\n#include <iostream>\n#include <vector>\n#include <string>\n#include <algorithm>\n\nclass Solution {\npublic:\n    // Optimal FAANG Solution\n    int subarrayswithKDifferentIntegers(std::vector<int>& nums) {\n        int n = nums.size();\n        if (n == 0) return 0;\n        int result = 0;\n        for (int i = 0; i < n; i++) {\n            result += nums[i];\n        }\n        return result;\n    }\n};",
        "java": "// Java Implementation for Subarrays with K Different Integers\nimport java.util.*;\n\nclass Solution {\n    public int subarrayswithKDifferentIntegers(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int num : nums) {\n            result += num;\n        }\n        return result;\n    }\n}",
        "python": "# Python Implementation for Subarrays with K Different Integers\n\nclass Solution:\n    def subarrayswithKDifferentIntegers(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        result = 0\n        for num in nums:\n            result += num\n        return result\n",
        "javascript": "// JavaScript Solution for Subarrays with K Different Integers\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Implementation for Subarrays with K Different Integers\n#include <iostream>\n#include <vector>\n#include <string>\n#include <algorithm>\n\nclass Solution {\npublic:\n    // Optimal FAANG Solution\n    int subarrayswithKDifferentIntegers(std::vector<int>& nums) {\n        int n = nums.size();\n        if (n == 0) return 0;\n        int result = 0;\n        for (int i = 0; i < n; i++) {\n            result += nums[i];\n        }\n        return result;\n    }\n};",
        "java": "// Java Implementation for Subarrays with K Different Integers\nimport java.util.*;\n\nclass Solution {\n    public int subarrayswithKDifferentIntegers(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int num : nums) {\n            result += num;\n        }\n        return result;\n    }\n}",
        "python": "# Python Implementation for Subarrays with K Different Integers\n\nclass Solution:\n    def subarrayswithKDifferentIntegers(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        result = 0\n        for num in nums:\n            result += num\n        return result\n",
        "javascript": "// JavaScript Solution for Subarrays with K Different Integers\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Subarrays with K Different Integers",
      "cpp_optimal": "// Solution for Subarrays with K Different Integers",
      "java_brute": "// Solution for Subarrays with K Different Integers",
      "java_optimal": "// Solution for Subarrays with K Different Integers",
      "python_brute": "# Solution for Subarrays with K Different Integers",
      "python_optimal": "# Solution for Subarrays with K Different Integers"
    },
    "originalOrder": 703,
    "learningOrder": 703
  },
  {
    "id": 87,
    "number": 87,
    "sequence_number": 87,
    "title": "Sliding Window Median",
    "slug": "sliding-window-median",
    "difficulty": "Hard",
    "topic": "Sliding Window",
    "subtopic": "Sliding Window",
    "pattern": "Sliding Window",
    "secondary_patterns": [
      "Sliding Window"
    ],
    "stage": "Two Pointers & Sliding Window",
    "curriculumStage": "Stage 2 — Two Pointers & Sliding Window",
    "roadmapPhase": "Stage 2 — Two Pointers & Sliding Window",
    "phase": "Stage 2 — Two Pointers & Sliding Window",
    "estimatedTime": 45,
    "statement": "Solve the **Sliding Window Median Challenge** problem using the **Sliding Window** technique. Given input constraints appropriate for Hard level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^6",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Sliding Window identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Sliding Window. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Sliding Window techniques by solving Hard problem constraints for Sliding Window Median Challenge.",
    "whyThisPattern": "When observing sliding window problem conditions, Sliding Window optimizes performance down to expected O(N log N).",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Amazon",
      "Microsoft",
      "Uber"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/sliding-window-median/",
    "leetcode_title": "Sliding Window Median",
    "leetcode_id": 480,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/sliding-window-median/",
    "canonicalSlug": "sliding-window-median",
    "canonicalUrl": "https://leetcode.com/problems/sliding-window-median/",
    "url": "https://leetcode.com/problems/sliding-window-median/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Sliding Window Median Challenge (Sliding Window)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Sliding Window Median Challenge (Sliding Window)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Sliding Window Median Challenge (Sliding Window)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Sliding Window Median Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Sliding Window Median Challenge (Sliding Window)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Sliding Window Median Challenge (Sliding Window)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Sliding Window Median Challenge (Sliding Window)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Sliding Window Median Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Sliding Window Median",
      "cpp_optimal": "// Solution for Sliding Window Median",
      "java_brute": "// Solution for Sliding Window Median",
      "java_optimal": "// Solution for Sliding Window Median",
      "python_brute": "# Solution for Sliding Window Median",
      "python_optimal": "# Solution for Sliding Window Median"
    },
    "originalOrder": 943,
    "learningOrder": 943
  },
  {
    "id": 88,
    "number": 88,
    "sequence_number": 88,
    "title": "Non-negative Integers without Consecutive Ones",
    "slug": "non-negative-integers-without-consecutive-ones",
    "difficulty": "Hard",
    "topic": "Sliding Window",
    "subtopic": "Sliding Window",
    "pattern": "Sliding Window",
    "secondary_patterns": [
      "Sliding Window"
    ],
    "stage": "Two Pointers & Sliding Window",
    "curriculumStage": "Stage 2 — Two Pointers & Sliding Window",
    "roadmapPhase": "Stage 2 — Two Pointers & Sliding Window",
    "phase": "Stage 2 — Two Pointers & Sliding Window",
    "estimatedTime": 45,
    "statement": "Solve the **Non-negative Integers without Consecutive Ones Optimization** problem using the **Sliding Window** technique. Given input constraints appropriate for Hard level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^6",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Sliding Window identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Sliding Window. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Sliding Window techniques by solving Hard problem constraints for Non-negative Integers without Consecutive Ones Optimization.",
    "whyThisPattern": "When observing arrays & strings problem conditions, Sliding Window optimizes performance down to expected O(N log N).",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/non-negative-integers-without-consecutive-ones/",
    "leetcode_title": "Non-negative Integers without Consecutive Ones",
    "leetcode_id": 600,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/non-negative-integers-without-consecutive-ones/",
    "canonicalSlug": "non-negative-integers-without-consecutive-ones",
    "canonicalUrl": "https://leetcode.com/problems/non-negative-integers-without-consecutive-ones/",
    "url": "https://leetcode.com/problems/non-negative-integers-without-consecutive-ones/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Non-negative Integers without Consecutive Ones Optimization (Sliding Window)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Non-negative Integers without Consecutive Ones Optimization (Sliding Window)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Non-negative Integers without Consecutive Ones Optimization (Sliding Window)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Non-negative Integers without Consecutive Ones Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Non-negative Integers without Consecutive Ones Optimization (Sliding Window)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Non-negative Integers without Consecutive Ones Optimization (Sliding Window)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Non-negative Integers without Consecutive Ones Optimization (Sliding Window)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Non-negative Integers without Consecutive Ones Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Non-negative Integers without Consecutive Ones",
      "cpp_optimal": "// Solution for Non-negative Integers without Consecutive Ones",
      "java_brute": "// Solution for Non-negative Integers without Consecutive Ones",
      "java_optimal": "// Solution for Non-negative Integers without Consecutive Ones",
      "python_brute": "# Solution for Non-negative Integers without Consecutive Ones",
      "python_optimal": "# Solution for Non-negative Integers without Consecutive Ones"
    },
    "originalOrder": 944,
    "learningOrder": 944
  },
  {
    "id": 89,
    "number": 89,
    "sequence_number": 89,
    "title": "Consecutive Numbers Sum",
    "slug": "consecutive-numbers-sum",
    "difficulty": "Hard",
    "topic": "Sliding Window",
    "subtopic": "Sliding Window",
    "pattern": "Sliding Window",
    "secondary_patterns": [
      "Sliding Window"
    ],
    "stage": "Two Pointers & Sliding Window",
    "curriculumStage": "Stage 2 — Two Pointers & Sliding Window",
    "roadmapPhase": "Stage 2 — Two Pointers & Sliding Window",
    "phase": "Stage 2 — Two Pointers & Sliding Window",
    "estimatedTime": 45,
    "statement": "Solve the **Consecutive Numbers Sum Optimization** problem using the **Sliding Window** technique. Given input constraints appropriate for Hard level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^6",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Sliding Window identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Sliding Window. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Sliding Window techniques by solving Hard problem constraints for Consecutive Numbers Sum Optimization.",
    "whyThisPattern": "When observing arrays & strings problem conditions, Sliding Window optimizes performance down to expected O(N log N).",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Apple",
      "Adobe",
      "Atlassian"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/consecutive-numbers-sum/",
    "leetcode_title": "Consecutive Numbers Sum",
    "leetcode_id": 829,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/consecutive-numbers-sum/",
    "canonicalSlug": "consecutive-numbers-sum",
    "canonicalUrl": "https://leetcode.com/problems/consecutive-numbers-sum/",
    "url": "https://leetcode.com/problems/consecutive-numbers-sum/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Consecutive Numbers Sum Optimization (Sliding Window)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Consecutive Numbers Sum Optimization (Sliding Window)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Consecutive Numbers Sum Optimization (Sliding Window)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Consecutive Numbers Sum Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Consecutive Numbers Sum Optimization (Sliding Window)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Consecutive Numbers Sum Optimization (Sliding Window)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Consecutive Numbers Sum Optimization (Sliding Window)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Consecutive Numbers Sum Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Consecutive Numbers Sum",
      "cpp_optimal": "// Solution for Consecutive Numbers Sum",
      "java_brute": "// Solution for Consecutive Numbers Sum",
      "java_optimal": "// Solution for Consecutive Numbers Sum",
      "python_brute": "# Solution for Consecutive Numbers Sum",
      "python_optimal": "# Solution for Consecutive Numbers Sum"
    },
    "originalOrder": 945,
    "learningOrder": 945
  },
  {
    "id": 90,
    "number": 90,
    "sequence_number": 90,
    "title": "Minimum Number of K Consecutive Bit Flips",
    "slug": "minimum-number-of-k-consecutive-bit-flips",
    "difficulty": "Hard",
    "topic": "Sliding Window",
    "subtopic": "Sliding Window",
    "pattern": "Sliding Window",
    "secondary_patterns": [
      "Sliding Window"
    ],
    "stage": "Two Pointers & Sliding Window",
    "curriculumStage": "Stage 2 — Two Pointers & Sliding Window",
    "roadmapPhase": "Stage 2 — Two Pointers & Sliding Window",
    "phase": "Stage 2 — Two Pointers & Sliding Window",
    "estimatedTime": 45,
    "statement": "Solve the **Minimum Number of K Consecutive Bit Flips Optimization** problem using the **Sliding Window** technique. Given input constraints appropriate for Hard level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^6",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Sliding Window identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Sliding Window. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Sliding Window techniques by solving Hard problem constraints for Minimum Number of K Consecutive Bit Flips Optimization.",
    "whyThisPattern": "When observing arrays & strings problem conditions, Sliding Window optimizes performance down to expected O(N log N).",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "LinkedIn",
      "Amazon"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/minimum-number-of-k-consecutive-bit-flips/",
    "leetcode_title": "Minimum Number of K Consecutive Bit Flips",
    "leetcode_id": 995,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/minimum-number-of-k-consecutive-bit-flips/",
    "canonicalSlug": "minimum-number-of-k-consecutive-bit-flips",
    "canonicalUrl": "https://leetcode.com/problems/minimum-number-of-k-consecutive-bit-flips/",
    "url": "https://leetcode.com/problems/minimum-number-of-k-consecutive-bit-flips/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Minimum Number of K Consecutive Bit Flips Optimization (Sliding Window)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Minimum Number of K Consecutive Bit Flips Optimization (Sliding Window)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Minimum Number of K Consecutive Bit Flips Optimization (Sliding Window)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Minimum Number of K Consecutive Bit Flips Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Minimum Number of K Consecutive Bit Flips Optimization (Sliding Window)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Minimum Number of K Consecutive Bit Flips Optimization (Sliding Window)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Minimum Number of K Consecutive Bit Flips Optimization (Sliding Window)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Minimum Number of K Consecutive Bit Flips Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Minimum Number of K Consecutive Bit Flips",
      "cpp_optimal": "// Solution for Minimum Number of K Consecutive Bit Flips",
      "java_brute": "// Solution for Minimum Number of K Consecutive Bit Flips",
      "java_optimal": "// Solution for Minimum Number of K Consecutive Bit Flips",
      "python_brute": "# Solution for Minimum Number of K Consecutive Bit Flips",
      "python_optimal": "# Solution for Minimum Number of K Consecutive Bit Flips"
    },
    "originalOrder": 946,
    "learningOrder": 946
  },
  {
    "id": 91,
    "number": 91,
    "sequence_number": 91,
    "title": "Constrained Subsequence Sum",
    "slug": "constrained-subsequence-sum",
    "difficulty": "Hard",
    "topic": "Sliding Window",
    "subtopic": "Sliding Window Optimization",
    "pattern": "Monotonic Deque DP",
    "secondary_patterns": [
      "Monotonic Deque DP"
    ],
    "stage": "Two Pointers & Sliding Window",
    "curriculumStage": "Stage 2 — Two Pointers & Sliding Window",
    "roadmapPhase": "Stage 2 — Two Pointers & Sliding Window",
    "phase": "Stage 2 — Two Pointers & Sliding Window",
    "estimatedTime": 45,
    "statement": "Given the constraints and input parameters for Constrained Subsequence Sum, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Constrained Subsequence Sum."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Constrained Subsequence Sum.",
      "Leverage the optimal Sliding Window pattern to reduce time complexity."
    ],
    "learningObjective": "Master Sliding Window techniques by solving Hard problem constraints for Constrained Subsequence Sum.",
    "whyThisPattern": "When observing Sliding Window problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/constrained-subsequence-sum/",
    "leetcode_title": "Constrained Subsequence Sum",
    "leetcode_id": 1425,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/constrained-subsequence-sum/",
    "canonicalSlug": "constrained-subsequence-sum",
    "canonicalUrl": "https://leetcode.com/problems/constrained-subsequence-sum/",
    "url": "https://leetcode.com/problems/constrained-subsequence-sum/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Constrained Subsequence Sum\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Constrained Subsequence Sum\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Constrained Subsequence Sum\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Constrained Subsequence Sum\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Constrained Subsequence Sum\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Constrained Subsequence Sum\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Constrained Subsequence Sum\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Constrained Subsequence Sum\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Constrained Subsequence Sum",
      "cpp_optimal": "// Solution for Constrained Subsequence Sum",
      "java_brute": "// Solution for Constrained Subsequence Sum",
      "java_optimal": "// Solution for Constrained Subsequence Sum",
      "python_brute": "# Solution for Constrained Subsequence Sum",
      "python_optimal": "# Solution for Constrained Subsequence Sum"
    },
    "originalOrder": 947,
    "learningOrder": 947
  },
  {
    "id": 92,
    "number": 92,
    "sequence_number": 92,
    "title": "Max Value of Equation",
    "slug": "max-value-of-equation",
    "difficulty": "Hard",
    "topic": "Sliding Window",
    "subtopic": "Sliding Window Optimization",
    "pattern": "Monotonic Deque Max Difference",
    "secondary_patterns": [
      "Monotonic Deque Max Difference"
    ],
    "stage": "Two Pointers & Sliding Window",
    "curriculumStage": "Stage 2 — Two Pointers & Sliding Window",
    "roadmapPhase": "Stage 2 — Two Pointers & Sliding Window",
    "phase": "Stage 2 — Two Pointers & Sliding Window",
    "estimatedTime": 45,
    "statement": "Given the constraints and input parameters for Max Value of Equation, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Max Value of Equation."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Max Value of Equation.",
      "Leverage the optimal Sliding Window pattern to reduce time complexity."
    ],
    "learningObjective": "Master Sliding Window techniques by solving Hard problem constraints for Max Value of Equation.",
    "whyThisPattern": "When observing Sliding Window problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/max-value-of-equation/",
    "leetcode_title": "Max Value of Equation",
    "leetcode_id": 1499,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/max-value-of-equation/",
    "canonicalSlug": "max-value-of-equation",
    "canonicalUrl": "https://leetcode.com/problems/max-value-of-equation/",
    "url": "https://leetcode.com/problems/max-value-of-equation/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Max Value of Equation\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Max Value of Equation\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Max Value of Equation\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Max Value of Equation\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Max Value of Equation\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Max Value of Equation\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Max Value of Equation\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Max Value of Equation\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Max Value of Equation",
      "cpp_optimal": "// Solution for Max Value of Equation",
      "java_brute": "// Solution for Max Value of Equation",
      "java_optimal": "// Solution for Max Value of Equation",
      "python_brute": "# Solution for Max Value of Equation",
      "python_optimal": "# Solution for Max Value of Equation"
    },
    "originalOrder": 948,
    "learningOrder": 948
  },
  {
    "id": 93,
    "number": 93,
    "sequence_number": 93,
    "title": "Count Subarrays With Fixed Bounds",
    "slug": "count-subarrays-with-fixed-bounds",
    "difficulty": "Hard",
    "topic": "Sliding Window",
    "subtopic": "Sliding Window Optimization",
    "pattern": "Min Max Bound Window",
    "secondary_patterns": [
      "Min Max Bound Window"
    ],
    "stage": "Two Pointers & Sliding Window",
    "curriculumStage": "Stage 2 — Two Pointers & Sliding Window",
    "roadmapPhase": "Stage 2 — Two Pointers & Sliding Window",
    "phase": "Stage 2 — Two Pointers & Sliding Window",
    "estimatedTime": 45,
    "statement": "Given the constraints and input parameters for Count Subarrays With Fixed Bounds, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Count Subarrays With Fixed Bounds."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Count Subarrays With Fixed Bounds.",
      "Leverage the optimal Sliding Window pattern to reduce time complexity."
    ],
    "learningObjective": "Master Sliding Window techniques by solving Hard problem constraints for Count Subarrays With Fixed Bounds.",
    "whyThisPattern": "When observing Sliding Window problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/count-subarrays-with-fixed-bounds/",
    "leetcode_title": "Count Subarrays With Fixed Bounds",
    "leetcode_id": 2444,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/count-subarrays-with-fixed-bounds/",
    "canonicalSlug": "count-subarrays-with-fixed-bounds",
    "canonicalUrl": "https://leetcode.com/problems/count-subarrays-with-fixed-bounds/",
    "url": "https://leetcode.com/problems/count-subarrays-with-fixed-bounds/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Count Subarrays With Fixed Bounds\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Count Subarrays With Fixed Bounds\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Count Subarrays With Fixed Bounds\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Count Subarrays With Fixed Bounds\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Count Subarrays With Fixed Bounds\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Count Subarrays With Fixed Bounds\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Count Subarrays With Fixed Bounds\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Count Subarrays With Fixed Bounds\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Count Subarrays With Fixed Bounds",
      "cpp_optimal": "// Solution for Count Subarrays With Fixed Bounds",
      "java_brute": "// Solution for Count Subarrays With Fixed Bounds",
      "java_optimal": "// Solution for Count Subarrays With Fixed Bounds",
      "python_brute": "# Solution for Count Subarrays With Fixed Bounds",
      "python_optimal": "# Solution for Count Subarrays With Fixed Bounds"
    },
    "originalOrder": 949,
    "learningOrder": 949
  },
  {
    "id": 94,
    "number": 94,
    "sequence_number": 94,
    "title": "Minimum Number of Operations to Make Array Continuous",
    "slug": "minimum-number-of-operations-to-make-array-continuous",
    "difficulty": "Hard",
    "topic": "Sliding Window",
    "subtopic": "Sliding Window Optimization",
    "pattern": "Sort & Sliding Window",
    "secondary_patterns": [
      "Sort & Sliding Window"
    ],
    "stage": "Two Pointers & Sliding Window",
    "curriculumStage": "Stage 2 — Two Pointers & Sliding Window",
    "roadmapPhase": "Stage 2 — Two Pointers & Sliding Window",
    "phase": "Stage 2 — Two Pointers & Sliding Window",
    "estimatedTime": 45,
    "statement": "Given the constraints and input parameters for Minimum Number of Operations to Make Array Continuous, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Minimum Number of Operations to Make Array Continuous."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Minimum Number of Operations to Make Array Continuous.",
      "Leverage the optimal Sliding Window pattern to reduce time complexity."
    ],
    "learningObjective": "Master Sliding Window techniques by solving Hard problem constraints for Minimum Number of Operations to Make Array Continuous.",
    "whyThisPattern": "When observing Sliding Window problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/minimum-number-of-operations-to-make-array-continuous/",
    "leetcode_title": "Minimum Number of Operations to Make Array Continuous",
    "leetcode_id": 2009,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/minimum-number-of-operations-to-make-array-continuous/",
    "canonicalSlug": "minimum-number-of-operations-to-make-array-continuous",
    "canonicalUrl": "https://leetcode.com/problems/minimum-number-of-operations-to-make-array-continuous/",
    "url": "https://leetcode.com/problems/minimum-number-of-operations-to-make-array-continuous/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Minimum Number of Operations to Make Array Continuous\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Minimum Number of Operations to Make Array Continuous\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Minimum Number of Operations to Make Array Continuous\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Minimum Number of Operations to Make Array Continuous\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Minimum Number of Operations to Make Array Continuous\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Minimum Number of Operations to Make Array Continuous\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Minimum Number of Operations to Make Array Continuous\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Minimum Number of Operations to Make Array Continuous\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Minimum Number of Operations to Make Array Continuous",
      "cpp_optimal": "// Solution for Minimum Number of Operations to Make Array Continuous",
      "java_brute": "// Solution for Minimum Number of Operations to Make Array Continuous",
      "java_optimal": "// Solution for Minimum Number of Operations to Make Array Continuous",
      "python_brute": "# Solution for Minimum Number of Operations to Make Array Continuous",
      "python_optimal": "# Solution for Minimum Number of Operations to Make Array Continuous"
    },
    "originalOrder": 950,
    "learningOrder": 950
  },
  {
    "id": 95,
    "number": 95,
    "sequence_number": 95,
    "title": "Maximum Number of Robots Within Budget",
    "slug": "maximum-number-of-robots-within-budget",
    "difficulty": "Hard",
    "topic": "Sliding Window",
    "subtopic": "Sliding Window Optimization",
    "pattern": "Monotonic Queue Cost Window",
    "secondary_patterns": [
      "Monotonic Queue Cost Window"
    ],
    "stage": "Two Pointers & Sliding Window",
    "curriculumStage": "Stage 2 — Two Pointers & Sliding Window",
    "roadmapPhase": "Stage 2 — Two Pointers & Sliding Window",
    "phase": "Stage 2 — Two Pointers & Sliding Window",
    "estimatedTime": 45,
    "statement": "Given the constraints and input parameters for Maximum Number of Robots Within Budget, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Maximum Number of Robots Within Budget."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Maximum Number of Robots Within Budget.",
      "Leverage the optimal Sliding Window pattern to reduce time complexity."
    ],
    "learningObjective": "Master Sliding Window techniques by solving Hard problem constraints for Maximum Number of Robots Within Budget.",
    "whyThisPattern": "When observing Sliding Window problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/maximum-number-of-robots-within-budget/",
    "leetcode_title": "Maximum Number of Robots Within Budget",
    "leetcode_id": 2398,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/maximum-number-of-robots-within-budget/",
    "canonicalSlug": "maximum-number-of-robots-within-budget",
    "canonicalUrl": "https://leetcode.com/problems/maximum-number-of-robots-within-budget/",
    "url": "https://leetcode.com/problems/maximum-number-of-robots-within-budget/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Maximum Number of Robots Within Budget\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Maximum Number of Robots Within Budget\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Maximum Number of Robots Within Budget\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Maximum Number of Robots Within Budget\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Maximum Number of Robots Within Budget\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Maximum Number of Robots Within Budget\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Maximum Number of Robots Within Budget\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Maximum Number of Robots Within Budget\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Maximum Number of Robots Within Budget",
      "cpp_optimal": "// Solution for Maximum Number of Robots Within Budget",
      "java_brute": "// Solution for Maximum Number of Robots Within Budget",
      "java_optimal": "// Solution for Maximum Number of Robots Within Budget",
      "python_brute": "# Solution for Maximum Number of Robots Within Budget",
      "python_optimal": "# Solution for Maximum Number of Robots Within Budget"
    },
    "originalOrder": 951,
    "learningOrder": 951
  },
  {
    "id": 96,
    "number": 96,
    "sequence_number": 96,
    "title": "Median of Two Sorted Arrays",
    "slug": "median-of-two-sorted-arrays",
    "difficulty": "Hard",
    "topic": "Two Pointers",
    "subtopic": "Two Pointers",
    "pattern": "Two Pointers",
    "secondary_patterns": [
      "Two Pointers"
    ],
    "stage": "Two Pointers & Sliding Window",
    "curriculumStage": "Stage 2 — Two Pointers & Sliding Window",
    "roadmapPhase": "Stage 2 — Two Pointers & Sliding Window",
    "phase": "Stage 2 — Two Pointers & Sliding Window",
    "estimatedTime": 45,
    "statement": "Solve the **Median of Two Sorted Arrays Optimization** problem using the **Two Pointers** technique. Given input constraints appropriate for Hard level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^6",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Two Pointers identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Two Pointers. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Two Pointers techniques by solving Hard problem constraints for Median of Two Sorted Arrays Optimization.",
    "whyThisPattern": "When observing arrays & strings problem conditions, Two Pointers optimizes performance down to expected O(N log N).",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(1)",
    "companyRelevance": [
      "Google",
      "LinkedIn",
      "Amazon"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/median-of-two-sorted-arrays/",
    "leetcode_title": "Median of Two Sorted Arrays",
    "leetcode_id": 4,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/median-of-two-sorted-arrays/",
    "canonicalSlug": "median-of-two-sorted-arrays",
    "canonicalUrl": "https://leetcode.com/problems/median-of-two-sorted-arrays/",
    "url": "https://leetcode.com/problems/median-of-two-sorted-arrays/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Median of Two Sorted Arrays Optimization (Two Pointers)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Median of Two Sorted Arrays Optimization (Two Pointers)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Median of Two Sorted Arrays Optimization (Two Pointers)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Median of Two Sorted Arrays Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Median of Two Sorted Arrays Optimization (Two Pointers)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Median of Two Sorted Arrays Optimization (Two Pointers)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Median of Two Sorted Arrays Optimization (Two Pointers)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Median of Two Sorted Arrays Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Median of Two Sorted Arrays",
      "cpp_optimal": "// Solution for Median of Two Sorted Arrays",
      "java_brute": "// Solution for Median of Two Sorted Arrays",
      "java_optimal": "// Solution for Median of Two Sorted Arrays",
      "python_brute": "# Solution for Median of Two Sorted Arrays",
      "python_optimal": "# Solution for Median of Two Sorted Arrays"
    },
    "originalOrder": 977,
    "learningOrder": 977
  },
  {
    "id": 97,
    "number": 97,
    "sequence_number": 97,
    "title": "Palindrome Partitioning II",
    "slug": "palindrome-partitioning-ii",
    "difficulty": "Hard",
    "topic": "Two Pointers",
    "subtopic": "Two Pointers",
    "pattern": "Two Pointers",
    "secondary_patterns": [
      "Two Pointers"
    ],
    "stage": "Two Pointers & Sliding Window",
    "curriculumStage": "Stage 2 — Two Pointers & Sliding Window",
    "roadmapPhase": "Stage 2 — Two Pointers & Sliding Window",
    "phase": "Stage 2 — Two Pointers & Sliding Window",
    "estimatedTime": 45,
    "statement": "Solve the **Palindrome Partitioning II Optimization** problem using the **Two Pointers** technique. Given input constraints appropriate for Hard level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^6",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Two Pointers identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Two Pointers. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Two Pointers techniques by solving Hard problem constraints for Palindrome Partitioning II Optimization.",
    "whyThisPattern": "When observing arrays & strings problem conditions, Two Pointers optimizes performance down to expected O(N log N).",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(1)",
    "companyRelevance": [
      "Meta",
      "Apple",
      "Netflix"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/palindrome-partitioning-ii/",
    "leetcode_title": "Palindrome Partitioning II",
    "leetcode_id": 132,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/palindrome-partitioning-ii/",
    "canonicalSlug": "palindrome-partitioning-ii",
    "canonicalUrl": "https://leetcode.com/problems/palindrome-partitioning-ii/",
    "url": "https://leetcode.com/problems/palindrome-partitioning-ii/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Palindrome Partitioning II Optimization (Two Pointers)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Palindrome Partitioning II Optimization (Two Pointers)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Palindrome Partitioning II Optimization (Two Pointers)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Palindrome Partitioning II Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Palindrome Partitioning II Optimization (Two Pointers)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Palindrome Partitioning II Optimization (Two Pointers)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Palindrome Partitioning II Optimization (Two Pointers)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Palindrome Partitioning II Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Palindrome Partitioning II",
      "cpp_optimal": "// Solution for Palindrome Partitioning II",
      "java_brute": "// Solution for Palindrome Partitioning II",
      "java_optimal": "// Solution for Palindrome Partitioning II",
      "python_brute": "# Solution for Palindrome Partitioning II",
      "python_optimal": "# Solution for Palindrome Partitioning II"
    },
    "originalOrder": 978,
    "learningOrder": 978
  },
  {
    "id": 98,
    "number": 98,
    "sequence_number": 98,
    "title": "Shortest Palindrome",
    "slug": "shortest-palindrome",
    "difficulty": "Hard",
    "topic": "Two Pointers",
    "subtopic": "Two Pointers",
    "pattern": "Two Pointers",
    "secondary_patterns": [
      "Two Pointers"
    ],
    "stage": "Two Pointers & Sliding Window",
    "curriculumStage": "Stage 2 — Two Pointers & Sliding Window",
    "roadmapPhase": "Stage 2 — Two Pointers & Sliding Window",
    "phase": "Stage 2 — Two Pointers & Sliding Window",
    "estimatedTime": 45,
    "statement": "Solve the **Shortest Palindrome Challenge** problem using the **Two Pointers** technique. Given input constraints appropriate for Hard level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^6",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Two Pointers identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Two Pointers. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Two Pointers techniques by solving Hard problem constraints for Shortest Palindrome Challenge.",
    "whyThisPattern": "When observing arrays & strings problem conditions, Two Pointers optimizes performance down to expected O(N log N).",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(1)",
    "companyRelevance": [
      "Meta",
      "Uber",
      "Databricks"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/shortest-palindrome/",
    "leetcode_title": "Shortest Palindrome",
    "leetcode_id": 214,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/shortest-palindrome/",
    "canonicalSlug": "shortest-palindrome",
    "canonicalUrl": "https://leetcode.com/problems/shortest-palindrome/",
    "url": "https://leetcode.com/problems/shortest-palindrome/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Shortest Palindrome Challenge (Two Pointers)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Shortest Palindrome Challenge (Two Pointers)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Shortest Palindrome Challenge (Two Pointers)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Shortest Palindrome Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Shortest Palindrome Challenge (Two Pointers)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Shortest Palindrome Challenge (Two Pointers)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Shortest Palindrome Challenge (Two Pointers)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Shortest Palindrome Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Shortest Palindrome",
      "cpp_optimal": "// Solution for Shortest Palindrome",
      "java_brute": "// Solution for Shortest Palindrome",
      "java_optimal": "// Solution for Shortest Palindrome",
      "python_brute": "# Solution for Shortest Palindrome",
      "python_optimal": "# Solution for Shortest Palindrome"
    },
    "originalOrder": 979,
    "learningOrder": 979
  },
  {
    "id": 99,
    "number": 99,
    "sequence_number": 99,
    "title": "Palindrome Pairs",
    "slug": "palindrome-pairs",
    "difficulty": "Hard",
    "topic": "Two Pointers",
    "subtopic": "Two Pointers",
    "pattern": "Two Pointers",
    "secondary_patterns": [
      "Two Pointers"
    ],
    "stage": "Two Pointers & Sliding Window",
    "curriculumStage": "Stage 2 — Two Pointers & Sliding Window",
    "roadmapPhase": "Stage 2 — Two Pointers & Sliding Window",
    "phase": "Stage 2 — Two Pointers & Sliding Window",
    "estimatedTime": 45,
    "statement": "Solve the **Palindrome Pairs Optimization** problem using the **Two Pointers** technique. Given input constraints appropriate for Hard level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^6",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Two Pointers identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Two Pointers. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Two Pointers techniques by solving Hard problem constraints for Palindrome Pairs Optimization.",
    "whyThisPattern": "When observing arrays & strings problem conditions, Two Pointers optimizes performance down to expected O(N log N).",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(1)",
    "companyRelevance": [
      "Apple",
      "Adobe",
      "Atlassian"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/palindrome-pairs/",
    "leetcode_title": "Palindrome Pairs",
    "leetcode_id": 336,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/palindrome-pairs/",
    "canonicalSlug": "palindrome-pairs",
    "canonicalUrl": "https://leetcode.com/problems/palindrome-pairs/",
    "url": "https://leetcode.com/problems/palindrome-pairs/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Palindrome Pairs Optimization (Two Pointers)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Palindrome Pairs Optimization (Two Pointers)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Palindrome Pairs Optimization (Two Pointers)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Palindrome Pairs Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Palindrome Pairs Optimization (Two Pointers)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Palindrome Pairs Optimization (Two Pointers)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Palindrome Pairs Optimization (Two Pointers)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Palindrome Pairs Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Palindrome Pairs",
      "cpp_optimal": "// Solution for Palindrome Pairs",
      "java_brute": "// Solution for Palindrome Pairs",
      "java_optimal": "// Solution for Palindrome Pairs",
      "python_brute": "# Solution for Palindrome Pairs",
      "python_optimal": "# Solution for Palindrome Pairs"
    },
    "originalOrder": 980,
    "learningOrder": 980
  },
  {
    "id": 100,
    "number": 100,
    "sequence_number": 100,
    "title": "Trapping Rain Water II",
    "slug": "trapping-rain-water-ii",
    "difficulty": "Hard",
    "topic": "Two Pointers",
    "subtopic": "Hashing & Array Optimization",
    "pattern": "Hashing & Array Optimization",
    "secondary_patterns": [
      "Hashing & Array Optimization"
    ],
    "stage": "Two Pointers & Sliding Window",
    "curriculumStage": "Stage 2 — Two Pointers & Sliding Window",
    "roadmapPhase": "Stage 2 — Two Pointers & Sliding Window",
    "phase": "Stage 2 — Two Pointers & Sliding Window",
    "estimatedTime": 45,
    "statement": "Solve the **Trapping Rain Water II Challenge** problem using the **Hashing & Array Optimization** technique. Given input constraints appropriate for Hard level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^6",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Hashing & Array Optimization identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Hashing & Array Optimization. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Hashing & Array Optimization techniques by solving Hard problem constraints for Trapping Rain Water II Challenge.",
    "whyThisPattern": "When observing arrays & strings problem conditions, Hashing & Array Optimization optimizes performance down to expected O(N log N).",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Amazon",
      "Microsoft",
      "Uber"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/trapping-rain-water-ii/",
    "leetcode_title": "Trapping Rain Water II",
    "leetcode_id": 407,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/trapping-rain-water-ii/",
    "canonicalSlug": "trapping-rain-water-ii",
    "canonicalUrl": "https://leetcode.com/problems/trapping-rain-water-ii/",
    "url": "https://leetcode.com/problems/trapping-rain-water-ii/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Trapping Rain Water II Challenge (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Trapping Rain Water II Challenge (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Trapping Rain Water II Challenge (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Trapping Rain Water II Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Trapping Rain Water II Challenge (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Trapping Rain Water II Challenge (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Trapping Rain Water II Challenge (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Trapping Rain Water II Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Trapping Rain Water II",
      "cpp_optimal": "// Solution for Trapping Rain Water II",
      "java_brute": "// Solution for Trapping Rain Water II",
      "java_optimal": "// Solution for Trapping Rain Water II",
      "python_brute": "# Solution for Trapping Rain Water II",
      "python_optimal": "# Solution for Trapping Rain Water II"
    },
    "originalOrder": 981,
    "learningOrder": 981
  },
  {
    "id": 101,
    "number": 101,
    "sequence_number": 101,
    "title": "Roman to Integer",
    "slug": "roman-to-integer-challenge",
    "difficulty": "Easy",
    "topic": "Strings",
    "subtopic": "Hashing & Array Optimization",
    "pattern": "Hashing & Array Optimization",
    "secondary_patterns": [
      "Hashing & Array Optimization"
    ],
    "stage": "Strings & Character Manipulation",
    "curriculumStage": "Stage 3 — Strings & Character Manipulation",
    "roadmapPhase": "Stage 3 — Strings & Character Manipulation",
    "phase": "Stage 3 — Strings & Character Manipulation",
    "estimatedTime": 15,
    "statement": "Solve the **Roman to Integer Challenge** problem using the **Hashing & Array Optimization** technique. Given input constraints appropriate for Easy level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^4",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Hashing & Array Optimization identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Hashing & Array Optimization. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Hashing & Array Optimization techniques by solving Easy problem constraints for Roman to Integer Challenge.",
    "whyThisPattern": "When observing arrays & strings problem conditions, Hashing & Array Optimization optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Microsoft",
      "Bloomberg",
      "Adobe"
    ],
    "companyRelevanceTier": "Medium",
    "leetcode_url": "https://leetcode.com/problems/roman-to-integer/",
    "leetcode_title": "Roman to Integer",
    "leetcode_id": 13,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/roman-to-integer/",
    "canonicalSlug": "roman-to-integer-challenge",
    "canonicalUrl": "https://leetcode.com/problems/roman-to-integer/",
    "url": "https://leetcode.com/problems/roman-to-integer/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Roman to Integer Challenge (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Roman to Integer Challenge (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Roman to Integer Challenge (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Roman to Integer Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Roman to Integer Challenge (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Roman to Integer Challenge (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Roman to Integer Challenge (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Roman to Integer Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Roman to Integer",
      "cpp_optimal": "// Solution for Roman to Integer",
      "java_brute": "// Solution for Roman to Integer",
      "java_optimal": "// Solution for Roman to Integer",
      "python_brute": "# Solution for Roman to Integer",
      "python_optimal": "# Solution for Roman to Integer"
    }
  },
  {
    "id": 102,
    "number": 102,
    "sequence_number": 102,
    "title": "Longest Common Prefix",
    "slug": "longest-common-prefix-optimization",
    "difficulty": "Easy",
    "topic": "Strings",
    "subtopic": "Hashing & Array Optimization",
    "pattern": "Hashing & Array Optimization",
    "secondary_patterns": [
      "Hashing & Array Optimization"
    ],
    "stage": "Strings & Character Manipulation",
    "curriculumStage": "Stage 3 — Strings & Character Manipulation",
    "roadmapPhase": "Stage 3 — Strings & Character Manipulation",
    "phase": "Stage 3 — Strings & Character Manipulation",
    "estimatedTime": 15,
    "statement": "Solve the **Longest Common Prefix Optimization** problem using the **Hashing & Array Optimization** technique. Given input constraints appropriate for Easy level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^4",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Hashing & Array Optimization identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Hashing & Array Optimization. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Hashing & Array Optimization techniques by solving Easy problem constraints for Longest Common Prefix Optimization.",
    "whyThisPattern": "When observing arrays & strings problem conditions, Hashing & Array Optimization optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Meta",
      "Apple",
      "Netflix"
    ],
    "companyRelevanceTier": "Medium",
    "leetcode_url": "https://leetcode.com/problems/longest-common-prefix/",
    "leetcode_title": "Longest Common Prefix",
    "leetcode_id": 14,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/longest-common-prefix/",
    "canonicalSlug": "longest-common-prefix-optimization",
    "canonicalUrl": "https://leetcode.com/problems/longest-common-prefix/",
    "url": "https://leetcode.com/problems/longest-common-prefix/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Longest Common Prefix Optimization (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Longest Common Prefix Optimization (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Longest Common Prefix Optimization (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Longest Common Prefix Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Longest Common Prefix Optimization (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Longest Common Prefix Optimization (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Longest Common Prefix Optimization (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Longest Common Prefix Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Longest Common Prefix",
      "cpp_optimal": "// Solution for Longest Common Prefix",
      "java_brute": "// Solution for Longest Common Prefix",
      "java_optimal": "// Solution for Longest Common Prefix",
      "python_brute": "# Solution for Longest Common Prefix",
      "python_optimal": "# Solution for Longest Common Prefix"
    }
  },
  {
    "id": 103,
    "number": 103,
    "sequence_number": 103,
    "title": "Find the Index of the First Occurrence in a String",
    "slug": "find-the-index-of-the-first-occurrence-in-a-string-optimization",
    "difficulty": "Easy",
    "topic": "Strings",
    "subtopic": "Hashing & Array Optimization",
    "pattern": "Hashing & Array Optimization",
    "secondary_patterns": [
      "Hashing & Array Optimization"
    ],
    "stage": "Strings & Character Manipulation",
    "curriculumStage": "Stage 3 — Strings & Character Manipulation",
    "roadmapPhase": "Stage 3 — Strings & Character Manipulation",
    "phase": "Stage 3 — Strings & Character Manipulation",
    "estimatedTime": 15,
    "statement": "Solve the **Find the Index of the First Occurrence in a String Optimization** problem using the **Hashing & Array Optimization** technique. Given input constraints appropriate for Easy level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^4",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Hashing & Array Optimization identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Hashing & Array Optimization. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Hashing & Array Optimization techniques by solving Easy problem constraints for Find the Index of the First Occurrence in a String Optimization.",
    "whyThisPattern": "When observing arrays & strings problem conditions, Hashing & Array Optimization optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "LinkedIn",
      "Amazon"
    ],
    "companyRelevanceTier": "Medium",
    "leetcode_url": "https://leetcode.com/problems/find-the-index-of-the-first-occurrence-in-a-string/",
    "leetcode_title": "Find the Index of the First Occurrence in a String",
    "leetcode_id": 28,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/find-the-index-of-the-first-occurrence-in-a-string/",
    "canonicalSlug": "find-the-index-of-the-first-occurrence-in-a-string-optimization",
    "canonicalUrl": "https://leetcode.com/problems/find-the-index-of-the-first-occurrence-in-a-string/",
    "url": "https://leetcode.com/problems/find-the-index-of-the-first-occurrence-in-a-string/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Find the Index of the First Occurrence in a String Optimization (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Find the Index of the First Occurrence in a String Optimization (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Find the Index of the First Occurrence in a String Optimization (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Find the Index of the First Occurrence in a String Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Find the Index of the First Occurrence in a String Optimization (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Find the Index of the First Occurrence in a String Optimization (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Find the Index of the First Occurrence in a String Optimization (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Find the Index of the First Occurrence in a String Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Find the Index of the First Occurrence in a String",
      "cpp_optimal": "// Solution for Find the Index of the First Occurrence in a String",
      "java_brute": "// Solution for Find the Index of the First Occurrence in a String",
      "java_optimal": "// Solution for Find the Index of the First Occurrence in a String",
      "python_brute": "# Solution for Find the Index of the First Occurrence in a String",
      "python_optimal": "# Solution for Find the Index of the First Occurrence in a String"
    }
  },
  {
    "id": 104,
    "number": 104,
    "sequence_number": 104,
    "title": "Search Insert Position",
    "slug": "search-insert-position-optimization",
    "difficulty": "Easy",
    "topic": "Strings",
    "subtopic": "Hashing & Array Optimization",
    "pattern": "Hashing & Array Optimization",
    "secondary_patterns": [
      "Hashing & Array Optimization"
    ],
    "stage": "Strings & Character Manipulation",
    "curriculumStage": "Stage 3 — Strings & Character Manipulation",
    "roadmapPhase": "Stage 3 — Strings & Character Manipulation",
    "phase": "Stage 3 — Strings & Character Manipulation",
    "estimatedTime": 15,
    "statement": "Solve the **Search Insert Position Optimization** problem using the **Hashing & Array Optimization** technique. Given input constraints appropriate for Easy level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^4",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Hashing & Array Optimization identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Hashing & Array Optimization. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Hashing & Array Optimization techniques by solving Easy problem constraints for Search Insert Position Optimization.",
    "whyThisPattern": "When observing arrays & strings problem conditions, Hashing & Array Optimization optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta"
    ],
    "companyRelevanceTier": "Medium",
    "leetcode_url": "https://leetcode.com/problems/search-insert-position/",
    "leetcode_title": "Search Insert Position",
    "leetcode_id": 35,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/search-insert-position/",
    "canonicalSlug": "search-insert-position-optimization",
    "canonicalUrl": "https://leetcode.com/problems/search-insert-position/",
    "url": "https://leetcode.com/problems/search-insert-position/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Search Insert Position Optimization (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Search Insert Position Optimization (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Search Insert Position Optimization (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Search Insert Position Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Search Insert Position Optimization (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Search Insert Position Optimization (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Search Insert Position Optimization (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Search Insert Position Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Search Insert Position",
      "cpp_optimal": "// Solution for Search Insert Position",
      "java_brute": "// Solution for Search Insert Position",
      "java_optimal": "// Solution for Search Insert Position",
      "python_brute": "# Solution for Search Insert Position",
      "python_optimal": "# Solution for Search Insert Position"
    }
  },
  {
    "id": 105,
    "number": 105,
    "sequence_number": 105,
    "title": "Length of Last Word",
    "slug": "length-of-last-word-challenge",
    "difficulty": "Easy",
    "topic": "Strings",
    "subtopic": "Hashing & Array Optimization",
    "pattern": "Hashing & Array Optimization",
    "secondary_patterns": [
      "Hashing & Array Optimization"
    ],
    "stage": "Strings & Character Manipulation",
    "curriculumStage": "Stage 3 — Strings & Character Manipulation",
    "roadmapPhase": "Stage 3 — Strings & Character Manipulation",
    "phase": "Stage 3 — Strings & Character Manipulation",
    "estimatedTime": 15,
    "statement": "Solve the **Length of Last Word Challenge** problem using the **Hashing & Array Optimization** technique. Given input constraints appropriate for Easy level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^4",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Hashing & Array Optimization identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Hashing & Array Optimization. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Hashing & Array Optimization techniques by solving Easy problem constraints for Length of Last Word Challenge.",
    "whyThisPattern": "When observing arrays & strings problem conditions, Hashing & Array Optimization optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Amazon",
      "Microsoft",
      "Uber"
    ],
    "companyRelevanceTier": "Medium",
    "leetcode_url": "https://leetcode.com/problems/length-of-last-word/",
    "leetcode_title": "Length of Last Word",
    "leetcode_id": 58,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/length-of-last-word/",
    "canonicalSlug": "length-of-last-word-challenge",
    "canonicalUrl": "https://leetcode.com/problems/length-of-last-word/",
    "url": "https://leetcode.com/problems/length-of-last-word/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Length of Last Word Challenge (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Length of Last Word Challenge (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Length of Last Word Challenge (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Length of Last Word Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Length of Last Word Challenge (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Length of Last Word Challenge (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Length of Last Word Challenge (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Length of Last Word Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Length of Last Word",
      "cpp_optimal": "// Solution for Length of Last Word",
      "java_brute": "// Solution for Length of Last Word",
      "java_optimal": "// Solution for Length of Last Word",
      "python_brute": "# Solution for Length of Last Word",
      "python_optimal": "# Solution for Length of Last Word"
    }
  },
  {
    "id": 106,
    "number": 106,
    "sequence_number": 106,
    "title": "Add Binary",
    "slug": "add-binary-challenge",
    "difficulty": "Easy",
    "topic": "Strings",
    "subtopic": "Hashing & Array Optimization",
    "pattern": "Hashing & Array Optimization",
    "secondary_patterns": [
      "Hashing & Array Optimization"
    ],
    "stage": "Strings & Character Manipulation",
    "curriculumStage": "Stage 3 — Strings & Character Manipulation",
    "roadmapPhase": "Stage 3 — Strings & Character Manipulation",
    "phase": "Stage 3 — Strings & Character Manipulation",
    "estimatedTime": 15,
    "statement": "Solve the **Add Binary Challenge** problem using the **Hashing & Array Optimization** technique. Given input constraints appropriate for Easy level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^4",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Hashing & Array Optimization identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Hashing & Array Optimization. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Hashing & Array Optimization techniques by solving Easy problem constraints for Add Binary Challenge.",
    "whyThisPattern": "When observing arrays & strings problem conditions, Hashing & Array Optimization optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Microsoft",
      "Bloomberg",
      "Adobe"
    ],
    "companyRelevanceTier": "Medium",
    "leetcode_url": "https://leetcode.com/problems/add-binary/",
    "leetcode_title": "Add Binary",
    "leetcode_id": 67,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/add-binary/",
    "canonicalSlug": "add-binary-challenge",
    "canonicalUrl": "https://leetcode.com/problems/add-binary/",
    "url": "https://leetcode.com/problems/add-binary/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Add Binary Challenge (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Add Binary Challenge (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Add Binary Challenge (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Add Binary Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Add Binary Challenge (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Add Binary Challenge (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Add Binary Challenge (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Add Binary Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Add Binary",
      "cpp_optimal": "// Solution for Add Binary",
      "java_brute": "// Solution for Add Binary",
      "java_optimal": "// Solution for Add Binary",
      "python_brute": "# Solution for Add Binary",
      "python_optimal": "# Solution for Add Binary"
    }
  },
  {
    "id": 107,
    "number": 107,
    "sequence_number": 107,
    "title": "Sqrt(x)",
    "slug": "sqrt-x-optimization",
    "difficulty": "Easy",
    "topic": "Strings",
    "subtopic": "Hashing & Array Optimization",
    "pattern": "Hashing & Array Optimization",
    "secondary_patterns": [
      "Hashing & Array Optimization"
    ],
    "stage": "Strings & Character Manipulation",
    "curriculumStage": "Stage 3 — Strings & Character Manipulation",
    "roadmapPhase": "Stage 3 — Strings & Character Manipulation",
    "phase": "Stage 3 — Strings & Character Manipulation",
    "estimatedTime": 15,
    "statement": "Solve the **Sqrt(x) Optimization** problem using the **Hashing & Array Optimization** technique. Given input constraints appropriate for Easy level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^4",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Hashing & Array Optimization identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Hashing & Array Optimization. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Hashing & Array Optimization techniques by solving Easy problem constraints for Sqrt(x) Optimization.",
    "whyThisPattern": "When observing arrays & strings problem conditions, Hashing & Array Optimization optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Meta",
      "Apple",
      "Netflix"
    ],
    "companyRelevanceTier": "Medium",
    "leetcode_url": "https://leetcode.com/problems/sqrtx/",
    "leetcode_title": "Sqrt(x)",
    "leetcode_id": 69,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/sqrtx/",
    "canonicalSlug": "sqrt-x-optimization",
    "canonicalUrl": "https://leetcode.com/problems/sqrtx/",
    "url": "https://leetcode.com/problems/sqrtx/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Sqrt(x) Optimization (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Sqrt(x) Optimization (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Sqrt(x) Optimization (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Sqrt(x) Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Sqrt(x) Optimization (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Sqrt(x) Optimization (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Sqrt(x) Optimization (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Sqrt(x) Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Sqrt(x)",
      "cpp_optimal": "// Solution for Sqrt(x)",
      "java_brute": "// Solution for Sqrt(x)",
      "java_optimal": "// Solution for Sqrt(x)",
      "python_brute": "# Solution for Sqrt(x)",
      "python_optimal": "# Solution for Sqrt(x)"
    }
  },
  {
    "id": 108,
    "number": 108,
    "sequence_number": 108,
    "title": "Excel Sheet Column Title",
    "slug": "excel-sheet-column-title-optimization",
    "difficulty": "Easy",
    "topic": "Strings",
    "subtopic": "Hashing & Array Optimization",
    "pattern": "Hashing & Array Optimization",
    "secondary_patterns": [
      "Hashing & Array Optimization"
    ],
    "stage": "Strings & Character Manipulation",
    "curriculumStage": "Stage 3 — Strings & Character Manipulation",
    "roadmapPhase": "Stage 3 — Strings & Character Manipulation",
    "phase": "Stage 3 — Strings & Character Manipulation",
    "estimatedTime": 15,
    "statement": "Solve the **Excel Sheet Column Title Optimization** problem using the **Hashing & Array Optimization** technique. Given input constraints appropriate for Easy level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^4",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Hashing & Array Optimization identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Hashing & Array Optimization. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Hashing & Array Optimization techniques by solving Easy problem constraints for Excel Sheet Column Title Optimization.",
    "whyThisPattern": "When observing arrays & strings problem conditions, Hashing & Array Optimization optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Meta",
      "Apple",
      "Netflix"
    ],
    "companyRelevanceTier": "Medium",
    "leetcode_url": "https://leetcode.com/problems/excel-sheet-column-title/",
    "leetcode_title": "Excel Sheet Column Title",
    "leetcode_id": 168,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/excel-sheet-column-title/",
    "canonicalSlug": "excel-sheet-column-title-optimization",
    "canonicalUrl": "https://leetcode.com/problems/excel-sheet-column-title/",
    "url": "https://leetcode.com/problems/excel-sheet-column-title/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Excel Sheet Column Title Optimization (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Excel Sheet Column Title Optimization (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Excel Sheet Column Title Optimization (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Excel Sheet Column Title Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Excel Sheet Column Title Optimization (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Excel Sheet Column Title Optimization (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Excel Sheet Column Title Optimization (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Excel Sheet Column Title Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Excel Sheet Column Title",
      "cpp_optimal": "// Solution for Excel Sheet Column Title",
      "java_brute": "// Solution for Excel Sheet Column Title",
      "java_optimal": "// Solution for Excel Sheet Column Title",
      "python_brute": "# Solution for Excel Sheet Column Title",
      "python_optimal": "# Solution for Excel Sheet Column Title"
    }
  },
  {
    "id": 109,
    "number": 109,
    "sequence_number": 109,
    "title": "Excel Sheet Column Number",
    "slug": "excel-sheet-column-number-optimization",
    "difficulty": "Easy",
    "topic": "Strings",
    "subtopic": "Hashing & Array Optimization",
    "pattern": "Hashing & Array Optimization",
    "secondary_patterns": [
      "Hashing & Array Optimization"
    ],
    "stage": "Strings & Character Manipulation",
    "curriculumStage": "Stage 3 — Strings & Character Manipulation",
    "roadmapPhase": "Stage 3 — Strings & Character Manipulation",
    "phase": "Stage 3 — Strings & Character Manipulation",
    "estimatedTime": 15,
    "statement": "Solve the **Excel Sheet Column Number Optimization** problem using the **Hashing & Array Optimization** technique. Given input constraints appropriate for Easy level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^4",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Hashing & Array Optimization identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Hashing & Array Optimization. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Hashing & Array Optimization techniques by solving Easy problem constraints for Excel Sheet Column Number Optimization.",
    "whyThisPattern": "When observing arrays & strings problem conditions, Hashing & Array Optimization optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "LinkedIn",
      "Amazon"
    ],
    "companyRelevanceTier": "Medium",
    "leetcode_url": "https://leetcode.com/problems/excel-sheet-column-number/",
    "leetcode_title": "Excel Sheet Column Number",
    "leetcode_id": 171,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/excel-sheet-column-number/",
    "canonicalSlug": "excel-sheet-column-number-optimization",
    "canonicalUrl": "https://leetcode.com/problems/excel-sheet-column-number/",
    "url": "https://leetcode.com/problems/excel-sheet-column-number/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Excel Sheet Column Number Optimization (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Excel Sheet Column Number Optimization (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Excel Sheet Column Number Optimization (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Excel Sheet Column Number Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Excel Sheet Column Number Optimization (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Excel Sheet Column Number Optimization (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Excel Sheet Column Number Optimization (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Excel Sheet Column Number Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Excel Sheet Column Number",
      "cpp_optimal": "// Solution for Excel Sheet Column Number",
      "java_brute": "// Solution for Excel Sheet Column Number",
      "java_optimal": "// Solution for Excel Sheet Column Number",
      "python_brute": "# Solution for Excel Sheet Column Number",
      "python_optimal": "# Solution for Excel Sheet Column Number"
    }
  },
  {
    "id": 110,
    "number": 110,
    "sequence_number": 110,
    "title": "Combine Two Tables",
    "slug": "combine-two-tables-challenge",
    "difficulty": "Easy",
    "topic": "Strings",
    "subtopic": "Hashing & Array Optimization",
    "pattern": "Hashing & Array Optimization",
    "secondary_patterns": [
      "Hashing & Array Optimization"
    ],
    "stage": "Strings & Character Manipulation",
    "curriculumStage": "Stage 3 — Strings & Character Manipulation",
    "roadmapPhase": "Stage 3 — Strings & Character Manipulation",
    "phase": "Stage 3 — Strings & Character Manipulation",
    "estimatedTime": 15,
    "statement": "Solve the **Combine Two Tables Challenge** problem using the **Hashing & Array Optimization** technique. Given input constraints appropriate for Easy level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^4",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Hashing & Array Optimization identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Hashing & Array Optimization. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Hashing & Array Optimization techniques by solving Easy problem constraints for Combine Two Tables Challenge.",
    "whyThisPattern": "When observing arrays & strings problem conditions, Hashing & Array Optimization optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Microsoft",
      "Bloomberg",
      "Adobe"
    ],
    "companyRelevanceTier": "Medium",
    "leetcode_url": "https://leetcode.com/problems/combine-two-tables/",
    "leetcode_title": "Combine Two Tables",
    "leetcode_id": 175,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/combine-two-tables/",
    "canonicalSlug": "combine-two-tables-challenge",
    "canonicalUrl": "https://leetcode.com/problems/combine-two-tables/",
    "url": "https://leetcode.com/problems/combine-two-tables/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Combine Two Tables Challenge (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Combine Two Tables Challenge (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Combine Two Tables Challenge (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Combine Two Tables Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Combine Two Tables Challenge (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Combine Two Tables Challenge (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Combine Two Tables Challenge (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Combine Two Tables Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Combine Two Tables",
      "cpp_optimal": "// Solution for Combine Two Tables",
      "java_brute": "// Solution for Combine Two Tables",
      "java_optimal": "// Solution for Combine Two Tables",
      "python_brute": "# Solution for Combine Two Tables",
      "python_optimal": "# Solution for Combine Two Tables"
    }
  },
  {
    "id": 111,
    "number": 111,
    "sequence_number": 111,
    "title": "Custom Sort String",
    "slug": "custom-sort-string",
    "difficulty": "Medium",
    "topic": "Strings",
    "subtopic": "Strings Optimization",
    "pattern": "Custom Priority Map Sort",
    "secondary_patterns": [
      "Custom Priority Map Sort"
    ],
    "stage": "Strings & Character Manipulation",
    "curriculumStage": "Stage 3 — Strings & Character Manipulation",
    "roadmapPhase": "Stage 3 — Strings & Character Manipulation",
    "phase": "Stage 3 — Strings & Character Manipulation",
    "estimatedTime": 30,
    "statement": "Given the constraints and input parameters for Custom Sort String, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Custom Sort String."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Custom Sort String.",
      "Leverage the optimal Strings pattern to reduce time complexity."
    ],
    "learningObjective": "Master Strings techniques by solving Medium problem constraints for Custom Sort String.",
    "whyThisPattern": "When observing Strings problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/custom-sort-string/",
    "leetcode_title": "Custom Sort String",
    "leetcode_id": 753,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/custom-sort-string/",
    "canonicalSlug": "custom-sort-string",
    "canonicalUrl": "https://leetcode.com/problems/custom-sort-string/",
    "url": "https://leetcode.com/problems/custom-sort-string/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Custom Sort String\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Custom Sort String\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Custom Sort String\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Custom Sort String\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Custom Sort String\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Custom Sort String\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Custom Sort String\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Custom Sort String\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Custom Sort String",
      "cpp_optimal": "// Solution for Custom Sort String",
      "java_brute": "// Solution for Custom Sort String",
      "java_optimal": "// Solution for Custom Sort String",
      "python_brute": "# Solution for Custom Sort String",
      "python_optimal": "# Solution for Custom Sort String"
    }
  },
  {
    "id": 112,
    "number": 112,
    "sequence_number": 112,
    "title": "Ambiguous Coordinates",
    "slug": "ambiguous-coordinates",
    "difficulty": "Medium",
    "topic": "Strings",
    "subtopic": "Strings Optimization",
    "pattern": "Decimal Insertion Backtracking",
    "secondary_patterns": [
      "Decimal Insertion Backtracking"
    ],
    "stage": "Strings & Character Manipulation",
    "curriculumStage": "Stage 3 — Strings & Character Manipulation",
    "roadmapPhase": "Stage 3 — Strings & Character Manipulation",
    "phase": "Stage 3 — Strings & Character Manipulation",
    "estimatedTime": 30,
    "statement": "Given the constraints and input parameters for Ambiguous Coordinates, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Ambiguous Coordinates."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Ambiguous Coordinates.",
      "Leverage the optimal Strings pattern to reduce time complexity."
    ],
    "learningObjective": "Master Strings techniques by solving Medium problem constraints for Ambiguous Coordinates.",
    "whyThisPattern": "When observing Strings problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/ambiguous-coordinates/",
    "leetcode_title": "Ambiguous Coordinates",
    "leetcode_id": 756,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/ambiguous-coordinates/",
    "canonicalSlug": "ambiguous-coordinates",
    "canonicalUrl": "https://leetcode.com/problems/ambiguous-coordinates/",
    "url": "https://leetcode.com/problems/ambiguous-coordinates/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Ambiguous Coordinates\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Ambiguous Coordinates\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Ambiguous Coordinates\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Ambiguous Coordinates\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Ambiguous Coordinates\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Ambiguous Coordinates\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Ambiguous Coordinates\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Ambiguous Coordinates\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Ambiguous Coordinates",
      "cpp_optimal": "// Solution for Ambiguous Coordinates",
      "java_brute": "// Solution for Ambiguous Coordinates",
      "java_optimal": "// Solution for Ambiguous Coordinates",
      "python_brute": "# Solution for Ambiguous Coordinates",
      "python_optimal": "# Solution for Ambiguous Coordinates"
    }
  },
  {
    "id": 113,
    "number": 113,
    "sequence_number": 113,
    "title": "Reordered Power of 2",
    "slug": "reordered-power-of-2",
    "difficulty": "Medium",
    "topic": "Strings",
    "subtopic": "Strings Optimization",
    "pattern": "Sorted Digit Count Match",
    "secondary_patterns": [
      "Sorted Digit Count Match"
    ],
    "stage": "Strings & Character Manipulation",
    "curriculumStage": "Stage 3 — Strings & Character Manipulation",
    "roadmapPhase": "Stage 3 — Strings & Character Manipulation",
    "phase": "Stage 3 — Strings & Character Manipulation",
    "estimatedTime": 30,
    "statement": "Given the constraints and input parameters for Reordered Power of 2, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Reordered Power of 2."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Reordered Power of 2.",
      "Leverage the optimal Strings pattern to reduce time complexity."
    ],
    "learningObjective": "Master Strings techniques by solving Medium problem constraints for Reordered Power of 2.",
    "whyThisPattern": "When observing Strings problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/reordered-power-of-2/",
    "leetcode_title": "Reordered Power of 2",
    "leetcode_id": 761,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/reordered-power-of-2/",
    "canonicalSlug": "reordered-power-of-2",
    "canonicalUrl": "https://leetcode.com/problems/reordered-power-of-2/",
    "url": "https://leetcode.com/problems/reordered-power-of-2/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Reordered Power of 2\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Reordered Power of 2\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Reordered Power of 2\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Reordered Power of 2\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Reordered Power of 2\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Reordered Power of 2\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Reordered Power of 2\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Reordered Power of 2\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Reordered Power of 2",
      "cpp_optimal": "// Solution for Reordered Power of 2",
      "java_brute": "// Solution for Reordered Power of 2",
      "java_optimal": "// Solution for Reordered Power of 2",
      "python_brute": "# Solution for Reordered Power of 2",
      "python_optimal": "# Solution for Reordered Power of 2"
    }
  },
  {
    "id": 114,
    "number": 114,
    "sequence_number": 114,
    "title": "Masking Personal Information",
    "slug": "masking-personal-information",
    "difficulty": "Medium",
    "topic": "Strings",
    "subtopic": "Strings Optimization",
    "pattern": "Regex Format Masking",
    "secondary_patterns": [
      "Regex Format Masking"
    ],
    "stage": "Strings & Character Manipulation",
    "curriculumStage": "Stage 3 — Strings & Character Manipulation",
    "roadmapPhase": "Stage 3 — Strings & Character Manipulation",
    "phase": "Stage 3 — Strings & Character Manipulation",
    "estimatedTime": 30,
    "statement": "Given the constraints and input parameters for Masking Personal Information, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Masking Personal Information."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Masking Personal Information.",
      "Leverage the optimal Strings pattern to reduce time complexity."
    ],
    "learningObjective": "Master Strings techniques by solving Medium problem constraints for Masking Personal Information.",
    "whyThisPattern": "When observing Strings problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/masking-personal-information/",
    "leetcode_title": "Masking Personal Information",
    "leetcode_id": 791,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/masking-personal-information/",
    "canonicalSlug": "masking-personal-information",
    "canonicalUrl": "https://leetcode.com/problems/masking-personal-information/",
    "url": "https://leetcode.com/problems/masking-personal-information/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Masking Personal Information\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Masking Personal Information\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Masking Personal Information\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Masking Personal Information\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Masking Personal Information\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Masking Personal Information\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Masking Personal Information\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Masking Personal Information\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Masking Personal Information",
      "cpp_optimal": "// Solution for Masking Personal Information",
      "java_brute": "// Solution for Masking Personal Information",
      "java_optimal": "// Solution for Masking Personal Information",
      "python_brute": "# Solution for Masking Personal Information",
      "python_optimal": "# Solution for Masking Personal Information"
    }
  },
  {
    "id": 115,
    "number": 115,
    "sequence_number": 115,
    "title": "Find And Replace in String",
    "slug": "find-and-replace-in-string",
    "difficulty": "Medium",
    "topic": "Strings",
    "subtopic": "Strings Optimization",
    "pattern": "Index Replacement Map",
    "secondary_patterns": [
      "Index Replacement Map"
    ],
    "stage": "Strings & Character Manipulation",
    "curriculumStage": "Stage 3 — Strings & Character Manipulation",
    "roadmapPhase": "Stage 3 — Strings & Character Manipulation",
    "phase": "Stage 3 — Strings & Character Manipulation",
    "estimatedTime": 30,
    "statement": "Given the constraints and input parameters for Find And Replace in String, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Find And Replace in String."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Find And Replace in String.",
      "Leverage the optimal Strings pattern to reduce time complexity."
    ],
    "learningObjective": "Master Strings techniques by solving Medium problem constraints for Find And Replace in String.",
    "whyThisPattern": "When observing Strings problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/find-and-replace-in-string/",
    "leetcode_title": "Find And Replace in String",
    "leetcode_id": 806,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/find-and-replace-in-string/",
    "canonicalSlug": "find-and-replace-in-string",
    "canonicalUrl": "https://leetcode.com/problems/find-and-replace-in-string/",
    "url": "https://leetcode.com/problems/find-and-replace-in-string/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Find And Replace in String\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Find And Replace in String\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Find And Replace in String\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Find And Replace in String\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Find And Replace in String\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Find And Replace in String\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Find And Replace in String\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Find And Replace in String\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Find And Replace in String",
      "cpp_optimal": "// Solution for Find And Replace in String",
      "java_brute": "// Solution for Find And Replace in String",
      "java_optimal": "// Solution for Find And Replace in String",
      "python_brute": "# Solution for Find And Replace in String",
      "python_optimal": "# Solution for Find And Replace in String"
    }
  },
  {
    "id": 116,
    "number": 116,
    "sequence_number": 116,
    "title": "Remove Comments",
    "slug": "remove-comments",
    "difficulty": "Medium",
    "topic": "Strings",
    "subtopic": "Strings Optimization",
    "pattern": "State Parsing Machine",
    "secondary_patterns": [
      "State Parsing Machine"
    ],
    "stage": "Strings & Character Manipulation",
    "curriculumStage": "Stage 3 — Strings & Character Manipulation",
    "roadmapPhase": "Stage 3 — Strings & Character Manipulation",
    "phase": "Stage 3 — Strings & Character Manipulation",
    "estimatedTime": 30,
    "statement": "Given the constraints and input parameters for Remove Comments, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Remove Comments."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Remove Comments.",
      "Leverage the optimal Strings pattern to reduce time complexity."
    ],
    "learningObjective": "Master Strings techniques by solving Medium problem constraints for Remove Comments.",
    "whyThisPattern": "When observing Strings problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/remove-comments/",
    "leetcode_title": "Remove Comments",
    "leetcode_id": 812,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/remove-comments/",
    "canonicalSlug": "remove-comments",
    "canonicalUrl": "https://leetcode.com/problems/remove-comments/",
    "url": "https://leetcode.com/problems/remove-comments/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Remove Comments\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Remove Comments\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Remove Comments\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Remove Comments\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Remove Comments\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Remove Comments\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Remove Comments\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Remove Comments\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Remove Comments",
      "cpp_optimal": "// Solution for Remove Comments",
      "java_brute": "// Solution for Remove Comments",
      "java_optimal": "// Solution for Remove Comments",
      "python_brute": "# Solution for Remove Comments",
      "python_optimal": "# Solution for Remove Comments"
    }
  },
  {
    "id": 117,
    "number": 117,
    "sequence_number": 117,
    "title": "Reorder Data in Log Files",
    "slug": "reorder-data-in-log-files",
    "difficulty": "Medium",
    "topic": "Strings",
    "subtopic": "Strings Optimization",
    "pattern": "Custom Log Comparator",
    "secondary_patterns": [
      "Custom Log Comparator"
    ],
    "stage": "Strings & Character Manipulation",
    "curriculumStage": "Stage 3 — Strings & Character Manipulation",
    "roadmapPhase": "Stage 3 — Strings & Character Manipulation",
    "phase": "Stage 3 — Strings & Character Manipulation",
    "estimatedTime": 30,
    "statement": "Given the constraints and input parameters for Reorder Data in Log Files, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Reorder Data in Log Files."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Reorder Data in Log Files.",
      "Leverage the optimal Strings pattern to reduce time complexity."
    ],
    "learningObjective": "Master Strings techniques by solving Medium problem constraints for Reorder Data in Log Files.",
    "whyThisPattern": "When observing Strings problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/reorder-data-in-log-files/",
    "leetcode_title": "Reorder Data in Log Files",
    "leetcode_id": 849,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/reorder-data-in-log-files/",
    "canonicalSlug": "reorder-data-in-log-files",
    "canonicalUrl": "https://leetcode.com/problems/reorder-data-in-log-files/",
    "url": "https://leetcode.com/problems/reorder-data-in-log-files/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Reorder Data in Log Files\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Reorder Data in Log Files\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Reorder Data in Log Files\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Reorder Data in Log Files\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Reorder Data in Log Files\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Reorder Data in Log Files\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Reorder Data in Log Files\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Reorder Data in Log Files\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Reorder Data in Log Files",
      "cpp_optimal": "// Solution for Reorder Data in Log Files",
      "java_brute": "// Solution for Reorder Data in Log Files",
      "java_optimal": "// Solution for Reorder Data in Log Files",
      "python_brute": "# Solution for Reorder Data in Log Files",
      "python_optimal": "# Solution for Reorder Data in Log Files"
    }
  },
  {
    "id": 118,
    "number": 118,
    "sequence_number": 118,
    "title": "HTML Entity Parser",
    "slug": "html-entity-parser",
    "difficulty": "Medium",
    "topic": "Strings",
    "subtopic": "Strings Optimization",
    "pattern": "Trie / Map Replacement",
    "secondary_patterns": [
      "Trie / Map Replacement"
    ],
    "stage": "Strings & Character Manipulation",
    "curriculumStage": "Stage 3 — Strings & Character Manipulation",
    "roadmapPhase": "Stage 3 — Strings & Character Manipulation",
    "phase": "Stage 3 — Strings & Character Manipulation",
    "estimatedTime": 30,
    "statement": "Given the constraints and input parameters for HTML Entity Parser, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for HTML Entity Parser."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for HTML Entity Parser.",
      "Leverage the optimal Strings pattern to reduce time complexity."
    ],
    "learningObjective": "Master Strings techniques by solving Medium problem constraints for HTML Entity Parser.",
    "whyThisPattern": "When observing Strings problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/html-entity-parser/",
    "leetcode_title": "HTML Entity Parser",
    "leetcode_id": 972,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/html-entity-parser/",
    "canonicalSlug": "html-entity-parser",
    "canonicalUrl": "https://leetcode.com/problems/html-entity-parser/",
    "url": "https://leetcode.com/problems/html-entity-parser/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for HTML Entity Parser\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for HTML Entity Parser\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for HTML Entity Parser\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for HTML Entity Parser\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for HTML Entity Parser\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for HTML Entity Parser\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for HTML Entity Parser\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for HTML Entity Parser\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for HTML Entity Parser",
      "cpp_optimal": "// Solution for HTML Entity Parser",
      "java_brute": "// Solution for HTML Entity Parser",
      "java_optimal": "// Solution for HTML Entity Parser",
      "python_brute": "# Solution for HTML Entity Parser",
      "python_optimal": "# Solution for HTML Entity Parser"
    }
  },
  {
    "id": 119,
    "number": 119,
    "sequence_number": 119,
    "title": "Multiply Strings",
    "slug": "multiply-strings",
    "difficulty": "Medium",
    "topic": "Strings",
    "subtopic": "Strings Optimization",
    "pattern": "Digit Array Column Multiplication",
    "secondary_patterns": [
      "Digit Array Column Multiplication"
    ],
    "stage": "Strings & Character Manipulation",
    "curriculumStage": "Stage 3 — Strings & Character Manipulation",
    "roadmapPhase": "Stage 3 — Strings & Character Manipulation",
    "phase": "Stage 3 — Strings & Character Manipulation",
    "estimatedTime": 30,
    "statement": "Given the constraints and input parameters for Multiply Strings, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Multiply Strings."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Multiply Strings.",
      "Leverage the optimal Strings pattern to reduce time complexity."
    ],
    "learningObjective": "Master Strings techniques by solving Medium problem constraints for Multiply Strings.",
    "whyThisPattern": "When observing Strings problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/multiply-strings/",
    "leetcode_title": "Multiply Strings",
    "leetcode_id": 988,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/multiply-strings/",
    "canonicalSlug": "multiply-strings",
    "canonicalUrl": "https://leetcode.com/problems/multiply-strings/",
    "url": "https://leetcode.com/problems/multiply-strings/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Multiply Strings\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Multiply Strings\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Multiply Strings\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Multiply Strings\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Multiply Strings\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Multiply Strings\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Multiply Strings\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Multiply Strings\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Multiply Strings",
      "cpp_optimal": "// Solution for Multiply Strings",
      "java_brute": "// Solution for Multiply Strings",
      "java_optimal": "// Solution for Multiply Strings",
      "python_brute": "# Solution for Multiply Strings",
      "python_optimal": "# Solution for Multiply Strings"
    }
  },
  {
    "id": 120,
    "number": 120,
    "sequence_number": 120,
    "title": "Spiral Matrix",
    "slug": "spiral-matrix",
    "difficulty": "Medium",
    "topic": "Simulation",
    "subtopic": "Binary Search",
    "pattern": "Binary Search",
    "secondary_patterns": [
      "Binary Search"
    ],
    "stage": "Strings & Character Manipulation",
    "curriculumStage": "Stage 3 — Strings & Character Manipulation",
    "roadmapPhase": "Stage 3 — Strings & Character Manipulation",
    "phase": "Stage 3 — Strings & Character Manipulation",
    "estimatedTime": 30,
    "statement": "Solve the **Spiral Matrix Challenge** problem using the **Binary Search** technique. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Binary Search identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Binary Search. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Binary Search techniques by solving Medium problem constraints for Spiral Matrix Challenge.",
    "whyThisPattern": "When observing arrays & strings problem conditions, Binary Search optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Amazon",
      "Microsoft",
      "Uber"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/spiral-matrix/",
    "leetcode_title": "Spiral Matrix",
    "leetcode_id": 54,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/spiral-matrix/",
    "canonicalSlug": "spiral-matrix",
    "canonicalUrl": "https://leetcode.com/problems/spiral-matrix/",
    "url": "https://leetcode.com/problems/spiral-matrix/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Spiral Matrix Challenge (Binary Search)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Spiral Matrix Challenge (Binary Search)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Spiral Matrix Challenge (Binary Search)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Spiral Matrix Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Spiral Matrix Challenge (Binary Search)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Spiral Matrix Challenge (Binary Search)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Spiral Matrix Challenge (Binary Search)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Spiral Matrix Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Spiral Matrix",
      "cpp_optimal": "// Solution for Spiral Matrix",
      "java_brute": "// Solution for Spiral Matrix",
      "java_optimal": "// Solution for Spiral Matrix",
      "python_brute": "# Solution for Spiral Matrix",
      "python_optimal": "# Solution for Spiral Matrix"
    },
    "originalOrder": 581,
    "learningOrder": 581
  },
  {
    "id": 121,
    "number": 121,
    "sequence_number": 121,
    "title": "Spiral Matrix II",
    "slug": "spiral-matrix-ii",
    "difficulty": "Medium",
    "topic": "Simulation",
    "subtopic": "Binary Search",
    "pattern": "Binary Search",
    "secondary_patterns": [
      "Binary Search"
    ],
    "stage": "Strings & Character Manipulation",
    "curriculumStage": "Stage 3 — Strings & Character Manipulation",
    "roadmapPhase": "Stage 3 — Strings & Character Manipulation",
    "phase": "Stage 3 — Strings & Character Manipulation",
    "estimatedTime": 30,
    "statement": "Solve the **Spiral Matrix II Challenge** problem using the **Binary Search** technique. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Binary Search identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Binary Search. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Binary Search techniques by solving Medium problem constraints for Spiral Matrix II Challenge.",
    "whyThisPattern": "When observing arrays & strings problem conditions, Binary Search optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Meta",
      "Uber",
      "Databricks"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/spiral-matrix-ii/",
    "leetcode_title": "Spiral Matrix II",
    "leetcode_id": 59,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/spiral-matrix-ii/",
    "canonicalSlug": "spiral-matrix-ii",
    "canonicalUrl": "https://leetcode.com/problems/spiral-matrix-ii/",
    "url": "https://leetcode.com/problems/spiral-matrix-ii/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Spiral Matrix II Challenge (Binary Search)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Spiral Matrix II Challenge (Binary Search)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Spiral Matrix II Challenge (Binary Search)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Spiral Matrix II Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Spiral Matrix II Challenge (Binary Search)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Spiral Matrix II Challenge (Binary Search)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Spiral Matrix II Challenge (Binary Search)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Spiral Matrix II Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Spiral Matrix II",
      "cpp_optimal": "// Solution for Spiral Matrix II",
      "java_brute": "// Solution for Spiral Matrix II",
      "java_optimal": "// Solution for Spiral Matrix II",
      "python_brute": "# Solution for Spiral Matrix II",
      "python_optimal": "# Solution for Spiral Matrix II"
    },
    "originalOrder": 582,
    "learningOrder": 582
  },
  {
    "id": 122,
    "number": 122,
    "sequence_number": 122,
    "title": "Incremental Memory Leak",
    "slug": "incremental-memory-leak",
    "difficulty": "Medium",
    "topic": "Simulation",
    "subtopic": "Simulation Optimization",
    "pattern": "Two Memory Stick Simulation",
    "secondary_patterns": [
      "Two Memory Stick Simulation"
    ],
    "stage": "Strings & Character Manipulation",
    "curriculumStage": "Stage 3 — Strings & Character Manipulation",
    "roadmapPhase": "Stage 3 — Strings & Character Manipulation",
    "phase": "Stage 3 — Strings & Character Manipulation",
    "estimatedTime": 30,
    "statement": "Given the constraints and input parameters for Incremental Memory Leak, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Incremental Memory Leak."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Incremental Memory Leak.",
      "Leverage the optimal Simulation pattern to reduce time complexity."
    ],
    "learningObjective": "Master Simulation techniques by solving Medium problem constraints for Incremental Memory Leak.",
    "whyThisPattern": "When observing Simulation problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/incremental-memory-leak/",
    "leetcode_title": "Incremental Memory Leak",
    "leetcode_id": 1860,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/incremental-memory-leak/",
    "canonicalSlug": "incremental-memory-leak",
    "canonicalUrl": "https://leetcode.com/problems/incremental-memory-leak/",
    "url": "https://leetcode.com/problems/incremental-memory-leak/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Incremental Memory Leak\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Incremental Memory Leak\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Incremental Memory Leak\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Incremental Memory Leak\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Incremental Memory Leak\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Incremental Memory Leak\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Incremental Memory Leak\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Incremental Memory Leak\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Incremental Memory Leak",
      "cpp_optimal": "// Solution for Incremental Memory Leak",
      "java_brute": "// Solution for Incremental Memory Leak",
      "java_optimal": "// Solution for Incremental Memory Leak",
      "python_brute": "# Solution for Incremental Memory Leak",
      "python_optimal": "# Solution for Incremental Memory Leak"
    },
    "originalOrder": 583,
    "learningOrder": 583
  },
  {
    "id": 123,
    "number": 123,
    "sequence_number": 123,
    "title": "Minimum Number of Operations to Reinitialize a Permutation",
    "slug": "minimum-number-of-operations-to-reinitialize-a-permutation",
    "difficulty": "Medium",
    "topic": "Simulation",
    "subtopic": "Simulation Optimization",
    "pattern": "Index Cycle Tracking",
    "secondary_patterns": [
      "Index Cycle Tracking"
    ],
    "stage": "Strings & Character Manipulation",
    "curriculumStage": "Stage 3 — Strings & Character Manipulation",
    "roadmapPhase": "Stage 3 — Strings & Character Manipulation",
    "phase": "Stage 3 — Strings & Character Manipulation",
    "estimatedTime": 30,
    "statement": "Given the constraints and input parameters for Minimum Number of Operations to Reinitialize a Permutation, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Minimum Number of Operations to Reinitialize a Permutation."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Minimum Number of Operations to Reinitialize a Permutation.",
      "Leverage the optimal Simulation pattern to reduce time complexity."
    ],
    "learningObjective": "Master Simulation techniques by solving Medium problem constraints for Minimum Number of Operations to Reinitialize a Permutation.",
    "whyThisPattern": "When observing Simulation problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/minimum-number-of-operations-to-reinitialize-a-permutation/",
    "leetcode_title": "Minimum Number of Operations to Reinitialize a Permutation",
    "leetcode_id": 1806,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/minimum-number-of-operations-to-reinitialize-a-permutation/",
    "canonicalSlug": "minimum-number-of-operations-to-reinitialize-a-permutation",
    "canonicalUrl": "https://leetcode.com/problems/minimum-number-of-operations-to-reinitialize-a-permutation/",
    "url": "https://leetcode.com/problems/minimum-number-of-operations-to-reinitialize-a-permutation/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Minimum Number of Operations to Reinitialize a Permutation\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Minimum Number of Operations to Reinitialize a Permutation\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Minimum Number of Operations to Reinitialize a Permutation\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Minimum Number of Operations to Reinitialize a Permutation\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Minimum Number of Operations to Reinitialize a Permutation\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Minimum Number of Operations to Reinitialize a Permutation\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Minimum Number of Operations to Reinitialize a Permutation\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Minimum Number of Operations to Reinitialize a Permutation\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Minimum Number of Operations to Reinitialize a Permutation",
      "cpp_optimal": "// Solution for Minimum Number of Operations to Reinitialize a Permutation",
      "java_brute": "// Solution for Minimum Number of Operations to Reinitialize a Permutation",
      "java_optimal": "// Solution for Minimum Number of Operations to Reinitialize a Permutation",
      "python_brute": "# Solution for Minimum Number of Operations to Reinitialize a Permutation",
      "python_optimal": "# Solution for Minimum Number of Operations to Reinitialize a Permutation"
    },
    "originalOrder": 584,
    "learningOrder": 584
  },
  {
    "id": 124,
    "number": 124,
    "sequence_number": 124,
    "title": "Game of Life",
    "slug": "game-of-life",
    "difficulty": "Medium",
    "topic": "Simulation",
    "subtopic": "Simulation Optimization",
    "pattern": "Simulation Pattern",
    "secondary_patterns": [
      "Simulation Pattern"
    ],
    "stage": "Strings & Character Manipulation",
    "curriculumStage": "Stage 3 — Strings & Character Manipulation",
    "roadmapPhase": "Stage 3 — Strings & Character Manipulation",
    "phase": "Stage 3 — Strings & Character Manipulation",
    "estimatedTime": 30,
    "statement": "Solve the **Game of Life** problem using standard Simulation techniques. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Simulation algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Simulation properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Simulation techniques by solving Medium problem constraints for Game of Life.",
    "whyThisPattern": "When observing Simulation problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/game-of-life/",
    "leetcode_title": "Game of Life",
    "leetcode_id": 289,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/game-of-life/",
    "canonicalSlug": "game-of-life",
    "canonicalUrl": "https://leetcode.com/problems/game-of-life/",
    "url": "https://leetcode.com/problems/game-of-life/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Game of Life\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Game of Life\n};",
        "java": "// Java Solution for Game of Life\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Game of Life\n}",
        "python": "# Python Solution for Game of Life\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Game of Life\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Game of Life\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Game of Life\n};",
        "java": "// Optimal Java Solution for Game of Life\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Game of Life\n}",
        "python": "# Optimal Python Solution for Game of Life\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Game of Life\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Game of Life",
      "cpp_optimal": "// Solution for Game of Life",
      "java_brute": "// Solution for Game of Life",
      "java_optimal": "// Solution for Game of Life",
      "python_brute": "# Solution for Game of Life",
      "python_optimal": "# Solution for Game of Life"
    },
    "originalOrder": 585,
    "learningOrder": 585
  },
  {
    "id": 125,
    "number": 125,
    "sequence_number": 125,
    "title": "Walking Robot Simulation",
    "slug": "walking-robot-simulation",
    "difficulty": "Medium",
    "topic": "Simulation",
    "subtopic": "Simulation Optimization",
    "pattern": "Simulation Pattern",
    "secondary_patterns": [
      "Simulation Pattern"
    ],
    "stage": "Strings & Character Manipulation",
    "curriculumStage": "Stage 3 — Strings & Character Manipulation",
    "roadmapPhase": "Stage 3 — Strings & Character Manipulation",
    "phase": "Stage 3 — Strings & Character Manipulation",
    "estimatedTime": 30,
    "statement": "Solve the **Walking Robot Simulation** problem using standard Simulation techniques. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Simulation algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Simulation properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Simulation techniques by solving Medium problem constraints for Walking Robot Simulation.",
    "whyThisPattern": "When observing Simulation problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/walking-robot-simulation/",
    "leetcode_title": "Walking Robot Simulation",
    "leetcode_id": 874,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/walking-robot-simulation/",
    "canonicalSlug": "walking-robot-simulation",
    "canonicalUrl": "https://leetcode.com/problems/walking-robot-simulation/",
    "url": "https://leetcode.com/problems/walking-robot-simulation/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Walking Robot Simulation\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Walking Robot Simulation\n};",
        "java": "// Java Solution for Walking Robot Simulation\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Walking Robot Simulation\n}",
        "python": "# Python Solution for Walking Robot Simulation\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Walking Robot Simulation\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Walking Robot Simulation\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Walking Robot Simulation\n};",
        "java": "// Optimal Java Solution for Walking Robot Simulation\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Walking Robot Simulation\n}",
        "python": "# Optimal Python Solution for Walking Robot Simulation\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Walking Robot Simulation\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Walking Robot Simulation",
      "cpp_optimal": "// Solution for Walking Robot Simulation",
      "java_brute": "// Solution for Walking Robot Simulation",
      "java_optimal": "// Solution for Walking Robot Simulation",
      "python_brute": "# Solution for Walking Robot Simulation",
      "python_optimal": "# Solution for Walking Robot Simulation"
    },
    "originalOrder": 586,
    "learningOrder": 586
  },
  {
    "id": 126,
    "number": 126,
    "sequence_number": 126,
    "title": "Fizz Buzz Multithreaded",
    "slug": "fizz-buzz-multithreaded",
    "difficulty": "Medium",
    "topic": "Simulation",
    "subtopic": "Simulation Optimization",
    "pattern": "Simulation Pattern",
    "secondary_patterns": [
      "Simulation Pattern"
    ],
    "stage": "Strings & Character Manipulation",
    "curriculumStage": "Stage 3 — Strings & Character Manipulation",
    "roadmapPhase": "Stage 3 — Strings & Character Manipulation",
    "phase": "Stage 3 — Strings & Character Manipulation",
    "estimatedTime": 30,
    "statement": "Solve the **Fizz Buzz Multithreaded** problem using standard Simulation techniques. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Simulation algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Simulation properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Simulation techniques by solving Medium problem constraints for Fizz Buzz Multithreaded.",
    "whyThisPattern": "When observing Simulation problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/fizz-buzz-multithreaded/",
    "leetcode_title": "Fizz Buzz Multithreaded",
    "leetcode_id": 1195,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/fizz-buzz-multithreaded/",
    "canonicalSlug": "fizz-buzz-multithreaded",
    "canonicalUrl": "https://leetcode.com/problems/fizz-buzz-multithreaded/",
    "url": "https://leetcode.com/problems/fizz-buzz-multithreaded/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Fizz Buzz Multithreaded\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Fizz Buzz Multithreaded\n};",
        "java": "// Java Solution for Fizz Buzz Multithreaded\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Fizz Buzz Multithreaded\n}",
        "python": "# Python Solution for Fizz Buzz Multithreaded\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Fizz Buzz Multithreaded\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Fizz Buzz Multithreaded\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Fizz Buzz Multithreaded\n};",
        "java": "// Optimal Java Solution for Fizz Buzz Multithreaded\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Fizz Buzz Multithreaded\n}",
        "python": "# Optimal Python Solution for Fizz Buzz Multithreaded\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Fizz Buzz Multithreaded\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Fizz Buzz Multithreaded",
      "cpp_optimal": "// Solution for Fizz Buzz Multithreaded",
      "java_brute": "// Solution for Fizz Buzz Multithreaded",
      "java_optimal": "// Solution for Fizz Buzz Multithreaded",
      "python_brute": "# Solution for Fizz Buzz Multithreaded",
      "python_optimal": "# Solution for Fizz Buzz Multithreaded"
    },
    "originalOrder": 587,
    "learningOrder": 587
  },
  {
    "id": 127,
    "number": 127,
    "sequence_number": 127,
    "title": "Where Will the Ball Fall",
    "slug": "where-will-the-ball-fall",
    "difficulty": "Medium",
    "topic": "Simulation",
    "subtopic": "Simulation Optimization",
    "pattern": "Simulation Pattern",
    "secondary_patterns": [
      "Simulation Pattern"
    ],
    "stage": "Strings & Character Manipulation",
    "curriculumStage": "Stage 3 — Strings & Character Manipulation",
    "roadmapPhase": "Stage 3 — Strings & Character Manipulation",
    "phase": "Stage 3 — Strings & Character Manipulation",
    "estimatedTime": 30,
    "statement": "Solve the **Where Will the Ball Fall** problem using standard Simulation techniques. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Simulation algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Simulation properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Simulation techniques by solving Medium problem constraints for Where Will the Ball Fall.",
    "whyThisPattern": "When observing Simulation problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/where-will-the-ball-fall/",
    "leetcode_title": "Where Will the Ball Fall",
    "leetcode_id": 1706,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/where-will-the-ball-fall/",
    "canonicalSlug": "where-will-the-ball-fall",
    "canonicalUrl": "https://leetcode.com/problems/where-will-the-ball-fall/",
    "url": "https://leetcode.com/problems/where-will-the-ball-fall/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Where Will the Ball Fall\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Where Will the Ball Fall\n};",
        "java": "// Java Solution for Where Will the Ball Fall\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Where Will the Ball Fall\n}",
        "python": "# Python Solution for Where Will the Ball Fall\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Where Will the Ball Fall\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Where Will the Ball Fall\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Where Will the Ball Fall\n};",
        "java": "// Optimal Java Solution for Where Will the Ball Fall\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Where Will the Ball Fall\n}",
        "python": "# Optimal Python Solution for Where Will the Ball Fall\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Where Will the Ball Fall\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Where Will the Ball Fall",
      "cpp_optimal": "// Solution for Where Will the Ball Fall",
      "java_brute": "// Solution for Where Will the Ball Fall",
      "java_optimal": "// Solution for Where Will the Ball Fall",
      "python_brute": "# Solution for Where Will the Ball Fall",
      "python_optimal": "# Solution for Where Will the Ball Fall"
    },
    "originalOrder": 588,
    "learningOrder": 588
  },
  {
    "id": 128,
    "number": 128,
    "sequence_number": 128,
    "title": "Walking Robot Simulation II",
    "slug": "walking-robot-simulation-ii",
    "difficulty": "Medium",
    "topic": "Simulation",
    "subtopic": "Simulation Optimization",
    "pattern": "Simulation Pattern",
    "secondary_patterns": [
      "Simulation Pattern"
    ],
    "stage": "Strings & Character Manipulation",
    "curriculumStage": "Stage 3 — Strings & Character Manipulation",
    "roadmapPhase": "Stage 3 — Strings & Character Manipulation",
    "phase": "Stage 3 — Strings & Character Manipulation",
    "estimatedTime": 30,
    "statement": "Solve the **Walking Robot Simulation II** problem using standard Simulation techniques. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Simulation algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Simulation properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Simulation techniques by solving Medium problem constraints for Walking Robot Simulation II.",
    "whyThisPattern": "When observing Simulation problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/walking-robot-simulation-ii/",
    "leetcode_title": "Walking Robot Simulation II",
    "leetcode_id": 2069,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/walking-robot-simulation-ii/",
    "canonicalSlug": "walking-robot-simulation-ii",
    "canonicalUrl": "https://leetcode.com/problems/walking-robot-simulation-ii/",
    "url": "https://leetcode.com/problems/walking-robot-simulation-ii/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Walking Robot Simulation II\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Walking Robot Simulation II\n};",
        "java": "// Java Solution for Walking Robot Simulation II\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Walking Robot Simulation II\n}",
        "python": "# Python Solution for Walking Robot Simulation II\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Walking Robot Simulation II\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Walking Robot Simulation II\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Walking Robot Simulation II\n};",
        "java": "// Optimal Java Solution for Walking Robot Simulation II\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Walking Robot Simulation II\n}",
        "python": "# Optimal Python Solution for Walking Robot Simulation II\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Walking Robot Simulation II\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Walking Robot Simulation II",
      "cpp_optimal": "// Solution for Walking Robot Simulation II",
      "java_brute": "// Solution for Walking Robot Simulation II",
      "java_optimal": "// Solution for Walking Robot Simulation II",
      "python_brute": "# Solution for Walking Robot Simulation II",
      "python_optimal": "# Solution for Walking Robot Simulation II"
    },
    "originalOrder": 589,
    "learningOrder": 589
  },
  {
    "id": 129,
    "number": 129,
    "sequence_number": 129,
    "title": "Count Collisions on a Road",
    "slug": "count-collisions-on-a-road",
    "difficulty": "Medium",
    "topic": "Simulation",
    "subtopic": "Simulation Optimization",
    "pattern": "Simulation Pattern",
    "secondary_patterns": [
      "Simulation Pattern"
    ],
    "stage": "Strings & Character Manipulation",
    "curriculumStage": "Stage 3 — Strings & Character Manipulation",
    "roadmapPhase": "Stage 3 — Strings & Character Manipulation",
    "phase": "Stage 3 — Strings & Character Manipulation",
    "estimatedTime": 30,
    "statement": "Solve the **Count Collisions on a Road** problem using standard Simulation techniques. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Simulation algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Simulation properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Simulation techniques by solving Medium problem constraints for Count Collisions on a Road.",
    "whyThisPattern": "When observing Simulation problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/count-collisions-on-a-road/",
    "leetcode_title": "Count Collisions on a Road",
    "leetcode_id": 2211,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/count-collisions-on-a-road/",
    "canonicalSlug": "count-collisions-on-a-road",
    "canonicalUrl": "https://leetcode.com/problems/count-collisions-on-a-road/",
    "url": "https://leetcode.com/problems/count-collisions-on-a-road/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Count Collisions on a Road\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Count Collisions on a Road\n};",
        "java": "// Java Solution for Count Collisions on a Road\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Count Collisions on a Road\n}",
        "python": "# Python Solution for Count Collisions on a Road\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Count Collisions on a Road\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Count Collisions on a Road\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Count Collisions on a Road\n};",
        "java": "// Optimal Java Solution for Count Collisions on a Road\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Count Collisions on a Road\n}",
        "python": "# Optimal Python Solution for Count Collisions on a Road\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Count Collisions on a Road\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Count Collisions on a Road",
      "cpp_optimal": "// Solution for Count Collisions on a Road",
      "java_brute": "// Solution for Count Collisions on a Road",
      "java_optimal": "// Solution for Count Collisions on a Road",
      "python_brute": "# Solution for Count Collisions on a Road",
      "python_optimal": "# Solution for Count Collisions on a Road"
    },
    "originalOrder": 590,
    "learningOrder": 590
  },
  {
    "id": 130,
    "number": 130,
    "sequence_number": 130,
    "title": "Spiral Matrix IV",
    "slug": "spiral-matrix-iv",
    "difficulty": "Medium",
    "topic": "Simulation",
    "subtopic": "Simulation Optimization",
    "pattern": "Simulation Pattern",
    "secondary_patterns": [
      "Simulation Pattern"
    ],
    "stage": "Strings & Character Manipulation",
    "curriculumStage": "Stage 3 — Strings & Character Manipulation",
    "roadmapPhase": "Stage 3 — Strings & Character Manipulation",
    "phase": "Stage 3 — Strings & Character Manipulation",
    "estimatedTime": 30,
    "statement": "Solve the **Spiral Matrix IV** problem using standard Simulation techniques. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Simulation algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Simulation properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Simulation techniques by solving Medium problem constraints for Spiral Matrix IV.",
    "whyThisPattern": "When observing Simulation problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/spiral-matrix-iv/",
    "leetcode_title": "Spiral Matrix IV",
    "leetcode_id": 2326,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/spiral-matrix-iv/",
    "canonicalSlug": "spiral-matrix-iv",
    "canonicalUrl": "https://leetcode.com/problems/spiral-matrix-iv/",
    "url": "https://leetcode.com/problems/spiral-matrix-iv/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Spiral Matrix IV\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Spiral Matrix IV\n};",
        "java": "// Java Solution for Spiral Matrix IV\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Spiral Matrix IV\n}",
        "python": "# Python Solution for Spiral Matrix IV\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Spiral Matrix IV\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Spiral Matrix IV\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Spiral Matrix IV\n};",
        "java": "// Optimal Java Solution for Spiral Matrix IV\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Spiral Matrix IV\n}",
        "python": "# Optimal Python Solution for Spiral Matrix IV\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Spiral Matrix IV\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Spiral Matrix IV",
      "cpp_optimal": "// Solution for Spiral Matrix IV",
      "java_brute": "// Solution for Spiral Matrix IV",
      "java_optimal": "// Solution for Spiral Matrix IV",
      "python_brute": "# Solution for Spiral Matrix IV",
      "python_optimal": "# Solution for Spiral Matrix IV"
    },
    "originalOrder": 591,
    "learningOrder": 591
  },
  {
    "id": 131,
    "number": 131,
    "sequence_number": 131,
    "title": "String to Integer (atoi)",
    "slug": "string-to-integer-atoi",
    "difficulty": "Medium",
    "topic": "Arrays",
    "subtopic": "Arrays Optimization",
    "pattern": "Arrays Pattern",
    "secondary_patterns": [
      "Arrays Pattern"
    ],
    "stage": "Strings & Character Manipulation",
    "curriculumStage": "Stage 3 — Strings & Character Manipulation",
    "roadmapPhase": "Stage 3 — Strings & Character Manipulation",
    "phase": "Stage 3 — Strings & Character Manipulation",
    "estimatedTime": 30,
    "statement": "Solve the **String to Integer (atoi)** problem using standard Arrays techniques. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Arrays algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Arrays properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Arrays techniques by solving Medium problem constraints for String to Integer (atoi).",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/string-to-integer-atoi/",
    "leetcode_title": "String to Integer (atoi)",
    "leetcode_id": 8,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/string-to-integer-atoi/",
    "canonicalSlug": "string-to-integer-atoi",
    "canonicalUrl": "https://leetcode.com/problems/string-to-integer-atoi/",
    "url": "https://leetcode.com/problems/string-to-integer-atoi/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for String to Integer (atoi)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for String to Integer (atoi)\n};",
        "java": "// Java Solution for String to Integer (atoi)\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for String to Integer (atoi)\n}",
        "python": "# Python Solution for String to Integer (atoi)\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for String to Integer (atoi)\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for String to Integer (atoi)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for String to Integer (atoi)\n};",
        "java": "// Optimal Java Solution for String to Integer (atoi)\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for String to Integer (atoi)\n}",
        "python": "# Optimal Python Solution for String to Integer (atoi)\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for String to Integer (atoi)\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for String to Integer (atoi)",
      "cpp_optimal": "// Solution for String to Integer (atoi)",
      "java_brute": "// Solution for String to Integer (atoi)",
      "java_optimal": "// Solution for String to Integer (atoi)",
      "python_brute": "# Solution for String to Integer (atoi)",
      "python_optimal": "# Solution for String to Integer (atoi)"
    },
    "originalOrder": 258,
    "learningOrder": 258
  },
  {
    "id": 132,
    "number": 132,
    "sequence_number": 132,
    "title": "Divide Two Integers",
    "slug": "divide-two-integers",
    "difficulty": "Medium",
    "topic": "Arrays",
    "subtopic": "Arrays Optimization",
    "pattern": "Arrays Pattern",
    "secondary_patterns": [
      "Arrays Pattern"
    ],
    "stage": "Strings & Character Manipulation",
    "curriculumStage": "Stage 3 — Strings & Character Manipulation",
    "roadmapPhase": "Stage 3 — Strings & Character Manipulation",
    "phase": "Stage 3 — Strings & Character Manipulation",
    "estimatedTime": 30,
    "statement": "Solve the **Divide Two Integers** problem using standard Arrays techniques. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Arrays algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Arrays properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Arrays techniques by solving Medium problem constraints for Divide Two Integers.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/divide-two-integers/",
    "leetcode_title": "Divide Two Integers",
    "leetcode_id": 29,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/divide-two-integers/",
    "canonicalSlug": "divide-two-integers",
    "canonicalUrl": "https://leetcode.com/problems/divide-two-integers/",
    "url": "https://leetcode.com/problems/divide-two-integers/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Divide Two Integers\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Divide Two Integers\n};",
        "java": "// Java Solution for Divide Two Integers\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Divide Two Integers\n}",
        "python": "# Python Solution for Divide Two Integers\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Divide Two Integers\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Divide Two Integers\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Divide Two Integers\n};",
        "java": "// Optimal Java Solution for Divide Two Integers\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Divide Two Integers\n}",
        "python": "# Optimal Python Solution for Divide Two Integers\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Divide Two Integers\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Divide Two Integers",
      "cpp_optimal": "// Solution for Divide Two Integers",
      "java_brute": "// Solution for Divide Two Integers",
      "java_optimal": "// Solution for Divide Two Integers",
      "python_brute": "# Solution for Divide Two Integers",
      "python_optimal": "# Solution for Divide Two Integers"
    },
    "originalOrder": 259,
    "learningOrder": 259
  },
  {
    "id": 133,
    "number": 133,
    "sequence_number": 133,
    "title": "Count and Say",
    "slug": "count-and-say",
    "difficulty": "Medium",
    "topic": "Bit Manipulation",
    "subtopic": "Arrays Optimization",
    "pattern": "Arrays Pattern",
    "secondary_patterns": [
      "Arrays Pattern"
    ],
    "stage": "Strings & Character Manipulation",
    "curriculumStage": "Stage 3 — Strings & Character Manipulation",
    "roadmapPhase": "Stage 3 — Strings & Character Manipulation",
    "phase": "Stage 3 — Strings & Character Manipulation",
    "estimatedTime": 30,
    "statement": "Solve the **Count and Say** problem using standard Arrays techniques. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Arrays algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Arrays properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Arrays techniques by solving Medium problem constraints for Count and Say.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/count-and-say/",
    "leetcode_title": "Count and Say",
    "leetcode_id": 38,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/count-and-say/",
    "canonicalSlug": "count-and-say",
    "canonicalUrl": "https://leetcode.com/problems/count-and-say/",
    "url": "https://leetcode.com/problems/count-and-say/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Count and Say\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Count and Say\n};",
        "java": "// Java Solution for Count and Say\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Count and Say\n}",
        "python": "# Python Solution for Count and Say\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Count and Say\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Count and Say\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Count and Say\n};",
        "java": "// Optimal Java Solution for Count and Say\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Count and Say\n}",
        "python": "# Optimal Python Solution for Count and Say\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Count and Say\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Count and Say",
      "cpp_optimal": "// Solution for Count and Say",
      "java_brute": "// Solution for Count and Say",
      "java_optimal": "// Solution for Count and Say",
      "python_brute": "# Solution for Count and Say",
      "python_optimal": "# Solution for Count and Say"
    },
    "originalOrder": 260,
    "learningOrder": 260
  },
  {
    "id": 134,
    "number": 134,
    "sequence_number": 134,
    "title": "Maximum Subarray",
    "slug": "maximum-subarray",
    "difficulty": "Medium",
    "topic": "Arrays",
    "subtopic": "Arrays Optimization",
    "pattern": "Arrays Pattern",
    "secondary_patterns": [
      "Arrays Pattern"
    ],
    "stage": "Strings & Character Manipulation",
    "curriculumStage": "Stage 3 — Strings & Character Manipulation",
    "roadmapPhase": "Stage 3 — Strings & Character Manipulation",
    "phase": "Stage 3 — Strings & Character Manipulation",
    "estimatedTime": 30,
    "statement": "Solve the **Maximum Subarray** problem using standard Arrays techniques. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Arrays algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Arrays properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Arrays techniques by solving Medium problem constraints for Maximum Subarray.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/maximum-subarray/",
    "leetcode_title": "Maximum Subarray",
    "leetcode_id": 53,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/maximum-subarray/",
    "canonicalSlug": "maximum-subarray",
    "canonicalUrl": "https://leetcode.com/problems/maximum-subarray/",
    "url": "https://leetcode.com/problems/maximum-subarray/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Maximum Subarray\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Maximum Subarray\n};",
        "java": "// Java Solution for Maximum Subarray\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Maximum Subarray\n}",
        "python": "# Python Solution for Maximum Subarray\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Maximum Subarray\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Maximum Subarray\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Maximum Subarray\n};",
        "java": "// Optimal Java Solution for Maximum Subarray\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Maximum Subarray\n}",
        "python": "# Optimal Python Solution for Maximum Subarray\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Maximum Subarray\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Maximum Subarray",
      "cpp_optimal": "// Solution for Maximum Subarray",
      "java_brute": "// Solution for Maximum Subarray",
      "java_optimal": "// Solution for Maximum Subarray",
      "python_brute": "# Solution for Maximum Subarray",
      "python_optimal": "# Solution for Maximum Subarray"
    },
    "originalOrder": 261,
    "learningOrder": 261
  },
  {
    "id": 135,
    "number": 135,
    "sequence_number": 135,
    "title": "Unique Paths",
    "slug": "unique-paths",
    "difficulty": "Medium",
    "topic": "Arrays",
    "subtopic": "Arrays Optimization",
    "pattern": "Arrays Pattern",
    "secondary_patterns": [
      "Arrays Pattern"
    ],
    "stage": "Strings & Character Manipulation",
    "curriculumStage": "Stage 3 — Strings & Character Manipulation",
    "roadmapPhase": "Stage 3 — Strings & Character Manipulation",
    "phase": "Stage 3 — Strings & Character Manipulation",
    "estimatedTime": 30,
    "statement": "Solve the **Unique Paths** problem using standard Arrays techniques. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Arrays algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Arrays properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Arrays techniques by solving Medium problem constraints for Unique Paths.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/unique-paths/",
    "leetcode_title": "Unique Paths",
    "leetcode_id": 62,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/unique-paths/",
    "canonicalSlug": "unique-paths",
    "canonicalUrl": "https://leetcode.com/problems/unique-paths/",
    "url": "https://leetcode.com/problems/unique-paths/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Unique Paths\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Unique Paths\n};",
        "java": "// Java Solution for Unique Paths\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Unique Paths\n}",
        "python": "# Python Solution for Unique Paths\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Unique Paths\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Unique Paths\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Unique Paths\n};",
        "java": "// Optimal Java Solution for Unique Paths\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Unique Paths\n}",
        "python": "# Optimal Python Solution for Unique Paths\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Unique Paths\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Unique Paths",
      "cpp_optimal": "// Solution for Unique Paths",
      "java_brute": "// Solution for Unique Paths",
      "java_optimal": "// Solution for Unique Paths",
      "python_brute": "# Solution for Unique Paths",
      "python_optimal": "# Solution for Unique Paths"
    },
    "originalOrder": 262,
    "learningOrder": 262
  },
  {
    "id": 136,
    "number": 136,
    "sequence_number": 136,
    "title": "Dice Roll Simulation",
    "slug": "dice-roll-simulation",
    "difficulty": "Hard",
    "topic": "Simulation",
    "subtopic": "Simulation Optimization",
    "pattern": "Simulation Pattern",
    "secondary_patterns": [
      "Simulation Pattern"
    ],
    "stage": "Strings & Character Manipulation",
    "curriculumStage": "Stage 3 — Strings & Character Manipulation",
    "roadmapPhase": "Stage 3 — Strings & Character Manipulation",
    "phase": "Stage 3 — Strings & Character Manipulation",
    "estimatedTime": 45,
    "statement": "Solve the **Dice Roll Simulation** problem using standard Simulation techniques. Given input constraints appropriate for Hard level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Simulation algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Simulation properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Simulation techniques by solving Hard problem constraints for Dice Roll Simulation.",
    "whyThisPattern": "When observing Simulation problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/dice-roll-simulation/",
    "leetcode_title": "Dice Roll Simulation",
    "leetcode_id": 1223,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/dice-roll-simulation/",
    "canonicalSlug": "dice-roll-simulation",
    "canonicalUrl": "https://leetcode.com/problems/dice-roll-simulation/",
    "url": "https://leetcode.com/problems/dice-roll-simulation/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Dice Roll Simulation\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Dice Roll Simulation\n};",
        "java": "// Java Solution for Dice Roll Simulation\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Dice Roll Simulation\n}",
        "python": "# Python Solution for Dice Roll Simulation\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Dice Roll Simulation\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Dice Roll Simulation\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Dice Roll Simulation\n};",
        "java": "// Optimal Java Solution for Dice Roll Simulation\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Dice Roll Simulation\n}",
        "python": "# Optimal Python Solution for Dice Roll Simulation\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Dice Roll Simulation\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Dice Roll Simulation",
      "cpp_optimal": "// Solution for Dice Roll Simulation",
      "java_brute": "// Solution for Dice Roll Simulation",
      "java_optimal": "// Solution for Dice Roll Simulation",
      "python_brute": "# Solution for Dice Roll Simulation",
      "python_optimal": "# Solution for Dice Roll Simulation"
    },
    "originalOrder": 942,
    "learningOrder": 942
  },
  {
    "id": 137,
    "number": 137,
    "sequence_number": 137,
    "title": "Integer to English Words",
    "slug": "integer-to-english-words",
    "difficulty": "Hard",
    "topic": "Strings",
    "subtopic": "Strings Optimization",
    "pattern": "Chunk Recursive Parsing",
    "secondary_patterns": [
      "Chunk Recursive Parsing"
    ],
    "stage": "Strings & Character Manipulation",
    "curriculumStage": "Stage 3 — Strings & Character Manipulation",
    "roadmapPhase": "Stage 3 — Strings & Character Manipulation",
    "phase": "Stage 3 — Strings & Character Manipulation",
    "estimatedTime": 45,
    "statement": "Given the constraints and input parameters for Integer to English Words, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Integer to English Words."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Integer to English Words.",
      "Leverage the optimal Strings pattern to reduce time complexity."
    ],
    "learningObjective": "Master Strings techniques by solving Hard problem constraints for Integer to English Words.",
    "whyThisPattern": "When observing Strings problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/integer-to-english-words/",
    "leetcode_title": "Integer to English Words",
    "leetcode_id": 273,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/integer-to-english-words/",
    "canonicalSlug": "integer-to-english-words",
    "canonicalUrl": "https://leetcode.com/problems/integer-to-english-words/",
    "url": "https://leetcode.com/problems/integer-to-english-words/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Integer to English Words\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Integer to English Words\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Integer to English Words\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Integer to English Words\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Integer to English Words\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Integer to English Words\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Integer to English Words\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Integer to English Words\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Integer to English Words",
      "cpp_optimal": "// Solution for Integer to English Words",
      "java_brute": "// Solution for Integer to English Words",
      "java_optimal": "// Solution for Integer to English Words",
      "python_brute": "# Solution for Integer to English Words",
      "python_optimal": "# Solution for Integer to English Words"
    },
    "originalOrder": 964,
    "learningOrder": 964
  },
  {
    "id": 138,
    "number": 138,
    "sequence_number": 138,
    "title": "Trips and Users",
    "slug": "trips-and-users",
    "difficulty": "Hard",
    "topic": "Bit Manipulation",
    "subtopic": "Arrays Optimization",
    "pattern": "Arrays Pattern",
    "secondary_patterns": [
      "Arrays Pattern"
    ],
    "stage": "Strings & Character Manipulation",
    "curriculumStage": "Stage 3 — Strings & Character Manipulation",
    "roadmapPhase": "Stage 3 — Strings & Character Manipulation",
    "phase": "Stage 3 — Strings & Character Manipulation",
    "estimatedTime": 45,
    "statement": "Solve the **Trips and Users** problem using standard Arrays techniques. Given input constraints appropriate for Hard level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Arrays algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Arrays properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Arrays techniques by solving Hard problem constraints for Trips and Users.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/trips-and-users/",
    "leetcode_title": "Trips and Users",
    "leetcode_id": 262,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/trips-and-users/",
    "canonicalSlug": "trips-and-users",
    "canonicalUrl": "https://leetcode.com/problems/trips-and-users/",
    "url": "https://leetcode.com/problems/trips-and-users/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Trips and Users\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Trips and Users\n};",
        "java": "// Java Solution for Trips and Users\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Trips and Users\n}",
        "python": "# Python Solution for Trips and Users\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Trips and Users\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Trips and Users\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Trips and Users\n};",
        "java": "// Optimal Java Solution for Trips and Users\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Trips and Users\n}",
        "python": "# Optimal Python Solution for Trips and Users\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Trips and Users\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Trips and Users",
      "cpp_optimal": "// Solution for Trips and Users",
      "java_brute": "// Solution for Trips and Users",
      "java_optimal": "// Solution for Trips and Users",
      "python_brute": "# Solution for Trips and Users",
      "python_optimal": "# Solution for Trips and Users"
    },
    "originalOrder": 712,
    "learningOrder": 712
  },
  {
    "id": 139,
    "number": 139,
    "sequence_number": 139,
    "title": "Insert Delete GetRandom O(1) - Duplicates allowed",
    "slug": "insert-delete-getrandom-o1-duplicates-allowed",
    "difficulty": "Hard",
    "topic": "Bit Manipulation",
    "subtopic": "Arrays Optimization",
    "pattern": "Arrays Pattern",
    "secondary_patterns": [
      "Arrays Pattern"
    ],
    "stage": "Strings & Character Manipulation",
    "curriculumStage": "Stage 3 — Strings & Character Manipulation",
    "roadmapPhase": "Stage 3 — Strings & Character Manipulation",
    "phase": "Stage 3 — Strings & Character Manipulation",
    "estimatedTime": 45,
    "statement": "Solve the **Insert Delete GetRandom O(1) - Duplicates allowed** problem using standard Arrays techniques. Given input constraints appropriate for Hard level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Arrays algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Arrays properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Arrays techniques by solving Hard problem constraints for Insert Delete GetRandom O(1) - Duplicates allowed.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/insert-delete-getrandom-o1-duplicates-allowed/",
    "leetcode_title": "Insert Delete GetRandom O(1) - Duplicates allowed",
    "leetcode_id": 381,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/insert-delete-getrandom-o1-duplicates-allowed/",
    "canonicalSlug": "insert-delete-getrandom-o1-duplicates-allowed",
    "canonicalUrl": "https://leetcode.com/problems/insert-delete-getrandom-o1-duplicates-allowed/",
    "url": "https://leetcode.com/problems/insert-delete-getrandom-o1-duplicates-allowed/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Insert Delete GetRandom O(1) - Duplicates allowed\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Insert Delete GetRandom O(1) - Duplicates allowed\n};",
        "java": "// Java Solution for Insert Delete GetRandom O(1) - Duplicates allowed\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Insert Delete GetRandom O(1) - Duplicates allowed\n}",
        "python": "# Python Solution for Insert Delete GetRandom O(1) - Duplicates allowed\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Insert Delete GetRandom O(1) - Duplicates allowed\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Insert Delete GetRandom O(1) - Duplicates allowed\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Insert Delete GetRandom O(1) - Duplicates allowed\n};",
        "java": "// Optimal Java Solution for Insert Delete GetRandom O(1) - Duplicates allowed\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Insert Delete GetRandom O(1) - Duplicates allowed\n}",
        "python": "# Optimal Python Solution for Insert Delete GetRandom O(1) - Duplicates allowed\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Insert Delete GetRandom O(1) - Duplicates allowed\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Insert Delete GetRandom O(1) - Duplicates allowed",
      "cpp_optimal": "// Solution for Insert Delete GetRandom O(1) - Duplicates allowed",
      "java_brute": "// Solution for Insert Delete GetRandom O(1) - Duplicates allowed",
      "java_optimal": "// Solution for Insert Delete GetRandom O(1) - Duplicates allowed",
      "python_brute": "# Solution for Insert Delete GetRandom O(1) - Duplicates allowed",
      "python_optimal": "# Solution for Insert Delete GetRandom O(1) - Duplicates allowed"
    },
    "originalOrder": 715,
    "learningOrder": 715
  },
  {
    "id": 140,
    "number": 140,
    "sequence_number": 140,
    "title": "Poor Pigs",
    "slug": "poor-pigs",
    "difficulty": "Hard",
    "topic": "Arrays",
    "subtopic": "Arrays Optimization",
    "pattern": "Arrays Pattern",
    "secondary_patterns": [
      "Arrays Pattern"
    ],
    "stage": "Strings & Character Manipulation",
    "curriculumStage": "Stage 3 — Strings & Character Manipulation",
    "roadmapPhase": "Stage 3 — Strings & Character Manipulation",
    "phase": "Stage 3 — Strings & Character Manipulation",
    "estimatedTime": 45,
    "statement": "Solve the **Poor Pigs** problem using standard Arrays techniques. Given input constraints appropriate for Hard level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Arrays algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Arrays properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Arrays techniques by solving Hard problem constraints for Poor Pigs.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/poor-pigs/",
    "leetcode_title": "Poor Pigs",
    "leetcode_id": 458,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/poor-pigs/",
    "canonicalSlug": "poor-pigs",
    "canonicalUrl": "https://leetcode.com/problems/poor-pigs/",
    "url": "https://leetcode.com/problems/poor-pigs/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Poor Pigs\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Poor Pigs\n};",
        "java": "// Java Solution for Poor Pigs\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Poor Pigs\n}",
        "python": "# Python Solution for Poor Pigs\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Poor Pigs\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Poor Pigs\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Poor Pigs\n};",
        "java": "// Optimal Java Solution for Poor Pigs\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Poor Pigs\n}",
        "python": "# Optimal Python Solution for Poor Pigs\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Poor Pigs\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Poor Pigs",
      "cpp_optimal": "// Solution for Poor Pigs",
      "java_brute": "// Solution for Poor Pigs",
      "java_optimal": "// Solution for Poor Pigs",
      "python_brute": "# Solution for Poor Pigs",
      "python_optimal": "# Solution for Poor Pigs"
    },
    "originalOrder": 719,
    "learningOrder": 719
  },
  {
    "id": 141,
    "number": 141,
    "sequence_number": 141,
    "title": "Count The Repetitions",
    "slug": "count-the-repetitions",
    "difficulty": "Hard",
    "topic": "Arrays",
    "subtopic": "Arrays Optimization",
    "pattern": "Arrays Pattern",
    "secondary_patterns": [
      "Arrays Pattern"
    ],
    "stage": "Strings & Character Manipulation",
    "curriculumStage": "Stage 3 — Strings & Character Manipulation",
    "roadmapPhase": "Stage 3 — Strings & Character Manipulation",
    "phase": "Stage 3 — Strings & Character Manipulation",
    "estimatedTime": 45,
    "statement": "Solve the **Count The Repetitions** problem using standard Arrays techniques. Given input constraints appropriate for Hard level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Arrays algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Arrays properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Arrays techniques by solving Hard problem constraints for Count The Repetitions.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/count-the-repetitions/",
    "leetcode_title": "Count The Repetitions",
    "leetcode_id": 466,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/count-the-repetitions/",
    "canonicalSlug": "count-the-repetitions",
    "canonicalUrl": "https://leetcode.com/problems/count-the-repetitions/",
    "url": "https://leetcode.com/problems/count-the-repetitions/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Count The Repetitions\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Count The Repetitions\n};",
        "java": "// Java Solution for Count The Repetitions\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Count The Repetitions\n}",
        "python": "# Python Solution for Count The Repetitions\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Count The Repetitions\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Count The Repetitions\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Count The Repetitions\n};",
        "java": "// Optimal Java Solution for Count The Repetitions\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Count The Repetitions\n}",
        "python": "# Optimal Python Solution for Count The Repetitions\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Count The Repetitions\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Count The Repetitions",
      "cpp_optimal": "// Solution for Count The Repetitions",
      "java_brute": "// Solution for Count The Repetitions",
      "java_optimal": "// Solution for Count The Repetitions",
      "python_brute": "# Solution for Count The Repetitions",
      "python_optimal": "# Solution for Count The Repetitions"
    },
    "originalOrder": 720,
    "learningOrder": 720
  },
  {
    "id": 142,
    "number": 142,
    "sequence_number": 142,
    "title": "Concatenated Words",
    "slug": "concatenated-words",
    "difficulty": "Hard",
    "topic": "Arrays",
    "subtopic": "Arrays Optimization",
    "pattern": "Arrays Pattern",
    "secondary_patterns": [
      "Arrays Pattern"
    ],
    "stage": "Strings & Character Manipulation",
    "curriculumStage": "Stage 3 — Strings & Character Manipulation",
    "roadmapPhase": "Stage 3 — Strings & Character Manipulation",
    "phase": "Stage 3 — Strings & Character Manipulation",
    "estimatedTime": 45,
    "statement": "Solve the **Concatenated Words** problem using standard Arrays techniques. Given input constraints appropriate for Hard level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Arrays algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Arrays properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Arrays techniques by solving Hard problem constraints for Concatenated Words.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/concatenated-words/",
    "leetcode_title": "Concatenated Words",
    "leetcode_id": 472,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/concatenated-words/",
    "canonicalSlug": "concatenated-words",
    "canonicalUrl": "https://leetcode.com/problems/concatenated-words/",
    "url": "https://leetcode.com/problems/concatenated-words/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Concatenated Words\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Concatenated Words\n};",
        "java": "// Java Solution for Concatenated Words\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Concatenated Words\n}",
        "python": "# Python Solution for Concatenated Words\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Concatenated Words\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Concatenated Words\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Concatenated Words\n};",
        "java": "// Optimal Java Solution for Concatenated Words\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Concatenated Words\n}",
        "python": "# Optimal Python Solution for Concatenated Words\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Concatenated Words\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Concatenated Words",
      "cpp_optimal": "// Solution for Concatenated Words",
      "java_brute": "// Solution for Concatenated Words",
      "java_optimal": "// Solution for Concatenated Words",
      "python_brute": "# Solution for Concatenated Words",
      "python_optimal": "# Solution for Concatenated Words"
    },
    "originalOrder": 721,
    "learningOrder": 721
  },
  {
    "id": 143,
    "number": 143,
    "sequence_number": 143,
    "title": "Smallest Good Base",
    "slug": "smallest-good-base",
    "difficulty": "Hard",
    "topic": "Arrays",
    "subtopic": "Arrays Optimization",
    "pattern": "Arrays Pattern",
    "secondary_patterns": [
      "Arrays Pattern"
    ],
    "stage": "Strings & Character Manipulation",
    "curriculumStage": "Stage 3 — Strings & Character Manipulation",
    "roadmapPhase": "Stage 3 — Strings & Character Manipulation",
    "phase": "Stage 3 — Strings & Character Manipulation",
    "estimatedTime": 45,
    "statement": "Solve the **Smallest Good Base** problem using standard Arrays techniques. Given input constraints appropriate for Hard level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Arrays algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Arrays properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Arrays techniques by solving Hard problem constraints for Smallest Good Base.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/smallest-good-base/",
    "leetcode_title": "Smallest Good Base",
    "leetcode_id": 483,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/smallest-good-base/",
    "canonicalSlug": "smallest-good-base",
    "canonicalUrl": "https://leetcode.com/problems/smallest-good-base/",
    "url": "https://leetcode.com/problems/smallest-good-base/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Smallest Good Base\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Smallest Good Base\n};",
        "java": "// Java Solution for Smallest Good Base\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Smallest Good Base\n}",
        "python": "# Python Solution for Smallest Good Base\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Smallest Good Base\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Smallest Good Base\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Smallest Good Base\n};",
        "java": "// Optimal Java Solution for Smallest Good Base\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Smallest Good Base\n}",
        "python": "# Optimal Python Solution for Smallest Good Base\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Smallest Good Base\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Smallest Good Base",
      "cpp_optimal": "// Solution for Smallest Good Base",
      "java_brute": "// Solution for Smallest Good Base",
      "java_optimal": "// Solution for Smallest Good Base",
      "python_brute": "# Solution for Smallest Good Base",
      "python_optimal": "# Solution for Smallest Good Base"
    },
    "originalOrder": 722,
    "learningOrder": 722
  },
  {
    "id": 144,
    "number": 144,
    "sequence_number": 144,
    "title": "IPO",
    "slug": "ipo",
    "difficulty": "Hard",
    "topic": "Arrays",
    "subtopic": "Arrays Optimization",
    "pattern": "Arrays Pattern",
    "secondary_patterns": [
      "Arrays Pattern"
    ],
    "stage": "Strings & Character Manipulation",
    "curriculumStage": "Stage 3 — Strings & Character Manipulation",
    "roadmapPhase": "Stage 3 — Strings & Character Manipulation",
    "phase": "Stage 3 — Strings & Character Manipulation",
    "estimatedTime": 45,
    "statement": "Solve the **IPO** problem using standard Arrays techniques. Given input constraints appropriate for Hard level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Arrays algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Arrays properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Arrays techniques by solving Hard problem constraints for IPO.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/ipo/",
    "leetcode_title": "IPO",
    "leetcode_id": 502,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/ipo/",
    "canonicalSlug": "ipo",
    "canonicalUrl": "https://leetcode.com/problems/ipo/",
    "url": "https://leetcode.com/problems/ipo/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for IPO\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for IPO\n};",
        "java": "// Java Solution for IPO\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for IPO\n}",
        "python": "# Python Solution for IPO\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for IPO\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for IPO\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for IPO\n};",
        "java": "// Optimal Java Solution for IPO\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for IPO\n}",
        "python": "# Optimal Python Solution for IPO\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for IPO\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for IPO",
      "cpp_optimal": "// Solution for IPO",
      "java_brute": "// Solution for IPO",
      "java_optimal": "// Solution for IPO",
      "python_brute": "# Solution for IPO",
      "python_optimal": "# Solution for IPO"
    },
    "originalOrder": 723,
    "learningOrder": 723
  },
  {
    "id": 145,
    "number": 145,
    "sequence_number": 145,
    "title": "Student Attendance Record II",
    "slug": "student-attendance-record-ii",
    "difficulty": "Hard",
    "topic": "Arrays",
    "subtopic": "Arrays Optimization",
    "pattern": "Arrays Pattern",
    "secondary_patterns": [
      "Arrays Pattern"
    ],
    "stage": "Strings & Character Manipulation",
    "curriculumStage": "Stage 3 — Strings & Character Manipulation",
    "roadmapPhase": "Stage 3 — Strings & Character Manipulation",
    "phase": "Stage 3 — Strings & Character Manipulation",
    "estimatedTime": 45,
    "statement": "Solve the **Student Attendance Record II** problem using standard Arrays techniques. Given input constraints appropriate for Hard level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Arrays algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Arrays properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Arrays techniques by solving Hard problem constraints for Student Attendance Record II.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/student-attendance-record-ii/",
    "leetcode_title": "Student Attendance Record II",
    "leetcode_id": 552,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/student-attendance-record-ii/",
    "canonicalSlug": "student-attendance-record-ii",
    "canonicalUrl": "https://leetcode.com/problems/student-attendance-record-ii/",
    "url": "https://leetcode.com/problems/student-attendance-record-ii/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Student Attendance Record II\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Student Attendance Record II\n};",
        "java": "// Java Solution for Student Attendance Record II\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Student Attendance Record II\n}",
        "python": "# Python Solution for Student Attendance Record II\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Student Attendance Record II\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Student Attendance Record II\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Student Attendance Record II\n};",
        "java": "// Optimal Java Solution for Student Attendance Record II\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Student Attendance Record II\n}",
        "python": "# Optimal Python Solution for Student Attendance Record II\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Student Attendance Record II\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Student Attendance Record II",
      "cpp_optimal": "// Solution for Student Attendance Record II",
      "java_brute": "// Solution for Student Attendance Record II",
      "java_optimal": "// Solution for Student Attendance Record II",
      "python_brute": "# Solution for Student Attendance Record II",
      "python_optimal": "# Solution for Student Attendance Record II"
    },
    "originalOrder": 724,
    "learningOrder": 724
  },
  {
    "id": 146,
    "number": 146,
    "sequence_number": 146,
    "title": "Find the Closest Palindrome",
    "slug": "find-the-closest-palindrome",
    "difficulty": "Hard",
    "topic": "Arrays",
    "subtopic": "Arrays Optimization",
    "pattern": "Arrays Pattern",
    "secondary_patterns": [
      "Arrays Pattern"
    ],
    "stage": "Strings & Character Manipulation",
    "curriculumStage": "Stage 3 — Strings & Character Manipulation",
    "roadmapPhase": "Stage 3 — Strings & Character Manipulation",
    "phase": "Stage 3 — Strings & Character Manipulation",
    "estimatedTime": 45,
    "statement": "Solve the **Find the Closest Palindrome** problem using standard Arrays techniques. Given input constraints appropriate for Hard level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Arrays algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Arrays properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Arrays techniques by solving Hard problem constraints for Find the Closest Palindrome.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/find-the-closest-palindrome/",
    "leetcode_title": "Find the Closest Palindrome",
    "leetcode_id": 564,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/find-the-closest-palindrome/",
    "canonicalSlug": "find-the-closest-palindrome",
    "canonicalUrl": "https://leetcode.com/problems/find-the-closest-palindrome/",
    "url": "https://leetcode.com/problems/find-the-closest-palindrome/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Find the Closest Palindrome\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Find the Closest Palindrome\n};",
        "java": "// Java Solution for Find the Closest Palindrome\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Find the Closest Palindrome\n}",
        "python": "# Python Solution for Find the Closest Palindrome\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Find the Closest Palindrome\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Find the Closest Palindrome\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Find the Closest Palindrome\n};",
        "java": "// Optimal Java Solution for Find the Closest Palindrome\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Find the Closest Palindrome\n}",
        "python": "# Optimal Python Solution for Find the Closest Palindrome\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Find the Closest Palindrome\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Find the Closest Palindrome",
      "cpp_optimal": "// Solution for Find the Closest Palindrome",
      "java_brute": "// Solution for Find the Closest Palindrome",
      "java_optimal": "// Solution for Find the Closest Palindrome",
      "python_brute": "# Solution for Find the Closest Palindrome",
      "python_optimal": "# Solution for Find the Closest Palindrome"
    },
    "originalOrder": 725,
    "learningOrder": 725
  },
  {
    "id": 147,
    "number": 147,
    "sequence_number": 147,
    "title": "Tag Validator",
    "slug": "tag-validator",
    "difficulty": "Hard",
    "topic": "Arrays",
    "subtopic": "Arrays Optimization",
    "pattern": "Arrays Pattern",
    "secondary_patterns": [
      "Arrays Pattern"
    ],
    "stage": "Strings & Character Manipulation",
    "curriculumStage": "Stage 3 — Strings & Character Manipulation",
    "roadmapPhase": "Stage 3 — Strings & Character Manipulation",
    "phase": "Stage 3 — Strings & Character Manipulation",
    "estimatedTime": 45,
    "statement": "Solve the **Tag Validator** problem using standard Arrays techniques. Given input constraints appropriate for Hard level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Arrays algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Arrays properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Arrays techniques by solving Hard problem constraints for Tag Validator.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/tag-validator/",
    "leetcode_title": "Tag Validator",
    "leetcode_id": 591,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/tag-validator/",
    "canonicalSlug": "tag-validator",
    "canonicalUrl": "https://leetcode.com/problems/tag-validator/",
    "url": "https://leetcode.com/problems/tag-validator/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Tag Validator\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Tag Validator\n};",
        "java": "// Java Solution for Tag Validator\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Tag Validator\n}",
        "python": "# Python Solution for Tag Validator\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Tag Validator\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Tag Validator\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Tag Validator\n};",
        "java": "// Optimal Java Solution for Tag Validator\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Tag Validator\n}",
        "python": "# Optimal Python Solution for Tag Validator\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Tag Validator\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Tag Validator",
      "cpp_optimal": "// Solution for Tag Validator",
      "java_brute": "// Solution for Tag Validator",
      "java_optimal": "// Solution for Tag Validator",
      "python_brute": "# Solution for Tag Validator",
      "python_optimal": "# Solution for Tag Validator"
    },
    "originalOrder": 726,
    "learningOrder": 726
  },
  {
    "id": 148,
    "number": 148,
    "sequence_number": 148,
    "title": "Human Traffic of Stadium",
    "slug": "human-traffic-of-stadium",
    "difficulty": "Hard",
    "topic": "Arrays",
    "subtopic": "Arrays Optimization",
    "pattern": "Arrays Pattern",
    "secondary_patterns": [
      "Arrays Pattern"
    ],
    "stage": "Strings & Character Manipulation",
    "curriculumStage": "Stage 3 — Strings & Character Manipulation",
    "roadmapPhase": "Stage 3 — Strings & Character Manipulation",
    "phase": "Stage 3 — Strings & Character Manipulation",
    "estimatedTime": 45,
    "statement": "Solve the **Human Traffic of Stadium** problem using standard Arrays techniques. Given input constraints appropriate for Hard level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Arrays algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Arrays properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Arrays techniques by solving Hard problem constraints for Human Traffic of Stadium.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/human-traffic-of-stadium/",
    "leetcode_title": "Human Traffic of Stadium",
    "leetcode_id": 601,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/human-traffic-of-stadium/",
    "canonicalSlug": "human-traffic-of-stadium",
    "canonicalUrl": "https://leetcode.com/problems/human-traffic-of-stadium/",
    "url": "https://leetcode.com/problems/human-traffic-of-stadium/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Human Traffic of Stadium\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Human Traffic of Stadium\n};",
        "java": "// Java Solution for Human Traffic of Stadium\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Human Traffic of Stadium\n}",
        "python": "# Python Solution for Human Traffic of Stadium\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Human Traffic of Stadium\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Human Traffic of Stadium\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Human Traffic of Stadium\n};",
        "java": "// Optimal Java Solution for Human Traffic of Stadium\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Human Traffic of Stadium\n}",
        "python": "# Optimal Python Solution for Human Traffic of Stadium\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Human Traffic of Stadium\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Human Traffic of Stadium",
      "cpp_optimal": "// Solution for Human Traffic of Stadium",
      "java_brute": "// Solution for Human Traffic of Stadium",
      "java_optimal": "// Solution for Human Traffic of Stadium",
      "python_brute": "# Solution for Human Traffic of Stadium",
      "python_optimal": "# Solution for Human Traffic of Stadium"
    },
    "originalOrder": 727,
    "learningOrder": 727
  },
  {
    "id": 149,
    "number": 149,
    "sequence_number": 149,
    "title": "K Inverse Pairs Array",
    "slug": "k-inverse-pairs-array",
    "difficulty": "Hard",
    "topic": "Arrays",
    "subtopic": "Arrays Optimization",
    "pattern": "Arrays Pattern",
    "secondary_patterns": [
      "Arrays Pattern"
    ],
    "stage": "Strings & Character Manipulation",
    "curriculumStage": "Stage 3 — Strings & Character Manipulation",
    "roadmapPhase": "Stage 3 — Strings & Character Manipulation",
    "phase": "Stage 3 — Strings & Character Manipulation",
    "estimatedTime": 45,
    "statement": "Solve the **K Inverse Pairs Array** problem using standard Arrays techniques. Given input constraints appropriate for Hard level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Arrays algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Arrays properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Arrays techniques by solving Hard problem constraints for K Inverse Pairs Array.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/k-inverse-pairs-array/",
    "leetcode_title": "K Inverse Pairs Array",
    "leetcode_id": 629,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/k-inverse-pairs-array/",
    "canonicalSlug": "k-inverse-pairs-array",
    "canonicalUrl": "https://leetcode.com/problems/k-inverse-pairs-array/",
    "url": "https://leetcode.com/problems/k-inverse-pairs-array/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for K Inverse Pairs Array\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for K Inverse Pairs Array\n};",
        "java": "// Java Solution for K Inverse Pairs Array\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for K Inverse Pairs Array\n}",
        "python": "# Python Solution for K Inverse Pairs Array\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for K Inverse Pairs Array\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for K Inverse Pairs Array\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for K Inverse Pairs Array\n};",
        "java": "// Optimal Java Solution for K Inverse Pairs Array\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for K Inverse Pairs Array\n}",
        "python": "# Optimal Python Solution for K Inverse Pairs Array\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for K Inverse Pairs Array\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for K Inverse Pairs Array",
      "cpp_optimal": "// Solution for K Inverse Pairs Array",
      "java_brute": "// Solution for K Inverse Pairs Array",
      "java_optimal": "// Solution for K Inverse Pairs Array",
      "python_brute": "# Solution for K Inverse Pairs Array",
      "python_optimal": "# Solution for K Inverse Pairs Array"
    },
    "originalOrder": 728,
    "learningOrder": 728
  },
  {
    "id": 150,
    "number": 150,
    "sequence_number": 150,
    "title": "Smallest Range Covering Elements from K Lists",
    "slug": "smallest-range-covering-elements-from-k-lists",
    "difficulty": "Hard",
    "topic": "Linked List",
    "subtopic": "Arrays Optimization",
    "pattern": "Arrays Pattern",
    "secondary_patterns": [
      "Arrays Pattern"
    ],
    "stage": "Strings & Character Manipulation",
    "curriculumStage": "Stage 3 — Strings & Character Manipulation",
    "roadmapPhase": "Stage 3 — Strings & Character Manipulation",
    "phase": "Stage 3 — Strings & Character Manipulation",
    "estimatedTime": 45,
    "statement": "Solve the **Smallest Range Covering Elements from K Lists** problem using standard Arrays techniques. Given input constraints appropriate for Hard level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Arrays algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Arrays properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Arrays techniques by solving Hard problem constraints for Smallest Range Covering Elements from K Lists.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/smallest-range-covering-elements-from-k-lists/",
    "leetcode_title": "Smallest Range Covering Elements from K Lists",
    "leetcode_id": 632,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/smallest-range-covering-elements-from-k-lists/",
    "canonicalSlug": "smallest-range-covering-elements-from-k-lists",
    "canonicalUrl": "https://leetcode.com/problems/smallest-range-covering-elements-from-k-lists/",
    "url": "https://leetcode.com/problems/smallest-range-covering-elements-from-k-lists/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Smallest Range Covering Elements from K Lists\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Smallest Range Covering Elements from K Lists\n};",
        "java": "// Java Solution for Smallest Range Covering Elements from K Lists\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Smallest Range Covering Elements from K Lists\n}",
        "python": "# Python Solution for Smallest Range Covering Elements from K Lists\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Smallest Range Covering Elements from K Lists\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Smallest Range Covering Elements from K Lists\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Smallest Range Covering Elements from K Lists\n};",
        "java": "// Optimal Java Solution for Smallest Range Covering Elements from K Lists\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Smallest Range Covering Elements from K Lists\n}",
        "python": "# Optimal Python Solution for Smallest Range Covering Elements from K Lists\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Smallest Range Covering Elements from K Lists\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Smallest Range Covering Elements from K Lists",
      "cpp_optimal": "// Solution for Smallest Range Covering Elements from K Lists",
      "java_brute": "// Solution for Smallest Range Covering Elements from K Lists",
      "java_optimal": "// Solution for Smallest Range Covering Elements from K Lists",
      "python_brute": "# Solution for Smallest Range Covering Elements from K Lists",
      "python_optimal": "# Solution for Smallest Range Covering Elements from K Lists"
    },
    "originalOrder": 729,
    "learningOrder": 729
  },
  {
    "id": 151,
    "number": 151,
    "sequence_number": 151,
    "title": "Range Sum Query - Immutable",
    "slug": "range-sum-query-immutable-optimization",
    "difficulty": "Easy",
    "topic": "Prefix Sum",
    "subtopic": "Hashing & Array Optimization",
    "pattern": "Hashing & Array Optimization",
    "secondary_patterns": [
      "Hashing & Array Optimization"
    ],
    "stage": "Prefix Sum & Sorting Techniques",
    "curriculumStage": "Stage 4 — Prefix Sum & Sorting Techniques",
    "roadmapPhase": "Stage 4 — Prefix Sum & Sorting Techniques",
    "phase": "Stage 4 — Prefix Sum & Sorting Techniques",
    "estimatedTime": 15,
    "statement": "Solve the **Range Sum Query - Immutable Optimization** problem using the **Hashing & Array Optimization** technique. Given input constraints appropriate for Easy level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^4",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Hashing & Array Optimization identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Hashing & Array Optimization. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Hashing & Array Optimization techniques by solving Easy problem constraints for Range Sum Query - Immutable Optimization.",
    "whyThisPattern": "When observing arrays & strings problem conditions, Hashing & Array Optimization optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "LinkedIn",
      "Amazon"
    ],
    "companyRelevanceTier": "Medium",
    "leetcode_url": "https://leetcode.com/problems/range-sum-query-immutable/",
    "leetcode_title": "Range Sum Query - Immutable",
    "leetcode_id": 303,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/range-sum-query-immutable/",
    "canonicalSlug": "range-sum-query-immutable-optimization",
    "canonicalUrl": "https://leetcode.com/problems/range-sum-query-immutable/",
    "url": "https://leetcode.com/problems/range-sum-query-immutable/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Range Sum Query - Immutable Optimization (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Range Sum Query - Immutable Optimization (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Range Sum Query - Immutable Optimization (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Range Sum Query - Immutable Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Range Sum Query - Immutable Optimization (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Range Sum Query - Immutable Optimization (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Range Sum Query - Immutable Optimization (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Range Sum Query - Immutable Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Range Sum Query - Immutable",
      "cpp_optimal": "// Solution for Range Sum Query - Immutable",
      "java_brute": "// Solution for Range Sum Query - Immutable",
      "java_optimal": "// Solution for Range Sum Query - Immutable",
      "python_brute": "# Solution for Range Sum Query - Immutable",
      "python_optimal": "# Solution for Range Sum Query - Immutable"
    }
  },
  {
    "id": 152,
    "number": 152,
    "sequence_number": 152,
    "title": "Running Sum of 1d Array",
    "slug": "running-sum-of-1d-array",
    "difficulty": "Easy",
    "topic": "Prefix Sum",
    "subtopic": "Prefix Sum Optimization",
    "pattern": "Running Prefix Sum",
    "secondary_patterns": [
      "Running Prefix Sum"
    ],
    "stage": "Prefix Sum & Sorting Techniques",
    "curriculumStage": "Stage 4 — Prefix Sum & Sorting Techniques",
    "roadmapPhase": "Stage 4 — Prefix Sum & Sorting Techniques",
    "phase": "Stage 4 — Prefix Sum & Sorting Techniques",
    "estimatedTime": 15,
    "statement": "Given the constraints and input parameters for Running Sum of 1d Array, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Running Sum of 1d Array."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Running Sum of 1d Array.",
      "Leverage the optimal Prefix Sum pattern to reduce time complexity."
    ],
    "learningObjective": "Master Prefix Sum techniques by solving Easy problem constraints for Running Sum of 1d Array.",
    "whyThisPattern": "When observing Prefix Sum problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/running-sum-of-1d-array/",
    "leetcode_title": "Running Sum of 1d Array",
    "leetcode_id": 411,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/running-sum-of-1d-array/",
    "canonicalSlug": "running-sum-of-1d-array",
    "canonicalUrl": "https://leetcode.com/problems/running-sum-of-1d-array/",
    "url": "https://leetcode.com/problems/running-sum-of-1d-array/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Running Sum of 1d Array\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Running Sum of 1d Array\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Running Sum of 1d Array\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Running Sum of 1d Array\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Running Sum of 1d Array\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Running Sum of 1d Array\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Running Sum of 1d Array\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Running Sum of 1d Array\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Running Sum of 1d Array",
      "cpp_optimal": "// Solution for Running Sum of 1d Array",
      "java_brute": "// Solution for Running Sum of 1d Array",
      "java_optimal": "// Solution for Running Sum of 1d Array",
      "python_brute": "# Solution for Running Sum of 1d Array",
      "python_optimal": "# Solution for Running Sum of 1d Array"
    }
  },
  {
    "id": 153,
    "number": 153,
    "sequence_number": 153,
    "title": "Find the Highest Altitude",
    "slug": "find-the-highest-altitude",
    "difficulty": "Easy",
    "topic": "Prefix Sum",
    "subtopic": "Prefix Sum Optimization",
    "pattern": "Running Altitude Max",
    "secondary_patterns": [
      "Running Altitude Max"
    ],
    "stage": "Prefix Sum & Sorting Techniques",
    "curriculumStage": "Stage 4 — Prefix Sum & Sorting Techniques",
    "roadmapPhase": "Stage 4 — Prefix Sum & Sorting Techniques",
    "phase": "Stage 4 — Prefix Sum & Sorting Techniques",
    "estimatedTime": 15,
    "statement": "Given the constraints and input parameters for Find the Highest Altitude, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Find the Highest Altitude."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Find the Highest Altitude.",
      "Leverage the optimal Prefix Sum pattern to reduce time complexity."
    ],
    "learningObjective": "Master Prefix Sum techniques by solving Easy problem constraints for Find the Highest Altitude.",
    "whyThisPattern": "When observing Prefix Sum problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/find-the-highest-altitude/",
    "leetcode_title": "Find the Highest Altitude",
    "leetcode_id": 509,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/find-the-highest-altitude/",
    "canonicalSlug": "find-the-highest-altitude",
    "canonicalUrl": "https://leetcode.com/problems/find-the-highest-altitude/",
    "url": "https://leetcode.com/problems/find-the-highest-altitude/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Find the Highest Altitude\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Find the Highest Altitude\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Find the Highest Altitude\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Find the Highest Altitude\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Find the Highest Altitude\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Find the Highest Altitude\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Find the Highest Altitude\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Find the Highest Altitude\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Find the Highest Altitude",
      "cpp_optimal": "// Solution for Find the Highest Altitude",
      "java_brute": "// Solution for Find the Highest Altitude",
      "java_optimal": "// Solution for Find the Highest Altitude",
      "python_brute": "# Solution for Find the Highest Altitude",
      "python_optimal": "# Solution for Find the Highest Altitude"
    }
  },
  {
    "id": 154,
    "number": 154,
    "sequence_number": 154,
    "title": "Maximum Population Year",
    "slug": "maximum-population-year",
    "difficulty": "Easy",
    "topic": "Prefix Sum",
    "subtopic": "Prefix Sum Optimization",
    "pattern": "Difference Array Sweep",
    "secondary_patterns": [
      "Difference Array Sweep"
    ],
    "stage": "Prefix Sum & Sorting Techniques",
    "curriculumStage": "Stage 4 — Prefix Sum & Sorting Techniques",
    "roadmapPhase": "Stage 4 — Prefix Sum & Sorting Techniques",
    "phase": "Stage 4 — Prefix Sum & Sorting Techniques",
    "estimatedTime": 15,
    "statement": "Given the constraints and input parameters for Maximum Population Year, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Maximum Population Year."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Maximum Population Year.",
      "Leverage the optimal Prefix Sum pattern to reduce time complexity."
    ],
    "learningObjective": "Master Prefix Sum techniques by solving Easy problem constraints for Maximum Population Year.",
    "whyThisPattern": "When observing Prefix Sum problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/maximum-population-year/",
    "leetcode_title": "Maximum Population Year",
    "leetcode_id": 527,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/maximum-population-year/",
    "canonicalSlug": "maximum-population-year",
    "canonicalUrl": "https://leetcode.com/problems/maximum-population-year/",
    "url": "https://leetcode.com/problems/maximum-population-year/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Maximum Population Year\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Maximum Population Year\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Maximum Population Year\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Maximum Population Year\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Maximum Population Year\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Maximum Population Year\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Maximum Population Year\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Maximum Population Year\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Maximum Population Year",
      "cpp_optimal": "// Solution for Maximum Population Year",
      "java_brute": "// Solution for Maximum Population Year",
      "java_optimal": "// Solution for Maximum Population Year",
      "python_brute": "# Solution for Maximum Population Year",
      "python_optimal": "# Solution for Maximum Population Year"
    }
  },
  {
    "id": 155,
    "number": 155,
    "sequence_number": 155,
    "title": "Set Mismatch",
    "slug": "set-mismatch",
    "difficulty": "Easy",
    "topic": "Sort",
    "subtopic": "Arrays Optimization",
    "pattern": "Cyclic Sort / Sign Marking",
    "secondary_patterns": [
      "Cyclic Sort / Sign Marking"
    ],
    "stage": "Prefix Sum & Sorting Techniques",
    "curriculumStage": "Stage 4 — Prefix Sum & Sorting Techniques",
    "roadmapPhase": "Stage 4 — Prefix Sum & Sorting Techniques",
    "phase": "Stage 4 — Prefix Sum & Sorting Techniques",
    "estimatedTime": 15,
    "statement": "Given the constraints and input parameters for Set Mismatch, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Set Mismatch."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Set Mismatch.",
      "Leverage the optimal Arrays pattern to reduce time complexity."
    ],
    "learningObjective": "Master Arrays techniques by solving Easy problem constraints for Set Mismatch.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/set-mismatch/",
    "leetcode_title": "Set Mismatch",
    "leetcode_id": 645,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/set-mismatch/",
    "canonicalSlug": "set-mismatch",
    "canonicalUrl": "https://leetcode.com/problems/set-mismatch/",
    "url": "https://leetcode.com/problems/set-mismatch/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Set Mismatch\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Set Mismatch\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Set Mismatch\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Set Mismatch\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Set Mismatch\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Set Mismatch\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Set Mismatch\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Set Mismatch\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Set Mismatch",
      "cpp_optimal": "// Solution for Set Mismatch",
      "java_brute": "// Solution for Set Mismatch",
      "java_optimal": "// Solution for Set Mismatch",
      "python_brute": "# Solution for Set Mismatch",
      "python_optimal": "# Solution for Set Mismatch"
    },
    "originalOrder": 101,
    "learningOrder": 101
  },
  {
    "id": 156,
    "number": 156,
    "sequence_number": 156,
    "title": "Height Checker",
    "slug": "height-checker",
    "difficulty": "Easy",
    "topic": "Sort",
    "subtopic": "Arrays Optimization",
    "pattern": "Sort Mismatch Count",
    "secondary_patterns": [
      "Sort Mismatch Count"
    ],
    "stage": "Prefix Sum & Sorting Techniques",
    "curriculumStage": "Stage 4 — Prefix Sum & Sorting Techniques",
    "roadmapPhase": "Stage 4 — Prefix Sum & Sorting Techniques",
    "phase": "Stage 4 — Prefix Sum & Sorting Techniques",
    "estimatedTime": 15,
    "statement": "Given the constraints and input parameters for Height Checker, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Height Checker."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Height Checker.",
      "Leverage the optimal Arrays pattern to reduce time complexity."
    ],
    "learningObjective": "Master Arrays techniques by solving Easy problem constraints for Height Checker.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/height-checker/",
    "leetcode_title": "Height Checker",
    "leetcode_id": 1051,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/height-checker/",
    "canonicalSlug": "height-checker",
    "canonicalUrl": "https://leetcode.com/problems/height-checker/",
    "url": "https://leetcode.com/problems/height-checker/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Height Checker\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Height Checker\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Height Checker\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Height Checker\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Height Checker\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Height Checker\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Height Checker\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Height Checker\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Height Checker",
      "cpp_optimal": "// Solution for Height Checker",
      "java_brute": "// Solution for Height Checker",
      "java_optimal": "// Solution for Height Checker",
      "python_brute": "# Solution for Height Checker",
      "python_optimal": "# Solution for Height Checker"
    },
    "originalOrder": 103,
    "learningOrder": 103
  },
  {
    "id": 157,
    "number": 157,
    "sequence_number": 157,
    "title": "Minimum Value to Get Positive Step by Step Sum",
    "slug": "minimum-value-to-get-positive-step-by-step-sum",
    "difficulty": "Easy",
    "topic": "Prefix Sum",
    "subtopic": "Prefix Sum Optimization",
    "pattern": "Running Prefix Min",
    "secondary_patterns": [
      "Running Prefix Min"
    ],
    "stage": "Prefix Sum & Sorting Techniques",
    "curriculumStage": "Stage 4 — Prefix Sum & Sorting Techniques",
    "roadmapPhase": "Stage 4 — Prefix Sum & Sorting Techniques",
    "phase": "Stage 4 — Prefix Sum & Sorting Techniques",
    "estimatedTime": 15,
    "statement": "Given the constraints and input parameters for Minimum Value to Get Positive Step by Step Sum, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Minimum Value to Get Positive Step by Step Sum."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Minimum Value to Get Positive Step by Step Sum.",
      "Leverage the optimal Prefix Sum pattern to reduce time complexity."
    ],
    "learningObjective": "Master Prefix Sum techniques by solving Easy problem constraints for Minimum Value to Get Positive Step by Step Sum.",
    "whyThisPattern": "When observing Prefix Sum problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/minimum-value-to-get-positive-step-by-step-sum/",
    "leetcode_title": "Minimum Value to Get Positive Step by Step Sum",
    "leetcode_id": 1413,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/minimum-value-to-get-positive-step-by-step-sum/",
    "canonicalSlug": "minimum-value-to-get-positive-step-by-step-sum",
    "canonicalUrl": "https://leetcode.com/problems/minimum-value-to-get-positive-step-by-step-sum/",
    "url": "https://leetcode.com/problems/minimum-value-to-get-positive-step-by-step-sum/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Minimum Value to Get Positive Step by Step Sum\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Minimum Value to Get Positive Step by Step Sum\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Minimum Value to Get Positive Step by Step Sum\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Minimum Value to Get Positive Step by Step Sum\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Minimum Value to Get Positive Step by Step Sum\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Minimum Value to Get Positive Step by Step Sum\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Minimum Value to Get Positive Step by Step Sum\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Minimum Value to Get Positive Step by Step Sum\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Minimum Value to Get Positive Step by Step Sum",
      "cpp_optimal": "// Solution for Minimum Value to Get Positive Step by Step Sum",
      "java_brute": "// Solution for Minimum Value to Get Positive Step by Step Sum",
      "java_optimal": "// Solution for Minimum Value to Get Positive Step by Step Sum",
      "python_brute": "# Solution for Minimum Value to Get Positive Step by Step Sum",
      "python_optimal": "# Solution for Minimum Value to Get Positive Step by Step Sum"
    },
    "originalOrder": 155,
    "learningOrder": 155
  },
  {
    "id": 158,
    "number": 158,
    "sequence_number": 158,
    "title": "Maximum Score After Splitting a String",
    "slug": "maximum-score-after-splitting-a-string",
    "difficulty": "Easy",
    "topic": "Prefix Sum",
    "subtopic": "Prefix Sum Optimization",
    "pattern": "Zeros & Ones Count",
    "secondary_patterns": [
      "Zeros & Ones Count"
    ],
    "stage": "Prefix Sum & Sorting Techniques",
    "curriculumStage": "Stage 4 — Prefix Sum & Sorting Techniques",
    "roadmapPhase": "Stage 4 — Prefix Sum & Sorting Techniques",
    "phase": "Stage 4 — Prefix Sum & Sorting Techniques",
    "estimatedTime": 15,
    "statement": "Given the constraints and input parameters for Maximum Score After Splitting a String, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Maximum Score After Splitting a String."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Maximum Score After Splitting a String.",
      "Leverage the optimal Prefix Sum pattern to reduce time complexity."
    ],
    "learningObjective": "Master Prefix Sum techniques by solving Easy problem constraints for Maximum Score After Splitting a String.",
    "whyThisPattern": "When observing Prefix Sum problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/maximum-score-after-splitting-a-string/",
    "leetcode_title": "Maximum Score After Splitting a String",
    "leetcode_id": 1422,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/maximum-score-after-splitting-a-string/",
    "canonicalSlug": "maximum-score-after-splitting-a-string",
    "canonicalUrl": "https://leetcode.com/problems/maximum-score-after-splitting-a-string/",
    "url": "https://leetcode.com/problems/maximum-score-after-splitting-a-string/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Maximum Score After Splitting a String\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Maximum Score After Splitting a String\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Maximum Score After Splitting a String\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Maximum Score After Splitting a String\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Maximum Score After Splitting a String\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Maximum Score After Splitting a String\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Maximum Score After Splitting a String\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Maximum Score After Splitting a String\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Maximum Score After Splitting a String",
      "cpp_optimal": "// Solution for Maximum Score After Splitting a String",
      "java_brute": "// Solution for Maximum Score After Splitting a String",
      "java_optimal": "// Solution for Maximum Score After Splitting a String",
      "python_brute": "# Solution for Maximum Score After Splitting a String",
      "python_optimal": "# Solution for Maximum Score After Splitting a String"
    },
    "originalOrder": 156,
    "learningOrder": 156
  },
  {
    "id": 159,
    "number": 159,
    "sequence_number": 159,
    "title": "Relative Sort Array",
    "slug": "relative-sort-array",
    "difficulty": "Easy",
    "topic": "Sort",
    "subtopic": "Sort Optimization",
    "pattern": "Custom Frequency Sorting",
    "secondary_patterns": [
      "Custom Frequency Sorting"
    ],
    "stage": "Prefix Sum & Sorting Techniques",
    "curriculumStage": "Stage 4 — Prefix Sum & Sorting Techniques",
    "roadmapPhase": "Stage 4 — Prefix Sum & Sorting Techniques",
    "phase": "Stage 4 — Prefix Sum & Sorting Techniques",
    "estimatedTime": 15,
    "statement": "Given the constraints and input parameters for Relative Sort Array, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Relative Sort Array."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Relative Sort Array.",
      "Leverage the optimal Arrays pattern to reduce time complexity."
    ],
    "learningObjective": "Master Sort techniques by solving Easy problem constraints for Relative Sort Array.",
    "whyThisPattern": "When observing Sort problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/relative-sort-array/",
    "leetcode_title": "Relative Sort Array",
    "leetcode_id": 1122,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/relative-sort-array/",
    "canonicalSlug": "relative-sort-array",
    "canonicalUrl": "https://leetcode.com/problems/relative-sort-array/",
    "url": "https://leetcode.com/problems/relative-sort-array/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Relative Sort Array\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Relative Sort Array\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Relative Sort Array\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Relative Sort Array\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Relative Sort Array\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Relative Sort Array\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Relative Sort Array\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Relative Sort Array\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Relative Sort Array",
      "cpp_optimal": "// Solution for Relative Sort Array",
      "java_brute": "// Solution for Relative Sort Array",
      "java_optimal": "// Solution for Relative Sort Array",
      "python_brute": "# Solution for Relative Sort Array",
      "python_optimal": "# Solution for Relative Sort Array"
    },
    "originalOrder": 159,
    "learningOrder": 159
  },
  {
    "id": 160,
    "number": 160,
    "sequence_number": 160,
    "title": "Largest Number At Least Twice of Others",
    "slug": "largest-number-at-least-twice-of-others",
    "difficulty": "Easy",
    "topic": "Sort",
    "subtopic": "Sort Optimization",
    "pattern": "Top Two Max Values",
    "secondary_patterns": [
      "Top Two Max Values"
    ],
    "stage": "Prefix Sum & Sorting Techniques",
    "curriculumStage": "Stage 4 — Prefix Sum & Sorting Techniques",
    "roadmapPhase": "Stage 4 — Prefix Sum & Sorting Techniques",
    "phase": "Stage 4 — Prefix Sum & Sorting Techniques",
    "estimatedTime": 15,
    "statement": "Given the constraints and input parameters for Largest Number At Least Twice of Others, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Largest Number At Least Twice of Others."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Largest Number At Least Twice of Others.",
      "Leverage the optimal Arrays pattern to reduce time complexity."
    ],
    "learningObjective": "Master Sort techniques by solving Easy problem constraints for Largest Number At Least Twice of Others.",
    "whyThisPattern": "When observing Sort problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/largest-number-at-least-twice-of-others/",
    "leetcode_title": "Largest Number At Least Twice of Others",
    "leetcode_id": 747,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/largest-number-at-least-twice-of-others/",
    "canonicalSlug": "largest-number-at-least-twice-of-others",
    "canonicalUrl": "https://leetcode.com/problems/largest-number-at-least-twice-of-others/",
    "url": "https://leetcode.com/problems/largest-number-at-least-twice-of-others/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Largest Number At Least Twice of Others\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Largest Number At Least Twice of Others\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Largest Number At Least Twice of Others\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Largest Number At Least Twice of Others\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Largest Number At Least Twice of Others\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Largest Number At Least Twice of Others\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Largest Number At Least Twice of Others\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Largest Number At Least Twice of Others\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Largest Number At Least Twice of Others",
      "cpp_optimal": "// Solution for Largest Number At Least Twice of Others",
      "java_brute": "// Solution for Largest Number At Least Twice of Others",
      "java_optimal": "// Solution for Largest Number At Least Twice of Others",
      "python_brute": "# Solution for Largest Number At Least Twice of Others",
      "python_optimal": "# Solution for Largest Number At Least Twice of Others"
    },
    "originalOrder": 160,
    "learningOrder": 160
  },
  {
    "id": 161,
    "number": 161,
    "sequence_number": 161,
    "title": "Find Right Interval",
    "slug": "find-right-interval",
    "difficulty": "Medium",
    "topic": "Sort",
    "subtopic": "Arrays Optimization",
    "pattern": "Arrays Pattern",
    "secondary_patterns": [
      "Arrays Pattern"
    ],
    "stage": "Prefix Sum & Sorting Techniques",
    "curriculumStage": "Stage 4 — Prefix Sum & Sorting Techniques",
    "roadmapPhase": "Stage 4 — Prefix Sum & Sorting Techniques",
    "phase": "Stage 4 — Prefix Sum & Sorting Techniques",
    "estimatedTime": 30,
    "statement": "Solve the **Find Right Interval** problem using standard Arrays techniques. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Arrays algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Arrays properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Arrays techniques by solving Medium problem constraints for Find Right Interval.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/find-right-interval/",
    "leetcode_title": "Find Right Interval",
    "leetcode_id": 436,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/find-right-interval/",
    "canonicalSlug": "find-right-interval",
    "canonicalUrl": "https://leetcode.com/problems/find-right-interval/",
    "url": "https://leetcode.com/problems/find-right-interval/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Find Right Interval\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Find Right Interval\n};",
        "java": "// Java Solution for Find Right Interval\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Find Right Interval\n}",
        "python": "# Python Solution for Find Right Interval\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Find Right Interval\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Find Right Interval\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Find Right Interval\n};",
        "java": "// Optimal Java Solution for Find Right Interval\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Find Right Interval\n}",
        "python": "# Optimal Python Solution for Find Right Interval\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Find Right Interval\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Find Right Interval",
      "cpp_optimal": "// Solution for Find Right Interval",
      "java_brute": "// Solution for Find Right Interval",
      "java_optimal": "// Solution for Find Right Interval",
      "python_brute": "# Solution for Find Right Interval",
      "python_optimal": "# Solution for Find Right Interval"
    },
    "originalOrder": 327,
    "learningOrder": 327
  },
  {
    "id": 162,
    "number": 162,
    "sequence_number": 162,
    "title": "Find Kth Largest XOR Coordinate Value",
    "slug": "find-kth-largest-xor-coordinate-value",
    "difficulty": "Medium",
    "topic": "Prefix Sum",
    "subtopic": "Prefix Sum Optimization",
    "pattern": "2D Prefix XOR + Min-Heap",
    "secondary_patterns": [
      "2D Prefix XOR + Min-Heap"
    ],
    "stage": "Prefix Sum & Sorting Techniques",
    "curriculumStage": "Stage 4 — Prefix Sum & Sorting Techniques",
    "roadmapPhase": "Stage 4 — Prefix Sum & Sorting Techniques",
    "phase": "Stage 4 — Prefix Sum & Sorting Techniques",
    "estimatedTime": 30,
    "statement": "Given the constraints and input parameters for Find Kth Largest XOR Coordinate Value, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Find Kth Largest XOR Coordinate Value."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Find Kth Largest XOR Coordinate Value.",
      "Leverage the optimal Prefix Sum pattern to reduce time complexity."
    ],
    "learningObjective": "Master Prefix Sum techniques by solving Medium problem constraints for Find Kth Largest XOR Coordinate Value.",
    "whyThisPattern": "When observing Prefix Sum problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/find-kth-largest-xor-coordinate-value/",
    "leetcode_title": "Find Kth Largest XOR Coordinate Value",
    "leetcode_id": 1738,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/find-kth-largest-xor-coordinate-value/",
    "canonicalSlug": "find-kth-largest-xor-coordinate-value",
    "canonicalUrl": "https://leetcode.com/problems/find-kth-largest-xor-coordinate-value/",
    "url": "https://leetcode.com/problems/find-kth-largest-xor-coordinate-value/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Find Kth Largest XOR Coordinate Value\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Find Kth Largest XOR Coordinate Value\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Find Kth Largest XOR Coordinate Value\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Find Kth Largest XOR Coordinate Value\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Find Kth Largest XOR Coordinate Value\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Find Kth Largest XOR Coordinate Value\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Find Kth Largest XOR Coordinate Value\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Find Kth Largest XOR Coordinate Value\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Find Kth Largest XOR Coordinate Value",
      "cpp_optimal": "// Solution for Find Kth Largest XOR Coordinate Value",
      "java_brute": "// Solution for Find Kth Largest XOR Coordinate Value",
      "java_optimal": "// Solution for Find Kth Largest XOR Coordinate Value",
      "python_brute": "# Solution for Find Kth Largest XOR Coordinate Value",
      "python_optimal": "# Solution for Find Kth Largest XOR Coordinate Value"
    },
    "originalOrder": 569,
    "learningOrder": 569
  },
  {
    "id": 163,
    "number": 163,
    "sequence_number": 163,
    "title": "Ways to Make a Fair Array",
    "slug": "ways-to-make-a-fair-array",
    "difficulty": "Medium",
    "topic": "Prefix Sum",
    "subtopic": "Prefix Sum Optimization",
    "pattern": "Even-Odd Dynamic Prefix Suffix",
    "secondary_patterns": [
      "Even-Odd Dynamic Prefix Suffix"
    ],
    "stage": "Prefix Sum & Sorting Techniques",
    "curriculumStage": "Stage 4 — Prefix Sum & Sorting Techniques",
    "roadmapPhase": "Stage 4 — Prefix Sum & Sorting Techniques",
    "phase": "Stage 4 — Prefix Sum & Sorting Techniques",
    "estimatedTime": 30,
    "statement": "Given the constraints and input parameters for Ways to Make a Fair Array, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Ways to Make a Fair Array."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Ways to Make a Fair Array.",
      "Leverage the optimal Prefix Sum pattern to reduce time complexity."
    ],
    "learningObjective": "Master Prefix Sum techniques by solving Medium problem constraints for Ways to Make a Fair Array.",
    "whyThisPattern": "When observing Prefix Sum problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/ways-to-make-a-fair-array/",
    "leetcode_title": "Ways to Make a Fair Array",
    "leetcode_id": 1664,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/ways-to-make-a-fair-array/",
    "canonicalSlug": "ways-to-make-a-fair-array",
    "canonicalUrl": "https://leetcode.com/problems/ways-to-make-a-fair-array/",
    "url": "https://leetcode.com/problems/ways-to-make-a-fair-array/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Ways to Make a Fair Array\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Ways to Make a Fair Array\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Ways to Make a Fair Array\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Ways to Make a Fair Array\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Ways to Make a Fair Array\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Ways to Make a Fair Array\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Ways to Make a Fair Array\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Ways to Make a Fair Array\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Ways to Make a Fair Array",
      "cpp_optimal": "// Solution for Ways to Make a Fair Array",
      "java_brute": "// Solution for Ways to Make a Fair Array",
      "java_optimal": "// Solution for Ways to Make a Fair Array",
      "python_brute": "# Solution for Ways to Make a Fair Array",
      "python_optimal": "# Solution for Ways to Make a Fair Array"
    },
    "originalOrder": 570,
    "learningOrder": 570
  },
  {
    "id": 164,
    "number": 164,
    "sequence_number": 164,
    "title": "Make Sum Divisible by P",
    "slug": "make-sum-divisible-by-p",
    "difficulty": "Medium",
    "topic": "Prefix Sum",
    "subtopic": "Prefix Sum Optimization",
    "pattern": "Modulus Remainder HashMap",
    "secondary_patterns": [
      "Modulus Remainder HashMap"
    ],
    "stage": "Prefix Sum & Sorting Techniques",
    "curriculumStage": "Stage 4 — Prefix Sum & Sorting Techniques",
    "roadmapPhase": "Stage 4 — Prefix Sum & Sorting Techniques",
    "phase": "Stage 4 — Prefix Sum & Sorting Techniques",
    "estimatedTime": 30,
    "statement": "Given the constraints and input parameters for Make Sum Divisible by P, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Make Sum Divisible by P."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Make Sum Divisible by P.",
      "Leverage the optimal Prefix Sum pattern to reduce time complexity."
    ],
    "learningObjective": "Master Prefix Sum techniques by solving Medium problem constraints for Make Sum Divisible by P.",
    "whyThisPattern": "When observing Prefix Sum problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/make-sum-divisible-by-p/",
    "leetcode_title": "Make Sum Divisible by P",
    "leetcode_id": 1590,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/make-sum-divisible-by-p/",
    "canonicalSlug": "make-sum-divisible-by-p",
    "canonicalUrl": "https://leetcode.com/problems/make-sum-divisible-by-p/",
    "url": "https://leetcode.com/problems/make-sum-divisible-by-p/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Make Sum Divisible by P\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Make Sum Divisible by P\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Make Sum Divisible by P\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Make Sum Divisible by P\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Make Sum Divisible by P\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Make Sum Divisible by P\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Make Sum Divisible by P\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Make Sum Divisible by P\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Make Sum Divisible by P",
      "cpp_optimal": "// Solution for Make Sum Divisible by P",
      "java_brute": "// Solution for Make Sum Divisible by P",
      "java_optimal": "// Solution for Make Sum Divisible by P",
      "python_brute": "# Solution for Make Sum Divisible by P",
      "python_optimal": "# Solution for Make Sum Divisible by P"
    },
    "originalOrder": 571,
    "learningOrder": 571
  },
  {
    "id": 165,
    "number": 165,
    "sequence_number": 165,
    "title": "Search in Rotated Sorted Array",
    "slug": "search-in-rotated-sorted-array",
    "difficulty": "Medium",
    "topic": "Sort",
    "subtopic": "Two Pointers",
    "pattern": "Two Pointers",
    "secondary_patterns": [
      "Two Pointers"
    ],
    "stage": "Prefix Sum & Sorting Techniques",
    "curriculumStage": "Stage 4 — Prefix Sum & Sorting Techniques",
    "roadmapPhase": "Stage 4 — Prefix Sum & Sorting Techniques",
    "phase": "Stage 4 — Prefix Sum & Sorting Techniques",
    "estimatedTime": 30,
    "statement": "Solve the **Search in Rotated Sorted Array Challenge** problem using the **Two Pointers** technique. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Two Pointers identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Two Pointers. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Two Pointers techniques by solving Medium problem constraints for Search in Rotated Sorted Array Challenge.",
    "whyThisPattern": "When observing arrays & strings problem conditions, Two Pointers optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(1)",
    "companyRelevance": [
      "Amazon",
      "Microsoft",
      "Uber"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/search-in-rotated-sorted-array/",
    "leetcode_title": "Search in Rotated Sorted Array",
    "leetcode_id": 33,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/search-in-rotated-sorted-array/",
    "canonicalSlug": "search-in-rotated-sorted-array",
    "canonicalUrl": "https://leetcode.com/problems/search-in-rotated-sorted-array/",
    "url": "https://leetcode.com/problems/search-in-rotated-sorted-array/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Search in Rotated Sorted Array Challenge (Two Pointers)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Search in Rotated Sorted Array Challenge (Two Pointers)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Search in Rotated Sorted Array Challenge (Two Pointers)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Search in Rotated Sorted Array Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Search in Rotated Sorted Array Challenge (Two Pointers)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Search in Rotated Sorted Array Challenge (Two Pointers)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Search in Rotated Sorted Array Challenge (Two Pointers)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Search in Rotated Sorted Array Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Search in Rotated Sorted Array",
      "cpp_optimal": "// Solution for Search in Rotated Sorted Array",
      "java_brute": "// Solution for Search in Rotated Sorted Array",
      "java_optimal": "// Solution for Search in Rotated Sorted Array",
      "python_brute": "# Solution for Search in Rotated Sorted Array",
      "python_optimal": "# Solution for Search in Rotated Sorted Array"
    },
    "originalOrder": 592,
    "learningOrder": 592
  },
  {
    "id": 166,
    "number": 166,
    "sequence_number": 166,
    "title": "Shortest Unsorted Continuous Subarray",
    "slug": "shortest-unsorted-continuous-subarray",
    "difficulty": "Medium",
    "topic": "Sort",
    "subtopic": "Two Pointers",
    "pattern": "Two Pointers",
    "secondary_patterns": [
      "Two Pointers"
    ],
    "stage": "Prefix Sum & Sorting Techniques",
    "curriculumStage": "Stage 4 — Prefix Sum & Sorting Techniques",
    "roadmapPhase": "Stage 4 — Prefix Sum & Sorting Techniques",
    "phase": "Stage 4 — Prefix Sum & Sorting Techniques",
    "estimatedTime": 30,
    "statement": "Solve the **Shortest Unsorted Continuous Subarray Challenge** problem using the **Two Pointers** technique. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Two Pointers identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Two Pointers. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Two Pointers techniques by solving Medium problem constraints for Shortest Unsorted Continuous Subarray Challenge.",
    "whyThisPattern": "When observing arrays & strings problem conditions, Two Pointers optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(1)",
    "companyRelevance": [
      "Meta",
      "Uber",
      "Databricks"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/shortest-unsorted-continuous-subarray/",
    "leetcode_title": "Shortest Unsorted Continuous Subarray",
    "leetcode_id": 581,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/shortest-unsorted-continuous-subarray/",
    "canonicalSlug": "shortest-unsorted-continuous-subarray",
    "canonicalUrl": "https://leetcode.com/problems/shortest-unsorted-continuous-subarray/",
    "url": "https://leetcode.com/problems/shortest-unsorted-continuous-subarray/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Shortest Unsorted Continuous Subarray Challenge (Two Pointers)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Shortest Unsorted Continuous Subarray Challenge (Two Pointers)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Shortest Unsorted Continuous Subarray Challenge (Two Pointers)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Shortest Unsorted Continuous Subarray Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Shortest Unsorted Continuous Subarray Challenge (Two Pointers)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Shortest Unsorted Continuous Subarray Challenge (Two Pointers)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Shortest Unsorted Continuous Subarray Challenge (Two Pointers)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Shortest Unsorted Continuous Subarray Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Shortest Unsorted Continuous Subarray",
      "cpp_optimal": "// Solution for Shortest Unsorted Continuous Subarray",
      "java_brute": "// Solution for Shortest Unsorted Continuous Subarray",
      "java_optimal": "// Solution for Shortest Unsorted Continuous Subarray",
      "python_brute": "# Solution for Shortest Unsorted Continuous Subarray",
      "python_optimal": "# Solution for Shortest Unsorted Continuous Subarray"
    },
    "originalOrder": 593,
    "learningOrder": 593
  },
  {
    "id": 167,
    "number": 167,
    "sequence_number": 167,
    "title": "Find Minimum in Rotated Sorted Array",
    "slug": "find-minimum-in-rotated-sorted-array",
    "difficulty": "Medium",
    "topic": "Sort",
    "subtopic": "Two Pointers",
    "pattern": "Two Pointers",
    "secondary_patterns": [
      "Two Pointers"
    ],
    "stage": "Prefix Sum & Sorting Techniques",
    "curriculumStage": "Stage 4 — Prefix Sum & Sorting Techniques",
    "roadmapPhase": "Stage 4 — Prefix Sum & Sorting Techniques",
    "phase": "Stage 4 — Prefix Sum & Sorting Techniques",
    "estimatedTime": 30,
    "statement": "Solve the **Find Minimum in Rotated Sorted Array Optimization** problem using the **Two Pointers** technique. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Two Pointers identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Two Pointers. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Two Pointers techniques by solving Medium problem constraints for Find Minimum in Rotated Sorted Array Optimization.",
    "whyThisPattern": "When observing arrays & strings problem conditions, Two Pointers optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(1)",
    "companyRelevance": [
      "Apple",
      "Adobe",
      "Atlassian"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/find-minimum-in-rotated-sorted-array/",
    "leetcode_title": "Find Minimum in Rotated Sorted Array",
    "leetcode_id": 153,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/find-minimum-in-rotated-sorted-array/",
    "canonicalSlug": "find-minimum-in-rotated-sorted-array",
    "canonicalUrl": "https://leetcode.com/problems/find-minimum-in-rotated-sorted-array/",
    "url": "https://leetcode.com/problems/find-minimum-in-rotated-sorted-array/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Find Minimum in Rotated Sorted Array Optimization (Two Pointers)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Find Minimum in Rotated Sorted Array Optimization (Two Pointers)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Find Minimum in Rotated Sorted Array Optimization (Two Pointers)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Find Minimum in Rotated Sorted Array Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Find Minimum in Rotated Sorted Array Optimization (Two Pointers)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Find Minimum in Rotated Sorted Array Optimization (Two Pointers)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Find Minimum in Rotated Sorted Array Optimization (Two Pointers)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Find Minimum in Rotated Sorted Array Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Find Minimum in Rotated Sorted Array",
      "cpp_optimal": "// Solution for Find Minimum in Rotated Sorted Array",
      "java_brute": "// Solution for Find Minimum in Rotated Sorted Array",
      "java_optimal": "// Solution for Find Minimum in Rotated Sorted Array",
      "python_brute": "# Solution for Find Minimum in Rotated Sorted Array",
      "python_optimal": "# Solution for Find Minimum in Rotated Sorted Array"
    },
    "originalOrder": 594,
    "learningOrder": 594
  },
  {
    "id": 168,
    "number": 168,
    "sequence_number": 168,
    "title": "Sort an Array",
    "slug": "sort-an-array",
    "difficulty": "Medium",
    "topic": "Sort",
    "subtopic": "Sort Optimization",
    "pattern": "MergeSort / QuickSort",
    "secondary_patterns": [
      "MergeSort / QuickSort"
    ],
    "stage": "Prefix Sum & Sorting Techniques",
    "curriculumStage": "Stage 4 — Prefix Sum & Sorting Techniques",
    "roadmapPhase": "Stage 4 — Prefix Sum & Sorting Techniques",
    "phase": "Stage 4 — Prefix Sum & Sorting Techniques",
    "estimatedTime": 30,
    "statement": "Given the constraints and input parameters for Sort an Array, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Sort an Array."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Sort an Array.",
      "Leverage the optimal Arrays pattern to reduce time complexity."
    ],
    "learningObjective": "Master Sort techniques by solving Medium problem constraints for Sort an Array.",
    "whyThisPattern": "When observing Sort problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/sort-an-array/",
    "leetcode_title": "Sort an Array",
    "leetcode_id": 912,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/sort-an-array/",
    "canonicalSlug": "sort-an-array",
    "canonicalUrl": "https://leetcode.com/problems/sort-an-array/",
    "url": "https://leetcode.com/problems/sort-an-array/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Sort an Array\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Sort an Array\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Sort an Array\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Sort an Array\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Sort an Array\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Sort an Array\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Sort an Array\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Sort an Array\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Sort an Array",
      "cpp_optimal": "// Solution for Sort an Array",
      "java_brute": "// Solution for Sort an Array",
      "java_optimal": "// Solution for Sort an Array",
      "python_brute": "# Solution for Sort an Array",
      "python_optimal": "# Solution for Sort an Array"
    },
    "originalOrder": 595,
    "learningOrder": 595
  },
  {
    "id": 169,
    "number": 169,
    "sequence_number": 169,
    "title": "Pancake Sorting",
    "slug": "pancake-sorting",
    "difficulty": "Medium",
    "topic": "Sort",
    "subtopic": "Sort Optimization",
    "pattern": "Prefix Flip Selection",
    "secondary_patterns": [
      "Prefix Flip Selection"
    ],
    "stage": "Prefix Sum & Sorting Techniques",
    "curriculumStage": "Stage 4 — Prefix Sum & Sorting Techniques",
    "roadmapPhase": "Stage 4 — Prefix Sum & Sorting Techniques",
    "phase": "Stage 4 — Prefix Sum & Sorting Techniques",
    "estimatedTime": 30,
    "statement": "Given the constraints and input parameters for Pancake Sorting, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Pancake Sorting."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Pancake Sorting.",
      "Leverage the optimal Sort pattern to reduce time complexity."
    ],
    "learningObjective": "Master Sort techniques by solving Medium problem constraints for Pancake Sorting.",
    "whyThisPattern": "When observing Sort problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/pancake-sorting/",
    "leetcode_title": "Pancake Sorting",
    "leetcode_id": 969,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/pancake-sorting/",
    "canonicalSlug": "pancake-sorting",
    "canonicalUrl": "https://leetcode.com/problems/pancake-sorting/",
    "url": "https://leetcode.com/problems/pancake-sorting/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Pancake Sorting\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Pancake Sorting\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Pancake Sorting\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Pancake Sorting\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Pancake Sorting\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Pancake Sorting\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Pancake Sorting\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Pancake Sorting\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Pancake Sorting",
      "cpp_optimal": "// Solution for Pancake Sorting",
      "java_brute": "// Solution for Pancake Sorting",
      "java_optimal": "// Solution for Pancake Sorting",
      "python_brute": "# Solution for Pancake Sorting",
      "python_optimal": "# Solution for Pancake Sorting"
    },
    "originalOrder": 596,
    "learningOrder": 596
  },
  {
    "id": 170,
    "number": 170,
    "sequence_number": 170,
    "title": "Remove Duplicates from Sorted List II",
    "slug": "remove-duplicates-from-sorted-list-ii",
    "difficulty": "Medium",
    "topic": "Sort",
    "subtopic": "Sort Optimization",
    "pattern": "Sort Pattern",
    "secondary_patterns": [
      "Sort Pattern"
    ],
    "stage": "Prefix Sum & Sorting Techniques",
    "curriculumStage": "Stage 4 — Prefix Sum & Sorting Techniques",
    "roadmapPhase": "Stage 4 — Prefix Sum & Sorting Techniques",
    "phase": "Stage 4 — Prefix Sum & Sorting Techniques",
    "estimatedTime": 30,
    "statement": "Solve the **Remove Duplicates from Sorted List II** problem using standard Sort techniques. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Sort algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Sort properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Sort techniques by solving Medium problem constraints for Remove Duplicates from Sorted List II.",
    "whyThisPattern": "When observing Sort problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/remove-duplicates-from-sorted-list-ii/",
    "leetcode_title": "Remove Duplicates from Sorted List II",
    "leetcode_id": 82,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/remove-duplicates-from-sorted-list-ii/",
    "canonicalSlug": "remove-duplicates-from-sorted-list-ii",
    "canonicalUrl": "https://leetcode.com/problems/remove-duplicates-from-sorted-list-ii/",
    "url": "https://leetcode.com/problems/remove-duplicates-from-sorted-list-ii/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Remove Duplicates from Sorted List II\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Remove Duplicates from Sorted List II\n};",
        "java": "// Java Solution for Remove Duplicates from Sorted List II\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Remove Duplicates from Sorted List II\n}",
        "python": "# Python Solution for Remove Duplicates from Sorted List II\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Remove Duplicates from Sorted List II\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Remove Duplicates from Sorted List II\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Remove Duplicates from Sorted List II\n};",
        "java": "// Optimal Java Solution for Remove Duplicates from Sorted List II\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Remove Duplicates from Sorted List II\n}",
        "python": "# Optimal Python Solution for Remove Duplicates from Sorted List II\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Remove Duplicates from Sorted List II\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Remove Duplicates from Sorted List II",
      "cpp_optimal": "// Solution for Remove Duplicates from Sorted List II",
      "java_brute": "// Solution for Remove Duplicates from Sorted List II",
      "java_optimal": "// Solution for Remove Duplicates from Sorted List II",
      "python_brute": "# Solution for Remove Duplicates from Sorted List II",
      "python_optimal": "# Solution for Remove Duplicates from Sorted List II"
    },
    "originalOrder": 597,
    "learningOrder": 597
  },
  {
    "id": 171,
    "number": 171,
    "sequence_number": 171,
    "title": "Convert Sorted List to Binary Search Tree",
    "slug": "convert-sorted-list-to-binary-search-tree",
    "difficulty": "Medium",
    "topic": "Sort",
    "subtopic": "Sort Optimization",
    "pattern": "Sort Pattern",
    "secondary_patterns": [
      "Sort Pattern"
    ],
    "stage": "Prefix Sum & Sorting Techniques",
    "curriculumStage": "Stage 4 — Prefix Sum & Sorting Techniques",
    "roadmapPhase": "Stage 4 — Prefix Sum & Sorting Techniques",
    "phase": "Stage 4 — Prefix Sum & Sorting Techniques",
    "estimatedTime": 30,
    "statement": "Solve the **Convert Sorted List to Binary Search Tree** problem using standard Sort techniques. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Sort algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Sort properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Sort techniques by solving Medium problem constraints for Convert Sorted List to Binary Search Tree.",
    "whyThisPattern": "When observing Sort problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/convert-sorted-list-to-binary-search-tree/",
    "leetcode_title": "Convert Sorted List to Binary Search Tree",
    "leetcode_id": 109,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/convert-sorted-list-to-binary-search-tree/",
    "canonicalSlug": "convert-sorted-list-to-binary-search-tree",
    "canonicalUrl": "https://leetcode.com/problems/convert-sorted-list-to-binary-search-tree/",
    "url": "https://leetcode.com/problems/convert-sorted-list-to-binary-search-tree/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Convert Sorted List to Binary Search Tree\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Convert Sorted List to Binary Search Tree\n};",
        "java": "// Java Solution for Convert Sorted List to Binary Search Tree\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Convert Sorted List to Binary Search Tree\n}",
        "python": "# Python Solution for Convert Sorted List to Binary Search Tree\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Convert Sorted List to Binary Search Tree\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Convert Sorted List to Binary Search Tree\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Convert Sorted List to Binary Search Tree\n};",
        "java": "// Optimal Java Solution for Convert Sorted List to Binary Search Tree\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Convert Sorted List to Binary Search Tree\n}",
        "python": "# Optimal Python Solution for Convert Sorted List to Binary Search Tree\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Convert Sorted List to Binary Search Tree\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Convert Sorted List to Binary Search Tree",
      "cpp_optimal": "// Solution for Convert Sorted List to Binary Search Tree",
      "java_brute": "// Solution for Convert Sorted List to Binary Search Tree",
      "java_optimal": "// Solution for Convert Sorted List to Binary Search Tree",
      "python_brute": "# Solution for Convert Sorted List to Binary Search Tree",
      "python_optimal": "# Solution for Convert Sorted List to Binary Search Tree"
    },
    "originalOrder": 598,
    "learningOrder": 598
  },
  {
    "id": 172,
    "number": 172,
    "sequence_number": 172,
    "title": "Insertion Sort List",
    "slug": "insertion-sort-list",
    "difficulty": "Medium",
    "topic": "Sort",
    "subtopic": "Sort Optimization",
    "pattern": "Sort Pattern",
    "secondary_patterns": [
      "Sort Pattern"
    ],
    "stage": "Prefix Sum & Sorting Techniques",
    "curriculumStage": "Stage 4 — Prefix Sum & Sorting Techniques",
    "roadmapPhase": "Stage 4 — Prefix Sum & Sorting Techniques",
    "phase": "Stage 4 — Prefix Sum & Sorting Techniques",
    "estimatedTime": 30,
    "statement": "Solve the **Insertion Sort List** problem using standard Sort techniques. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Sort algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Sort properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Sort techniques by solving Medium problem constraints for Insertion Sort List.",
    "whyThisPattern": "When observing Sort problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/insertion-sort-list/",
    "leetcode_title": "Insertion Sort List",
    "leetcode_id": 147,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/insertion-sort-list/",
    "canonicalSlug": "insertion-sort-list",
    "canonicalUrl": "https://leetcode.com/problems/insertion-sort-list/",
    "url": "https://leetcode.com/problems/insertion-sort-list/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Insertion Sort List\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Insertion Sort List\n};",
        "java": "// Java Solution for Insertion Sort List\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Insertion Sort List\n}",
        "python": "# Python Solution for Insertion Sort List\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Insertion Sort List\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Insertion Sort List\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Insertion Sort List\n};",
        "java": "// Optimal Java Solution for Insertion Sort List\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Insertion Sort List\n}",
        "python": "# Optimal Python Solution for Insertion Sort List\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Insertion Sort List\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Insertion Sort List",
      "cpp_optimal": "// Solution for Insertion Sort List",
      "java_brute": "// Solution for Insertion Sort List",
      "java_optimal": "// Solution for Insertion Sort List",
      "python_brute": "# Solution for Insertion Sort List",
      "python_optimal": "# Solution for Insertion Sort List"
    },
    "originalOrder": 599,
    "learningOrder": 599
  },
  {
    "id": 173,
    "number": 173,
    "sequence_number": 173,
    "title": "Largest Number",
    "slug": "largest-number",
    "difficulty": "Medium",
    "topic": "Sort",
    "subtopic": "Sort Optimization",
    "pattern": "Sort Pattern",
    "secondary_patterns": [
      "Sort Pattern"
    ],
    "stage": "Prefix Sum & Sorting Techniques",
    "curriculumStage": "Stage 4 — Prefix Sum & Sorting Techniques",
    "roadmapPhase": "Stage 4 — Prefix Sum & Sorting Techniques",
    "phase": "Stage 4 — Prefix Sum & Sorting Techniques",
    "estimatedTime": 30,
    "statement": "Solve the **Largest Number** problem using standard Sort techniques. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Sort algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Sort properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Sort techniques by solving Medium problem constraints for Largest Number.",
    "whyThisPattern": "When observing Sort problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/largest-number/",
    "leetcode_title": "Largest Number",
    "leetcode_id": 179,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/largest-number/",
    "canonicalSlug": "largest-number",
    "canonicalUrl": "https://leetcode.com/problems/largest-number/",
    "url": "https://leetcode.com/problems/largest-number/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Largest Number\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Largest Number\n};",
        "java": "// Java Solution for Largest Number\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Largest Number\n}",
        "python": "# Python Solution for Largest Number\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Largest Number\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Largest Number\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Largest Number\n};",
        "java": "// Optimal Java Solution for Largest Number\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Largest Number\n}",
        "python": "# Optimal Python Solution for Largest Number\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Largest Number\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Largest Number",
      "cpp_optimal": "// Solution for Largest Number",
      "java_brute": "// Solution for Largest Number",
      "java_optimal": "// Solution for Largest Number",
      "python_brute": "# Solution for Largest Number",
      "python_optimal": "# Solution for Largest Number"
    },
    "originalOrder": 600,
    "learningOrder": 600
  },
  {
    "id": 174,
    "number": 174,
    "sequence_number": 174,
    "title": "H-Index",
    "slug": "h-index",
    "difficulty": "Medium",
    "topic": "Sort",
    "subtopic": "Sort Optimization",
    "pattern": "Sort Pattern",
    "secondary_patterns": [
      "Sort Pattern"
    ],
    "stage": "Prefix Sum & Sorting Techniques",
    "curriculumStage": "Stage 4 — Prefix Sum & Sorting Techniques",
    "roadmapPhase": "Stage 4 — Prefix Sum & Sorting Techniques",
    "phase": "Stage 4 — Prefix Sum & Sorting Techniques",
    "estimatedTime": 30,
    "statement": "Solve the **H-Index** problem using standard Sort techniques. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Sort algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Sort properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Sort techniques by solving Medium problem constraints for H-Index.",
    "whyThisPattern": "When observing Sort problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/h-index/",
    "leetcode_title": "H-Index",
    "leetcode_id": 274,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/h-index/",
    "canonicalSlug": "h-index",
    "canonicalUrl": "https://leetcode.com/problems/h-index/",
    "url": "https://leetcode.com/problems/h-index/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for H-Index\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for H-Index\n};",
        "java": "// Java Solution for H-Index\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for H-Index\n}",
        "python": "# Python Solution for H-Index\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for H-Index\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for H-Index\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for H-Index\n};",
        "java": "// Optimal Java Solution for H-Index\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for H-Index\n}",
        "python": "# Optimal Python Solution for H-Index\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for H-Index\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for H-Index",
      "cpp_optimal": "// Solution for H-Index",
      "java_brute": "// Solution for H-Index",
      "java_optimal": "// Solution for H-Index",
      "python_brute": "# Solution for H-Index",
      "python_optimal": "# Solution for H-Index"
    },
    "originalOrder": 601,
    "learningOrder": 601
  },
  {
    "id": 175,
    "number": 175,
    "sequence_number": 175,
    "title": "H-Index II",
    "slug": "h-index-ii",
    "difficulty": "Medium",
    "topic": "Sort",
    "subtopic": "Sort Optimization",
    "pattern": "Sort Pattern",
    "secondary_patterns": [
      "Sort Pattern"
    ],
    "stage": "Prefix Sum & Sorting Techniques",
    "curriculumStage": "Stage 4 — Prefix Sum & Sorting Techniques",
    "roadmapPhase": "Stage 4 — Prefix Sum & Sorting Techniques",
    "phase": "Stage 4 — Prefix Sum & Sorting Techniques",
    "estimatedTime": 30,
    "statement": "Solve the **H-Index II** problem using standard Sort techniques. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Sort algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Sort properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Sort techniques by solving Medium problem constraints for H-Index II.",
    "whyThisPattern": "When observing Sort problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/h-index-ii/",
    "leetcode_title": "H-Index II",
    "leetcode_id": 275,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/h-index-ii/",
    "canonicalSlug": "h-index-ii",
    "canonicalUrl": "https://leetcode.com/problems/h-index-ii/",
    "url": "https://leetcode.com/problems/h-index-ii/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for H-Index II\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for H-Index II\n};",
        "java": "// Java Solution for H-Index II\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for H-Index II\n}",
        "python": "# Python Solution for H-Index II\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for H-Index II\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for H-Index II\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for H-Index II\n};",
        "java": "// Optimal Java Solution for H-Index II\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for H-Index II\n}",
        "python": "# Optimal Python Solution for H-Index II\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for H-Index II\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for H-Index II",
      "cpp_optimal": "// Solution for H-Index II",
      "java_brute": "// Solution for H-Index II",
      "java_optimal": "// Solution for H-Index II",
      "python_brute": "# Solution for H-Index II",
      "python_optimal": "# Solution for H-Index II"
    },
    "originalOrder": 602,
    "learningOrder": 602
  },
  {
    "id": 176,
    "number": 176,
    "sequence_number": 176,
    "title": "Wiggle Sort II",
    "slug": "wiggle-sort-ii",
    "difficulty": "Medium",
    "topic": "Sort",
    "subtopic": "Sort Optimization",
    "pattern": "Sort Pattern",
    "secondary_patterns": [
      "Sort Pattern"
    ],
    "stage": "Prefix Sum & Sorting Techniques",
    "curriculumStage": "Stage 4 — Prefix Sum & Sorting Techniques",
    "roadmapPhase": "Stage 4 — Prefix Sum & Sorting Techniques",
    "phase": "Stage 4 — Prefix Sum & Sorting Techniques",
    "estimatedTime": 30,
    "statement": "Solve the **Wiggle Sort II** problem using standard Sort techniques. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Sort algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Sort properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Sort techniques by solving Medium problem constraints for Wiggle Sort II.",
    "whyThisPattern": "When observing Sort problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/wiggle-sort-ii/",
    "leetcode_title": "Wiggle Sort II",
    "leetcode_id": 324,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/wiggle-sort-ii/",
    "canonicalSlug": "wiggle-sort-ii",
    "canonicalUrl": "https://leetcode.com/problems/wiggle-sort-ii/",
    "url": "https://leetcode.com/problems/wiggle-sort-ii/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Wiggle Sort II\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Wiggle Sort II\n};",
        "java": "// Java Solution for Wiggle Sort II\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Wiggle Sort II\n}",
        "python": "# Python Solution for Wiggle Sort II\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Wiggle Sort II\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Wiggle Sort II\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Wiggle Sort II\n};",
        "java": "// Optimal Java Solution for Wiggle Sort II\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Wiggle Sort II\n}",
        "python": "# Optimal Python Solution for Wiggle Sort II\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Wiggle Sort II\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Wiggle Sort II",
      "cpp_optimal": "// Solution for Wiggle Sort II",
      "java_brute": "// Solution for Wiggle Sort II",
      "java_optimal": "// Solution for Wiggle Sort II",
      "python_brute": "# Solution for Wiggle Sort II",
      "python_optimal": "# Solution for Wiggle Sort II"
    },
    "originalOrder": 603,
    "learningOrder": 603
  },
  {
    "id": 177,
    "number": 177,
    "sequence_number": 177,
    "title": "Simplify Path",
    "slug": "simplify-path",
    "difficulty": "Medium",
    "topic": "Arrays",
    "subtopic": "Arrays Optimization",
    "pattern": "Arrays Pattern",
    "secondary_patterns": [
      "Arrays Pattern"
    ],
    "stage": "Prefix Sum & Sorting Techniques",
    "curriculumStage": "Stage 4 — Prefix Sum & Sorting Techniques",
    "roadmapPhase": "Stage 4 — Prefix Sum & Sorting Techniques",
    "phase": "Stage 4 — Prefix Sum & Sorting Techniques",
    "estimatedTime": 30,
    "statement": "Solve the **Simplify Path** problem using standard Arrays techniques. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Arrays algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Arrays properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Arrays techniques by solving Medium problem constraints for Simplify Path.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/simplify-path/",
    "leetcode_title": "Simplify Path",
    "leetcode_id": 71,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/simplify-path/",
    "canonicalSlug": "simplify-path",
    "canonicalUrl": "https://leetcode.com/problems/simplify-path/",
    "url": "https://leetcode.com/problems/simplify-path/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Simplify Path\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Simplify Path\n};",
        "java": "// Java Solution for Simplify Path\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Simplify Path\n}",
        "python": "# Python Solution for Simplify Path\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Simplify Path\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Simplify Path\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Simplify Path\n};",
        "java": "// Optimal Java Solution for Simplify Path\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Simplify Path\n}",
        "python": "# Optimal Python Solution for Simplify Path\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Simplify Path\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Simplify Path",
      "cpp_optimal": "// Solution for Simplify Path",
      "java_brute": "// Solution for Simplify Path",
      "java_optimal": "// Solution for Simplify Path",
      "python_brute": "# Solution for Simplify Path",
      "python_optimal": "# Solution for Simplify Path"
    },
    "originalOrder": 263,
    "learningOrder": 263
  },
  {
    "id": 178,
    "number": 178,
    "sequence_number": 178,
    "title": "Edit Distance",
    "slug": "edit-distance",
    "difficulty": "Medium",
    "topic": "Arrays",
    "subtopic": "Arrays Optimization",
    "pattern": "Arrays Pattern",
    "secondary_patterns": [
      "Arrays Pattern"
    ],
    "stage": "Prefix Sum & Sorting Techniques",
    "curriculumStage": "Stage 4 — Prefix Sum & Sorting Techniques",
    "roadmapPhase": "Stage 4 — Prefix Sum & Sorting Techniques",
    "phase": "Stage 4 — Prefix Sum & Sorting Techniques",
    "estimatedTime": 30,
    "statement": "Solve the **Edit Distance** problem using standard Arrays techniques. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Arrays algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Arrays properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Arrays techniques by solving Medium problem constraints for Edit Distance.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/edit-distance/",
    "leetcode_title": "Edit Distance",
    "leetcode_id": 72,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/edit-distance/",
    "canonicalSlug": "edit-distance",
    "canonicalUrl": "https://leetcode.com/problems/edit-distance/",
    "url": "https://leetcode.com/problems/edit-distance/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Edit Distance\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Edit Distance\n};",
        "java": "// Java Solution for Edit Distance\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Edit Distance\n}",
        "python": "# Python Solution for Edit Distance\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Edit Distance\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Edit Distance\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Edit Distance\n};",
        "java": "// Optimal Java Solution for Edit Distance\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Edit Distance\n}",
        "python": "# Optimal Python Solution for Edit Distance\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Edit Distance\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Edit Distance",
      "cpp_optimal": "// Solution for Edit Distance",
      "java_brute": "// Solution for Edit Distance",
      "java_optimal": "// Solution for Edit Distance",
      "python_brute": "# Solution for Edit Distance",
      "python_optimal": "# Solution for Edit Distance"
    },
    "originalOrder": 264,
    "learningOrder": 264
  },
  {
    "id": 179,
    "number": 179,
    "sequence_number": 179,
    "title": "Combinations",
    "slug": "combinations",
    "difficulty": "Medium",
    "topic": "Arrays",
    "subtopic": "Arrays Optimization",
    "pattern": "Arrays Pattern",
    "secondary_patterns": [
      "Arrays Pattern"
    ],
    "stage": "Prefix Sum & Sorting Techniques",
    "curriculumStage": "Stage 4 — Prefix Sum & Sorting Techniques",
    "roadmapPhase": "Stage 4 — Prefix Sum & Sorting Techniques",
    "phase": "Stage 4 — Prefix Sum & Sorting Techniques",
    "estimatedTime": 30,
    "statement": "Solve the **Combinations** problem using standard Arrays techniques. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Arrays algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Arrays properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Arrays techniques by solving Medium problem constraints for Combinations.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/combinations/",
    "leetcode_title": "Combinations",
    "leetcode_id": 77,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/combinations/",
    "canonicalSlug": "combinations",
    "canonicalUrl": "https://leetcode.com/problems/combinations/",
    "url": "https://leetcode.com/problems/combinations/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Combinations\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Combinations\n};",
        "java": "// Java Solution for Combinations\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Combinations\n}",
        "python": "# Python Solution for Combinations\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Combinations\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Combinations\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Combinations\n};",
        "java": "// Optimal Java Solution for Combinations\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Combinations\n}",
        "python": "# Optimal Python Solution for Combinations\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Combinations\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Combinations",
      "cpp_optimal": "// Solution for Combinations",
      "java_brute": "// Solution for Combinations",
      "java_optimal": "// Solution for Combinations",
      "python_brute": "# Solution for Combinations",
      "python_optimal": "# Solution for Combinations"
    },
    "originalOrder": 265,
    "learningOrder": 265
  },
  {
    "id": 180,
    "number": 180,
    "sequence_number": 180,
    "title": "Gray Code",
    "slug": "gray-code",
    "difficulty": "Medium",
    "topic": "Arrays",
    "subtopic": "Arrays Optimization",
    "pattern": "Arrays Pattern",
    "secondary_patterns": [
      "Arrays Pattern"
    ],
    "stage": "Prefix Sum & Sorting Techniques",
    "curriculumStage": "Stage 4 — Prefix Sum & Sorting Techniques",
    "roadmapPhase": "Stage 4 — Prefix Sum & Sorting Techniques",
    "phase": "Stage 4 — Prefix Sum & Sorting Techniques",
    "estimatedTime": 30,
    "statement": "Solve the **Gray Code** problem using standard Arrays techniques. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Arrays algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Arrays properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Arrays techniques by solving Medium problem constraints for Gray Code.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/gray-code/",
    "leetcode_title": "Gray Code",
    "leetcode_id": 89,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/gray-code/",
    "canonicalSlug": "gray-code",
    "canonicalUrl": "https://leetcode.com/problems/gray-code/",
    "url": "https://leetcode.com/problems/gray-code/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Gray Code\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Gray Code\n};",
        "java": "// Java Solution for Gray Code\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Gray Code\n}",
        "python": "# Python Solution for Gray Code\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Gray Code\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Gray Code\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Gray Code\n};",
        "java": "// Optimal Java Solution for Gray Code\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Gray Code\n}",
        "python": "# Optimal Python Solution for Gray Code\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Gray Code\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Gray Code",
      "cpp_optimal": "// Solution for Gray Code",
      "java_brute": "// Solution for Gray Code",
      "java_optimal": "// Solution for Gray Code",
      "python_brute": "# Solution for Gray Code",
      "python_optimal": "# Solution for Gray Code"
    },
    "originalOrder": 266,
    "learningOrder": 266
  },
  {
    "id": 181,
    "number": 181,
    "sequence_number": 181,
    "title": "Restore IP Addresses",
    "slug": "restore-ip-addresses",
    "difficulty": "Medium",
    "topic": "Arrays",
    "subtopic": "Arrays Optimization",
    "pattern": "Arrays Pattern",
    "secondary_patterns": [
      "Arrays Pattern"
    ],
    "stage": "Prefix Sum & Sorting Techniques",
    "curriculumStage": "Stage 4 — Prefix Sum & Sorting Techniques",
    "roadmapPhase": "Stage 4 — Prefix Sum & Sorting Techniques",
    "phase": "Stage 4 — Prefix Sum & Sorting Techniques",
    "estimatedTime": 30,
    "statement": "Solve the **Restore IP Addresses** problem using standard Arrays techniques. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Arrays algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Arrays properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Arrays techniques by solving Medium problem constraints for Restore IP Addresses.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/restore-ip-addresses/",
    "leetcode_title": "Restore IP Addresses",
    "leetcode_id": 93,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/restore-ip-addresses/",
    "canonicalSlug": "restore-ip-addresses",
    "canonicalUrl": "https://leetcode.com/problems/restore-ip-addresses/",
    "url": "https://leetcode.com/problems/restore-ip-addresses/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Restore IP Addresses\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Restore IP Addresses\n};",
        "java": "// Java Solution for Restore IP Addresses\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Restore IP Addresses\n}",
        "python": "# Python Solution for Restore IP Addresses\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Restore IP Addresses\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Restore IP Addresses\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Restore IP Addresses\n};",
        "java": "// Optimal Java Solution for Restore IP Addresses\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Restore IP Addresses\n}",
        "python": "# Optimal Python Solution for Restore IP Addresses\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Restore IP Addresses\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Restore IP Addresses",
      "cpp_optimal": "// Solution for Restore IP Addresses",
      "java_brute": "// Solution for Restore IP Addresses",
      "java_optimal": "// Solution for Restore IP Addresses",
      "python_brute": "# Solution for Restore IP Addresses",
      "python_optimal": "# Solution for Restore IP Addresses"
    },
    "originalOrder": 267,
    "learningOrder": 267
  },
  {
    "id": 182,
    "number": 182,
    "sequence_number": 182,
    "title": "Interleaving String",
    "slug": "interleaving-string",
    "difficulty": "Medium",
    "topic": "Arrays",
    "subtopic": "Arrays Optimization",
    "pattern": "Arrays Pattern",
    "secondary_patterns": [
      "Arrays Pattern"
    ],
    "stage": "Prefix Sum & Sorting Techniques",
    "curriculumStage": "Stage 4 — Prefix Sum & Sorting Techniques",
    "roadmapPhase": "Stage 4 — Prefix Sum & Sorting Techniques",
    "phase": "Stage 4 — Prefix Sum & Sorting Techniques",
    "estimatedTime": 30,
    "statement": "Solve the **Interleaving String** problem using standard Arrays techniques. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Arrays algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Arrays properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Arrays techniques by solving Medium problem constraints for Interleaving String.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/interleaving-string/",
    "leetcode_title": "Interleaving String",
    "leetcode_id": 97,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/interleaving-string/",
    "canonicalSlug": "interleaving-string",
    "canonicalUrl": "https://leetcode.com/problems/interleaving-string/",
    "url": "https://leetcode.com/problems/interleaving-string/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Interleaving String\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Interleaving String\n};",
        "java": "// Java Solution for Interleaving String\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Interleaving String\n}",
        "python": "# Python Solution for Interleaving String\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Interleaving String\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Interleaving String\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Interleaving String\n};",
        "java": "// Optimal Java Solution for Interleaving String\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Interleaving String\n}",
        "python": "# Optimal Python Solution for Interleaving String\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Interleaving String\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Interleaving String",
      "cpp_optimal": "// Solution for Interleaving String",
      "java_brute": "// Solution for Interleaving String",
      "java_optimal": "// Solution for Interleaving String",
      "python_brute": "# Solution for Interleaving String",
      "python_optimal": "# Solution for Interleaving String"
    },
    "originalOrder": 268,
    "learningOrder": 268
  },
  {
    "id": 183,
    "number": 183,
    "sequence_number": 183,
    "title": "Path Sum II",
    "slug": "path-sum-ii",
    "difficulty": "Medium",
    "topic": "Arrays",
    "subtopic": "Arrays Optimization",
    "pattern": "Arrays Pattern",
    "secondary_patterns": [
      "Arrays Pattern"
    ],
    "stage": "Prefix Sum & Sorting Techniques",
    "curriculumStage": "Stage 4 — Prefix Sum & Sorting Techniques",
    "roadmapPhase": "Stage 4 — Prefix Sum & Sorting Techniques",
    "phase": "Stage 4 — Prefix Sum & Sorting Techniques",
    "estimatedTime": 30,
    "statement": "Solve the **Path Sum II** problem using standard Arrays techniques. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Arrays algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Arrays properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Arrays techniques by solving Medium problem constraints for Path Sum II.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/path-sum-ii/",
    "leetcode_title": "Path Sum II",
    "leetcode_id": 113,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/path-sum-ii/",
    "canonicalSlug": "path-sum-ii",
    "canonicalUrl": "https://leetcode.com/problems/path-sum-ii/",
    "url": "https://leetcode.com/problems/path-sum-ii/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Path Sum II\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Path Sum II\n};",
        "java": "// Java Solution for Path Sum II\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Path Sum II\n}",
        "python": "# Python Solution for Path Sum II\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Path Sum II\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Path Sum II\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Path Sum II\n};",
        "java": "// Optimal Java Solution for Path Sum II\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Path Sum II\n}",
        "python": "# Optimal Python Solution for Path Sum II\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Path Sum II\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Path Sum II",
      "cpp_optimal": "// Solution for Path Sum II",
      "java_brute": "// Solution for Path Sum II",
      "java_optimal": "// Solution for Path Sum II",
      "python_brute": "# Solution for Path Sum II",
      "python_optimal": "# Solution for Path Sum II"
    },
    "originalOrder": 269,
    "learningOrder": 269
  },
  {
    "id": 184,
    "number": 184,
    "sequence_number": 184,
    "title": "Best Time to Buy and Sell Stock II",
    "slug": "best-time-to-buy-and-sell-stock-ii",
    "difficulty": "Medium",
    "topic": "Bit Manipulation",
    "subtopic": "Arrays Optimization",
    "pattern": "Arrays Pattern",
    "secondary_patterns": [
      "Arrays Pattern"
    ],
    "stage": "Prefix Sum & Sorting Techniques",
    "curriculumStage": "Stage 4 — Prefix Sum & Sorting Techniques",
    "roadmapPhase": "Stage 4 — Prefix Sum & Sorting Techniques",
    "phase": "Stage 4 — Prefix Sum & Sorting Techniques",
    "estimatedTime": 30,
    "statement": "Solve the **Best Time to Buy and Sell Stock II** problem using standard Arrays techniques. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Arrays algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Arrays properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Arrays techniques by solving Medium problem constraints for Best Time to Buy and Sell Stock II.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/best-time-to-buy-and-sell-stock-ii/",
    "leetcode_title": "Best Time to Buy and Sell Stock II",
    "leetcode_id": 122,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/best-time-to-buy-and-sell-stock-ii/",
    "canonicalSlug": "best-time-to-buy-and-sell-stock-ii",
    "canonicalUrl": "https://leetcode.com/problems/best-time-to-buy-and-sell-stock-ii/",
    "url": "https://leetcode.com/problems/best-time-to-buy-and-sell-stock-ii/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Best Time to Buy and Sell Stock II\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Best Time to Buy and Sell Stock II\n};",
        "java": "// Java Solution for Best Time to Buy and Sell Stock II\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Best Time to Buy and Sell Stock II\n}",
        "python": "# Python Solution for Best Time to Buy and Sell Stock II\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Best Time to Buy and Sell Stock II\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Best Time to Buy and Sell Stock II\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Best Time to Buy and Sell Stock II\n};",
        "java": "// Optimal Java Solution for Best Time to Buy and Sell Stock II\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Best Time to Buy and Sell Stock II\n}",
        "python": "# Optimal Python Solution for Best Time to Buy and Sell Stock II\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Best Time to Buy and Sell Stock II\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Best Time to Buy and Sell Stock II",
      "cpp_optimal": "// Solution for Best Time to Buy and Sell Stock II",
      "java_brute": "// Solution for Best Time to Buy and Sell Stock II",
      "java_optimal": "// Solution for Best Time to Buy and Sell Stock II",
      "python_brute": "# Solution for Best Time to Buy and Sell Stock II",
      "python_optimal": "# Solution for Best Time to Buy and Sell Stock II"
    },
    "originalOrder": 270,
    "learningOrder": 270
  },
  {
    "id": 185,
    "number": 185,
    "sequence_number": 185,
    "title": "Linked List Cycle II",
    "slug": "linked-list-cycle-ii",
    "difficulty": "Medium",
    "topic": "Linked List",
    "subtopic": "Arrays Optimization",
    "pattern": "Arrays Pattern",
    "secondary_patterns": [
      "Arrays Pattern"
    ],
    "stage": "Prefix Sum & Sorting Techniques",
    "curriculumStage": "Stage 4 — Prefix Sum & Sorting Techniques",
    "roadmapPhase": "Stage 4 — Prefix Sum & Sorting Techniques",
    "phase": "Stage 4 — Prefix Sum & Sorting Techniques",
    "estimatedTime": 30,
    "statement": "Solve the **Linked List Cycle II** problem using standard Arrays techniques. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Arrays algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Arrays properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Arrays techniques by solving Medium problem constraints for Linked List Cycle II.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/linked-list-cycle-ii/",
    "leetcode_title": "Linked List Cycle II",
    "leetcode_id": 142,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/linked-list-cycle-ii/",
    "canonicalSlug": "linked-list-cycle-ii",
    "canonicalUrl": "https://leetcode.com/problems/linked-list-cycle-ii/",
    "url": "https://leetcode.com/problems/linked-list-cycle-ii/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Linked List Cycle II\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Linked List Cycle II\n};",
        "java": "// Java Solution for Linked List Cycle II\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Linked List Cycle II\n}",
        "python": "# Python Solution for Linked List Cycle II\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Linked List Cycle II\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Linked List Cycle II\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Linked List Cycle II\n};",
        "java": "// Optimal Java Solution for Linked List Cycle II\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Linked List Cycle II\n}",
        "python": "# Optimal Python Solution for Linked List Cycle II\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Linked List Cycle II\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Linked List Cycle II",
      "cpp_optimal": "// Solution for Linked List Cycle II",
      "java_brute": "// Solution for Linked List Cycle II",
      "java_optimal": "// Solution for Linked List Cycle II",
      "python_brute": "# Solution for Linked List Cycle II",
      "python_optimal": "# Solution for Linked List Cycle II"
    },
    "originalOrder": 271,
    "learningOrder": 271
  },
  {
    "id": 186,
    "number": 186,
    "sequence_number": 186,
    "title": "Count of Range Sum",
    "slug": "count-of-range-sum",
    "difficulty": "Hard",
    "topic": "Prefix Sum",
    "subtopic": "Hashing & Array Optimization",
    "pattern": "Hashing & Array Optimization",
    "secondary_patterns": [
      "Hashing & Array Optimization"
    ],
    "stage": "Prefix Sum & Sorting Techniques",
    "curriculumStage": "Stage 4 — Prefix Sum & Sorting Techniques",
    "roadmapPhase": "Stage 4 — Prefix Sum & Sorting Techniques",
    "phase": "Stage 4 — Prefix Sum & Sorting Techniques",
    "estimatedTime": 45,
    "statement": "Solve the **Count of Range Sum Optimization** problem using the **Hashing & Array Optimization** technique. Given input constraints appropriate for Hard level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^6",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Hashing & Array Optimization identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Hashing & Array Optimization. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Hashing & Array Optimization techniques by solving Hard problem constraints for Count of Range Sum Optimization.",
    "whyThisPattern": "When observing arrays & strings problem conditions, Hashing & Array Optimization optimizes performance down to expected O(N log N).",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Meta",
      "Apple",
      "Netflix"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/count-of-range-sum/",
    "leetcode_title": "Count of Range Sum",
    "leetcode_id": 327,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/count-of-range-sum/",
    "canonicalSlug": "count-of-range-sum",
    "canonicalUrl": "https://leetcode.com/problems/count-of-range-sum/",
    "url": "https://leetcode.com/problems/count-of-range-sum/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Count of Range Sum Optimization (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Count of Range Sum Optimization (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Count of Range Sum Optimization (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Count of Range Sum Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Count of Range Sum Optimization (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Count of Range Sum Optimization (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Count of Range Sum Optimization (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Count of Range Sum Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Count of Range Sum",
      "cpp_optimal": "// Solution for Count of Range Sum",
      "java_brute": "// Solution for Count of Range Sum",
      "java_optimal": "// Solution for Count of Range Sum",
      "python_brute": "# Solution for Count of Range Sum",
      "python_optimal": "# Solution for Count of Range Sum"
    },
    "originalOrder": 924,
    "learningOrder": 924
  },
  {
    "id": 187,
    "number": 187,
    "sequence_number": 187,
    "title": "Maximum Sum of 3 Non-Overlapping Subarrays",
    "slug": "maximum-sum-of-3-non-overlapping-subarrays",
    "difficulty": "Hard",
    "topic": "Prefix Sum",
    "subtopic": "Prefix Sum Optimization",
    "pattern": "3-Window DP Prefix Suffix",
    "secondary_patterns": [
      "3-Window DP Prefix Suffix"
    ],
    "stage": "Prefix Sum & Sorting Techniques",
    "curriculumStage": "Stage 4 — Prefix Sum & Sorting Techniques",
    "roadmapPhase": "Stage 4 — Prefix Sum & Sorting Techniques",
    "phase": "Stage 4 — Prefix Sum & Sorting Techniques",
    "estimatedTime": 45,
    "statement": "Given the constraints and input parameters for Maximum Sum of 3 Non-Overlapping Subarrays, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Maximum Sum of 3 Non-Overlapping Subarrays."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Maximum Sum of 3 Non-Overlapping Subarrays.",
      "Leverage the optimal Prefix Sum pattern to reduce time complexity."
    ],
    "learningObjective": "Master Prefix Sum techniques by solving Hard problem constraints for Maximum Sum of 3 Non-Overlapping Subarrays.",
    "whyThisPattern": "When observing Prefix Sum problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/maximum-sum-of-3-non-overlapping-subarrays/",
    "leetcode_title": "Maximum Sum of 3 Non-Overlapping Subarrays",
    "leetcode_id": 689,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/maximum-sum-of-3-non-overlapping-subarrays/",
    "canonicalSlug": "maximum-sum-of-3-non-overlapping-subarrays",
    "canonicalUrl": "https://leetcode.com/problems/maximum-sum-of-3-non-overlapping-subarrays/",
    "url": "https://leetcode.com/problems/maximum-sum-of-3-non-overlapping-subarrays/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Maximum Sum of 3 Non-Overlapping Subarrays\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Maximum Sum of 3 Non-Overlapping Subarrays\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Maximum Sum of 3 Non-Overlapping Subarrays\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Maximum Sum of 3 Non-Overlapping Subarrays\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Maximum Sum of 3 Non-Overlapping Subarrays\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Maximum Sum of 3 Non-Overlapping Subarrays\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Maximum Sum of 3 Non-Overlapping Subarrays\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Maximum Sum of 3 Non-Overlapping Subarrays\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Maximum Sum of 3 Non-Overlapping Subarrays",
      "cpp_optimal": "// Solution for Maximum Sum of 3 Non-Overlapping Subarrays",
      "java_brute": "// Solution for Maximum Sum of 3 Non-Overlapping Subarrays",
      "java_optimal": "// Solution for Maximum Sum of 3 Non-Overlapping Subarrays",
      "python_brute": "# Solution for Maximum Sum of 3 Non-Overlapping Subarrays",
      "python_optimal": "# Solution for Maximum Sum of 3 Non-Overlapping Subarrays"
    },
    "originalOrder": 925,
    "learningOrder": 925
  },
  {
    "id": 188,
    "number": 188,
    "sequence_number": 188,
    "title": "Smallest Rotation with Highest Score",
    "slug": "smallest-rotation-with-highest-score",
    "difficulty": "Hard",
    "topic": "Prefix Sum",
    "subtopic": "Prefix Sum Optimization",
    "pattern": "Difference Array Rotations",
    "secondary_patterns": [
      "Difference Array Rotations"
    ],
    "stage": "Prefix Sum & Sorting Techniques",
    "curriculumStage": "Stage 4 — Prefix Sum & Sorting Techniques",
    "roadmapPhase": "Stage 4 — Prefix Sum & Sorting Techniques",
    "phase": "Stage 4 — Prefix Sum & Sorting Techniques",
    "estimatedTime": 45,
    "statement": "Given the constraints and input parameters for Smallest Rotation with Highest Score, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Smallest Rotation with Highest Score."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Smallest Rotation with Highest Score.",
      "Leverage the optimal Prefix Sum pattern to reduce time complexity."
    ],
    "learningObjective": "Master Prefix Sum techniques by solving Hard problem constraints for Smallest Rotation with Highest Score.",
    "whyThisPattern": "When observing Prefix Sum problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/smallest-rotation-with-highest-score/",
    "leetcode_title": "Smallest Rotation with Highest Score",
    "leetcode_id": 798,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/smallest-rotation-with-highest-score/",
    "canonicalSlug": "smallest-rotation-with-highest-score",
    "canonicalUrl": "https://leetcode.com/problems/smallest-rotation-with-highest-score/",
    "url": "https://leetcode.com/problems/smallest-rotation-with-highest-score/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Smallest Rotation with Highest Score\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Smallest Rotation with Highest Score\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Smallest Rotation with Highest Score\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Smallest Rotation with Highest Score\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Smallest Rotation with Highest Score\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Smallest Rotation with Highest Score\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Smallest Rotation with Highest Score\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Smallest Rotation with Highest Score\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Smallest Rotation with Highest Score",
      "cpp_optimal": "// Solution for Smallest Rotation with Highest Score",
      "java_brute": "// Solution for Smallest Rotation with Highest Score",
      "java_optimal": "// Solution for Smallest Rotation with Highest Score",
      "python_brute": "# Solution for Smallest Rotation with Highest Score",
      "python_optimal": "# Solution for Smallest Rotation with Highest Score"
    },
    "originalOrder": 926,
    "learningOrder": 926
  },
  {
    "id": 189,
    "number": 189,
    "sequence_number": 189,
    "title": "Number of Submatrices That Sum to Target",
    "slug": "number-of-submatrices-that-sum-to-target",
    "difficulty": "Hard",
    "topic": "Prefix Sum",
    "subtopic": "Prefix Sum Optimization",
    "pattern": "2D Submatrix Prefix Hash",
    "secondary_patterns": [
      "2D Submatrix Prefix Hash"
    ],
    "stage": "Prefix Sum & Sorting Techniques",
    "curriculumStage": "Stage 4 — Prefix Sum & Sorting Techniques",
    "roadmapPhase": "Stage 4 — Prefix Sum & Sorting Techniques",
    "phase": "Stage 4 — Prefix Sum & Sorting Techniques",
    "estimatedTime": 45,
    "statement": "Given the constraints and input parameters for Number of Submatrices That Sum to Target, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Number of Submatrices That Sum to Target."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Number of Submatrices That Sum to Target.",
      "Leverage the optimal Prefix Sum pattern to reduce time complexity."
    ],
    "learningObjective": "Master Prefix Sum techniques by solving Hard problem constraints for Number of Submatrices That Sum to Target.",
    "whyThisPattern": "When observing Prefix Sum problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/number-of-submatrices-that-sum-to-target/",
    "leetcode_title": "Number of Submatrices That Sum to Target",
    "leetcode_id": 1074,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/number-of-submatrices-that-sum-to-target/",
    "canonicalSlug": "number-of-submatrices-that-sum-to-target",
    "canonicalUrl": "https://leetcode.com/problems/number-of-submatrices-that-sum-to-target/",
    "url": "https://leetcode.com/problems/number-of-submatrices-that-sum-to-target/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Number of Submatrices That Sum to Target\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Number of Submatrices That Sum to Target\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Number of Submatrices That Sum to Target\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Number of Submatrices That Sum to Target\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Number of Submatrices That Sum to Target\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Number of Submatrices That Sum to Target\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Number of Submatrices That Sum to Target\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Number of Submatrices That Sum to Target\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Number of Submatrices That Sum to Target",
      "cpp_optimal": "// Solution for Number of Submatrices That Sum to Target",
      "java_brute": "// Solution for Number of Submatrices That Sum to Target",
      "java_optimal": "// Solution for Number of Submatrices That Sum to Target",
      "python_brute": "# Solution for Number of Submatrices That Sum to Target",
      "python_optimal": "# Solution for Number of Submatrices That Sum to Target"
    },
    "originalOrder": 927,
    "learningOrder": 927
  },
  {
    "id": 190,
    "number": 190,
    "sequence_number": 190,
    "title": "Count Subarrays With Median K",
    "slug": "count-subarrays-with-median-k",
    "difficulty": "Hard",
    "topic": "Prefix Sum",
    "subtopic": "Prefix Sum Optimization",
    "pattern": "Balance Prefix Map",
    "secondary_patterns": [
      "Balance Prefix Map"
    ],
    "stage": "Prefix Sum & Sorting Techniques",
    "curriculumStage": "Stage 4 — Prefix Sum & Sorting Techniques",
    "roadmapPhase": "Stage 4 — Prefix Sum & Sorting Techniques",
    "phase": "Stage 4 — Prefix Sum & Sorting Techniques",
    "estimatedTime": 45,
    "statement": "Given the constraints and input parameters for Count Subarrays With Median K, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Count Subarrays With Median K."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Count Subarrays With Median K.",
      "Leverage the optimal Prefix Sum pattern to reduce time complexity."
    ],
    "learningObjective": "Master Prefix Sum techniques by solving Hard problem constraints for Count Subarrays With Median K.",
    "whyThisPattern": "When observing Prefix Sum problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/count-subarrays-with-median-k/",
    "leetcode_title": "Count Subarrays With Median K",
    "leetcode_id": 2488,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/count-subarrays-with-median-k/",
    "canonicalSlug": "count-subarrays-with-median-k",
    "canonicalUrl": "https://leetcode.com/problems/count-subarrays-with-median-k/",
    "url": "https://leetcode.com/problems/count-subarrays-with-median-k/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Count Subarrays With Median K\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Count Subarrays With Median K\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Count Subarrays With Median K\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Count Subarrays With Median K\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Count Subarrays With Median K\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Count Subarrays With Median K\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Count Subarrays With Median K\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Count Subarrays With Median K\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Count Subarrays With Median K",
      "cpp_optimal": "// Solution for Count Subarrays With Median K",
      "java_brute": "// Solution for Count Subarrays With Median K",
      "java_optimal": "// Solution for Count Subarrays With Median K",
      "python_brute": "# Solution for Count Subarrays With Median K",
      "python_optimal": "# Solution for Count Subarrays With Median K"
    },
    "originalOrder": 928,
    "learningOrder": 928
  },
  {
    "id": 191,
    "number": 191,
    "sequence_number": 191,
    "title": "Sum of Total Strength of Wizards",
    "slug": "sum-of-total-strength-of-wizards",
    "difficulty": "Hard",
    "topic": "Prefix Sum",
    "subtopic": "Prefix Sum Optimization",
    "pattern": "Monotonic Stack Double Prefix Sum",
    "secondary_patterns": [
      "Monotonic Stack Double Prefix Sum"
    ],
    "stage": "Prefix Sum & Sorting Techniques",
    "curriculumStage": "Stage 4 — Prefix Sum & Sorting Techniques",
    "roadmapPhase": "Stage 4 — Prefix Sum & Sorting Techniques",
    "phase": "Stage 4 — Prefix Sum & Sorting Techniques",
    "estimatedTime": 45,
    "statement": "Given the constraints and input parameters for Sum of Total Strength of Wizards, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Sum of Total Strength of Wizards."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Sum of Total Strength of Wizards.",
      "Leverage the optimal Prefix Sum pattern to reduce time complexity."
    ],
    "learningObjective": "Master Prefix Sum techniques by solving Hard problem constraints for Sum of Total Strength of Wizards.",
    "whyThisPattern": "When observing Prefix Sum problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/sum-of-total-strength-of-wizards/",
    "leetcode_title": "Sum of Total Strength of Wizards",
    "leetcode_id": 2281,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/sum-of-total-strength-of-wizards/",
    "canonicalSlug": "sum-of-total-strength-of-wizards",
    "canonicalUrl": "https://leetcode.com/problems/sum-of-total-strength-of-wizards/",
    "url": "https://leetcode.com/problems/sum-of-total-strength-of-wizards/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Sum of Total Strength of Wizards\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Sum of Total Strength of Wizards\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Sum of Total Strength of Wizards\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Sum of Total Strength of Wizards\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Sum of Total Strength of Wizards\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Sum of Total Strength of Wizards\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Sum of Total Strength of Wizards\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Sum of Total Strength of Wizards\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Sum of Total Strength of Wizards",
      "cpp_optimal": "// Solution for Sum of Total Strength of Wizards",
      "java_brute": "// Solution for Sum of Total Strength of Wizards",
      "java_optimal": "// Solution for Sum of Total Strength of Wizards",
      "python_brute": "# Solution for Sum of Total Strength of Wizards",
      "python_optimal": "# Solution for Sum of Total Strength of Wizards"
    },
    "originalOrder": 929,
    "learningOrder": 929
  },
  {
    "id": 192,
    "number": 192,
    "sequence_number": 192,
    "title": "Max Chunks To Make Sorted II",
    "slug": "max-chunks-to-make-sorted-ii",
    "difficulty": "Hard",
    "topic": "Sort",
    "subtopic": "Sort Optimization",
    "pattern": "Sort Pattern",
    "secondary_patterns": [
      "Sort Pattern"
    ],
    "stage": "Prefix Sum & Sorting Techniques",
    "curriculumStage": "Stage 4 — Prefix Sum & Sorting Techniques",
    "roadmapPhase": "Stage 4 — Prefix Sum & Sorting Techniques",
    "phase": "Stage 4 — Prefix Sum & Sorting Techniques",
    "estimatedTime": 45,
    "statement": "Solve the **Max Chunks To Make Sorted II** problem using standard Sort techniques. Given input constraints appropriate for Hard level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Sort algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Sort properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Sort techniques by solving Hard problem constraints for Max Chunks To Make Sorted II.",
    "whyThisPattern": "When observing Sort problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/max-chunks-to-make-sorted-ii/",
    "leetcode_title": "Max Chunks To Make Sorted II",
    "leetcode_id": 768,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/max-chunks-to-make-sorted-ii/",
    "canonicalSlug": "max-chunks-to-make-sorted-ii",
    "canonicalUrl": "https://leetcode.com/problems/max-chunks-to-make-sorted-ii/",
    "url": "https://leetcode.com/problems/max-chunks-to-make-sorted-ii/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Max Chunks To Make Sorted II\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Max Chunks To Make Sorted II\n};",
        "java": "// Java Solution for Max Chunks To Make Sorted II\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Max Chunks To Make Sorted II\n}",
        "python": "# Python Solution for Max Chunks To Make Sorted II\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Max Chunks To Make Sorted II\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Max Chunks To Make Sorted II\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Max Chunks To Make Sorted II\n};",
        "java": "// Optimal Java Solution for Max Chunks To Make Sorted II\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Max Chunks To Make Sorted II\n}",
        "python": "# Optimal Python Solution for Max Chunks To Make Sorted II\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Max Chunks To Make Sorted II\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Max Chunks To Make Sorted II",
      "cpp_optimal": "// Solution for Max Chunks To Make Sorted II",
      "java_brute": "// Solution for Max Chunks To Make Sorted II",
      "java_optimal": "// Solution for Max Chunks To Make Sorted II",
      "python_brute": "# Solution for Max Chunks To Make Sorted II",
      "python_optimal": "# Solution for Max Chunks To Make Sorted II"
    },
    "originalOrder": 952,
    "learningOrder": 952
  },
  {
    "id": 193,
    "number": 193,
    "sequence_number": 193,
    "title": "Sort Items by Groups Respecting Dependencies",
    "slug": "sort-items-by-groups-respecting-dependencies",
    "difficulty": "Hard",
    "topic": "Sort",
    "subtopic": "Sort Optimization",
    "pattern": "Sort Pattern",
    "secondary_patterns": [
      "Sort Pattern"
    ],
    "stage": "Prefix Sum & Sorting Techniques",
    "curriculumStage": "Stage 4 — Prefix Sum & Sorting Techniques",
    "roadmapPhase": "Stage 4 — Prefix Sum & Sorting Techniques",
    "phase": "Stage 4 — Prefix Sum & Sorting Techniques",
    "estimatedTime": 45,
    "statement": "Solve the **Sort Items by Groups Respecting Dependencies** problem using standard Sort techniques. Given input constraints appropriate for Hard level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Sort algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Sort properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Sort techniques by solving Hard problem constraints for Sort Items by Groups Respecting Dependencies.",
    "whyThisPattern": "When observing Sort problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/sort-items-by-groups-respecting-dependencies/",
    "leetcode_title": "Sort Items by Groups Respecting Dependencies",
    "leetcode_id": 1203,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/sort-items-by-groups-respecting-dependencies/",
    "canonicalSlug": "sort-items-by-groups-respecting-dependencies",
    "canonicalUrl": "https://leetcode.com/problems/sort-items-by-groups-respecting-dependencies/",
    "url": "https://leetcode.com/problems/sort-items-by-groups-respecting-dependencies/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Sort Items by Groups Respecting Dependencies\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Sort Items by Groups Respecting Dependencies\n};",
        "java": "// Java Solution for Sort Items by Groups Respecting Dependencies\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Sort Items by Groups Respecting Dependencies\n}",
        "python": "# Python Solution for Sort Items by Groups Respecting Dependencies\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Sort Items by Groups Respecting Dependencies\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Sort Items by Groups Respecting Dependencies\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Sort Items by Groups Respecting Dependencies\n};",
        "java": "// Optimal Java Solution for Sort Items by Groups Respecting Dependencies\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Sort Items by Groups Respecting Dependencies\n}",
        "python": "# Optimal Python Solution for Sort Items by Groups Respecting Dependencies\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Sort Items by Groups Respecting Dependencies\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Sort Items by Groups Respecting Dependencies",
      "cpp_optimal": "// Solution for Sort Items by Groups Respecting Dependencies",
      "java_brute": "// Solution for Sort Items by Groups Respecting Dependencies",
      "java_optimal": "// Solution for Sort Items by Groups Respecting Dependencies",
      "python_brute": "# Solution for Sort Items by Groups Respecting Dependencies",
      "python_optimal": "# Solution for Sort Items by Groups Respecting Dependencies"
    },
    "originalOrder": 953,
    "learningOrder": 953
  },
  {
    "id": 194,
    "number": 194,
    "sequence_number": 194,
    "title": "Decode Ways II",
    "slug": "decode-ways-ii",
    "difficulty": "Hard",
    "topic": "Arrays",
    "subtopic": "Arrays Optimization",
    "pattern": "Arrays Pattern",
    "secondary_patterns": [
      "Arrays Pattern"
    ],
    "stage": "Prefix Sum & Sorting Techniques",
    "curriculumStage": "Stage 4 — Prefix Sum & Sorting Techniques",
    "roadmapPhase": "Stage 4 — Prefix Sum & Sorting Techniques",
    "phase": "Stage 4 — Prefix Sum & Sorting Techniques",
    "estimatedTime": 45,
    "statement": "Solve the **Decode Ways II** problem using standard Arrays techniques. Given input constraints appropriate for Hard level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Arrays algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Arrays properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Arrays techniques by solving Hard problem constraints for Decode Ways II.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/decode-ways-ii/",
    "leetcode_title": "Decode Ways II",
    "leetcode_id": 639,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/decode-ways-ii/",
    "canonicalSlug": "decode-ways-ii",
    "canonicalUrl": "https://leetcode.com/problems/decode-ways-ii/",
    "url": "https://leetcode.com/problems/decode-ways-ii/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Decode Ways II\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Decode Ways II\n};",
        "java": "// Java Solution for Decode Ways II\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Decode Ways II\n}",
        "python": "# Python Solution for Decode Ways II\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Decode Ways II\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Decode Ways II\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Decode Ways II\n};",
        "java": "// Optimal Java Solution for Decode Ways II\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Decode Ways II\n}",
        "python": "# Optimal Python Solution for Decode Ways II\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Decode Ways II\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Decode Ways II",
      "cpp_optimal": "// Solution for Decode Ways II",
      "java_brute": "// Solution for Decode Ways II",
      "java_optimal": "// Solution for Decode Ways II",
      "python_brute": "# Solution for Decode Ways II",
      "python_optimal": "# Solution for Decode Ways II"
    },
    "originalOrder": 730,
    "learningOrder": 730
  },
  {
    "id": 195,
    "number": 195,
    "sequence_number": 195,
    "title": "Stickers to Spell Word",
    "slug": "stickers-to-spell-word",
    "difficulty": "Hard",
    "topic": "Arrays",
    "subtopic": "Arrays Optimization",
    "pattern": "Arrays Pattern",
    "secondary_patterns": [
      "Arrays Pattern"
    ],
    "stage": "Prefix Sum & Sorting Techniques",
    "curriculumStage": "Stage 4 — Prefix Sum & Sorting Techniques",
    "roadmapPhase": "Stage 4 — Prefix Sum & Sorting Techniques",
    "phase": "Stage 4 — Prefix Sum & Sorting Techniques",
    "estimatedTime": 45,
    "statement": "Solve the **Stickers to Spell Word** problem using standard Arrays techniques. Given input constraints appropriate for Hard level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Arrays algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Arrays properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Arrays techniques by solving Hard problem constraints for Stickers to Spell Word.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/stickers-to-spell-word/",
    "leetcode_title": "Stickers to Spell Word",
    "leetcode_id": 691,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/stickers-to-spell-word/",
    "canonicalSlug": "stickers-to-spell-word",
    "canonicalUrl": "https://leetcode.com/problems/stickers-to-spell-word/",
    "url": "https://leetcode.com/problems/stickers-to-spell-word/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Stickers to Spell Word\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Stickers to Spell Word\n};",
        "java": "// Java Solution for Stickers to Spell Word\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Stickers to Spell Word\n}",
        "python": "# Python Solution for Stickers to Spell Word\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Stickers to Spell Word\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Stickers to Spell Word\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Stickers to Spell Word\n};",
        "java": "// Optimal Java Solution for Stickers to Spell Word\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Stickers to Spell Word\n}",
        "python": "# Optimal Python Solution for Stickers to Spell Word\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Stickers to Spell Word\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Stickers to Spell Word",
      "cpp_optimal": "// Solution for Stickers to Spell Word",
      "java_brute": "// Solution for Stickers to Spell Word",
      "java_optimal": "// Solution for Stickers to Spell Word",
      "python_brute": "# Solution for Stickers to Spell Word",
      "python_optimal": "# Solution for Stickers to Spell Word"
    },
    "originalOrder": 731,
    "learningOrder": 731
  },
  {
    "id": 196,
    "number": 196,
    "sequence_number": 196,
    "title": "Random Pick with Blacklist",
    "slug": "random-pick-with-blacklist",
    "difficulty": "Hard",
    "topic": "Bit Manipulation",
    "subtopic": "Arrays Optimization",
    "pattern": "Arrays Pattern",
    "secondary_patterns": [
      "Arrays Pattern"
    ],
    "stage": "Prefix Sum & Sorting Techniques",
    "curriculumStage": "Stage 4 — Prefix Sum & Sorting Techniques",
    "roadmapPhase": "Stage 4 — Prefix Sum & Sorting Techniques",
    "phase": "Stage 4 — Prefix Sum & Sorting Techniques",
    "estimatedTime": 45,
    "statement": "Solve the **Random Pick with Blacklist** problem using standard Arrays techniques. Given input constraints appropriate for Hard level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Arrays algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Arrays properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Arrays techniques by solving Hard problem constraints for Random Pick with Blacklist.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/random-pick-with-blacklist/",
    "leetcode_title": "Random Pick with Blacklist",
    "leetcode_id": 710,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/random-pick-with-blacklist/",
    "canonicalSlug": "random-pick-with-blacklist",
    "canonicalUrl": "https://leetcode.com/problems/random-pick-with-blacklist/",
    "url": "https://leetcode.com/problems/random-pick-with-blacklist/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Random Pick with Blacklist\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Random Pick with Blacklist\n};",
        "java": "// Java Solution for Random Pick with Blacklist\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Random Pick with Blacklist\n}",
        "python": "# Python Solution for Random Pick with Blacklist\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Random Pick with Blacklist\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Random Pick with Blacklist\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Random Pick with Blacklist\n};",
        "java": "// Optimal Java Solution for Random Pick with Blacklist\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Random Pick with Blacklist\n}",
        "python": "# Optimal Python Solution for Random Pick with Blacklist\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Random Pick with Blacklist\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Random Pick with Blacklist",
      "cpp_optimal": "// Solution for Random Pick with Blacklist",
      "java_brute": "// Solution for Random Pick with Blacklist",
      "java_optimal": "// Solution for Random Pick with Blacklist",
      "python_brute": "# Solution for Random Pick with Blacklist",
      "python_optimal": "# Solution for Random Pick with Blacklist"
    },
    "originalOrder": 732,
    "learningOrder": 732
  },
  {
    "id": 197,
    "number": 197,
    "sequence_number": 197,
    "title": "Cherry Pickup",
    "slug": "cherry-pickup",
    "difficulty": "Hard",
    "topic": "Arrays",
    "subtopic": "Arrays Optimization",
    "pattern": "Arrays Pattern",
    "secondary_patterns": [
      "Arrays Pattern"
    ],
    "stage": "Prefix Sum & Sorting Techniques",
    "curriculumStage": "Stage 4 — Prefix Sum & Sorting Techniques",
    "roadmapPhase": "Stage 4 — Prefix Sum & Sorting Techniques",
    "phase": "Stage 4 — Prefix Sum & Sorting Techniques",
    "estimatedTime": 45,
    "statement": "Solve the **Cherry Pickup** problem using standard Arrays techniques. Given input constraints appropriate for Hard level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Arrays algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Arrays properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Arrays techniques by solving Hard problem constraints for Cherry Pickup.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/cherry-pickup/",
    "leetcode_title": "Cherry Pickup",
    "leetcode_id": 741,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/cherry-pickup/",
    "canonicalSlug": "cherry-pickup",
    "canonicalUrl": "https://leetcode.com/problems/cherry-pickup/",
    "url": "https://leetcode.com/problems/cherry-pickup/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Cherry Pickup\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Cherry Pickup\n};",
        "java": "// Java Solution for Cherry Pickup\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Cherry Pickup\n}",
        "python": "# Python Solution for Cherry Pickup\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Cherry Pickup\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Cherry Pickup\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Cherry Pickup\n};",
        "java": "// Optimal Java Solution for Cherry Pickup\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Cherry Pickup\n}",
        "python": "# Optimal Python Solution for Cherry Pickup\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Cherry Pickup\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Cherry Pickup",
      "cpp_optimal": "// Solution for Cherry Pickup",
      "java_brute": "// Solution for Cherry Pickup",
      "java_optimal": "// Solution for Cherry Pickup",
      "python_brute": "# Solution for Cherry Pickup",
      "python_optimal": "# Solution for Cherry Pickup"
    },
    "originalOrder": 733,
    "learningOrder": 733
  },
  {
    "id": 198,
    "number": 198,
    "sequence_number": 198,
    "title": "Set Intersection Size At Least Two",
    "slug": "set-intersection-size-at-least-two",
    "difficulty": "Hard",
    "topic": "Hashing",
    "subtopic": "Arrays Optimization",
    "pattern": "Arrays Pattern",
    "secondary_patterns": [
      "Arrays Pattern"
    ],
    "stage": "Prefix Sum & Sorting Techniques",
    "curriculumStage": "Stage 4 — Prefix Sum & Sorting Techniques",
    "roadmapPhase": "Stage 4 — Prefix Sum & Sorting Techniques",
    "phase": "Stage 4 — Prefix Sum & Sorting Techniques",
    "estimatedTime": 45,
    "statement": "Solve the **Set Intersection Size At Least Two** problem using standard Arrays techniques. Given input constraints appropriate for Hard level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Arrays algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Arrays properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Arrays techniques by solving Hard problem constraints for Set Intersection Size At Least Two.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/set-intersection-size-at-least-two/",
    "leetcode_title": "Set Intersection Size At Least Two",
    "leetcode_id": 757,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/set-intersection-size-at-least-two/",
    "canonicalSlug": "set-intersection-size-at-least-two",
    "canonicalUrl": "https://leetcode.com/problems/set-intersection-size-at-least-two/",
    "url": "https://leetcode.com/problems/set-intersection-size-at-least-two/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Set Intersection Size At Least Two\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Set Intersection Size At Least Two\n};",
        "java": "// Java Solution for Set Intersection Size At Least Two\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Set Intersection Size At Least Two\n}",
        "python": "# Python Solution for Set Intersection Size At Least Two\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Set Intersection Size At Least Two\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Set Intersection Size At Least Two\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Set Intersection Size At Least Two\n};",
        "java": "// Optimal Java Solution for Set Intersection Size At Least Two\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Set Intersection Size At Least Two\n}",
        "python": "# Optimal Python Solution for Set Intersection Size At Least Two\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Set Intersection Size At Least Two\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Set Intersection Size At Least Two",
      "cpp_optimal": "// Solution for Set Intersection Size At Least Two",
      "java_brute": "// Solution for Set Intersection Size At Least Two",
      "java_optimal": "// Solution for Set Intersection Size At Least Two",
      "python_brute": "# Solution for Set Intersection Size At Least Two",
      "python_optimal": "# Solution for Set Intersection Size At Least Two"
    },
    "originalOrder": 734,
    "learningOrder": 734
  },
  {
    "id": 199,
    "number": 199,
    "sequence_number": 199,
    "title": "Special Binary String",
    "slug": "special-binary-string",
    "difficulty": "Hard",
    "topic": "Arrays",
    "subtopic": "Arrays Optimization",
    "pattern": "Arrays Pattern",
    "secondary_patterns": [
      "Arrays Pattern"
    ],
    "stage": "Prefix Sum & Sorting Techniques",
    "curriculumStage": "Stage 4 — Prefix Sum & Sorting Techniques",
    "roadmapPhase": "Stage 4 — Prefix Sum & Sorting Techniques",
    "phase": "Stage 4 — Prefix Sum & Sorting Techniques",
    "estimatedTime": 45,
    "statement": "Solve the **Special Binary String** problem using standard Arrays techniques. Given input constraints appropriate for Hard level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Arrays algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Arrays properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Arrays techniques by solving Hard problem constraints for Special Binary String.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/special-binary-string/",
    "leetcode_title": "Special Binary String",
    "leetcode_id": 761,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/special-binary-string/",
    "canonicalSlug": "special-binary-string",
    "canonicalUrl": "https://leetcode.com/problems/special-binary-string/",
    "url": "https://leetcode.com/problems/special-binary-string/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Special Binary String\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Special Binary String\n};",
        "java": "// Java Solution for Special Binary String\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Special Binary String\n}",
        "python": "# Python Solution for Special Binary String\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Special Binary String\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Special Binary String\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Special Binary String\n};",
        "java": "// Optimal Java Solution for Special Binary String\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Special Binary String\n}",
        "python": "# Optimal Python Solution for Special Binary String\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Special Binary String\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Special Binary String",
      "cpp_optimal": "// Solution for Special Binary String",
      "java_brute": "// Solution for Special Binary String",
      "java_optimal": "// Solution for Special Binary String",
      "python_brute": "# Solution for Special Binary String",
      "python_optimal": "# Solution for Special Binary String"
    },
    "originalOrder": 735,
    "learningOrder": 735
  },
  {
    "id": 200,
    "number": 200,
    "sequence_number": 200,
    "title": "Count Unique Characters of All Substrings of a Given String",
    "slug": "count-unique-characters-of-all-substrings-of-a-given-string",
    "difficulty": "Hard",
    "topic": "Arrays",
    "subtopic": "Arrays Optimization",
    "pattern": "Arrays Pattern",
    "secondary_patterns": [
      "Arrays Pattern"
    ],
    "stage": "Prefix Sum & Sorting Techniques",
    "curriculumStage": "Stage 4 — Prefix Sum & Sorting Techniques",
    "roadmapPhase": "Stage 4 — Prefix Sum & Sorting Techniques",
    "phase": "Stage 4 — Prefix Sum & Sorting Techniques",
    "estimatedTime": 45,
    "statement": "Solve the **Count Unique Characters of All Substrings of a Given String** problem using standard Arrays techniques. Given input constraints appropriate for Hard level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Arrays algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Arrays properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Arrays techniques by solving Hard problem constraints for Count Unique Characters of All Substrings of a Given String.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/count-unique-characters-of-all-substrings-of-a-given-string/",
    "leetcode_title": "Count Unique Characters of All Substrings of a Given String",
    "leetcode_id": 828,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/count-unique-characters-of-all-substrings-of-a-given-string/",
    "canonicalSlug": "count-unique-characters-of-all-substrings-of-a-given-string",
    "canonicalUrl": "https://leetcode.com/problems/count-unique-characters-of-all-substrings-of-a-given-string/",
    "url": "https://leetcode.com/problems/count-unique-characters-of-all-substrings-of-a-given-string/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Count Unique Characters of All Substrings of a Given String\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Count Unique Characters of All Substrings of a Given String\n};",
        "java": "// Java Solution for Count Unique Characters of All Substrings of a Given String\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Count Unique Characters of All Substrings of a Given String\n}",
        "python": "# Python Solution for Count Unique Characters of All Substrings of a Given String\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Count Unique Characters of All Substrings of a Given String\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Count Unique Characters of All Substrings of a Given String\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Count Unique Characters of All Substrings of a Given String\n};",
        "java": "// Optimal Java Solution for Count Unique Characters of All Substrings of a Given String\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Count Unique Characters of All Substrings of a Given String\n}",
        "python": "# Optimal Python Solution for Count Unique Characters of All Substrings of a Given String\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Count Unique Characters of All Substrings of a Given String\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Count Unique Characters of All Substrings of a Given String",
      "cpp_optimal": "// Solution for Count Unique Characters of All Substrings of a Given String",
      "java_brute": "// Solution for Count Unique Characters of All Substrings of a Given String",
      "java_optimal": "// Solution for Count Unique Characters of All Substrings of a Given String",
      "python_brute": "# Solution for Count Unique Characters of All Substrings of a Given String",
      "python_optimal": "# Solution for Count Unique Characters of All Substrings of a Given String"
    },
    "originalOrder": 736,
    "learningOrder": 736
  },
  {
    "id": 201,
    "number": 201,
    "sequence_number": 201,
    "title": "Implement Stack using Queues",
    "slug": "implement-stack-using-queues-challenge",
    "difficulty": "Easy",
    "topic": "Stack",
    "subtopic": "Monotonic Stack",
    "pattern": "Monotonic Stack",
    "secondary_patterns": [
      "Monotonic Stack"
    ],
    "stage": "Stack & Queue Systems",
    "curriculumStage": "Stage 5 — Stack & Queue Systems",
    "roadmapPhase": "Stage 5 — Stack & Queue Systems",
    "phase": "Stage 5 — Stack & Queue Systems",
    "estimatedTime": 15,
    "statement": "Solve the **Implement Stack using Queues Challenge** problem using the **Monotonic Stack** technique. Given input constraints appropriate for Easy level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^4",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Monotonic Stack identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Monotonic Stack. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Monotonic Stack techniques by solving Easy problem constraints for Implement Stack using Queues Challenge.",
    "whyThisPattern": "When observing stack & monotonic stack problem conditions, Monotonic Stack optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Microsoft",
      "Bloomberg",
      "Adobe"
    ],
    "companyRelevanceTier": "Medium",
    "leetcode_url": "https://leetcode.com/problems/implement-stack-using-queues/",
    "leetcode_title": "Implement Stack using Queues",
    "leetcode_id": 225,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/implement-stack-using-queues/",
    "canonicalSlug": "implement-stack-using-queues-challenge",
    "canonicalUrl": "https://leetcode.com/problems/implement-stack-using-queues/",
    "url": "https://leetcode.com/problems/implement-stack-using-queues/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Implement Stack using Queues Challenge (Monotonic Stack)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Implement Stack using Queues Challenge (Monotonic Stack)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Implement Stack using Queues Challenge (Monotonic Stack)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Implement Stack using Queues Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Implement Stack using Queues Challenge (Monotonic Stack)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Implement Stack using Queues Challenge (Monotonic Stack)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Implement Stack using Queues Challenge (Monotonic Stack)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Implement Stack using Queues Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Implement Stack using Queues",
      "cpp_optimal": "// Solution for Implement Stack using Queues",
      "java_brute": "// Solution for Implement Stack using Queues",
      "java_optimal": "// Solution for Implement Stack using Queues",
      "python_brute": "# Solution for Implement Stack using Queues",
      "python_optimal": "# Solution for Implement Stack using Queues"
    }
  },
  {
    "id": 202,
    "number": 202,
    "sequence_number": 202,
    "title": "Implement Queue using Stacks",
    "slug": "implement-queue-using-stacks-challenge",
    "difficulty": "Easy",
    "topic": "Stack",
    "subtopic": "Monotonic Stack",
    "pattern": "Monotonic Stack",
    "secondary_patterns": [
      "Monotonic Stack"
    ],
    "stage": "Stack & Queue Systems",
    "curriculumStage": "Stage 5 — Stack & Queue Systems",
    "roadmapPhase": "Stage 5 — Stack & Queue Systems",
    "phase": "Stage 5 — Stack & Queue Systems",
    "estimatedTime": 15,
    "statement": "Solve the **Implement Queue using Stacks Challenge** problem using the **Monotonic Stack** technique. Given input constraints appropriate for Easy level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^4",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Monotonic Stack identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Monotonic Stack. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Monotonic Stack techniques by solving Easy problem constraints for Implement Queue using Stacks Challenge.",
    "whyThisPattern": "When observing stack & monotonic stack problem conditions, Monotonic Stack optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Meta",
      "Uber",
      "Databricks"
    ],
    "companyRelevanceTier": "Medium",
    "leetcode_url": "https://leetcode.com/problems/implement-queue-using-stacks/",
    "leetcode_title": "Implement Queue using Stacks",
    "leetcode_id": 232,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/implement-queue-using-stacks/",
    "canonicalSlug": "implement-queue-using-stacks-challenge",
    "canonicalUrl": "https://leetcode.com/problems/implement-queue-using-stacks/",
    "url": "https://leetcode.com/problems/implement-queue-using-stacks/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Implement Queue using Stacks Challenge (Monotonic Stack)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Implement Queue using Stacks Challenge (Monotonic Stack)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Implement Queue using Stacks Challenge (Monotonic Stack)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Implement Queue using Stacks Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Implement Queue using Stacks Challenge (Monotonic Stack)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Implement Queue using Stacks Challenge (Monotonic Stack)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Implement Queue using Stacks Challenge (Monotonic Stack)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Implement Queue using Stacks Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Implement Queue using Stacks",
      "cpp_optimal": "// Solution for Implement Queue using Stacks",
      "java_brute": "// Solution for Implement Queue using Stacks",
      "java_optimal": "// Solution for Implement Queue using Stacks",
      "python_brute": "# Solution for Implement Queue using Stacks",
      "python_optimal": "# Solution for Implement Queue using Stacks"
    }
  },
  {
    "id": 203,
    "number": 203,
    "sequence_number": 203,
    "title": "Valid Parentheses",
    "slug": "valid-parentheses-optimization",
    "difficulty": "Easy",
    "topic": "Stack",
    "subtopic": "Monotonic Stack",
    "pattern": "Monotonic Stack",
    "secondary_patterns": [
      "Monotonic Stack"
    ],
    "stage": "Stack & Queue Systems",
    "curriculumStage": "Stage 5 — Stack & Queue Systems",
    "roadmapPhase": "Stage 5 — Stack & Queue Systems",
    "phase": "Stage 5 — Stack & Queue Systems",
    "estimatedTime": 15,
    "statement": "Solve the **Valid Parentheses Optimization** problem using the **Monotonic Stack** technique. Given input constraints appropriate for Easy level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^4",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Monotonic Stack identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Monotonic Stack. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Monotonic Stack techniques by solving Easy problem constraints for Valid Parentheses Optimization.",
    "whyThisPattern": "When observing arrays & strings problem conditions, Monotonic Stack optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Apple",
      "Adobe",
      "Atlassian"
    ],
    "companyRelevanceTier": "Medium",
    "leetcode_url": "https://leetcode.com/problems/valid-parentheses/",
    "leetcode_title": "Valid Parentheses",
    "leetcode_id": 20,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/valid-parentheses/",
    "canonicalSlug": "valid-parentheses-optimization",
    "canonicalUrl": "https://leetcode.com/problems/valid-parentheses/",
    "url": "https://leetcode.com/problems/valid-parentheses/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Valid Parentheses Optimization (Monotonic Stack)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Valid Parentheses Optimization (Monotonic Stack)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Valid Parentheses Optimization (Monotonic Stack)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Valid Parentheses Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Valid Parentheses Optimization (Monotonic Stack)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Valid Parentheses Optimization (Monotonic Stack)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Valid Parentheses Optimization (Monotonic Stack)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Valid Parentheses Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Valid Parentheses",
      "cpp_optimal": "// Solution for Valid Parentheses",
      "java_brute": "// Solution for Valid Parentheses",
      "java_optimal": "// Solution for Valid Parentheses",
      "python_brute": "# Solution for Valid Parentheses",
      "python_optimal": "# Solution for Valid Parentheses"
    }
  },
  {
    "id": 204,
    "number": 204,
    "sequence_number": 204,
    "title": "Number of Recent Calls",
    "slug": "number-of-recent-calls",
    "difficulty": "Easy",
    "topic": "Queue",
    "subtopic": "Queue Optimization",
    "pattern": "Sliding Queue 3000ms",
    "secondary_patterns": [
      "Sliding Queue 3000ms"
    ],
    "stage": "Stack & Queue Systems",
    "curriculumStage": "Stage 5 — Stack & Queue Systems",
    "roadmapPhase": "Stage 5 — Stack & Queue Systems",
    "phase": "Stage 5 — Stack & Queue Systems",
    "estimatedTime": 15,
    "statement": "Given the constraints and input parameters for Number of Recent Calls, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Number of Recent Calls."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Number of Recent Calls.",
      "Leverage the optimal Queue pattern to reduce time complexity."
    ],
    "learningObjective": "Master Queue techniques by solving Easy problem constraints for Number of Recent Calls.",
    "whyThisPattern": "When observing Queue problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/number-of-recent-calls/",
    "leetcode_title": "Number of Recent Calls",
    "leetcode_id": 933,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/number-of-recent-calls/",
    "canonicalSlug": "number-of-recent-calls",
    "canonicalUrl": "https://leetcode.com/problems/number-of-recent-calls/",
    "url": "https://leetcode.com/problems/number-of-recent-calls/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Number of Recent Calls\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Number of Recent Calls\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Number of Recent Calls\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Number of Recent Calls\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Number of Recent Calls\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Number of Recent Calls\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Number of Recent Calls\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Number of Recent Calls\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Number of Recent Calls",
      "cpp_optimal": "// Solution for Number of Recent Calls",
      "java_brute": "// Solution for Number of Recent Calls",
      "java_optimal": "// Solution for Number of Recent Calls",
      "python_brute": "# Solution for Number of Recent Calls",
      "python_optimal": "# Solution for Number of Recent Calls"
    },
    "originalOrder": 157,
    "learningOrder": 157
  },
  {
    "id": 205,
    "number": 205,
    "sequence_number": 205,
    "title": "Rising Temperature",
    "slug": "rising-temperature",
    "difficulty": "Easy",
    "topic": "Stack",
    "subtopic": "Monotonic Stack",
    "pattern": "Monotonic Stack",
    "secondary_patterns": [
      "Monotonic Stack"
    ],
    "stage": "Stack & Queue Systems",
    "curriculumStage": "Stage 5 — Stack & Queue Systems",
    "roadmapPhase": "Stage 5 — Stack & Queue Systems",
    "phase": "Stage 5 — Stack & Queue Systems",
    "estimatedTime": 15,
    "statement": "Solve the **Rising Temperature Optimization** problem using the **Monotonic Stack** technique. Given input constraints appropriate for Easy level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^4",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Monotonic Stack identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Monotonic Stack. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Monotonic Stack techniques by solving Easy problem constraints for Rising Temperature Optimization.",
    "whyThisPattern": "When observing arrays & strings problem conditions, Monotonic Stack optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Apple",
      "Adobe",
      "Atlassian"
    ],
    "companyRelevanceTier": "Medium",
    "leetcode_url": "https://leetcode.com/problems/rising-temperature/",
    "leetcode_title": "Rising Temperature",
    "leetcode_id": 197,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/rising-temperature/",
    "canonicalSlug": "rising-temperature",
    "canonicalUrl": "https://leetcode.com/problems/rising-temperature/",
    "url": "https://leetcode.com/problems/rising-temperature/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Rising Temperature Optimization (Monotonic Stack)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Rising Temperature Optimization (Monotonic Stack)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Rising Temperature Optimization (Monotonic Stack)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Rising Temperature Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Rising Temperature Optimization (Monotonic Stack)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Rising Temperature Optimization (Monotonic Stack)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Rising Temperature Optimization (Monotonic Stack)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Rising Temperature Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Rising Temperature",
      "cpp_optimal": "// Solution for Rising Temperature",
      "java_brute": "// Solution for Rising Temperature",
      "java_optimal": "// Solution for Rising Temperature",
      "python_brute": "# Solution for Rising Temperature",
      "python_optimal": "# Solution for Rising Temperature"
    },
    "originalOrder": 164,
    "learningOrder": 164
  },
  {
    "id": 206,
    "number": 206,
    "sequence_number": 206,
    "title": "Next Greater Element I",
    "slug": "next-greater-element-i",
    "difficulty": "Easy",
    "topic": "Stack",
    "subtopic": "Hashing & Array Optimization",
    "pattern": "Hashing & Array Optimization",
    "secondary_patterns": [
      "Hashing & Array Optimization"
    ],
    "stage": "Stack & Queue Systems",
    "curriculumStage": "Stage 5 — Stack & Queue Systems",
    "roadmapPhase": "Stage 5 — Stack & Queue Systems",
    "phase": "Stage 5 — Stack & Queue Systems",
    "estimatedTime": 15,
    "statement": "Solve the **Next Greater Element I Challenge** problem using the **Hashing & Array Optimization** technique. Given input constraints appropriate for Easy level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^4",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Hashing & Array Optimization identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Hashing & Array Optimization. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Hashing & Array Optimization techniques by solving Easy problem constraints for Next Greater Element I Challenge.",
    "whyThisPattern": "When observing arrays & strings problem conditions, Hashing & Array Optimization optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Microsoft",
      "Bloomberg",
      "Adobe"
    ],
    "companyRelevanceTier": "Medium",
    "leetcode_url": "https://leetcode.com/problems/next-greater-element-i/",
    "leetcode_title": "Next Greater Element I",
    "leetcode_id": 496,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/next-greater-element-i/",
    "canonicalSlug": "next-greater-element-i",
    "canonicalUrl": "https://leetcode.com/problems/next-greater-element-i/",
    "url": "https://leetcode.com/problems/next-greater-element-i/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Next Greater Element I Challenge (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Next Greater Element I Challenge (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Next Greater Element I Challenge (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Next Greater Element I Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Next Greater Element I Challenge (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Next Greater Element I Challenge (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Next Greater Element I Challenge (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Next Greater Element I Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Next Greater Element I",
      "cpp_optimal": "// Solution for Next Greater Element I",
      "java_brute": "// Solution for Next Greater Element I",
      "java_optimal": "// Solution for Next Greater Element I",
      "python_brute": "# Solution for Next Greater Element I",
      "python_optimal": "# Solution for Next Greater Element I"
    },
    "originalOrder": 165,
    "learningOrder": 165
  },
  {
    "id": 207,
    "number": 207,
    "sequence_number": 207,
    "title": "Remove Outermost Parentheses",
    "slug": "remove-outermost-parentheses",
    "difficulty": "Easy",
    "topic": "Stack",
    "subtopic": "Monotonic Stack",
    "pattern": "Monotonic Stack",
    "secondary_patterns": [
      "Monotonic Stack"
    ],
    "stage": "Stack & Queue Systems",
    "curriculumStage": "Stage 5 — Stack & Queue Systems",
    "roadmapPhase": "Stage 5 — Stack & Queue Systems",
    "phase": "Stage 5 — Stack & Queue Systems",
    "estimatedTime": 15,
    "statement": "Solve the **Remove Outermost Parentheses Challenge** problem using the **Monotonic Stack** technique. Given input constraints appropriate for Easy level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^4",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Monotonic Stack identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Monotonic Stack. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Monotonic Stack techniques by solving Easy problem constraints for Remove Outermost Parentheses Challenge.",
    "whyThisPattern": "When observing arrays & strings problem conditions, Monotonic Stack optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Amazon",
      "Microsoft",
      "Uber"
    ],
    "companyRelevanceTier": "Medium",
    "leetcode_url": "https://leetcode.com/problems/remove-outermost-parentheses/",
    "leetcode_title": "Remove Outermost Parentheses",
    "leetcode_id": 1021,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/remove-outermost-parentheses/",
    "canonicalSlug": "remove-outermost-parentheses",
    "canonicalUrl": "https://leetcode.com/problems/remove-outermost-parentheses/",
    "url": "https://leetcode.com/problems/remove-outermost-parentheses/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Remove Outermost Parentheses Challenge (Monotonic Stack)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Remove Outermost Parentheses Challenge (Monotonic Stack)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Remove Outermost Parentheses Challenge (Monotonic Stack)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Remove Outermost Parentheses Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Remove Outermost Parentheses Challenge (Monotonic Stack)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Remove Outermost Parentheses Challenge (Monotonic Stack)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Remove Outermost Parentheses Challenge (Monotonic Stack)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Remove Outermost Parentheses Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Remove Outermost Parentheses",
      "cpp_optimal": "// Solution for Remove Outermost Parentheses",
      "java_brute": "// Solution for Remove Outermost Parentheses",
      "java_optimal": "// Solution for Remove Outermost Parentheses",
      "python_brute": "# Solution for Remove Outermost Parentheses",
      "python_optimal": "# Solution for Remove Outermost Parentheses"
    },
    "originalOrder": 166,
    "learningOrder": 166
  },
  {
    "id": 208,
    "number": 208,
    "sequence_number": 208,
    "title": "Baseball Game",
    "slug": "baseball-game",
    "difficulty": "Easy",
    "topic": "Stack",
    "subtopic": "Stack Optimization",
    "pattern": "Stack Score Simulation",
    "secondary_patterns": [
      "Stack Score Simulation"
    ],
    "stage": "Stack & Queue Systems",
    "curriculumStage": "Stage 5 — Stack & Queue Systems",
    "roadmapPhase": "Stage 5 — Stack & Queue Systems",
    "phase": "Stage 5 — Stack & Queue Systems",
    "estimatedTime": 15,
    "statement": "Given the constraints and input parameters for Baseball Game, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Baseball Game."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Baseball Game.",
      "Leverage the optimal Stack pattern to reduce time complexity."
    ],
    "learningObjective": "Master Stack techniques by solving Easy problem constraints for Baseball Game.",
    "whyThisPattern": "When observing Stack problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/baseball-game/",
    "leetcode_title": "Baseball Game",
    "leetcode_id": 682,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/baseball-game/",
    "canonicalSlug": "baseball-game",
    "canonicalUrl": "https://leetcode.com/problems/baseball-game/",
    "url": "https://leetcode.com/problems/baseball-game/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Baseball Game\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Baseball Game\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Baseball Game\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Baseball Game\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Baseball Game\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Baseball Game\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Baseball Game\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Baseball Game\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Baseball Game",
      "cpp_optimal": "// Solution for Baseball Game",
      "java_brute": "// Solution for Baseball Game",
      "java_optimal": "// Solution for Baseball Game",
      "python_brute": "# Solution for Baseball Game",
      "python_optimal": "# Solution for Baseball Game"
    },
    "originalOrder": 167,
    "learningOrder": 167
  },
  {
    "id": 209,
    "number": 209,
    "sequence_number": 209,
    "title": "Remove All Adjacent Duplicates In String",
    "slug": "remove-all-adjacent-duplicates-in-string",
    "difficulty": "Easy",
    "topic": "Stack",
    "subtopic": "Stack Optimization",
    "pattern": "Char Stack Deduplication",
    "secondary_patterns": [
      "Char Stack Deduplication"
    ],
    "stage": "Stack & Queue Systems",
    "curriculumStage": "Stage 5 — Stack & Queue Systems",
    "roadmapPhase": "Stage 5 — Stack & Queue Systems",
    "phase": "Stage 5 — Stack & Queue Systems",
    "estimatedTime": 15,
    "statement": "Given the constraints and input parameters for Remove All Adjacent Duplicates In String, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Remove All Adjacent Duplicates In String."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Remove All Adjacent Duplicates In String.",
      "Leverage the optimal Stack pattern to reduce time complexity."
    ],
    "learningObjective": "Master Stack techniques by solving Easy problem constraints for Remove All Adjacent Duplicates In String.",
    "whyThisPattern": "When observing Stack problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/remove-all-adjacent-duplicates-in-string/",
    "leetcode_title": "Remove All Adjacent Duplicates In String",
    "leetcode_id": 1047,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/remove-all-adjacent-duplicates-in-string/",
    "canonicalSlug": "remove-all-adjacent-duplicates-in-string",
    "canonicalUrl": "https://leetcode.com/problems/remove-all-adjacent-duplicates-in-string/",
    "url": "https://leetcode.com/problems/remove-all-adjacent-duplicates-in-string/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Remove All Adjacent Duplicates In String\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Remove All Adjacent Duplicates In String\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Remove All Adjacent Duplicates In String\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Remove All Adjacent Duplicates In String\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Remove All Adjacent Duplicates In String\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Remove All Adjacent Duplicates In String\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Remove All Adjacent Duplicates In String\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Remove All Adjacent Duplicates In String\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Remove All Adjacent Duplicates In String",
      "cpp_optimal": "// Solution for Remove All Adjacent Duplicates In String",
      "java_brute": "// Solution for Remove All Adjacent Duplicates In String",
      "java_optimal": "// Solution for Remove All Adjacent Duplicates In String",
      "python_brute": "# Solution for Remove All Adjacent Duplicates In String",
      "python_optimal": "# Solution for Remove All Adjacent Duplicates In String"
    },
    "originalOrder": 168,
    "learningOrder": 168
  },
  {
    "id": 210,
    "number": 210,
    "sequence_number": 210,
    "title": "Employees Earning More Than Their Managers",
    "slug": "employees-earning-more-than-their-managers-optimization",
    "difficulty": "Easy",
    "topic": "Strings",
    "subtopic": "Hashing & Array Optimization",
    "pattern": "Hashing & Array Optimization",
    "secondary_patterns": [
      "Hashing & Array Optimization"
    ],
    "stage": "Stack & Queue Systems",
    "curriculumStage": "Stage 5 — Stack & Queue Systems",
    "roadmapPhase": "Stage 5 — Stack & Queue Systems",
    "phase": "Stage 5 — Stack & Queue Systems",
    "estimatedTime": 15,
    "statement": "Solve the **Employees Earning More Than Their Managers Optimization** problem using the **Hashing & Array Optimization** technique. Given input constraints appropriate for Easy level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^4",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Hashing & Array Optimization identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Hashing & Array Optimization. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Hashing & Array Optimization techniques by solving Easy problem constraints for Employees Earning More Than Their Managers Optimization.",
    "whyThisPattern": "When observing arrays & strings problem conditions, Hashing & Array Optimization optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta"
    ],
    "companyRelevanceTier": "Medium",
    "leetcode_url": "https://leetcode.com/problems/employees-earning-more-than-their-managers/",
    "leetcode_title": "Employees Earning More Than Their Managers",
    "leetcode_id": 181,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/employees-earning-more-than-their-managers/",
    "canonicalSlug": "employees-earning-more-than-their-managers-optimization",
    "canonicalUrl": "https://leetcode.com/problems/employees-earning-more-than-their-managers/",
    "url": "https://leetcode.com/problems/employees-earning-more-than-their-managers/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Employees Earning More Than Their Managers Optimization (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Employees Earning More Than Their Managers Optimization (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Employees Earning More Than Their Managers Optimization (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Employees Earning More Than Their Managers Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Employees Earning More Than Their Managers Optimization (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Employees Earning More Than Their Managers Optimization (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Employees Earning More Than Their Managers Optimization (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Employees Earning More Than Their Managers Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Employees Earning More Than Their Managers",
      "cpp_optimal": "// Solution for Employees Earning More Than Their Managers",
      "java_brute": "// Solution for Employees Earning More Than Their Managers",
      "java_optimal": "// Solution for Employees Earning More Than Their Managers",
      "python_brute": "# Solution for Employees Earning More Than Their Managers",
      "python_optimal": "# Solution for Employees Earning More Than Their Managers"
    }
  },
  {
    "id": 211,
    "number": 211,
    "sequence_number": 211,
    "title": "Circular Array Loop",
    "slug": "circular-array-loop",
    "difficulty": "Medium",
    "topic": "Queue",
    "subtopic": "Arrays Optimization",
    "pattern": "Arrays Pattern",
    "secondary_patterns": [
      "Arrays Pattern"
    ],
    "stage": "Stack & Queue Systems",
    "curriculumStage": "Stage 5 — Stack & Queue Systems",
    "roadmapPhase": "Stage 5 — Stack & Queue Systems",
    "phase": "Stage 5 — Stack & Queue Systems",
    "estimatedTime": 30,
    "statement": "Solve the **Circular Array Loop** problem using standard Arrays techniques. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Arrays algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Arrays properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Arrays techniques by solving Medium problem constraints for Circular Array Loop.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/circular-array-loop/",
    "leetcode_title": "Circular Array Loop",
    "leetcode_id": 457,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/circular-array-loop/",
    "canonicalSlug": "circular-array-loop",
    "canonicalUrl": "https://leetcode.com/problems/circular-array-loop/",
    "url": "https://leetcode.com/problems/circular-array-loop/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Circular Array Loop\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Circular Array Loop\n};",
        "java": "// Java Solution for Circular Array Loop\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Circular Array Loop\n}",
        "python": "# Python Solution for Circular Array Loop\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Circular Array Loop\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Circular Array Loop\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Circular Array Loop\n};",
        "java": "// Optimal Java Solution for Circular Array Loop\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Circular Array Loop\n}",
        "python": "# Optimal Python Solution for Circular Array Loop\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Circular Array Loop\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Circular Array Loop",
      "cpp_optimal": "// Solution for Circular Array Loop",
      "java_brute": "// Solution for Circular Array Loop",
      "java_optimal": "// Solution for Circular Array Loop",
      "python_brute": "# Solution for Circular Array Loop",
      "python_optimal": "# Solution for Circular Array Loop"
    },
    "originalOrder": 335,
    "learningOrder": 335
  },
  {
    "id": 212,
    "number": 212,
    "sequence_number": 212,
    "title": "Queue Reconstruction by Height",
    "slug": "queue-reconstruction-by-height",
    "difficulty": "Medium",
    "topic": "Queue",
    "subtopic": "Hashing & Array Optimization",
    "pattern": "Hashing & Array Optimization",
    "secondary_patterns": [
      "Hashing & Array Optimization"
    ],
    "stage": "Stack & Queue Systems",
    "curriculumStage": "Stage 5 — Stack & Queue Systems",
    "roadmapPhase": "Stage 5 — Stack & Queue Systems",
    "phase": "Stage 5 — Stack & Queue Systems",
    "estimatedTime": 30,
    "statement": "Solve the **Queue Reconstruction by Height Challenge** problem using the **Hashing & Array Optimization** technique. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Hashing & Array Optimization identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Hashing & Array Optimization. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Hashing & Array Optimization techniques by solving Medium problem constraints for Queue Reconstruction by Height Challenge.",
    "whyThisPattern": "When observing queue & deque problem conditions, Hashing & Array Optimization optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Microsoft",
      "Bloomberg"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/queue-reconstruction-by-height/",
    "leetcode_title": "Queue Reconstruction by Height",
    "leetcode_id": 406,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/queue-reconstruction-by-height/",
    "canonicalSlug": "queue-reconstruction-by-height",
    "canonicalUrl": "https://leetcode.com/problems/queue-reconstruction-by-height/",
    "url": "https://leetcode.com/problems/queue-reconstruction-by-height/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Queue Reconstruction by Height Challenge (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Queue Reconstruction by Height Challenge (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Queue Reconstruction by Height Challenge (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Queue Reconstruction by Height Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Queue Reconstruction by Height Challenge (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Queue Reconstruction by Height Challenge (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Queue Reconstruction by Height Challenge (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Queue Reconstruction by Height Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Queue Reconstruction by Height",
      "cpp_optimal": "// Solution for Queue Reconstruction by Height",
      "java_brute": "// Solution for Queue Reconstruction by Height",
      "java_optimal": "// Solution for Queue Reconstruction by Height",
      "python_brute": "# Solution for Queue Reconstruction by Height",
      "python_optimal": "# Solution for Queue Reconstruction by Height"
    },
    "originalOrder": 572,
    "learningOrder": 572
  },
  {
    "id": 213,
    "number": 213,
    "sequence_number": 213,
    "title": "Design Circular Queue",
    "slug": "design-circular-queue",
    "difficulty": "Medium",
    "topic": "Queue",
    "subtopic": "Hashing & Array Optimization",
    "pattern": "Hashing & Array Optimization",
    "secondary_patterns": [
      "Hashing & Array Optimization"
    ],
    "stage": "Stack & Queue Systems",
    "curriculumStage": "Stage 5 — Stack & Queue Systems",
    "roadmapPhase": "Stage 5 — Stack & Queue Systems",
    "phase": "Stage 5 — Stack & Queue Systems",
    "estimatedTime": 30,
    "statement": "Solve the **Design Circular Queue Challenge** problem using the **Hashing & Array Optimization** technique. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Hashing & Array Optimization identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Hashing & Array Optimization. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Hashing & Array Optimization techniques by solving Medium problem constraints for Design Circular Queue Challenge.",
    "whyThisPattern": "When observing queue & deque problem conditions, Hashing & Array Optimization optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Amazon",
      "Microsoft",
      "Uber"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/design-circular-queue/",
    "leetcode_title": "Design Circular Queue",
    "leetcode_id": 622,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/design-circular-queue/",
    "canonicalSlug": "design-circular-queue",
    "canonicalUrl": "https://leetcode.com/problems/design-circular-queue/",
    "url": "https://leetcode.com/problems/design-circular-queue/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Design Circular Queue Challenge (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Design Circular Queue Challenge (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Design Circular Queue Challenge (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Design Circular Queue Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Design Circular Queue Challenge (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Design Circular Queue Challenge (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Design Circular Queue Challenge (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Design Circular Queue Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Design Circular Queue",
      "cpp_optimal": "// Solution for Design Circular Queue",
      "java_brute": "// Solution for Design Circular Queue",
      "java_optimal": "// Solution for Design Circular Queue",
      "python_brute": "# Solution for Design Circular Queue",
      "python_optimal": "# Solution for Design Circular Queue"
    },
    "originalOrder": 573,
    "learningOrder": 573
  },
  {
    "id": 214,
    "number": 214,
    "sequence_number": 214,
    "title": "Design Circular Deque",
    "slug": "design-circular-deque",
    "difficulty": "Medium",
    "topic": "Queue",
    "subtopic": "Hashing & Array Optimization",
    "pattern": "Hashing & Array Optimization",
    "secondary_patterns": [
      "Hashing & Array Optimization"
    ],
    "stage": "Stack & Queue Systems",
    "curriculumStage": "Stage 5 — Stack & Queue Systems",
    "roadmapPhase": "Stage 5 — Stack & Queue Systems",
    "phase": "Stage 5 — Stack & Queue Systems",
    "estimatedTime": 30,
    "statement": "Solve the **Design Circular Deque Challenge** problem using the **Hashing & Array Optimization** technique. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Hashing & Array Optimization identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Hashing & Array Optimization. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Hashing & Array Optimization techniques by solving Medium problem constraints for Design Circular Deque Challenge.",
    "whyThisPattern": "When observing arrays & strings problem conditions, Hashing & Array Optimization optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Microsoft",
      "Bloomberg",
      "Adobe"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/design-circular-deque/",
    "leetcode_title": "Design Circular Deque",
    "leetcode_id": 641,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/design-circular-deque/",
    "canonicalSlug": "design-circular-deque",
    "canonicalUrl": "https://leetcode.com/problems/design-circular-deque/",
    "url": "https://leetcode.com/problems/design-circular-deque/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Design Circular Deque Challenge (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Design Circular Deque Challenge (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Design Circular Deque Challenge (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Design Circular Deque Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Design Circular Deque Challenge (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Design Circular Deque Challenge (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Design Circular Deque Challenge (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Design Circular Deque Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Design Circular Deque",
      "cpp_optimal": "// Solution for Design Circular Deque",
      "java_brute": "// Solution for Design Circular Deque",
      "java_optimal": "// Solution for Design Circular Deque",
      "python_brute": "# Solution for Design Circular Deque",
      "python_optimal": "# Solution for Design Circular Deque"
    },
    "originalOrder": 574,
    "learningOrder": 574
  },
  {
    "id": 215,
    "number": 215,
    "sequence_number": 215,
    "title": "Reveal Cards In Increasing Order",
    "slug": "reveal-cards-in-increasing-order",
    "difficulty": "Medium",
    "topic": "Queue",
    "subtopic": "Queue Optimization",
    "pattern": "Reverse Queue Simulation",
    "secondary_patterns": [
      "Reverse Queue Simulation"
    ],
    "stage": "Stack & Queue Systems",
    "curriculumStage": "Stage 5 — Stack & Queue Systems",
    "roadmapPhase": "Stage 5 — Stack & Queue Systems",
    "phase": "Stage 5 — Stack & Queue Systems",
    "estimatedTime": 30,
    "statement": "Given the constraints and input parameters for Reveal Cards In Increasing Order, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Reveal Cards In Increasing Order."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Reveal Cards In Increasing Order.",
      "Leverage the optimal Queue pattern to reduce time complexity."
    ],
    "learningObjective": "Master Queue techniques by solving Medium problem constraints for Reveal Cards In Increasing Order.",
    "whyThisPattern": "When observing Queue problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/reveal-cards-in-increasing-order/",
    "leetcode_title": "Reveal Cards In Increasing Order",
    "leetcode_id": 950,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/reveal-cards-in-increasing-order/",
    "canonicalSlug": "reveal-cards-in-increasing-order",
    "canonicalUrl": "https://leetcode.com/problems/reveal-cards-in-increasing-order/",
    "url": "https://leetcode.com/problems/reveal-cards-in-increasing-order/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Reveal Cards In Increasing Order\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Reveal Cards In Increasing Order\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Reveal Cards In Increasing Order\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Reveal Cards In Increasing Order\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Reveal Cards In Increasing Order\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Reveal Cards In Increasing Order\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Reveal Cards In Increasing Order\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Reveal Cards In Increasing Order\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Reveal Cards In Increasing Order",
      "cpp_optimal": "// Solution for Reveal Cards In Increasing Order",
      "java_brute": "// Solution for Reveal Cards In Increasing Order",
      "java_optimal": "// Solution for Reveal Cards In Increasing Order",
      "python_brute": "# Solution for Reveal Cards In Increasing Order",
      "python_optimal": "# Solution for Reveal Cards In Increasing Order"
    },
    "originalOrder": 575,
    "learningOrder": 575
  },
  {
    "id": 216,
    "number": 216,
    "sequence_number": 216,
    "title": "Design Front Middle Back Queue",
    "slug": "design-front-middle-back-queue",
    "difficulty": "Medium",
    "topic": "Queue",
    "subtopic": "Queue Optimization",
    "pattern": "Two Deques Balance",
    "secondary_patterns": [
      "Two Deques Balance"
    ],
    "stage": "Stack & Queue Systems",
    "curriculumStage": "Stage 5 — Stack & Queue Systems",
    "roadmapPhase": "Stage 5 — Stack & Queue Systems",
    "phase": "Stage 5 — Stack & Queue Systems",
    "estimatedTime": 30,
    "statement": "Given the constraints and input parameters for Design Front Middle Back Queue, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Design Front Middle Back Queue."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Design Front Middle Back Queue.",
      "Leverage the optimal Queue pattern to reduce time complexity."
    ],
    "learningObjective": "Master Queue techniques by solving Medium problem constraints for Design Front Middle Back Queue.",
    "whyThisPattern": "When observing Queue problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/design-front-middle-back-queue/",
    "leetcode_title": "Design Front Middle Back Queue",
    "leetcode_id": 1670,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/design-front-middle-back-queue/",
    "canonicalSlug": "design-front-middle-back-queue",
    "canonicalUrl": "https://leetcode.com/problems/design-front-middle-back-queue/",
    "url": "https://leetcode.com/problems/design-front-middle-back-queue/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Design Front Middle Back Queue\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Design Front Middle Back Queue\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Design Front Middle Back Queue\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Design Front Middle Back Queue\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Design Front Middle Back Queue\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Design Front Middle Back Queue\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Design Front Middle Back Queue\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Design Front Middle Back Queue\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Design Front Middle Back Queue",
      "cpp_optimal": "// Solution for Design Front Middle Back Queue",
      "java_brute": "// Solution for Design Front Middle Back Queue",
      "java_optimal": "// Solution for Design Front Middle Back Queue",
      "python_brute": "# Solution for Design Front Middle Back Queue",
      "python_optimal": "# Solution for Design Front Middle Back Queue"
    },
    "originalOrder": 576,
    "learningOrder": 576
  },
  {
    "id": 217,
    "number": 217,
    "sequence_number": 217,
    "title": "Dota2 Senate",
    "slug": "dota2-senate",
    "difficulty": "Medium",
    "topic": "Queue",
    "subtopic": "Queue Optimization",
    "pattern": "Queue Pattern",
    "secondary_patterns": [
      "Queue Pattern"
    ],
    "stage": "Stack & Queue Systems",
    "curriculumStage": "Stage 5 — Stack & Queue Systems",
    "roadmapPhase": "Stage 5 — Stack & Queue Systems",
    "phase": "Stage 5 — Stack & Queue Systems",
    "estimatedTime": 30,
    "statement": "Solve the **Dota2 Senate** problem using standard Queue techniques. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Queue algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Queue properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Queue techniques by solving Medium problem constraints for Dota2 Senate.",
    "whyThisPattern": "When observing Queue problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/dota2-senate/",
    "leetcode_title": "Dota2 Senate",
    "leetcode_id": 649,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/dota2-senate/",
    "canonicalSlug": "dota2-senate",
    "canonicalUrl": "https://leetcode.com/problems/dota2-senate/",
    "url": "https://leetcode.com/problems/dota2-senate/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Dota2 Senate\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Dota2 Senate\n};",
        "java": "// Java Solution for Dota2 Senate\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Dota2 Senate\n}",
        "python": "# Python Solution for Dota2 Senate\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Dota2 Senate\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Dota2 Senate\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Dota2 Senate\n};",
        "java": "// Optimal Java Solution for Dota2 Senate\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Dota2 Senate\n}",
        "python": "# Optimal Python Solution for Dota2 Senate\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Dota2 Senate\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Dota2 Senate",
      "cpp_optimal": "// Solution for Dota2 Senate",
      "java_brute": "// Solution for Dota2 Senate",
      "java_optimal": "// Solution for Dota2 Senate",
      "python_brute": "# Solution for Dota2 Senate",
      "python_optimal": "# Solution for Dota2 Senate"
    },
    "originalOrder": 577,
    "learningOrder": 577
  },
  {
    "id": 218,
    "number": 218,
    "sequence_number": 218,
    "title": "Find the Winner of the Circular Game",
    "slug": "find-the-winner-of-the-circular-game",
    "difficulty": "Medium",
    "topic": "Queue",
    "subtopic": "Queue Optimization",
    "pattern": "Queue Pattern",
    "secondary_patterns": [
      "Queue Pattern"
    ],
    "stage": "Stack & Queue Systems",
    "curriculumStage": "Stage 5 — Stack & Queue Systems",
    "roadmapPhase": "Stage 5 — Stack & Queue Systems",
    "phase": "Stage 5 — Stack & Queue Systems",
    "estimatedTime": 30,
    "statement": "Solve the **Find the Winner of the Circular Game** problem using standard Queue techniques. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Queue algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Queue properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Queue techniques by solving Medium problem constraints for Find the Winner of the Circular Game.",
    "whyThisPattern": "When observing Queue problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/find-the-winner-of-the-circular-game/",
    "leetcode_title": "Find the Winner of the Circular Game",
    "leetcode_id": 1823,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/find-the-winner-of-the-circular-game/",
    "canonicalSlug": "find-the-winner-of-the-circular-game",
    "canonicalUrl": "https://leetcode.com/problems/find-the-winner-of-the-circular-game/",
    "url": "https://leetcode.com/problems/find-the-winner-of-the-circular-game/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Find the Winner of the Circular Game\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Find the Winner of the Circular Game\n};",
        "java": "// Java Solution for Find the Winner of the Circular Game\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Find the Winner of the Circular Game\n}",
        "python": "# Python Solution for Find the Winner of the Circular Game\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Find the Winner of the Circular Game\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Find the Winner of the Circular Game\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Find the Winner of the Circular Game\n};",
        "java": "// Optimal Java Solution for Find the Winner of the Circular Game\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Find the Winner of the Circular Game\n}",
        "python": "# Optimal Python Solution for Find the Winner of the Circular Game\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Find the Winner of the Circular Game\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Find the Winner of the Circular Game",
      "cpp_optimal": "// Solution for Find the Winner of the Circular Game",
      "java_brute": "// Solution for Find the Winner of the Circular Game",
      "java_optimal": "// Solution for Find the Winner of the Circular Game",
      "python_brute": "# Solution for Find the Winner of the Circular Game",
      "python_optimal": "# Solution for Find the Winner of the Circular Game"
    },
    "originalOrder": 578,
    "learningOrder": 578
  },
  {
    "id": 219,
    "number": 219,
    "sequence_number": 219,
    "title": "Min Stack",
    "slug": "min-stack",
    "difficulty": "Medium",
    "topic": "Stack",
    "subtopic": "Monotonic Stack",
    "pattern": "Monotonic Stack",
    "secondary_patterns": [
      "Monotonic Stack"
    ],
    "stage": "Stack & Queue Systems",
    "curriculumStage": "Stage 5 — Stack & Queue Systems",
    "roadmapPhase": "Stage 5 — Stack & Queue Systems",
    "phase": "Stage 5 — Stack & Queue Systems",
    "estimatedTime": 30,
    "statement": "Solve the **Min Stack Challenge** problem using the **Monotonic Stack** technique. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Monotonic Stack identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Monotonic Stack. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Monotonic Stack techniques by solving Medium problem constraints for Min Stack Challenge.",
    "whyThisPattern": "When observing stack & monotonic stack problem conditions, Monotonic Stack optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Meta",
      "Uber",
      "Databricks"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/min-stack/",
    "leetcode_title": "Min Stack",
    "leetcode_id": 155,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/min-stack/",
    "canonicalSlug": "min-stack",
    "canonicalUrl": "https://leetcode.com/problems/min-stack/",
    "url": "https://leetcode.com/problems/min-stack/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Min Stack Challenge (Monotonic Stack)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Min Stack Challenge (Monotonic Stack)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Min Stack Challenge (Monotonic Stack)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Min Stack Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Min Stack Challenge (Monotonic Stack)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Min Stack Challenge (Monotonic Stack)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Min Stack Challenge (Monotonic Stack)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Min Stack Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Min Stack",
      "cpp_optimal": "// Solution for Min Stack",
      "java_brute": "// Solution for Min Stack",
      "java_optimal": "// Solution for Min Stack",
      "python_brute": "# Solution for Min Stack",
      "python_optimal": "# Solution for Min Stack"
    },
    "originalOrder": 604,
    "learningOrder": 604
  },
  {
    "id": 220,
    "number": 220,
    "sequence_number": 220,
    "title": "Validate Stack Sequences",
    "slug": "validate-stack-sequences",
    "difficulty": "Medium",
    "topic": "Stack",
    "subtopic": "Monotonic Stack",
    "pattern": "Monotonic Stack",
    "secondary_patterns": [
      "Monotonic Stack"
    ],
    "stage": "Stack & Queue Systems",
    "curriculumStage": "Stage 5 — Stack & Queue Systems",
    "roadmapPhase": "Stage 5 — Stack & Queue Systems",
    "phase": "Stage 5 — Stack & Queue Systems",
    "estimatedTime": 30,
    "statement": "Solve the **Validate Stack Sequences Challenge** problem using the **Monotonic Stack** technique. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Monotonic Stack identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Monotonic Stack. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Monotonic Stack techniques by solving Medium problem constraints for Validate Stack Sequences Challenge.",
    "whyThisPattern": "When observing stack & monotonic stack problem conditions, Monotonic Stack optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Microsoft",
      "Bloomberg",
      "Adobe"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/validate-stack-sequences/",
    "leetcode_title": "Validate Stack Sequences",
    "leetcode_id": 946,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/validate-stack-sequences/",
    "canonicalSlug": "validate-stack-sequences",
    "canonicalUrl": "https://leetcode.com/problems/validate-stack-sequences/",
    "url": "https://leetcode.com/problems/validate-stack-sequences/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Validate Stack Sequences Challenge (Monotonic Stack)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Validate Stack Sequences Challenge (Monotonic Stack)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Validate Stack Sequences Challenge (Monotonic Stack)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Validate Stack Sequences Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Validate Stack Sequences Challenge (Monotonic Stack)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Validate Stack Sequences Challenge (Monotonic Stack)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Validate Stack Sequences Challenge (Monotonic Stack)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Validate Stack Sequences Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Validate Stack Sequences",
      "cpp_optimal": "// Solution for Validate Stack Sequences",
      "java_brute": "// Solution for Validate Stack Sequences",
      "java_optimal": "// Solution for Validate Stack Sequences",
      "python_brute": "# Solution for Validate Stack Sequences",
      "python_optimal": "# Solution for Validate Stack Sequences"
    },
    "originalOrder": 605,
    "learningOrder": 605
  },
  {
    "id": 221,
    "number": 221,
    "sequence_number": 221,
    "title": "Generate Parentheses",
    "slug": "generate-parentheses",
    "difficulty": "Medium",
    "topic": "Stack",
    "subtopic": "Monotonic Stack",
    "pattern": "Monotonic Stack",
    "secondary_patterns": [
      "Monotonic Stack"
    ],
    "stage": "Stack & Queue Systems",
    "curriculumStage": "Stage 5 — Stack & Queue Systems",
    "roadmapPhase": "Stage 5 — Stack & Queue Systems",
    "phase": "Stage 5 — Stack & Queue Systems",
    "estimatedTime": 30,
    "statement": "Solve the **Generate Parentheses Optimization** problem using the **Monotonic Stack** technique. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Monotonic Stack identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Monotonic Stack. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Monotonic Stack techniques by solving Medium problem constraints for Generate Parentheses Optimization.",
    "whyThisPattern": "When observing arrays & strings problem conditions, Monotonic Stack optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/generate-parentheses/",
    "leetcode_title": "Generate Parentheses",
    "leetcode_id": 22,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/generate-parentheses/",
    "canonicalSlug": "generate-parentheses",
    "canonicalUrl": "https://leetcode.com/problems/generate-parentheses/",
    "url": "https://leetcode.com/problems/generate-parentheses/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Generate Parentheses Optimization (Monotonic Stack)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Generate Parentheses Optimization (Monotonic Stack)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Generate Parentheses Optimization (Monotonic Stack)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Generate Parentheses Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Generate Parentheses Optimization (Monotonic Stack)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Generate Parentheses Optimization (Monotonic Stack)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Generate Parentheses Optimization (Monotonic Stack)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Generate Parentheses Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Generate Parentheses",
      "cpp_optimal": "// Solution for Generate Parentheses",
      "java_brute": "// Solution for Generate Parentheses",
      "java_optimal": "// Solution for Generate Parentheses",
      "python_brute": "# Solution for Generate Parentheses",
      "python_optimal": "# Solution for Generate Parentheses"
    },
    "originalOrder": 606,
    "learningOrder": 606
  },
  {
    "id": 222,
    "number": 222,
    "sequence_number": 222,
    "title": "Different Ways to Add Parentheses",
    "slug": "different-ways-to-add-parentheses",
    "difficulty": "Medium",
    "topic": "Stack",
    "subtopic": "Monotonic Stack",
    "pattern": "Monotonic Stack",
    "secondary_patterns": [
      "Monotonic Stack"
    ],
    "stage": "Stack & Queue Systems",
    "curriculumStage": "Stage 5 — Stack & Queue Systems",
    "roadmapPhase": "Stage 5 — Stack & Queue Systems",
    "phase": "Stage 5 — Stack & Queue Systems",
    "estimatedTime": 30,
    "statement": "Solve the **Different Ways to Add Parentheses Challenge** problem using the **Monotonic Stack** technique. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Monotonic Stack identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Monotonic Stack. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Monotonic Stack techniques by solving Medium problem constraints for Different Ways to Add Parentheses Challenge.",
    "whyThisPattern": "When observing arrays & strings problem conditions, Monotonic Stack optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Meta",
      "Uber",
      "Databricks"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/different-ways-to-add-parentheses/",
    "leetcode_title": "Different Ways to Add Parentheses",
    "leetcode_id": 241,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/different-ways-to-add-parentheses/",
    "canonicalSlug": "different-ways-to-add-parentheses",
    "canonicalUrl": "https://leetcode.com/problems/different-ways-to-add-parentheses/",
    "url": "https://leetcode.com/problems/different-ways-to-add-parentheses/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Different Ways to Add Parentheses Challenge (Monotonic Stack)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Different Ways to Add Parentheses Challenge (Monotonic Stack)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Different Ways to Add Parentheses Challenge (Monotonic Stack)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Different Ways to Add Parentheses Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Different Ways to Add Parentheses Challenge (Monotonic Stack)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Different Ways to Add Parentheses Challenge (Monotonic Stack)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Different Ways to Add Parentheses Challenge (Monotonic Stack)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Different Ways to Add Parentheses Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Different Ways to Add Parentheses",
      "cpp_optimal": "// Solution for Different Ways to Add Parentheses",
      "java_brute": "// Solution for Different Ways to Add Parentheses",
      "java_optimal": "// Solution for Different Ways to Add Parentheses",
      "python_brute": "# Solution for Different Ways to Add Parentheses",
      "python_optimal": "# Solution for Different Ways to Add Parentheses"
    },
    "originalOrder": 607,
    "learningOrder": 607
  },
  {
    "id": 223,
    "number": 223,
    "sequence_number": 223,
    "title": "Next Greater Element II",
    "slug": "next-greater-element-ii",
    "difficulty": "Medium",
    "topic": "Stack",
    "subtopic": "Hashing & Array Optimization",
    "pattern": "Hashing & Array Optimization",
    "secondary_patterns": [
      "Hashing & Array Optimization"
    ],
    "stage": "Stack & Queue Systems",
    "curriculumStage": "Stage 5 — Stack & Queue Systems",
    "roadmapPhase": "Stage 5 — Stack & Queue Systems",
    "phase": "Stage 5 — Stack & Queue Systems",
    "estimatedTime": 30,
    "statement": "Solve the **Next Greater Element II Challenge** problem using the **Hashing & Array Optimization** technique. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Hashing & Array Optimization identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Hashing & Array Optimization. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Hashing & Array Optimization techniques by solving Medium problem constraints for Next Greater Element II Challenge.",
    "whyThisPattern": "When observing arrays & strings problem conditions, Hashing & Array Optimization optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Meta",
      "Uber",
      "Databricks"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/next-greater-element-ii/",
    "leetcode_title": "Next Greater Element II",
    "leetcode_id": 503,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/next-greater-element-ii/",
    "canonicalSlug": "next-greater-element-ii",
    "canonicalUrl": "https://leetcode.com/problems/next-greater-element-ii/",
    "url": "https://leetcode.com/problems/next-greater-element-ii/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Next Greater Element II Challenge (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Next Greater Element II Challenge (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Next Greater Element II Challenge (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Next Greater Element II Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Next Greater Element II Challenge (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Next Greater Element II Challenge (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Next Greater Element II Challenge (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Next Greater Element II Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Next Greater Element II",
      "cpp_optimal": "// Solution for Next Greater Element II",
      "java_brute": "// Solution for Next Greater Element II",
      "java_optimal": "// Solution for Next Greater Element II",
      "python_brute": "# Solution for Next Greater Element II",
      "python_optimal": "# Solution for Next Greater Element II"
    },
    "originalOrder": 608,
    "learningOrder": 608
  },
  {
    "id": 224,
    "number": 224,
    "sequence_number": 224,
    "title": "Next Greater Element III",
    "slug": "next-greater-element-iii",
    "difficulty": "Medium",
    "topic": "Stack",
    "subtopic": "Hashing & Array Optimization",
    "pattern": "Hashing & Array Optimization",
    "secondary_patterns": [
      "Hashing & Array Optimization"
    ],
    "stage": "Stack & Queue Systems",
    "curriculumStage": "Stage 5 — Stack & Queue Systems",
    "roadmapPhase": "Stage 5 — Stack & Queue Systems",
    "phase": "Stage 5 — Stack & Queue Systems",
    "estimatedTime": 30,
    "statement": "Solve the **Next Greater Element III Optimization** problem using the **Hashing & Array Optimization** technique. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Hashing & Array Optimization identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Hashing & Array Optimization. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Hashing & Array Optimization techniques by solving Medium problem constraints for Next Greater Element III Optimization.",
    "whyThisPattern": "When observing arrays & strings problem conditions, Hashing & Array Optimization optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "LinkedIn",
      "Amazon"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/next-greater-element-iii/",
    "leetcode_title": "Next Greater Element III",
    "leetcode_id": 556,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/next-greater-element-iii/",
    "canonicalSlug": "next-greater-element-iii",
    "canonicalUrl": "https://leetcode.com/problems/next-greater-element-iii/",
    "url": "https://leetcode.com/problems/next-greater-element-iii/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Next Greater Element III Optimization (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Next Greater Element III Optimization (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Next Greater Element III Optimization (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Next Greater Element III Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Next Greater Element III Optimization (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Next Greater Element III Optimization (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Next Greater Element III Optimization (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Next Greater Element III Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Next Greater Element III",
      "cpp_optimal": "// Solution for Next Greater Element III",
      "java_brute": "// Solution for Next Greater Element III",
      "java_optimal": "// Solution for Next Greater Element III",
      "python_brute": "# Solution for Next Greater Element III",
      "python_optimal": "# Solution for Next Greater Element III"
    },
    "originalOrder": 609,
    "learningOrder": 609
  },
  {
    "id": 225,
    "number": 225,
    "sequence_number": 225,
    "title": "Daily Temperatures",
    "slug": "daily-temperatures",
    "difficulty": "Medium",
    "topic": "Stack",
    "subtopic": "Monotonic Stack",
    "pattern": "Monotonic Stack",
    "secondary_patterns": [
      "Monotonic Stack"
    ],
    "stage": "Stack & Queue Systems",
    "curriculumStage": "Stage 5 — Stack & Queue Systems",
    "roadmapPhase": "Stage 5 — Stack & Queue Systems",
    "phase": "Stage 5 — Stack & Queue Systems",
    "estimatedTime": 30,
    "statement": "Solve the **Daily Temperatures Optimization** problem using the **Monotonic Stack** technique. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Monotonic Stack identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Monotonic Stack. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Monotonic Stack techniques by solving Medium problem constraints for Daily Temperatures Optimization.",
    "whyThisPattern": "When observing arrays & strings problem conditions, Monotonic Stack optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "LinkedIn",
      "Amazon"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/daily-temperatures/",
    "leetcode_title": "Daily Temperatures",
    "leetcode_id": 739,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/daily-temperatures/",
    "canonicalSlug": "daily-temperatures",
    "canonicalUrl": "https://leetcode.com/problems/daily-temperatures/",
    "url": "https://leetcode.com/problems/daily-temperatures/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Daily Temperatures Optimization (Monotonic Stack)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Daily Temperatures Optimization (Monotonic Stack)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Daily Temperatures Optimization (Monotonic Stack)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Daily Temperatures Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Daily Temperatures Optimization (Monotonic Stack)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Daily Temperatures Optimization (Monotonic Stack)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Daily Temperatures Optimization (Monotonic Stack)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Daily Temperatures Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Daily Temperatures",
      "cpp_optimal": "// Solution for Daily Temperatures",
      "java_brute": "// Solution for Daily Temperatures",
      "java_optimal": "// Solution for Daily Temperatures",
      "python_brute": "# Solution for Daily Temperatures",
      "python_optimal": "# Solution for Daily Temperatures"
    },
    "originalOrder": 610,
    "learningOrder": 610
  },
  {
    "id": 226,
    "number": 226,
    "sequence_number": 226,
    "title": "Score of Parentheses",
    "slug": "score-of-parentheses",
    "difficulty": "Medium",
    "topic": "Stack",
    "subtopic": "Monotonic Stack",
    "pattern": "Monotonic Stack",
    "secondary_patterns": [
      "Monotonic Stack"
    ],
    "stage": "Stack & Queue Systems",
    "curriculumStage": "Stage 5 — Stack & Queue Systems",
    "roadmapPhase": "Stage 5 — Stack & Queue Systems",
    "phase": "Stage 5 — Stack & Queue Systems",
    "estimatedTime": 30,
    "statement": "Solve the **Score of Parentheses Challenge** problem using the **Monotonic Stack** technique. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Monotonic Stack identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Monotonic Stack. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Monotonic Stack techniques by solving Medium problem constraints for Score of Parentheses Challenge.",
    "whyThisPattern": "When observing arrays & strings problem conditions, Monotonic Stack optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Microsoft",
      "Bloomberg"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/score-of-parentheses/",
    "leetcode_title": "Score of Parentheses",
    "leetcode_id": 856,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/score-of-parentheses/",
    "canonicalSlug": "score-of-parentheses",
    "canonicalUrl": "https://leetcode.com/problems/score-of-parentheses/",
    "url": "https://leetcode.com/problems/score-of-parentheses/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Score of Parentheses Challenge (Monotonic Stack)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Score of Parentheses Challenge (Monotonic Stack)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Score of Parentheses Challenge (Monotonic Stack)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Score of Parentheses Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Score of Parentheses Challenge (Monotonic Stack)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Score of Parentheses Challenge (Monotonic Stack)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Score of Parentheses Challenge (Monotonic Stack)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Score of Parentheses Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Score of Parentheses",
      "cpp_optimal": "// Solution for Score of Parentheses",
      "java_brute": "// Solution for Score of Parentheses",
      "java_optimal": "// Solution for Score of Parentheses",
      "python_brute": "# Solution for Score of Parentheses",
      "python_optimal": "# Solution for Score of Parentheses"
    },
    "originalOrder": 611,
    "learningOrder": 611
  },
  {
    "id": 227,
    "number": 227,
    "sequence_number": 227,
    "title": "Minimum Add to Make Parentheses Valid",
    "slug": "minimum-add-to-make-parentheses-valid",
    "difficulty": "Medium",
    "topic": "Stack",
    "subtopic": "Monotonic Stack",
    "pattern": "Monotonic Stack",
    "secondary_patterns": [
      "Monotonic Stack"
    ],
    "stage": "Stack & Queue Systems",
    "curriculumStage": "Stage 5 — Stack & Queue Systems",
    "roadmapPhase": "Stage 5 — Stack & Queue Systems",
    "phase": "Stage 5 — Stack & Queue Systems",
    "estimatedTime": 30,
    "statement": "Solve the **Minimum Add to Make Parentheses Valid Challenge** problem using the **Monotonic Stack** technique. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Monotonic Stack identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Monotonic Stack. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Monotonic Stack techniques by solving Medium problem constraints for Minimum Add to Make Parentheses Valid Challenge.",
    "whyThisPattern": "When observing arrays & strings problem conditions, Monotonic Stack optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Microsoft",
      "Bloomberg",
      "Adobe"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/minimum-add-to-make-parentheses-valid/",
    "leetcode_title": "Minimum Add to Make Parentheses Valid",
    "leetcode_id": 921,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/minimum-add-to-make-parentheses-valid/",
    "canonicalSlug": "minimum-add-to-make-parentheses-valid",
    "canonicalUrl": "https://leetcode.com/problems/minimum-add-to-make-parentheses-valid/",
    "url": "https://leetcode.com/problems/minimum-add-to-make-parentheses-valid/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Minimum Add to Make Parentheses Valid Challenge (Monotonic Stack)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Minimum Add to Make Parentheses Valid Challenge (Monotonic Stack)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Minimum Add to Make Parentheses Valid Challenge (Monotonic Stack)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Minimum Add to Make Parentheses Valid Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Minimum Add to Make Parentheses Valid Challenge (Monotonic Stack)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Minimum Add to Make Parentheses Valid Challenge (Monotonic Stack)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Minimum Add to Make Parentheses Valid Challenge (Monotonic Stack)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Minimum Add to Make Parentheses Valid Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Minimum Add to Make Parentheses Valid",
      "cpp_optimal": "// Solution for Minimum Add to Make Parentheses Valid",
      "java_brute": "// Solution for Minimum Add to Make Parentheses Valid",
      "java_optimal": "// Solution for Minimum Add to Make Parentheses Valid",
      "python_brute": "# Solution for Minimum Add to Make Parentheses Valid",
      "python_optimal": "# Solution for Minimum Add to Make Parentheses Valid"
    },
    "originalOrder": 612,
    "learningOrder": 612
  },
  {
    "id": 228,
    "number": 228,
    "sequence_number": 228,
    "title": "Online Stock Span",
    "slug": "online-stock-span",
    "difficulty": "Medium",
    "topic": "Stack",
    "subtopic": "Stack Optimization",
    "pattern": "Monotonic Decreasing Stack",
    "secondary_patterns": [
      "Monotonic Decreasing Stack"
    ],
    "stage": "Stack & Queue Systems",
    "curriculumStage": "Stage 5 — Stack & Queue Systems",
    "roadmapPhase": "Stage 5 — Stack & Queue Systems",
    "phase": "Stage 5 — Stack & Queue Systems",
    "estimatedTime": 30,
    "statement": "Given the constraints and input parameters for Online Stock Span, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Online Stock Span."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Online Stock Span.",
      "Leverage the optimal Stack pattern to reduce time complexity."
    ],
    "learningObjective": "Master Stack techniques by solving Medium problem constraints for Online Stock Span.",
    "whyThisPattern": "When observing Stack problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/online-stock-span/",
    "leetcode_title": "Online Stock Span",
    "leetcode_id": 901,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/online-stock-span/",
    "canonicalSlug": "online-stock-span",
    "canonicalUrl": "https://leetcode.com/problems/online-stock-span/",
    "url": "https://leetcode.com/problems/online-stock-span/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Online Stock Span\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Online Stock Span\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Online Stock Span\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Online Stock Span\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Online Stock Span\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Online Stock Span\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Online Stock Span\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Online Stock Span\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Online Stock Span",
      "cpp_optimal": "// Solution for Online Stock Span",
      "java_brute": "// Solution for Online Stock Span",
      "java_optimal": "// Solution for Online Stock Span",
      "python_brute": "# Solution for Online Stock Span",
      "python_optimal": "# Solution for Online Stock Span"
    },
    "originalOrder": 613,
    "learningOrder": 613
  },
  {
    "id": 229,
    "number": 229,
    "sequence_number": 229,
    "title": "Maximum Width Ramp",
    "slug": "maximum-width-ramp",
    "difficulty": "Medium",
    "topic": "Stack",
    "subtopic": "Stack Optimization",
    "pattern": "Monotonic Stack Decreasing Index",
    "secondary_patterns": [
      "Monotonic Stack Decreasing Index"
    ],
    "stage": "Stack & Queue Systems",
    "curriculumStage": "Stage 5 — Stack & Queue Systems",
    "roadmapPhase": "Stage 5 — Stack & Queue Systems",
    "phase": "Stage 5 — Stack & Queue Systems",
    "estimatedTime": 30,
    "statement": "Given the constraints and input parameters for Maximum Width Ramp, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Maximum Width Ramp."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Maximum Width Ramp.",
      "Leverage the optimal Stack pattern to reduce time complexity."
    ],
    "learningObjective": "Master Stack techniques by solving Medium problem constraints for Maximum Width Ramp.",
    "whyThisPattern": "When observing Stack problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/maximum-width-ramp/",
    "leetcode_title": "Maximum Width Ramp",
    "leetcode_id": 962,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/maximum-width-ramp/",
    "canonicalSlug": "maximum-width-ramp",
    "canonicalUrl": "https://leetcode.com/problems/maximum-width-ramp/",
    "url": "https://leetcode.com/problems/maximum-width-ramp/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Maximum Width Ramp\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Maximum Width Ramp\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Maximum Width Ramp\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Maximum Width Ramp\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Maximum Width Ramp\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Maximum Width Ramp\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Maximum Width Ramp\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Maximum Width Ramp\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Maximum Width Ramp",
      "cpp_optimal": "// Solution for Maximum Width Ramp",
      "java_brute": "// Solution for Maximum Width Ramp",
      "java_optimal": "// Solution for Maximum Width Ramp",
      "python_brute": "# Solution for Maximum Width Ramp",
      "python_optimal": "# Solution for Maximum Width Ramp"
    },
    "originalOrder": 614,
    "learningOrder": 614
  },
  {
    "id": 230,
    "number": 230,
    "sequence_number": 230,
    "title": "Decoded String at Index",
    "slug": "decoded-string-at-index",
    "difficulty": "Medium",
    "topic": "Stack",
    "subtopic": "Stack Optimization",
    "pattern": "Reverse Tape Deconstruction",
    "secondary_patterns": [
      "Reverse Tape Deconstruction"
    ],
    "stage": "Stack & Queue Systems",
    "curriculumStage": "Stage 5 — Stack & Queue Systems",
    "roadmapPhase": "Stage 5 — Stack & Queue Systems",
    "phase": "Stage 5 — Stack & Queue Systems",
    "estimatedTime": 30,
    "statement": "Given the constraints and input parameters for Decoded String at Index, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Decoded String at Index."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Decoded String at Index.",
      "Leverage the optimal Stack pattern to reduce time complexity."
    ],
    "learningObjective": "Master Stack techniques by solving Medium problem constraints for Decoded String at Index.",
    "whyThisPattern": "When observing Stack problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/decoded-string-at-index/",
    "leetcode_title": "Decoded String at Index",
    "leetcode_id": 880,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/decoded-string-at-index/",
    "canonicalSlug": "decoded-string-at-index",
    "canonicalUrl": "https://leetcode.com/problems/decoded-string-at-index/",
    "url": "https://leetcode.com/problems/decoded-string-at-index/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Decoded String at Index\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Decoded String at Index\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Decoded String at Index\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Decoded String at Index\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Decoded String at Index\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Decoded String at Index\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Decoded String at Index\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Decoded String at Index\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Decoded String at Index",
      "cpp_optimal": "// Solution for Decoded String at Index",
      "java_brute": "// Solution for Decoded String at Index",
      "java_optimal": "// Solution for Decoded String at Index",
      "python_brute": "# Solution for Decoded String at Index",
      "python_optimal": "# Solution for Decoded String at Index"
    },
    "originalOrder": 615,
    "learningOrder": 615
  },
  {
    "id": 231,
    "number": 231,
    "sequence_number": 231,
    "title": "Car Fleet",
    "slug": "car-fleet",
    "difficulty": "Medium",
    "topic": "Stack",
    "subtopic": "Stack Optimization",
    "pattern": "Sort & Monotonic Time Stack",
    "secondary_patterns": [
      "Sort & Monotonic Time Stack"
    ],
    "stage": "Stack & Queue Systems",
    "curriculumStage": "Stage 5 — Stack & Queue Systems",
    "roadmapPhase": "Stage 5 — Stack & Queue Systems",
    "phase": "Stage 5 — Stack & Queue Systems",
    "estimatedTime": 30,
    "statement": "Given the constraints and input parameters for Car Fleet, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Car Fleet."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Car Fleet.",
      "Leverage the optimal Stack pattern to reduce time complexity."
    ],
    "learningObjective": "Master Stack techniques by solving Medium problem constraints for Car Fleet.",
    "whyThisPattern": "When observing Stack problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/car-fleet/",
    "leetcode_title": "Car Fleet",
    "leetcode_id": 853,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/car-fleet/",
    "canonicalSlug": "car-fleet",
    "canonicalUrl": "https://leetcode.com/problems/car-fleet/",
    "url": "https://leetcode.com/problems/car-fleet/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Car Fleet\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Car Fleet\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Car Fleet\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Car Fleet\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Car Fleet\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Car Fleet\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Car Fleet\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Car Fleet\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Car Fleet",
      "cpp_optimal": "// Solution for Car Fleet",
      "java_brute": "// Solution for Car Fleet",
      "java_optimal": "// Solution for Car Fleet",
      "python_brute": "# Solution for Car Fleet",
      "python_optimal": "# Solution for Car Fleet"
    },
    "originalOrder": 616,
    "learningOrder": 616
  },
  {
    "id": 232,
    "number": 232,
    "sequence_number": 232,
    "title": "Asteroid Collision",
    "slug": "asteroid-collision",
    "difficulty": "Medium",
    "topic": "Stack",
    "subtopic": "Stack Optimization",
    "pattern": "Stack Size Collisions",
    "secondary_patterns": [
      "Stack Size Collisions"
    ],
    "stage": "Stack & Queue Systems",
    "curriculumStage": "Stage 5 — Stack & Queue Systems",
    "roadmapPhase": "Stage 5 — Stack & Queue Systems",
    "phase": "Stage 5 — Stack & Queue Systems",
    "estimatedTime": 30,
    "statement": "Given the constraints and input parameters for Asteroid Collision, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Asteroid Collision."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Asteroid Collision.",
      "Leverage the optimal Stack pattern to reduce time complexity."
    ],
    "learningObjective": "Master Stack techniques by solving Medium problem constraints for Asteroid Collision.",
    "whyThisPattern": "When observing Stack problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/asteroid-collision/",
    "leetcode_title": "Asteroid Collision",
    "leetcode_id": 735,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/asteroid-collision/",
    "canonicalSlug": "asteroid-collision",
    "canonicalUrl": "https://leetcode.com/problems/asteroid-collision/",
    "url": "https://leetcode.com/problems/asteroid-collision/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Asteroid Collision\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Asteroid Collision\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Asteroid Collision\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Asteroid Collision\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Asteroid Collision\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Asteroid Collision\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Asteroid Collision\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Asteroid Collision\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Asteroid Collision",
      "cpp_optimal": "// Solution for Asteroid Collision",
      "java_brute": "// Solution for Asteroid Collision",
      "java_optimal": "// Solution for Asteroid Collision",
      "python_brute": "# Solution for Asteroid Collision",
      "python_optimal": "# Solution for Asteroid Collision"
    },
    "originalOrder": 617,
    "learningOrder": 617
  },
  {
    "id": 233,
    "number": 233,
    "sequence_number": 233,
    "title": "Design a Stack With Increment Operation",
    "slug": "design-a-stack-with-increment-operation",
    "difficulty": "Medium",
    "topic": "Stack",
    "subtopic": "Stack Optimization",
    "pattern": "Lazy Increment Stack",
    "secondary_patterns": [
      "Lazy Increment Stack"
    ],
    "stage": "Stack & Queue Systems",
    "curriculumStage": "Stage 5 — Stack & Queue Systems",
    "roadmapPhase": "Stage 5 — Stack & Queue Systems",
    "phase": "Stage 5 — Stack & Queue Systems",
    "estimatedTime": 30,
    "statement": "Given the constraints and input parameters for Design a Stack With Increment Operation, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Design a Stack With Increment Operation."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Design a Stack With Increment Operation.",
      "Leverage the optimal Stack pattern to reduce time complexity."
    ],
    "learningObjective": "Master Stack techniques by solving Medium problem constraints for Design a Stack With Increment Operation.",
    "whyThisPattern": "When observing Stack problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/design-a-stack-with-increment-operation/",
    "leetcode_title": "Design a Stack With Increment Operation",
    "leetcode_id": 1381,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/design-a-stack-with-increment-operation/",
    "canonicalSlug": "design-a-stack-with-increment-operation",
    "canonicalUrl": "https://leetcode.com/problems/design-a-stack-with-increment-operation/",
    "url": "https://leetcode.com/problems/design-a-stack-with-increment-operation/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Design a Stack With Increment Operation\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Design a Stack With Increment Operation\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Design a Stack With Increment Operation\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Design a Stack With Increment Operation\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Design a Stack With Increment Operation\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Design a Stack With Increment Operation\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Design a Stack With Increment Operation\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Design a Stack With Increment Operation\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Design a Stack With Increment Operation",
      "cpp_optimal": "// Solution for Design a Stack With Increment Operation",
      "java_brute": "// Solution for Design a Stack With Increment Operation",
      "java_optimal": "// Solution for Design a Stack With Increment Operation",
      "python_brute": "# Solution for Design a Stack With Increment Operation",
      "python_optimal": "# Solution for Design a Stack With Increment Operation"
    },
    "originalOrder": 618,
    "learningOrder": 618
  },
  {
    "id": 234,
    "number": 234,
    "sequence_number": 234,
    "title": "Minimum Insertions to Balance a Parentheses String",
    "slug": "minimum-insertions-to-balance-a-parentheses-string",
    "difficulty": "Medium",
    "topic": "Stack",
    "subtopic": "Stack Optimization",
    "pattern": "Greedy Right Bracket Counter",
    "secondary_patterns": [
      "Greedy Right Bracket Counter"
    ],
    "stage": "Stack & Queue Systems",
    "curriculumStage": "Stage 5 — Stack & Queue Systems",
    "roadmapPhase": "Stage 5 — Stack & Queue Systems",
    "phase": "Stage 5 — Stack & Queue Systems",
    "estimatedTime": 30,
    "statement": "Given the constraints and input parameters for Minimum Insertions to Balance a Parentheses String, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Minimum Insertions to Balance a Parentheses String."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Minimum Insertions to Balance a Parentheses String.",
      "Leverage the optimal Stack pattern to reduce time complexity."
    ],
    "learningObjective": "Master Stack techniques by solving Medium problem constraints for Minimum Insertions to Balance a Parentheses String.",
    "whyThisPattern": "When observing Stack problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/minimum-insertions-to-balance-a-parentheses-string/",
    "leetcode_title": "Minimum Insertions to Balance a Parentheses String",
    "leetcode_id": 1541,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/minimum-insertions-to-balance-a-parentheses-string/",
    "canonicalSlug": "minimum-insertions-to-balance-a-parentheses-string",
    "canonicalUrl": "https://leetcode.com/problems/minimum-insertions-to-balance-a-parentheses-string/",
    "url": "https://leetcode.com/problems/minimum-insertions-to-balance-a-parentheses-string/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Minimum Insertions to Balance a Parentheses String\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Minimum Insertions to Balance a Parentheses String\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Minimum Insertions to Balance a Parentheses String\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Minimum Insertions to Balance a Parentheses String\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Minimum Insertions to Balance a Parentheses String\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Minimum Insertions to Balance a Parentheses String\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Minimum Insertions to Balance a Parentheses String\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Minimum Insertions to Balance a Parentheses String\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Minimum Insertions to Balance a Parentheses String",
      "cpp_optimal": "// Solution for Minimum Insertions to Balance a Parentheses String",
      "java_brute": "// Solution for Minimum Insertions to Balance a Parentheses String",
      "java_optimal": "// Solution for Minimum Insertions to Balance a Parentheses String",
      "python_brute": "# Solution for Minimum Insertions to Balance a Parentheses String",
      "python_optimal": "# Solution for Minimum Insertions to Balance a Parentheses String"
    },
    "originalOrder": 619,
    "learningOrder": 619
  },
  {
    "id": 235,
    "number": 235,
    "sequence_number": 235,
    "title": "Maximum Score From Removing Substrings",
    "slug": "maximum-score-from-removing-substrings",
    "difficulty": "Medium",
    "topic": "Stack",
    "subtopic": "Stack Optimization",
    "pattern": "Two-Pass Greedy Stack",
    "secondary_patterns": [
      "Two-Pass Greedy Stack"
    ],
    "stage": "Stack & Queue Systems",
    "curriculumStage": "Stage 5 — Stack & Queue Systems",
    "roadmapPhase": "Stage 5 — Stack & Queue Systems",
    "phase": "Stage 5 — Stack & Queue Systems",
    "estimatedTime": 30,
    "statement": "Given the constraints and input parameters for Maximum Score From Removing Substrings, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Maximum Score From Removing Substrings."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Maximum Score From Removing Substrings.",
      "Leverage the optimal Stack pattern to reduce time complexity."
    ],
    "learningObjective": "Master Stack techniques by solving Medium problem constraints for Maximum Score From Removing Substrings.",
    "whyThisPattern": "When observing Stack problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/maximum-score-from-removing-substrings/",
    "leetcode_title": "Maximum Score From Removing Substrings",
    "leetcode_id": 1717,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/maximum-score-from-removing-substrings/",
    "canonicalSlug": "maximum-score-from-removing-substrings",
    "canonicalUrl": "https://leetcode.com/problems/maximum-score-from-removing-substrings/",
    "url": "https://leetcode.com/problems/maximum-score-from-removing-substrings/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Maximum Score From Removing Substrings\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Maximum Score From Removing Substrings\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Maximum Score From Removing Substrings\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Maximum Score From Removing Substrings\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Maximum Score From Removing Substrings\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Maximum Score From Removing Substrings\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Maximum Score From Removing Substrings\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Maximum Score From Removing Substrings\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Maximum Score From Removing Substrings",
      "cpp_optimal": "// Solution for Maximum Score From Removing Substrings",
      "java_brute": "// Solution for Maximum Score From Removing Substrings",
      "java_optimal": "// Solution for Maximum Score From Removing Substrings",
      "python_brute": "# Solution for Maximum Score From Removing Substrings",
      "python_optimal": "# Solution for Maximum Score From Removing Substrings"
    },
    "originalOrder": 620,
    "learningOrder": 620
  },
  {
    "id": 236,
    "number": 236,
    "sequence_number": 236,
    "title": "Sliding Window Maximum",
    "slug": "sliding-window-maximum",
    "difficulty": "Hard",
    "topic": "Queue",
    "subtopic": "Sliding Window",
    "pattern": "Sliding Window",
    "secondary_patterns": [
      "Sliding Window"
    ],
    "stage": "Stack & Queue Systems",
    "curriculumStage": "Stage 5 — Stack & Queue Systems",
    "roadmapPhase": "Stage 5 — Stack & Queue Systems",
    "phase": "Stage 5 — Stack & Queue Systems",
    "estimatedTime": 45,
    "statement": "Solve the **Sliding Window Maximum Optimization** problem using the **Sliding Window** technique. Given input constraints appropriate for Hard level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^6",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Sliding Window identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Sliding Window. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Sliding Window techniques by solving Hard problem constraints for Sliding Window Maximum Optimization.",
    "whyThisPattern": "When observing sliding window problem conditions, Sliding Window optimizes performance down to expected O(N log N).",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "LinkedIn",
      "Amazon"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/sliding-window-maximum/",
    "leetcode_title": "Sliding Window Maximum",
    "leetcode_id": 239,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/sliding-window-maximum/",
    "canonicalSlug": "sliding-window-maximum",
    "canonicalUrl": "https://leetcode.com/problems/sliding-window-maximum/",
    "url": "https://leetcode.com/problems/sliding-window-maximum/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Sliding Window Maximum Optimization (Sliding Window)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Sliding Window Maximum Optimization (Sliding Window)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Sliding Window Maximum Optimization (Sliding Window)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Sliding Window Maximum Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Sliding Window Maximum Optimization (Sliding Window)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Sliding Window Maximum Optimization (Sliding Window)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Sliding Window Maximum Optimization (Sliding Window)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Sliding Window Maximum Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Sliding Window Maximum",
      "cpp_optimal": "// Solution for Sliding Window Maximum",
      "java_brute": "// Solution for Sliding Window Maximum",
      "java_optimal": "// Solution for Sliding Window Maximum",
      "python_brute": "# Solution for Sliding Window Maximum",
      "python_optimal": "# Solution for Sliding Window Maximum"
    },
    "originalOrder": 930,
    "learningOrder": 930
  },
  {
    "id": 237,
    "number": 237,
    "sequence_number": 237,
    "title": "Orderly Queue",
    "slug": "orderly-queue",
    "difficulty": "Hard",
    "topic": "Queue",
    "subtopic": "Hashing & Array Optimization",
    "pattern": "Hashing & Array Optimization",
    "secondary_patterns": [
      "Hashing & Array Optimization"
    ],
    "stage": "Stack & Queue Systems",
    "curriculumStage": "Stage 5 — Stack & Queue Systems",
    "roadmapPhase": "Stage 5 — Stack & Queue Systems",
    "phase": "Stage 5 — Stack & Queue Systems",
    "estimatedTime": 45,
    "statement": "Solve the **Orderly Queue Optimization** problem using the **Hashing & Array Optimization** technique. Given input constraints appropriate for Hard level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^6",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Hashing & Array Optimization identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Hashing & Array Optimization. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Hashing & Array Optimization techniques by solving Hard problem constraints for Orderly Queue Optimization.",
    "whyThisPattern": "When observing queue & deque problem conditions, Hashing & Array Optimization optimizes performance down to expected O(N log N).",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "LinkedIn",
      "Amazon"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/orderly-queue/",
    "leetcode_title": "Orderly Queue",
    "leetcode_id": 899,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/orderly-queue/",
    "canonicalSlug": "orderly-queue",
    "canonicalUrl": "https://leetcode.com/problems/orderly-queue/",
    "url": "https://leetcode.com/problems/orderly-queue/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Orderly Queue Optimization (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Orderly Queue Optimization (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Orderly Queue Optimization (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Orderly Queue Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Orderly Queue Optimization (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Orderly Queue Optimization (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Orderly Queue Optimization (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Orderly Queue Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Orderly Queue",
      "cpp_optimal": "// Solution for Orderly Queue",
      "java_brute": "// Solution for Orderly Queue",
      "java_optimal": "// Solution for Orderly Queue",
      "python_brute": "# Solution for Orderly Queue",
      "python_optimal": "# Solution for Orderly Queue"
    },
    "originalOrder": 931,
    "learningOrder": 931
  },
  {
    "id": 238,
    "number": 238,
    "sequence_number": 238,
    "title": "Number of Visible People in a Queue",
    "slug": "number-of-visible-people-in-a-queue",
    "difficulty": "Hard",
    "topic": "Queue",
    "subtopic": "Queue Optimization",
    "pattern": "Queue Pattern",
    "secondary_patterns": [
      "Queue Pattern"
    ],
    "stage": "Stack & Queue Systems",
    "curriculumStage": "Stage 5 — Stack & Queue Systems",
    "roadmapPhase": "Stage 5 — Stack & Queue Systems",
    "phase": "Stage 5 — Stack & Queue Systems",
    "estimatedTime": 45,
    "statement": "Solve the **Number of Visible People in a Queue** problem using standard Queue techniques. Given input constraints appropriate for Hard level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Queue algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Queue properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Queue techniques by solving Hard problem constraints for Number of Visible People in a Queue.",
    "whyThisPattern": "When observing Queue problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/number-of-visible-people-in-a-queue/",
    "leetcode_title": "Number of Visible People in a Queue",
    "leetcode_id": 1944,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/number-of-visible-people-in-a-queue/",
    "canonicalSlug": "number-of-visible-people-in-a-queue",
    "canonicalUrl": "https://leetcode.com/problems/number-of-visible-people-in-a-queue/",
    "url": "https://leetcode.com/problems/number-of-visible-people-in-a-queue/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Number of Visible People in a Queue\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Number of Visible People in a Queue\n};",
        "java": "// Java Solution for Number of Visible People in a Queue\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Number of Visible People in a Queue\n}",
        "python": "# Python Solution for Number of Visible People in a Queue\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Number of Visible People in a Queue\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Number of Visible People in a Queue\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Number of Visible People in a Queue\n};",
        "java": "// Optimal Java Solution for Number of Visible People in a Queue\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Number of Visible People in a Queue\n}",
        "python": "# Optimal Python Solution for Number of Visible People in a Queue\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Number of Visible People in a Queue\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Number of Visible People in a Queue",
      "cpp_optimal": "// Solution for Number of Visible People in a Queue",
      "java_brute": "// Solution for Number of Visible People in a Queue",
      "java_optimal": "// Solution for Number of Visible People in a Queue",
      "python_brute": "# Solution for Number of Visible People in a Queue",
      "python_optimal": "# Solution for Number of Visible People in a Queue"
    },
    "originalOrder": 932,
    "learningOrder": 932
  },
  {
    "id": 239,
    "number": 239,
    "sequence_number": 239,
    "title": "Maximum Frequency Stack",
    "slug": "maximum-frequency-stack",
    "difficulty": "Hard",
    "topic": "Stack",
    "subtopic": "Monotonic Stack",
    "pattern": "Monotonic Stack",
    "secondary_patterns": [
      "Monotonic Stack"
    ],
    "stage": "Stack & Queue Systems",
    "curriculumStage": "Stage 5 — Stack & Queue Systems",
    "roadmapPhase": "Stage 5 — Stack & Queue Systems",
    "phase": "Stage 5 — Stack & Queue Systems",
    "estimatedTime": 45,
    "statement": "Solve the **Maximum Frequency Stack Challenge** problem using the **Monotonic Stack** technique. Given input constraints appropriate for Hard level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^6",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Monotonic Stack identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Monotonic Stack. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Monotonic Stack techniques by solving Hard problem constraints for Maximum Frequency Stack Challenge.",
    "whyThisPattern": "When observing stack & monotonic stack problem conditions, Monotonic Stack optimizes performance down to expected O(N log N).",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Meta",
      "Uber",
      "Databricks"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/maximum-frequency-stack/",
    "leetcode_title": "Maximum Frequency Stack",
    "leetcode_id": 895,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/maximum-frequency-stack/",
    "canonicalSlug": "maximum-frequency-stack",
    "canonicalUrl": "https://leetcode.com/problems/maximum-frequency-stack/",
    "url": "https://leetcode.com/problems/maximum-frequency-stack/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Maximum Frequency Stack Challenge (Monotonic Stack)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Maximum Frequency Stack Challenge (Monotonic Stack)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Maximum Frequency Stack Challenge (Monotonic Stack)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Maximum Frequency Stack Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Maximum Frequency Stack Challenge (Monotonic Stack)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Maximum Frequency Stack Challenge (Monotonic Stack)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Maximum Frequency Stack Challenge (Monotonic Stack)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Maximum Frequency Stack Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Maximum Frequency Stack",
      "cpp_optimal": "// Solution for Maximum Frequency Stack",
      "java_brute": "// Solution for Maximum Frequency Stack",
      "java_optimal": "// Solution for Maximum Frequency Stack",
      "python_brute": "# Solution for Maximum Frequency Stack",
      "python_optimal": "# Solution for Maximum Frequency Stack"
    },
    "originalOrder": 954,
    "learningOrder": 954
  },
  {
    "id": 240,
    "number": 240,
    "sequence_number": 240,
    "title": "Dinner Plate Stacks",
    "slug": "dinner-plate-stacks",
    "difficulty": "Hard",
    "topic": "Stack",
    "subtopic": "Monotonic Stack",
    "pattern": "Monotonic Stack",
    "secondary_patterns": [
      "Monotonic Stack"
    ],
    "stage": "Stack & Queue Systems",
    "curriculumStage": "Stage 5 — Stack & Queue Systems",
    "roadmapPhase": "Stage 5 — Stack & Queue Systems",
    "phase": "Stage 5 — Stack & Queue Systems",
    "estimatedTime": 45,
    "statement": "Solve the **Dinner Plate Stacks Optimization** problem using the **Monotonic Stack** technique. Given input constraints appropriate for Hard level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^6",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Monotonic Stack identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Monotonic Stack. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Monotonic Stack techniques by solving Hard problem constraints for Dinner Plate Stacks Optimization.",
    "whyThisPattern": "When observing stack & monotonic stack problem conditions, Monotonic Stack optimizes performance down to expected O(N log N).",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/dinner-plate-stacks/",
    "leetcode_title": "Dinner Plate Stacks",
    "leetcode_id": 1172,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/dinner-plate-stacks/",
    "canonicalSlug": "dinner-plate-stacks",
    "canonicalUrl": "https://leetcode.com/problems/dinner-plate-stacks/",
    "url": "https://leetcode.com/problems/dinner-plate-stacks/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Dinner Plate Stacks Optimization (Monotonic Stack)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Dinner Plate Stacks Optimization (Monotonic Stack)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Dinner Plate Stacks Optimization (Monotonic Stack)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Dinner Plate Stacks Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Dinner Plate Stacks Optimization (Monotonic Stack)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Dinner Plate Stacks Optimization (Monotonic Stack)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Dinner Plate Stacks Optimization (Monotonic Stack)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Dinner Plate Stacks Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Dinner Plate Stacks",
      "cpp_optimal": "// Solution for Dinner Plate Stacks",
      "java_brute": "// Solution for Dinner Plate Stacks",
      "java_optimal": "// Solution for Dinner Plate Stacks",
      "python_brute": "# Solution for Dinner Plate Stacks",
      "python_optimal": "# Solution for Dinner Plate Stacks"
    },
    "originalOrder": 955,
    "learningOrder": 955
  },
  {
    "id": 241,
    "number": 241,
    "sequence_number": 241,
    "title": "Longest Valid Parentheses",
    "slug": "longest-valid-parentheses",
    "difficulty": "Hard",
    "topic": "Stack",
    "subtopic": "Monotonic Stack",
    "pattern": "Monotonic Stack",
    "secondary_patterns": [
      "Monotonic Stack"
    ],
    "stage": "Stack & Queue Systems",
    "curriculumStage": "Stage 5 — Stack & Queue Systems",
    "roadmapPhase": "Stage 5 — Stack & Queue Systems",
    "phase": "Stage 5 — Stack & Queue Systems",
    "estimatedTime": 45,
    "statement": "Solve the **Longest Valid Parentheses Challenge** problem using the **Monotonic Stack** technique. Given input constraints appropriate for Hard level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^6",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Monotonic Stack identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Monotonic Stack. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Monotonic Stack techniques by solving Hard problem constraints for Longest Valid Parentheses Challenge.",
    "whyThisPattern": "When observing arrays & strings problem conditions, Monotonic Stack optimizes performance down to expected O(N log N).",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Amazon",
      "Microsoft",
      "Uber"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/longest-valid-parentheses/",
    "leetcode_title": "Longest Valid Parentheses",
    "leetcode_id": 32,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/longest-valid-parentheses/",
    "canonicalSlug": "longest-valid-parentheses",
    "canonicalUrl": "https://leetcode.com/problems/longest-valid-parentheses/",
    "url": "https://leetcode.com/problems/longest-valid-parentheses/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Longest Valid Parentheses Challenge (Monotonic Stack)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Longest Valid Parentheses Challenge (Monotonic Stack)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Longest Valid Parentheses Challenge (Monotonic Stack)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Longest Valid Parentheses Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Longest Valid Parentheses Challenge (Monotonic Stack)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Longest Valid Parentheses Challenge (Monotonic Stack)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Longest Valid Parentheses Challenge (Monotonic Stack)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Longest Valid Parentheses Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Longest Valid Parentheses",
      "cpp_optimal": "// Solution for Longest Valid Parentheses",
      "java_brute": "// Solution for Longest Valid Parentheses",
      "java_optimal": "// Solution for Longest Valid Parentheses",
      "python_brute": "# Solution for Longest Valid Parentheses",
      "python_optimal": "# Solution for Longest Valid Parentheses"
    },
    "originalOrder": 956,
    "learningOrder": 956
  },
  {
    "id": 242,
    "number": 242,
    "sequence_number": 242,
    "title": "Largest Rectangle in Histogram",
    "slug": "largest-rectangle-in-histogram",
    "difficulty": "Hard",
    "topic": "Stack",
    "subtopic": "Monotonic Stack",
    "pattern": "Monotonic Stack",
    "secondary_patterns": [
      "Monotonic Stack"
    ],
    "stage": "Stack & Queue Systems",
    "curriculumStage": "Stage 5 — Stack & Queue Systems",
    "roadmapPhase": "Stage 5 — Stack & Queue Systems",
    "phase": "Stage 5 — Stack & Queue Systems",
    "estimatedTime": 45,
    "statement": "Solve the **Largest Rectangle in Histogram Optimization** problem using the **Monotonic Stack** technique. Given input constraints appropriate for Hard level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^6",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Monotonic Stack identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Monotonic Stack. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Monotonic Stack techniques by solving Hard problem constraints for Largest Rectangle in Histogram Optimization.",
    "whyThisPattern": "When observing arrays & strings problem conditions, Monotonic Stack optimizes performance down to expected O(N log N).",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Meta",
      "Apple",
      "Netflix"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/largest-rectangle-in-histogram/",
    "leetcode_title": "Largest Rectangle in Histogram",
    "leetcode_id": 84,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/largest-rectangle-in-histogram/",
    "canonicalSlug": "largest-rectangle-in-histogram",
    "canonicalUrl": "https://leetcode.com/problems/largest-rectangle-in-histogram/",
    "url": "https://leetcode.com/problems/largest-rectangle-in-histogram/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Largest Rectangle in Histogram Optimization (Monotonic Stack)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Largest Rectangle in Histogram Optimization (Monotonic Stack)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Largest Rectangle in Histogram Optimization (Monotonic Stack)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Largest Rectangle in Histogram Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Largest Rectangle in Histogram Optimization (Monotonic Stack)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Largest Rectangle in Histogram Optimization (Monotonic Stack)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Largest Rectangle in Histogram Optimization (Monotonic Stack)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Largest Rectangle in Histogram Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Largest Rectangle in Histogram",
      "cpp_optimal": "// Solution for Largest Rectangle in Histogram",
      "java_brute": "// Solution for Largest Rectangle in Histogram",
      "java_optimal": "// Solution for Largest Rectangle in Histogram",
      "python_brute": "# Solution for Largest Rectangle in Histogram",
      "python_optimal": "# Solution for Largest Rectangle in Histogram"
    },
    "originalOrder": 957,
    "learningOrder": 957
  },
  {
    "id": 243,
    "number": 243,
    "sequence_number": 243,
    "title": "Remove Invalid Parentheses",
    "slug": "remove-invalid-parentheses",
    "difficulty": "Hard",
    "topic": "Stack",
    "subtopic": "Monotonic Stack",
    "pattern": "Monotonic Stack",
    "secondary_patterns": [
      "Monotonic Stack"
    ],
    "stage": "Stack & Queue Systems",
    "curriculumStage": "Stage 5 — Stack & Queue Systems",
    "roadmapPhase": "Stage 5 — Stack & Queue Systems",
    "phase": "Stage 5 — Stack & Queue Systems",
    "estimatedTime": 45,
    "statement": "Solve the **Remove Invalid Parentheses Optimization** problem using the **Monotonic Stack** technique. Given input constraints appropriate for Hard level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^6",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Monotonic Stack identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Monotonic Stack. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Monotonic Stack techniques by solving Hard problem constraints for Remove Invalid Parentheses Optimization.",
    "whyThisPattern": "When observing arrays & strings problem conditions, Monotonic Stack optimizes performance down to expected O(N log N).",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Meta",
      "Apple",
      "Netflix"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/remove-invalid-parentheses/",
    "leetcode_title": "Remove Invalid Parentheses",
    "leetcode_id": 301,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/remove-invalid-parentheses/",
    "canonicalSlug": "remove-invalid-parentheses",
    "canonicalUrl": "https://leetcode.com/problems/remove-invalid-parentheses/",
    "url": "https://leetcode.com/problems/remove-invalid-parentheses/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Remove Invalid Parentheses Optimization (Monotonic Stack)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Remove Invalid Parentheses Optimization (Monotonic Stack)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Remove Invalid Parentheses Optimization (Monotonic Stack)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Remove Invalid Parentheses Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Remove Invalid Parentheses Optimization (Monotonic Stack)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Remove Invalid Parentheses Optimization (Monotonic Stack)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Remove Invalid Parentheses Optimization (Monotonic Stack)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Remove Invalid Parentheses Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Remove Invalid Parentheses",
      "cpp_optimal": "// Solution for Remove Invalid Parentheses",
      "java_brute": "// Solution for Remove Invalid Parentheses",
      "java_optimal": "// Solution for Remove Invalid Parentheses",
      "python_brute": "# Solution for Remove Invalid Parentheses",
      "python_optimal": "# Solution for Remove Invalid Parentheses"
    },
    "originalOrder": 958,
    "learningOrder": 958
  },
  {
    "id": 244,
    "number": 244,
    "sequence_number": 244,
    "title": "Number of Atoms",
    "slug": "number-of-atoms",
    "difficulty": "Hard",
    "topic": "Stack",
    "subtopic": "Stack Optimization",
    "pattern": "Nested Bracket Parsing Stack",
    "secondary_patterns": [
      "Nested Bracket Parsing Stack"
    ],
    "stage": "Stack & Queue Systems",
    "curriculumStage": "Stage 5 — Stack & Queue Systems",
    "roadmapPhase": "Stage 5 — Stack & Queue Systems",
    "phase": "Stage 5 — Stack & Queue Systems",
    "estimatedTime": 45,
    "statement": "Given the constraints and input parameters for Number of Atoms, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Number of Atoms."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Number of Atoms.",
      "Leverage the optimal Stack pattern to reduce time complexity."
    ],
    "learningObjective": "Master Stack techniques by solving Hard problem constraints for Number of Atoms.",
    "whyThisPattern": "When observing Stack problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/number-of-atoms/",
    "leetcode_title": "Number of Atoms",
    "leetcode_id": 726,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/number-of-atoms/",
    "canonicalSlug": "number-of-atoms",
    "canonicalUrl": "https://leetcode.com/problems/number-of-atoms/",
    "url": "https://leetcode.com/problems/number-of-atoms/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Number of Atoms\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Number of Atoms\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Number of Atoms\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Number of Atoms\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Number of Atoms\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Number of Atoms\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Number of Atoms\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Number of Atoms\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Number of Atoms",
      "cpp_optimal": "// Solution for Number of Atoms",
      "java_brute": "// Solution for Number of Atoms",
      "java_optimal": "// Solution for Number of Atoms",
      "python_brute": "# Solution for Number of Atoms",
      "python_optimal": "# Solution for Number of Atoms"
    },
    "originalOrder": 959,
    "learningOrder": 959
  },
  {
    "id": 245,
    "number": 245,
    "sequence_number": 245,
    "title": "Parse Lisp Expression",
    "slug": "parse-lisp-expression",
    "difficulty": "Hard",
    "topic": "Stack",
    "subtopic": "Stack Optimization",
    "pattern": "Scope Map Recursion Stack",
    "secondary_patterns": [
      "Scope Map Recursion Stack"
    ],
    "stage": "Stack & Queue Systems",
    "curriculumStage": "Stage 5 — Stack & Queue Systems",
    "roadmapPhase": "Stage 5 — Stack & Queue Systems",
    "phase": "Stage 5 — Stack & Queue Systems",
    "estimatedTime": 45,
    "statement": "Given the constraints and input parameters for Parse Lisp Expression, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Parse Lisp Expression."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Parse Lisp Expression.",
      "Leverage the optimal Stack pattern to reduce time complexity."
    ],
    "learningObjective": "Master Stack techniques by solving Hard problem constraints for Parse Lisp Expression.",
    "whyThisPattern": "When observing Stack problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/parse-lisp-expression/",
    "leetcode_title": "Parse Lisp Expression",
    "leetcode_id": 736,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/parse-lisp-expression/",
    "canonicalSlug": "parse-lisp-expression",
    "canonicalUrl": "https://leetcode.com/problems/parse-lisp-expression/",
    "url": "https://leetcode.com/problems/parse-lisp-expression/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Parse Lisp Expression\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Parse Lisp Expression\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Parse Lisp Expression\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Parse Lisp Expression\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Parse Lisp Expression\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Parse Lisp Expression\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Parse Lisp Expression\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Parse Lisp Expression\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Parse Lisp Expression",
      "cpp_optimal": "// Solution for Parse Lisp Expression",
      "java_brute": "// Solution for Parse Lisp Expression",
      "java_optimal": "// Solution for Parse Lisp Expression",
      "python_brute": "# Solution for Parse Lisp Expression",
      "python_optimal": "# Solution for Parse Lisp Expression"
    },
    "originalOrder": 960,
    "learningOrder": 960
  },
  {
    "id": 246,
    "number": 246,
    "sequence_number": 246,
    "title": "Maximal Rectangle",
    "slug": "maximal-rectangle",
    "difficulty": "Hard",
    "topic": "Stack",
    "subtopic": "Stack Optimization",
    "pattern": "Histogram Height Monotonic Stack",
    "secondary_patterns": [
      "Histogram Height Monotonic Stack"
    ],
    "stage": "Stack & Queue Systems",
    "curriculumStage": "Stage 5 — Stack & Queue Systems",
    "roadmapPhase": "Stage 5 — Stack & Queue Systems",
    "phase": "Stage 5 — Stack & Queue Systems",
    "estimatedTime": 45,
    "statement": "Given the constraints and input parameters for Maximal Rectangle, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Maximal Rectangle."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Maximal Rectangle.",
      "Leverage the optimal Stack pattern to reduce time complexity."
    ],
    "learningObjective": "Master Stack techniques by solving Hard problem constraints for Maximal Rectangle.",
    "whyThisPattern": "When observing Stack problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/maximal-rectangle/",
    "leetcode_title": "Maximal Rectangle",
    "leetcode_id": 85,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/maximal-rectangle/",
    "canonicalSlug": "maximal-rectangle",
    "canonicalUrl": "https://leetcode.com/problems/maximal-rectangle/",
    "url": "https://leetcode.com/problems/maximal-rectangle/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Maximal Rectangle\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Maximal Rectangle\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Maximal Rectangle\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Maximal Rectangle\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Maximal Rectangle\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Maximal Rectangle\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Maximal Rectangle\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Maximal Rectangle\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Maximal Rectangle",
      "cpp_optimal": "// Solution for Maximal Rectangle",
      "java_brute": "// Solution for Maximal Rectangle",
      "java_optimal": "// Solution for Maximal Rectangle",
      "python_brute": "# Solution for Maximal Rectangle",
      "python_optimal": "# Solution for Maximal Rectangle"
    },
    "originalOrder": 961,
    "learningOrder": 961
  },
  {
    "id": 247,
    "number": 247,
    "sequence_number": 247,
    "title": "Basic Calculator IV",
    "slug": "basic-calculator-iv",
    "difficulty": "Hard",
    "topic": "Stack",
    "subtopic": "Stack Optimization",
    "pattern": "Polynomial Expression Parsing",
    "secondary_patterns": [
      "Polynomial Expression Parsing"
    ],
    "stage": "Stack & Queue Systems",
    "curriculumStage": "Stage 5 — Stack & Queue Systems",
    "roadmapPhase": "Stage 5 — Stack & Queue Systems",
    "phase": "Stage 5 — Stack & Queue Systems",
    "estimatedTime": 45,
    "statement": "Given the constraints and input parameters for Basic Calculator IV, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Basic Calculator IV."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Basic Calculator IV.",
      "Leverage the optimal Stack pattern to reduce time complexity."
    ],
    "learningObjective": "Master Stack techniques by solving Hard problem constraints for Basic Calculator IV.",
    "whyThisPattern": "When observing Stack problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/basic-calculator-iv/",
    "leetcode_title": "Basic Calculator IV",
    "leetcode_id": 770,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/basic-calculator-iv/",
    "canonicalSlug": "basic-calculator-iv",
    "canonicalUrl": "https://leetcode.com/problems/basic-calculator-iv/",
    "url": "https://leetcode.com/problems/basic-calculator-iv/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Basic Calculator IV\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Basic Calculator IV\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Basic Calculator IV\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Basic Calculator IV\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Basic Calculator IV\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Basic Calculator IV\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Basic Calculator IV\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Basic Calculator IV\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Basic Calculator IV",
      "cpp_optimal": "// Solution for Basic Calculator IV",
      "java_brute": "// Solution for Basic Calculator IV",
      "java_optimal": "// Solution for Basic Calculator IV",
      "python_brute": "# Solution for Basic Calculator IV",
      "python_optimal": "# Solution for Basic Calculator IV"
    },
    "originalOrder": 962,
    "learningOrder": 962
  },
  {
    "id": 248,
    "number": 248,
    "sequence_number": 248,
    "title": "Smallest K-Length Subsequence With Occurrences of a Letter",
    "slug": "smallest-k-length-subsequence-with-occurrences-of-a-letter",
    "difficulty": "Hard",
    "topic": "Stack",
    "subtopic": "Stack Optimization",
    "pattern": "Monotonic Stack Frequency",
    "secondary_patterns": [
      "Monotonic Stack Frequency"
    ],
    "stage": "Stack & Queue Systems",
    "curriculumStage": "Stage 5 — Stack & Queue Systems",
    "roadmapPhase": "Stage 5 — Stack & Queue Systems",
    "phase": "Stage 5 — Stack & Queue Systems",
    "estimatedTime": 45,
    "statement": "Given the constraints and input parameters for Smallest K-Length Subsequence With Occurrences of a Letter, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Smallest K-Length Subsequence With Occurrences of a Letter."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Smallest K-Length Subsequence With Occurrences of a Letter.",
      "Leverage the optimal Stack pattern to reduce time complexity."
    ],
    "learningObjective": "Master Stack techniques by solving Hard problem constraints for Smallest K-Length Subsequence With Occurrences of a Letter.",
    "whyThisPattern": "When observing Stack problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/smallest-k-length-subsequence-with-occurrences-of-a-letter/",
    "leetcode_title": "Smallest K-Length Subsequence With Occurrences of a Letter",
    "leetcode_id": 2030,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/smallest-k-length-subsequence-with-occurrences-of-a-letter/",
    "canonicalSlug": "smallest-k-length-subsequence-with-occurrences-of-a-letter",
    "canonicalUrl": "https://leetcode.com/problems/smallest-k-length-subsequence-with-occurrences-of-a-letter/",
    "url": "https://leetcode.com/problems/smallest-k-length-subsequence-with-occurrences-of-a-letter/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Smallest K-Length Subsequence With Occurrences of a Letter\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Smallest K-Length Subsequence With Occurrences of a Letter\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Smallest K-Length Subsequence With Occurrences of a Letter\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Smallest K-Length Subsequence With Occurrences of a Letter\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Smallest K-Length Subsequence With Occurrences of a Letter\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Smallest K-Length Subsequence With Occurrences of a Letter\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Smallest K-Length Subsequence With Occurrences of a Letter\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Smallest K-Length Subsequence With Occurrences of a Letter\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Smallest K-Length Subsequence With Occurrences of a Letter",
      "cpp_optimal": "// Solution for Smallest K-Length Subsequence With Occurrences of a Letter",
      "java_brute": "// Solution for Smallest K-Length Subsequence With Occurrences of a Letter",
      "java_optimal": "// Solution for Smallest K-Length Subsequence With Occurrences of a Letter",
      "python_brute": "# Solution for Smallest K-Length Subsequence With Occurrences of a Letter",
      "python_optimal": "# Solution for Smallest K-Length Subsequence With Occurrences of a Letter"
    },
    "originalOrder": 963,
    "learningOrder": 963
  },
  {
    "id": 249,
    "number": 249,
    "sequence_number": 249,
    "title": "Shortest Subarray with Sum at Least K",
    "slug": "shortest-subarray-with-sum-at-least-k",
    "difficulty": "Hard",
    "topic": "Arrays",
    "subtopic": "Arrays Optimization",
    "pattern": "Arrays Pattern",
    "secondary_patterns": [
      "Arrays Pattern"
    ],
    "stage": "Stack & Queue Systems",
    "curriculumStage": "Stage 5 — Stack & Queue Systems",
    "roadmapPhase": "Stage 5 — Stack & Queue Systems",
    "phase": "Stage 5 — Stack & Queue Systems",
    "estimatedTime": 45,
    "statement": "Solve the **Shortest Subarray with Sum at Least K** problem using standard Arrays techniques. Given input constraints appropriate for Hard level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Arrays algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Arrays properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Arrays techniques by solving Hard problem constraints for Shortest Subarray with Sum at Least K.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/shortest-subarray-with-sum-at-least-k/",
    "leetcode_title": "Shortest Subarray with Sum at Least K",
    "leetcode_id": 862,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/shortest-subarray-with-sum-at-least-k/",
    "canonicalSlug": "shortest-subarray-with-sum-at-least-k",
    "canonicalUrl": "https://leetcode.com/problems/shortest-subarray-with-sum-at-least-k/",
    "url": "https://leetcode.com/problems/shortest-subarray-with-sum-at-least-k/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Shortest Subarray with Sum at Least K\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Shortest Subarray with Sum at Least K\n};",
        "java": "// Java Solution for Shortest Subarray with Sum at Least K\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Shortest Subarray with Sum at Least K\n}",
        "python": "# Python Solution for Shortest Subarray with Sum at Least K\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Shortest Subarray with Sum at Least K\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Shortest Subarray with Sum at Least K\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Shortest Subarray with Sum at Least K\n};",
        "java": "// Optimal Java Solution for Shortest Subarray with Sum at Least K\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Shortest Subarray with Sum at Least K\n}",
        "python": "# Optimal Python Solution for Shortest Subarray with Sum at Least K\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Shortest Subarray with Sum at Least K\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Shortest Subarray with Sum at Least K",
      "cpp_optimal": "// Solution for Shortest Subarray with Sum at Least K",
      "java_brute": "// Solution for Shortest Subarray with Sum at Least K",
      "java_optimal": "// Solution for Shortest Subarray with Sum at Least K",
      "python_brute": "# Solution for Shortest Subarray with Sum at Least K",
      "python_optimal": "# Solution for Shortest Subarray with Sum at Least K"
    },
    "originalOrder": 737,
    "learningOrder": 737
  },
  {
    "id": 250,
    "number": 250,
    "sequence_number": 250,
    "title": "Nth Magical Number",
    "slug": "nth-magical-number",
    "difficulty": "Hard",
    "topic": "Arrays",
    "subtopic": "Arrays Optimization",
    "pattern": "Arrays Pattern",
    "secondary_patterns": [
      "Arrays Pattern"
    ],
    "stage": "Stack & Queue Systems",
    "curriculumStage": "Stage 5 — Stack & Queue Systems",
    "roadmapPhase": "Stage 5 — Stack & Queue Systems",
    "phase": "Stage 5 — Stack & Queue Systems",
    "estimatedTime": 45,
    "statement": "Solve the **Nth Magical Number** problem using standard Arrays techniques. Given input constraints appropriate for Hard level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Arrays algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Arrays properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Arrays techniques by solving Hard problem constraints for Nth Magical Number.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/nth-magical-number/",
    "leetcode_title": "Nth Magical Number",
    "leetcode_id": 878,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/nth-magical-number/",
    "canonicalSlug": "nth-magical-number",
    "canonicalUrl": "https://leetcode.com/problems/nth-magical-number/",
    "url": "https://leetcode.com/problems/nth-magical-number/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Nth Magical Number\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Nth Magical Number\n};",
        "java": "// Java Solution for Nth Magical Number\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Nth Magical Number\n}",
        "python": "# Python Solution for Nth Magical Number\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Nth Magical Number\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Nth Magical Number\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Nth Magical Number\n};",
        "java": "// Optimal Java Solution for Nth Magical Number\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Nth Magical Number\n}",
        "python": "# Optimal Python Solution for Nth Magical Number\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Nth Magical Number\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Nth Magical Number",
      "cpp_optimal": "// Solution for Nth Magical Number",
      "java_brute": "// Solution for Nth Magical Number",
      "java_optimal": "// Solution for Nth Magical Number",
      "python_brute": "# Solution for Nth Magical Number",
      "python_optimal": "# Solution for Nth Magical Number"
    },
    "originalOrder": 738,
    "learningOrder": 738
  },
  {
    "id": 251,
    "number": 251,
    "sequence_number": 251,
    "title": "Duplicate Zeros",
    "slug": "duplicate-zeros",
    "difficulty": "Easy",
    "topic": "Two Pointers",
    "subtopic": "Two Pointers Optimization",
    "pattern": "In-Place Right Shift",
    "secondary_patterns": [
      "In-Place Right Shift"
    ],
    "stage": "Linked Lists & Fast-Slow Pointers",
    "curriculumStage": "Stage 6 — Linked Lists & Fast-Slow Pointers",
    "roadmapPhase": "Stage 6 — Linked Lists & Fast-Slow Pointers",
    "phase": "Stage 6 — Linked Lists & Fast-Slow Pointers",
    "estimatedTime": 15,
    "statement": "Given the constraints and input parameters for Duplicate Zeros, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Duplicate Zeros."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Duplicate Zeros.",
      "Leverage the optimal Two Pointers pattern to reduce time complexity."
    ],
    "learningObjective": "Master Two Pointers techniques by solving Easy problem constraints for Duplicate Zeros.",
    "whyThisPattern": "When observing Two Pointers problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/duplicate-zeros/",
    "leetcode_title": "Duplicate Zeros",
    "leetcode_id": 395,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/duplicate-zeros/",
    "canonicalSlug": "duplicate-zeros",
    "canonicalUrl": "https://leetcode.com/problems/duplicate-zeros/",
    "url": "https://leetcode.com/problems/duplicate-zeros/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Duplicate Zeros\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Duplicate Zeros\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Duplicate Zeros\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Duplicate Zeros\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Duplicate Zeros\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Duplicate Zeros\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Duplicate Zeros\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Duplicate Zeros\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Duplicate Zeros",
      "cpp_optimal": "// Solution for Duplicate Zeros",
      "java_brute": "// Solution for Duplicate Zeros",
      "java_optimal": "// Solution for Duplicate Zeros",
      "python_brute": "# Solution for Duplicate Zeros",
      "python_optimal": "# Solution for Duplicate Zeros"
    }
  },
  {
    "id": 252,
    "number": 252,
    "sequence_number": 252,
    "title": "Missing Number",
    "slug": "missing-number-optimization",
    "difficulty": "Easy",
    "topic": "Arrays",
    "subtopic": "Hashing & Array Optimization",
    "pattern": "Hashing & Array Optimization",
    "secondary_patterns": [
      "Hashing & Array Optimization"
    ],
    "stage": "Linked Lists & Fast-Slow Pointers",
    "curriculumStage": "Stage 6 — Linked Lists & Fast-Slow Pointers",
    "roadmapPhase": "Stage 6 — Linked Lists & Fast-Slow Pointers",
    "phase": "Stage 6 — Linked Lists & Fast-Slow Pointers",
    "estimatedTime": 15,
    "statement": "Solve the **Missing Number Optimization** problem using the **Hashing & Array Optimization** technique. Given input constraints appropriate for Easy level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^4",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Hashing & Array Optimization identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Hashing & Array Optimization. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Hashing & Array Optimization techniques by solving Easy problem constraints for Missing Number Optimization.",
    "whyThisPattern": "When observing arrays & strings problem conditions, Hashing & Array Optimization optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "LinkedIn",
      "Amazon"
    ],
    "companyRelevanceTier": "Medium",
    "leetcode_url": "https://leetcode.com/problems/missing-number/",
    "leetcode_title": "Missing Number",
    "leetcode_id": 268,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/missing-number/",
    "canonicalSlug": "missing-number-optimization",
    "canonicalUrl": "https://leetcode.com/problems/missing-number/",
    "url": "https://leetcode.com/problems/missing-number/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Missing Number Optimization (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Missing Number Optimization (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Missing Number Optimization (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Missing Number Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Missing Number Optimization (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Missing Number Optimization (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Missing Number Optimization (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Missing Number Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Missing Number",
      "cpp_optimal": "// Solution for Missing Number",
      "java_brute": "// Solution for Missing Number",
      "java_optimal": "// Solution for Missing Number",
      "python_brute": "# Solution for Missing Number",
      "python_optimal": "# Solution for Missing Number"
    }
  },
  {
    "id": 253,
    "number": 253,
    "sequence_number": 253,
    "title": "Intersection of Two Arrays",
    "slug": "intersection-of-two-arrays-optimization",
    "difficulty": "Easy",
    "topic": "Arrays",
    "subtopic": "Hashing & Array Optimization",
    "pattern": "Hashing & Array Optimization",
    "secondary_patterns": [
      "Hashing & Array Optimization"
    ],
    "stage": "Linked Lists & Fast-Slow Pointers",
    "curriculumStage": "Stage 6 — Linked Lists & Fast-Slow Pointers",
    "roadmapPhase": "Stage 6 — Linked Lists & Fast-Slow Pointers",
    "phase": "Stage 6 — Linked Lists & Fast-Slow Pointers",
    "estimatedTime": 15,
    "statement": "Solve the **Intersection of Two Arrays Optimization** problem using the **Hashing & Array Optimization** technique. Given input constraints appropriate for Easy level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^4",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Hashing & Array Optimization identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Hashing & Array Optimization. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Hashing & Array Optimization techniques by solving Easy problem constraints for Intersection of Two Arrays Optimization.",
    "whyThisPattern": "When observing arrays & strings problem conditions, Hashing & Array Optimization optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "LinkedIn",
      "Amazon"
    ],
    "companyRelevanceTier": "Medium",
    "leetcode_url": "https://leetcode.com/problems/intersection-of-two-arrays/",
    "leetcode_title": "Intersection of Two Arrays",
    "leetcode_id": 349,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/intersection-of-two-arrays/",
    "canonicalSlug": "intersection-of-two-arrays-optimization",
    "canonicalUrl": "https://leetcode.com/problems/intersection-of-two-arrays/",
    "url": "https://leetcode.com/problems/intersection-of-two-arrays/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Intersection of Two Arrays Optimization (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Intersection of Two Arrays Optimization (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Intersection of Two Arrays Optimization (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Intersection of Two Arrays Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Intersection of Two Arrays Optimization (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Intersection of Two Arrays Optimization (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Intersection of Two Arrays Optimization (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Intersection of Two Arrays Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Intersection of Two Arrays",
      "cpp_optimal": "// Solution for Intersection of Two Arrays",
      "java_brute": "// Solution for Intersection of Two Arrays",
      "java_optimal": "// Solution for Intersection of Two Arrays",
      "python_brute": "# Solution for Intersection of Two Arrays",
      "python_optimal": "# Solution for Intersection of Two Arrays"
    }
  },
  {
    "id": 254,
    "number": 254,
    "sequence_number": 254,
    "title": "Intersection of Two Arrays II",
    "slug": "intersection-of-two-arrays-ii-optimization",
    "difficulty": "Easy",
    "topic": "Arrays",
    "subtopic": "Hashing & Array Optimization",
    "pattern": "Hashing & Array Optimization",
    "secondary_patterns": [
      "Hashing & Array Optimization"
    ],
    "stage": "Linked Lists & Fast-Slow Pointers",
    "curriculumStage": "Stage 6 — Linked Lists & Fast-Slow Pointers",
    "roadmapPhase": "Stage 6 — Linked Lists & Fast-Slow Pointers",
    "phase": "Stage 6 — Linked Lists & Fast-Slow Pointers",
    "estimatedTime": 15,
    "statement": "Solve the **Intersection of Two Arrays II Optimization** problem using the **Hashing & Array Optimization** technique. Given input constraints appropriate for Easy level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^4",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Hashing & Array Optimization identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Hashing & Array Optimization. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Hashing & Array Optimization techniques by solving Easy problem constraints for Intersection of Two Arrays II Optimization.",
    "whyThisPattern": "When observing arrays & strings problem conditions, Hashing & Array Optimization optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta"
    ],
    "companyRelevanceTier": "Medium",
    "leetcode_url": "https://leetcode.com/problems/intersection-of-two-arrays-ii/",
    "leetcode_title": "Intersection of Two Arrays II",
    "leetcode_id": 350,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/intersection-of-two-arrays-ii/",
    "canonicalSlug": "intersection-of-two-arrays-ii-optimization",
    "canonicalUrl": "https://leetcode.com/problems/intersection-of-two-arrays-ii/",
    "url": "https://leetcode.com/problems/intersection-of-two-arrays-ii/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Intersection of Two Arrays II Optimization (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Intersection of Two Arrays II Optimization (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Intersection of Two Arrays II Optimization (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Intersection of Two Arrays II Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Intersection of Two Arrays II Optimization (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Intersection of Two Arrays II Optimization (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Intersection of Two Arrays II Optimization (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Intersection of Two Arrays II Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Intersection of Two Arrays II",
      "cpp_optimal": "// Solution for Intersection of Two Arrays II",
      "java_brute": "// Solution for Intersection of Two Arrays II",
      "java_optimal": "// Solution for Intersection of Two Arrays II",
      "python_brute": "# Solution for Intersection of Two Arrays II",
      "python_optimal": "# Solution for Intersection of Two Arrays II"
    }
  },
  {
    "id": 255,
    "number": 255,
    "sequence_number": 255,
    "title": "Third Maximum Number",
    "slug": "third-maximum-number-optimization",
    "difficulty": "Easy",
    "topic": "Arrays",
    "subtopic": "Hashing & Array Optimization",
    "pattern": "Hashing & Array Optimization",
    "secondary_patterns": [
      "Hashing & Array Optimization"
    ],
    "stage": "Linked Lists & Fast-Slow Pointers",
    "curriculumStage": "Stage 6 — Linked Lists & Fast-Slow Pointers",
    "roadmapPhase": "Stage 6 — Linked Lists & Fast-Slow Pointers",
    "phase": "Stage 6 — Linked Lists & Fast-Slow Pointers",
    "estimatedTime": 15,
    "statement": "Solve the **Third Maximum Number Optimization** problem using the **Hashing & Array Optimization** technique. Given input constraints appropriate for Easy level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^4",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Hashing & Array Optimization identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Hashing & Array Optimization. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Hashing & Array Optimization techniques by solving Easy problem constraints for Third Maximum Number Optimization.",
    "whyThisPattern": "When observing arrays & strings problem conditions, Hashing & Array Optimization optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Meta",
      "Apple",
      "Netflix"
    ],
    "companyRelevanceTier": "Medium",
    "leetcode_url": "https://leetcode.com/problems/third-maximum-number/",
    "leetcode_title": "Third Maximum Number",
    "leetcode_id": 414,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/third-maximum-number/",
    "canonicalSlug": "third-maximum-number-optimization",
    "canonicalUrl": "https://leetcode.com/problems/third-maximum-number/",
    "url": "https://leetcode.com/problems/third-maximum-number/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Third Maximum Number Optimization (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Third Maximum Number Optimization (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Third Maximum Number Optimization (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Third Maximum Number Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Third Maximum Number Optimization (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Third Maximum Number Optimization (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Third Maximum Number Optimization (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Third Maximum Number Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Third Maximum Number",
      "cpp_optimal": "// Solution for Third Maximum Number",
      "java_brute": "// Solution for Third Maximum Number",
      "java_optimal": "// Solution for Third Maximum Number",
      "python_brute": "# Solution for Third Maximum Number",
      "python_optimal": "# Solution for Third Maximum Number"
    }
  },
  {
    "id": 256,
    "number": 256,
    "sequence_number": 256,
    "title": "Merge Sorted Array",
    "slug": "merge-sorted-array-optimization",
    "difficulty": "Easy",
    "topic": "Arrays",
    "subtopic": "Two Pointers",
    "pattern": "Two Pointers",
    "secondary_patterns": [
      "Two Pointers"
    ],
    "stage": "Linked Lists & Fast-Slow Pointers",
    "curriculumStage": "Stage 6 — Linked Lists & Fast-Slow Pointers",
    "roadmapPhase": "Stage 6 — Linked Lists & Fast-Slow Pointers",
    "phase": "Stage 6 — Linked Lists & Fast-Slow Pointers",
    "estimatedTime": 15,
    "statement": "Solve the **Merge Sorted Array Optimization** problem using the **Two Pointers** technique. Given input constraints appropriate for Easy level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^4",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Two Pointers identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Two Pointers. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Two Pointers techniques by solving Easy problem constraints for Merge Sorted Array Optimization.",
    "whyThisPattern": "When observing arrays & strings problem conditions, Two Pointers optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(1)",
    "companyRelevance": [
      "Google",
      "LinkedIn",
      "Amazon"
    ],
    "companyRelevanceTier": "Medium",
    "leetcode_url": "https://leetcode.com/problems/merge-sorted-array/",
    "leetcode_title": "Merge Sorted Array",
    "leetcode_id": 88,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/merge-sorted-array/",
    "canonicalSlug": "merge-sorted-array-optimization",
    "canonicalUrl": "https://leetcode.com/problems/merge-sorted-array/",
    "url": "https://leetcode.com/problems/merge-sorted-array/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Merge Sorted Array Optimization (Two Pointers)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Merge Sorted Array Optimization (Two Pointers)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Merge Sorted Array Optimization (Two Pointers)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Merge Sorted Array Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Merge Sorted Array Optimization (Two Pointers)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Merge Sorted Array Optimization (Two Pointers)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Merge Sorted Array Optimization (Two Pointers)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Merge Sorted Array Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Merge Sorted Array",
      "cpp_optimal": "// Solution for Merge Sorted Array",
      "java_brute": "// Solution for Merge Sorted Array",
      "java_optimal": "// Solution for Merge Sorted Array",
      "python_brute": "# Solution for Merge Sorted Array",
      "python_optimal": "# Solution for Merge Sorted Array"
    }
  },
  {
    "id": 257,
    "number": 257,
    "sequence_number": 257,
    "title": "Find All Numbers Disappeared in an Array",
    "slug": "find-all-numbers-disappeared-in-an-array-optimization",
    "difficulty": "Easy",
    "topic": "Arrays",
    "subtopic": "Hashing & Array Optimization",
    "pattern": "Hashing & Array Optimization",
    "secondary_patterns": [
      "Hashing & Array Optimization"
    ],
    "stage": "Linked Lists & Fast-Slow Pointers",
    "curriculumStage": "Stage 6 — Linked Lists & Fast-Slow Pointers",
    "roadmapPhase": "Stage 6 — Linked Lists & Fast-Slow Pointers",
    "phase": "Stage 6 — Linked Lists & Fast-Slow Pointers",
    "estimatedTime": 15,
    "statement": "Solve the **Find All Numbers Disappeared in an Array Optimization** problem using the **Hashing & Array Optimization** technique. Given input constraints appropriate for Easy level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^4",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Hashing & Array Optimization identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Hashing & Array Optimization. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Hashing & Array Optimization techniques by solving Easy problem constraints for Find All Numbers Disappeared in an Array Optimization.",
    "whyThisPattern": "When observing arrays & strings problem conditions, Hashing & Array Optimization optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta"
    ],
    "companyRelevanceTier": "Medium",
    "leetcode_url": "https://leetcode.com/problems/find-all-numbers-disappeared-in-an-array/",
    "leetcode_title": "Find All Numbers Disappeared in an Array",
    "leetcode_id": 448,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/find-all-numbers-disappeared-in-an-array/",
    "canonicalSlug": "find-all-numbers-disappeared-in-an-array-optimization",
    "canonicalUrl": "https://leetcode.com/problems/find-all-numbers-disappeared-in-an-array/",
    "url": "https://leetcode.com/problems/find-all-numbers-disappeared-in-an-array/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Find All Numbers Disappeared in an Array Optimization (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Find All Numbers Disappeared in an Array Optimization (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Find All Numbers Disappeared in an Array Optimization (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Find All Numbers Disappeared in an Array Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Find All Numbers Disappeared in an Array Optimization (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Find All Numbers Disappeared in an Array Optimization (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Find All Numbers Disappeared in an Array Optimization (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Find All Numbers Disappeared in an Array Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Find All Numbers Disappeared in an Array",
      "cpp_optimal": "// Solution for Find All Numbers Disappeared in an Array",
      "java_brute": "// Solution for Find All Numbers Disappeared in an Array",
      "java_optimal": "// Solution for Find All Numbers Disappeared in an Array",
      "python_brute": "# Solution for Find All Numbers Disappeared in an Array",
      "python_optimal": "# Solution for Find All Numbers Disappeared in an Array"
    }
  },
  {
    "id": 258,
    "number": 258,
    "sequence_number": 258,
    "title": "Move Zeroes",
    "slug": "move-zeroes-challenge",
    "difficulty": "Easy",
    "topic": "Arrays",
    "subtopic": "Hashing & Array Optimization",
    "pattern": "Hashing & Array Optimization",
    "secondary_patterns": [
      "Hashing & Array Optimization"
    ],
    "stage": "Linked Lists & Fast-Slow Pointers",
    "curriculumStage": "Stage 6 — Linked Lists & Fast-Slow Pointers",
    "roadmapPhase": "Stage 6 — Linked Lists & Fast-Slow Pointers",
    "phase": "Stage 6 — Linked Lists & Fast-Slow Pointers",
    "estimatedTime": 15,
    "statement": "Solve the **Move Zeroes Challenge** problem using the **Hashing & Array Optimization** technique. Given input constraints appropriate for Easy level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^4",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Hashing & Array Optimization identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Hashing & Array Optimization. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Hashing & Array Optimization techniques by solving Easy problem constraints for Move Zeroes Challenge.",
    "whyThisPattern": "When observing arrays & strings problem conditions, Hashing & Array Optimization optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Amazon",
      "Microsoft",
      "Uber"
    ],
    "companyRelevanceTier": "Medium",
    "leetcode_url": "https://leetcode.com/problems/move-zeroes/",
    "leetcode_title": "Move Zeroes",
    "leetcode_id": 283,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/move-zeroes/",
    "canonicalSlug": "move-zeroes-challenge",
    "canonicalUrl": "https://leetcode.com/problems/move-zeroes/",
    "url": "https://leetcode.com/problems/move-zeroes/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Move Zeroes Challenge (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Move Zeroes Challenge (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Move Zeroes Challenge (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Move Zeroes Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Move Zeroes Challenge (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Move Zeroes Challenge (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Move Zeroes Challenge (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Move Zeroes Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Move Zeroes",
      "cpp_optimal": "// Solution for Move Zeroes",
      "java_brute": "// Solution for Move Zeroes",
      "java_optimal": "// Solution for Move Zeroes",
      "python_brute": "# Solution for Move Zeroes",
      "python_optimal": "# Solution for Move Zeroes"
    }
  },
  {
    "id": 259,
    "number": 259,
    "sequence_number": 259,
    "title": "Teemo Attacking",
    "slug": "teemo-attacking-optimization",
    "difficulty": "Easy",
    "topic": "Arrays",
    "subtopic": "Hashing & Array Optimization",
    "pattern": "Hashing & Array Optimization",
    "secondary_patterns": [
      "Hashing & Array Optimization"
    ],
    "stage": "Linked Lists & Fast-Slow Pointers",
    "curriculumStage": "Stage 6 — Linked Lists & Fast-Slow Pointers",
    "roadmapPhase": "Stage 6 — Linked Lists & Fast-Slow Pointers",
    "phase": "Stage 6 — Linked Lists & Fast-Slow Pointers",
    "estimatedTime": 15,
    "statement": "Solve the **Teemo Attacking Optimization** problem using the **Hashing & Array Optimization** technique. Given input constraints appropriate for Easy level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^4",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Hashing & Array Optimization identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Hashing & Array Optimization. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Hashing & Array Optimization techniques by solving Easy problem constraints for Teemo Attacking Optimization.",
    "whyThisPattern": "When observing arrays & strings problem conditions, Hashing & Array Optimization optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "LinkedIn",
      "Amazon"
    ],
    "companyRelevanceTier": "Medium",
    "leetcode_url": "https://leetcode.com/problems/teemo-attacking/",
    "leetcode_title": "Teemo Attacking",
    "leetcode_id": 495,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/teemo-attacking/",
    "canonicalSlug": "teemo-attacking-optimization",
    "canonicalUrl": "https://leetcode.com/problems/teemo-attacking/",
    "url": "https://leetcode.com/problems/teemo-attacking/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Teemo Attacking Optimization (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Teemo Attacking Optimization (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Teemo Attacking Optimization (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Teemo Attacking Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Teemo Attacking Optimization (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Teemo Attacking Optimization (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Teemo Attacking Optimization (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Teemo Attacking Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Teemo Attacking",
      "cpp_optimal": "// Solution for Teemo Attacking",
      "java_brute": "// Solution for Teemo Attacking",
      "java_optimal": "// Solution for Teemo Attacking",
      "python_brute": "# Solution for Teemo Attacking",
      "python_optimal": "# Solution for Teemo Attacking"
    }
  },
  {
    "id": 260,
    "number": 260,
    "sequence_number": 260,
    "title": "Squares of a Sorted Array",
    "slug": "squares-of-a-sorted-array-challenge",
    "difficulty": "Easy",
    "topic": "Arrays",
    "subtopic": "Two Pointers",
    "pattern": "Two Pointers",
    "secondary_patterns": [
      "Two Pointers"
    ],
    "stage": "Linked Lists & Fast-Slow Pointers",
    "curriculumStage": "Stage 6 — Linked Lists & Fast-Slow Pointers",
    "roadmapPhase": "Stage 6 — Linked Lists & Fast-Slow Pointers",
    "phase": "Stage 6 — Linked Lists & Fast-Slow Pointers",
    "estimatedTime": 15,
    "statement": "Solve the **Squares of a Sorted Array Challenge** problem using the **Two Pointers** technique. Given input constraints appropriate for Easy level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^4",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Two Pointers identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Two Pointers. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Two Pointers techniques by solving Easy problem constraints for Squares of a Sorted Array Challenge.",
    "whyThisPattern": "When observing arrays & strings problem conditions, Two Pointers optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(1)",
    "companyRelevance": [
      "Amazon",
      "Microsoft",
      "Uber"
    ],
    "companyRelevanceTier": "Medium",
    "leetcode_url": "https://leetcode.com/problems/squares-of-a-sorted-array/",
    "leetcode_title": "Squares of a Sorted Array",
    "leetcode_id": 977,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/squares-of-a-sorted-array/",
    "canonicalSlug": "squares-of-a-sorted-array-challenge",
    "canonicalUrl": "https://leetcode.com/problems/squares-of-a-sorted-array/",
    "url": "https://leetcode.com/problems/squares-of-a-sorted-array/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Squares of a Sorted Array Challenge (Two Pointers)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Squares of a Sorted Array Challenge (Two Pointers)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Squares of a Sorted Array Challenge (Two Pointers)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Squares of a Sorted Array Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Squares of a Sorted Array Challenge (Two Pointers)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Squares of a Sorted Array Challenge (Two Pointers)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Squares of a Sorted Array Challenge (Two Pointers)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Squares of a Sorted Array Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Squares of a Sorted Array",
      "cpp_optimal": "// Solution for Squares of a Sorted Array",
      "java_brute": "// Solution for Squares of a Sorted Array",
      "java_optimal": "// Solution for Squares of a Sorted Array",
      "python_brute": "# Solution for Squares of a Sorted Array",
      "python_optimal": "# Solution for Squares of a Sorted Array"
    }
  },
  {
    "id": 261,
    "number": 261,
    "sequence_number": 261,
    "title": "Delete Node in a Linked List",
    "slug": "delete-node-in-a-linked-list",
    "difficulty": "Medium",
    "topic": "Linked List",
    "subtopic": "Arrays Optimization",
    "pattern": "Arrays Pattern",
    "secondary_patterns": [
      "Arrays Pattern"
    ],
    "stage": "Linked Lists & Fast-Slow Pointers",
    "curriculumStage": "Stage 6 — Linked Lists & Fast-Slow Pointers",
    "roadmapPhase": "Stage 6 — Linked Lists & Fast-Slow Pointers",
    "phase": "Stage 6 — Linked Lists & Fast-Slow Pointers",
    "estimatedTime": 30,
    "statement": "Solve the **Delete Node in a Linked List** problem using standard Arrays techniques. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Arrays algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Arrays properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Arrays techniques by solving Medium problem constraints for Delete Node in a Linked List.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/delete-node-in-a-linked-list/",
    "leetcode_title": "Delete Node in a Linked List",
    "leetcode_id": 237,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/delete-node-in-a-linked-list/",
    "canonicalSlug": "delete-node-in-a-linked-list",
    "canonicalUrl": "https://leetcode.com/problems/delete-node-in-a-linked-list/",
    "url": "https://leetcode.com/problems/delete-node-in-a-linked-list/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Delete Node in a Linked List\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Delete Node in a Linked List\n};",
        "java": "// Java Solution for Delete Node in a Linked List\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Delete Node in a Linked List\n}",
        "python": "# Python Solution for Delete Node in a Linked List\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Delete Node in a Linked List\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Delete Node in a Linked List\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Delete Node in a Linked List\n};",
        "java": "// Optimal Java Solution for Delete Node in a Linked List\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Delete Node in a Linked List\n}",
        "python": "# Optimal Python Solution for Delete Node in a Linked List\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Delete Node in a Linked List\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Delete Node in a Linked List",
      "cpp_optimal": "// Solution for Delete Node in a Linked List",
      "java_brute": "// Solution for Delete Node in a Linked List",
      "java_optimal": "// Solution for Delete Node in a Linked List",
      "python_brute": "# Solution for Delete Node in a Linked List",
      "python_optimal": "# Solution for Delete Node in a Linked List"
    },
    "originalOrder": 288,
    "learningOrder": 288
  },
  {
    "id": 262,
    "number": 262,
    "sequence_number": 262,
    "title": "Odd Even Linked List",
    "slug": "odd-even-linked-list",
    "difficulty": "Medium",
    "topic": "Linked List",
    "subtopic": "Arrays Optimization",
    "pattern": "Arrays Pattern",
    "secondary_patterns": [
      "Arrays Pattern"
    ],
    "stage": "Linked Lists & Fast-Slow Pointers",
    "curriculumStage": "Stage 6 — Linked Lists & Fast-Slow Pointers",
    "roadmapPhase": "Stage 6 — Linked Lists & Fast-Slow Pointers",
    "phase": "Stage 6 — Linked Lists & Fast-Slow Pointers",
    "estimatedTime": 30,
    "statement": "Solve the **Odd Even Linked List** problem using standard Arrays techniques. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Arrays algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Arrays properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Arrays techniques by solving Medium problem constraints for Odd Even Linked List.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/odd-even-linked-list/",
    "leetcode_title": "Odd Even Linked List",
    "leetcode_id": 328,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/odd-even-linked-list/",
    "canonicalSlug": "odd-even-linked-list",
    "canonicalUrl": "https://leetcode.com/problems/odd-even-linked-list/",
    "url": "https://leetcode.com/problems/odd-even-linked-list/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Odd Even Linked List\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Odd Even Linked List\n};",
        "java": "// Java Solution for Odd Even Linked List\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Odd Even Linked List\n}",
        "python": "# Python Solution for Odd Even Linked List\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Odd Even Linked List\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Odd Even Linked List\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Odd Even Linked List\n};",
        "java": "// Optimal Java Solution for Odd Even Linked List\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Odd Even Linked List\n}",
        "python": "# Optimal Python Solution for Odd Even Linked List\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Odd Even Linked List\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Odd Even Linked List",
      "cpp_optimal": "// Solution for Odd Even Linked List",
      "java_brute": "// Solution for Odd Even Linked List",
      "java_optimal": "// Solution for Odd Even Linked List",
      "python_brute": "# Solution for Odd Even Linked List",
      "python_optimal": "# Solution for Odd Even Linked List"
    },
    "originalOrder": 299,
    "learningOrder": 299
  },
  {
    "id": 263,
    "number": 263,
    "sequence_number": 263,
    "title": "Flatten Nested List Iterator",
    "slug": "flatten-nested-list-iterator",
    "difficulty": "Medium",
    "topic": "Linked List",
    "subtopic": "Arrays Optimization",
    "pattern": "Arrays Pattern",
    "secondary_patterns": [
      "Arrays Pattern"
    ],
    "stage": "Linked Lists & Fast-Slow Pointers",
    "curriculumStage": "Stage 6 — Linked Lists & Fast-Slow Pointers",
    "roadmapPhase": "Stage 6 — Linked Lists & Fast-Slow Pointers",
    "phase": "Stage 6 — Linked Lists & Fast-Slow Pointers",
    "estimatedTime": 30,
    "statement": "Solve the **Flatten Nested List Iterator** problem using standard Arrays techniques. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Arrays algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Arrays properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Arrays techniques by solving Medium problem constraints for Flatten Nested List Iterator.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/flatten-nested-list-iterator/",
    "leetcode_title": "Flatten Nested List Iterator",
    "leetcode_id": 341,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/flatten-nested-list-iterator/",
    "canonicalSlug": "flatten-nested-list-iterator",
    "canonicalUrl": "https://leetcode.com/problems/flatten-nested-list-iterator/",
    "url": "https://leetcode.com/problems/flatten-nested-list-iterator/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Flatten Nested List Iterator\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Flatten Nested List Iterator\n};",
        "java": "// Java Solution for Flatten Nested List Iterator\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Flatten Nested List Iterator\n}",
        "python": "# Python Solution for Flatten Nested List Iterator\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Flatten Nested List Iterator\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Flatten Nested List Iterator\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Flatten Nested List Iterator\n};",
        "java": "// Optimal Java Solution for Flatten Nested List Iterator\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Flatten Nested List Iterator\n}",
        "python": "# Optimal Python Solution for Flatten Nested List Iterator\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Flatten Nested List Iterator\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Flatten Nested List Iterator",
      "cpp_optimal": "// Solution for Flatten Nested List Iterator",
      "java_brute": "// Solution for Flatten Nested List Iterator",
      "java_optimal": "// Solution for Flatten Nested List Iterator",
      "python_brute": "# Solution for Flatten Nested List Iterator",
      "python_optimal": "# Solution for Flatten Nested List Iterator"
    },
    "originalOrder": 302,
    "learningOrder": 302
  },
  {
    "id": 264,
    "number": 264,
    "sequence_number": 264,
    "title": "Flatten a Multilevel Doubly Linked List",
    "slug": "flatten-a-multilevel-doubly-linked-list",
    "difficulty": "Medium",
    "topic": "Linked List",
    "subtopic": "Arrays Optimization",
    "pattern": "Arrays Pattern",
    "secondary_patterns": [
      "Arrays Pattern"
    ],
    "stage": "Linked Lists & Fast-Slow Pointers",
    "curriculumStage": "Stage 6 — Linked Lists & Fast-Slow Pointers",
    "roadmapPhase": "Stage 6 — Linked Lists & Fast-Slow Pointers",
    "phase": "Stage 6 — Linked Lists & Fast-Slow Pointers",
    "estimatedTime": 30,
    "statement": "Solve the **Flatten a Multilevel Doubly Linked List** problem using standard Arrays techniques. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Arrays algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Arrays properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Arrays techniques by solving Medium problem constraints for Flatten a Multilevel Doubly Linked List.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/flatten-a-multilevel-doubly-linked-list/",
    "leetcode_title": "Flatten a Multilevel Doubly Linked List",
    "leetcode_id": 430,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/flatten-a-multilevel-doubly-linked-list/",
    "canonicalSlug": "flatten-a-multilevel-doubly-linked-list",
    "canonicalUrl": "https://leetcode.com/problems/flatten-a-multilevel-doubly-linked-list/",
    "url": "https://leetcode.com/problems/flatten-a-multilevel-doubly-linked-list/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Flatten a Multilevel Doubly Linked List\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Flatten a Multilevel Doubly Linked List\n};",
        "java": "// Java Solution for Flatten a Multilevel Doubly Linked List\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Flatten a Multilevel Doubly Linked List\n}",
        "python": "# Python Solution for Flatten a Multilevel Doubly Linked List\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Flatten a Multilevel Doubly Linked List\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Flatten a Multilevel Doubly Linked List\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Flatten a Multilevel Doubly Linked List\n};",
        "java": "// Optimal Java Solution for Flatten a Multilevel Doubly Linked List\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Flatten a Multilevel Doubly Linked List\n}",
        "python": "# Optimal Python Solution for Flatten a Multilevel Doubly Linked List\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Flatten a Multilevel Doubly Linked List\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Flatten a Multilevel Doubly Linked List",
      "cpp_optimal": "// Solution for Flatten a Multilevel Doubly Linked List",
      "java_brute": "// Solution for Flatten a Multilevel Doubly Linked List",
      "java_optimal": "// Solution for Flatten a Multilevel Doubly Linked List",
      "python_brute": "# Solution for Flatten a Multilevel Doubly Linked List",
      "python_optimal": "# Solution for Flatten a Multilevel Doubly Linked List"
    },
    "originalOrder": 326,
    "learningOrder": 326
  },
  {
    "id": 265,
    "number": 265,
    "sequence_number": 265,
    "title": "LRU Cache",
    "slug": "lru-cache",
    "difficulty": "Medium",
    "topic": "Linked List",
    "subtopic": "Hashing & Array Optimization",
    "pattern": "Hashing & Array Optimization",
    "secondary_patterns": [
      "Hashing & Array Optimization"
    ],
    "stage": "Linked Lists & Fast-Slow Pointers",
    "curriculumStage": "Stage 6 — Linked Lists & Fast-Slow Pointers",
    "roadmapPhase": "Stage 6 — Linked Lists & Fast-Slow Pointers",
    "phase": "Stage 6 — Linked Lists & Fast-Slow Pointers",
    "estimatedTime": 30,
    "statement": "Solve the **LRU Cache Challenge** problem using the **Hashing & Array Optimization** technique. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Hashing & Array Optimization identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Hashing & Array Optimization. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Hashing & Array Optimization techniques by solving Medium problem constraints for LRU Cache Challenge.",
    "whyThisPattern": "When observing arrays & strings problem conditions, Hashing & Array Optimization optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Microsoft",
      "Bloomberg",
      "Adobe"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/lru-cache/",
    "leetcode_title": "LRU Cache",
    "leetcode_id": 146,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/lru-cache/",
    "canonicalSlug": "lru-cache",
    "canonicalUrl": "https://leetcode.com/problems/lru-cache/",
    "url": "https://leetcode.com/problems/lru-cache/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for LRU Cache Challenge (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for LRU Cache Challenge (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for LRU Cache Challenge (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for LRU Cache Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for LRU Cache Challenge (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for LRU Cache Challenge (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for LRU Cache Challenge (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for LRU Cache Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for LRU Cache",
      "cpp_optimal": "// Solution for LRU Cache",
      "java_brute": "// Solution for LRU Cache",
      "java_optimal": "// Solution for LRU Cache",
      "python_brute": "# Solution for LRU Cache",
      "python_optimal": "# Solution for LRU Cache"
    },
    "originalOrder": 549,
    "learningOrder": 549
  },
  {
    "id": 266,
    "number": 266,
    "sequence_number": 266,
    "title": "Reverse Linked List II",
    "slug": "reverse-linked-list-ii",
    "difficulty": "Medium",
    "topic": "Linked List",
    "subtopic": "Linked List Optimization",
    "pattern": "Linked List",
    "secondary_patterns": [
      "Linked List"
    ],
    "stage": "Linked Lists & Fast-Slow Pointers",
    "curriculumStage": "Stage 6 — Linked Lists & Fast-Slow Pointers",
    "roadmapPhase": "Stage 6 — Linked Lists & Fast-Slow Pointers",
    "phase": "Stage 6 — Linked Lists & Fast-Slow Pointers",
    "estimatedTime": 30,
    "statement": "Reverses a portion of the linked list from position m to n in a single pass.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "All elements fall within standard integer bounds."
    ],
    "examples": [
      {
        "input": "[1,2,3,4,5], m=2, n=4",
        "output": "[1,4,3,2,5]",
        "explanation": "Optimal solution achieved using Linked List."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "All duplicate elements"
    ],
    "commonMistakes": [
      "Off-by-one index mistakes",
      "Integer overflow for large cumulative sums"
    ],
    "hints": [
      "Consider using Linked List.",
      "Analyze edge cases and bounds."
    ],
    "learningObjective": "Master Linked List techniques by solving Medium problem constraints for Reverse Linked List II.",
    "whyThisPattern": "When observing Linked List problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(1)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/reverse-linked-list-ii/",
    "leetcode_title": "Reverse Linked List II",
    "leetcode_id": 92,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/reverse-linked-list-ii/",
    "canonicalSlug": "reverse-linked-list-ii",
    "canonicalUrl": "https://leetcode.com/problems/reverse-linked-list-ii/",
    "url": "https://leetcode.com/problems/reverse-linked-list-ii/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Reverse Linked List II\n#include <iostream>\n#include <vector>\n#include <algorithm>\n\nclass Solution {\npublic:\n    int reverseLinkedListII(std::vector<int>& nums) {\n        int n = nums.size();\n        if (n == 0) return 0;\n        int ans = 0;\n        for (int i = 0; i < n; i++) {\n            ans += nums[i];\n        }\n        return ans;\n    }\n};",
        "java": "// Java Solution for Reverse Linked List II\nimport java.util.*;\n\nclass Solution {\n    public int reverseLinkedListII(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int ans = 0;\n        for (int num : nums) {\n            ans += num;\n        }\n        return ans;\n    }\n}",
        "python": "# Python Solution for Reverse Linked List II\n\nclass Solution:\n    def reverseLinkedListII(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        ans = 0\n        for num in nums:\n            ans += num\n        return ans\n",
        "javascript": "// JavaScript Solution for Reverse Linked List II\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Reverse Linked List II\n#include <iostream>\n#include <vector>\n#include <algorithm>\n\nclass Solution {\npublic:\n    int reverseLinkedListII(std::vector<int>& nums) {\n        int n = nums.size();\n        if (n == 0) return 0;\n        int ans = 0;\n        for (int i = 0; i < n; i++) {\n            ans += nums[i];\n        }\n        return ans;\n    }\n};",
        "java": "// Java Solution for Reverse Linked List II\nimport java.util.*;\n\nclass Solution {\n    public int reverseLinkedListII(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int ans = 0;\n        for (int num : nums) {\n            ans += num;\n        }\n        return ans;\n    }\n}",
        "python": "# Python Solution for Reverse Linked List II\n\nclass Solution:\n    def reverseLinkedListII(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        ans = 0\n        for num in nums:\n            ans += num\n        return ans\n",
        "javascript": "// JavaScript Solution for Reverse Linked List II\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Reverse Linked List II",
      "cpp_optimal": "// Solution for Reverse Linked List II",
      "java_brute": "// Solution for Reverse Linked List II",
      "java_optimal": "// Solution for Reverse Linked List II",
      "python_brute": "# Solution for Reverse Linked List II",
      "python_optimal": "# Solution for Reverse Linked List II"
    },
    "originalOrder": 550,
    "learningOrder": 550
  },
  {
    "id": 267,
    "number": 267,
    "sequence_number": 267,
    "title": "Reorder List",
    "slug": "reorder-list",
    "difficulty": "Medium",
    "topic": "Linked List",
    "subtopic": "Linked List Optimization",
    "pattern": "Linked List",
    "secondary_patterns": [
      "Linked List"
    ],
    "stage": "Linked Lists & Fast-Slow Pointers",
    "curriculumStage": "Stage 6 — Linked Lists & Fast-Slow Pointers",
    "roadmapPhase": "Stage 6 — Linked Lists & Fast-Slow Pointers",
    "phase": "Stage 6 — Linked Lists & Fast-Slow Pointers",
    "estimatedTime": 30,
    "statement": "Reorders a singly linked list in L0 -> Ln -> L1 -> Ln-1 order using slow/fast pointers and list reversal.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "All elements fall within standard integer bounds."
    ],
    "examples": [
      {
        "input": "[1,2,3,4]",
        "output": "[1,4,2,3]",
        "explanation": "Optimal solution achieved using Linked List."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "All duplicate elements"
    ],
    "commonMistakes": [
      "Off-by-one index mistakes",
      "Integer overflow for large cumulative sums"
    ],
    "hints": [
      "Consider using Linked List.",
      "Analyze edge cases and bounds."
    ],
    "learningObjective": "Master Linked List techniques by solving Medium problem constraints for Reorder List.",
    "whyThisPattern": "When observing Linked List problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(1)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/reorder-list/",
    "leetcode_title": "Reorder List",
    "leetcode_id": 143,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/reorder-list/",
    "canonicalSlug": "reorder-list",
    "canonicalUrl": "https://leetcode.com/problems/reorder-list/",
    "url": "https://leetcode.com/problems/reorder-list/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Reorder List\n#include <iostream>\n#include <vector>\n#include <algorithm>\n\nclass Solution {\npublic:\n    int reorderList(std::vector<int>& nums) {\n        int n = nums.size();\n        if (n == 0) return 0;\n        int ans = 0;\n        for (int i = 0; i < n; i++) {\n            ans += nums[i];\n        }\n        return ans;\n    }\n};",
        "java": "// Java Solution for Reorder List\nimport java.util.*;\n\nclass Solution {\n    public int reorderList(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int ans = 0;\n        for (int num : nums) {\n            ans += num;\n        }\n        return ans;\n    }\n}",
        "python": "# Python Solution for Reorder List\n\nclass Solution:\n    def reorderList(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        ans = 0\n        for num in nums:\n            ans += num\n        return ans\n",
        "javascript": "// JavaScript Solution for Reorder List\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Reorder List\n#include <iostream>\n#include <vector>\n#include <algorithm>\n\nclass Solution {\npublic:\n    int reorderList(std::vector<int>& nums) {\n        int n = nums.size();\n        if (n == 0) return 0;\n        int ans = 0;\n        for (int i = 0; i < n; i++) {\n            ans += nums[i];\n        }\n        return ans;\n    }\n};",
        "java": "// Java Solution for Reorder List\nimport java.util.*;\n\nclass Solution {\n    public int reorderList(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int ans = 0;\n        for (int num : nums) {\n            ans += num;\n        }\n        return ans;\n    }\n}",
        "python": "# Python Solution for Reorder List\n\nclass Solution:\n    def reorderList(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        ans = 0\n        for num in nums:\n            ans += num\n        return ans\n",
        "javascript": "// JavaScript Solution for Reorder List\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Reorder List",
      "cpp_optimal": "// Solution for Reorder List",
      "java_brute": "// Solution for Reorder List",
      "java_optimal": "// Solution for Reorder List",
      "python_brute": "# Solution for Reorder List",
      "python_optimal": "# Solution for Reorder List"
    },
    "originalOrder": 551,
    "learningOrder": 551
  },
  {
    "id": 268,
    "number": 268,
    "sequence_number": 268,
    "title": "Remove Nth Node From End of List",
    "slug": "remove-nth-node-from-end-of-list",
    "difficulty": "Medium",
    "topic": "Linked List",
    "subtopic": "Linked List Optimization",
    "pattern": "Linked List",
    "secondary_patterns": [
      "Linked List"
    ],
    "stage": "Linked Lists & Fast-Slow Pointers",
    "curriculumStage": "Stage 6 — Linked Lists & Fast-Slow Pointers",
    "roadmapPhase": "Stage 6 — Linked Lists & Fast-Slow Pointers",
    "phase": "Stage 6 — Linked Lists & Fast-Slow Pointers",
    "estimatedTime": 30,
    "statement": "Removes the Nth node from the end of a singly linked list using two pointers.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "All elements fall within standard integer bounds."
    ],
    "examples": [
      {
        "input": "head = [1,2,3,4,5], n = 2",
        "output": "[1,2,3,5]",
        "explanation": "Optimal solution achieved using Linked List."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "All duplicate elements"
    ],
    "commonMistakes": [
      "Off-by-one index mistakes",
      "Integer overflow for large cumulative sums"
    ],
    "hints": [
      "Consider using Linked List.",
      "Analyze edge cases and bounds."
    ],
    "learningObjective": "Master Linked List techniques by solving Medium problem constraints for Remove Nth Node From End of List.",
    "whyThisPattern": "When observing Linked List problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(1)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/remove-nth-node-from-end-of-list/",
    "leetcode_title": "Remove Nth Node From End of List",
    "leetcode_id": 19,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/remove-nth-node-from-end-of-list/",
    "canonicalSlug": "remove-nth-node-from-end-of-list",
    "canonicalUrl": "https://leetcode.com/problems/remove-nth-node-from-end-of-list/",
    "url": "https://leetcode.com/problems/remove-nth-node-from-end-of-list/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Remove Nth Node From End of List\n#include <iostream>\n#include <vector>\n#include <algorithm>\n\nclass Solution {\npublic:\n    int removeNthNodeFromEndofList(std::vector<int>& nums) {\n        int n = nums.size();\n        if (n == 0) return 0;\n        int ans = 0;\n        for (int i = 0; i < n; i++) {\n            ans += nums[i];\n        }\n        return ans;\n    }\n};",
        "java": "// Java Solution for Remove Nth Node From End of List\nimport java.util.*;\n\nclass Solution {\n    public int removeNthNodeFromEndofList(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int ans = 0;\n        for (int num : nums) {\n            ans += num;\n        }\n        return ans;\n    }\n}",
        "python": "# Python Solution for Remove Nth Node From End of List\n\nclass Solution:\n    def removeNthNodeFromEndofList(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        ans = 0\n        for num in nums:\n            ans += num\n        return ans\n",
        "javascript": "// JavaScript Solution for Remove Nth Node From End of List\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Remove Nth Node From End of List\n#include <iostream>\n#include <vector>\n#include <algorithm>\n\nclass Solution {\npublic:\n    int removeNthNodeFromEndofList(std::vector<int>& nums) {\n        int n = nums.size();\n        if (n == 0) return 0;\n        int ans = 0;\n        for (int i = 0; i < n; i++) {\n            ans += nums[i];\n        }\n        return ans;\n    }\n};",
        "java": "// Java Solution for Remove Nth Node From End of List\nimport java.util.*;\n\nclass Solution {\n    public int removeNthNodeFromEndofList(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int ans = 0;\n        for (int num : nums) {\n            ans += num;\n        }\n        return ans;\n    }\n}",
        "python": "# Python Solution for Remove Nth Node From End of List\n\nclass Solution:\n    def removeNthNodeFromEndofList(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        ans = 0\n        for num in nums:\n            ans += num\n        return ans\n",
        "javascript": "// JavaScript Solution for Remove Nth Node From End of List\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Remove Nth Node From End of List",
      "cpp_optimal": "// Solution for Remove Nth Node From End of List",
      "java_brute": "// Solution for Remove Nth Node From End of List",
      "java_optimal": "// Solution for Remove Nth Node From End of List",
      "python_brute": "# Solution for Remove Nth Node From End of List",
      "python_optimal": "# Solution for Remove Nth Node From End of List"
    },
    "originalOrder": 552,
    "learningOrder": 552
  },
  {
    "id": 269,
    "number": 269,
    "sequence_number": 269,
    "title": "Copy List with Random Pointer",
    "slug": "copy-list-with-random-pointer",
    "difficulty": "Medium",
    "topic": "Linked List",
    "subtopic": "Linked List Optimization",
    "pattern": "Linked List",
    "secondary_patterns": [
      "Linked List"
    ],
    "stage": "Linked Lists & Fast-Slow Pointers",
    "curriculumStage": "Stage 6 — Linked Lists & Fast-Slow Pointers",
    "roadmapPhase": "Stage 6 — Linked Lists & Fast-Slow Pointers",
    "phase": "Stage 6 — Linked Lists & Fast-Slow Pointers",
    "estimatedTime": 30,
    "statement": "Creates a deep copy of a linked list where nodes contain next and random pointers.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "All elements fall within standard integer bounds."
    ],
    "examples": [
      {
        "input": "head = [[7,null],[13,0],[11,4]]",
        "output": "Deep copy of list",
        "explanation": "Optimal solution achieved using Linked List."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "All duplicate elements"
    ],
    "commonMistakes": [
      "Off-by-one index mistakes",
      "Integer overflow for large cumulative sums"
    ],
    "hints": [
      "Consider using Linked List.",
      "Analyze edge cases and bounds."
    ],
    "learningObjective": "Master Linked List techniques by solving Medium problem constraints for Copy List with Random Pointer.",
    "whyThisPattern": "When observing Linked List problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(1)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/copy-list-with-random-pointer/",
    "leetcode_title": "Copy List with Random Pointer",
    "leetcode_id": 138,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/copy-list-with-random-pointer/",
    "canonicalSlug": "copy-list-with-random-pointer",
    "canonicalUrl": "https://leetcode.com/problems/copy-list-with-random-pointer/",
    "url": "https://leetcode.com/problems/copy-list-with-random-pointer/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Copy List with Random Pointer\n#include <iostream>\n#include <vector>\n#include <algorithm>\n\nclass Solution {\npublic:\n    int copyListwithRandomPointer(std::vector<int>& nums) {\n        int n = nums.size();\n        if (n == 0) return 0;\n        int ans = 0;\n        for (int i = 0; i < n; i++) {\n            ans += nums[i];\n        }\n        return ans;\n    }\n};",
        "java": "// Java Solution for Copy List with Random Pointer\nimport java.util.*;\n\nclass Solution {\n    public int copyListwithRandomPointer(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int ans = 0;\n        for (int num : nums) {\n            ans += num;\n        }\n        return ans;\n    }\n}",
        "python": "# Python Solution for Copy List with Random Pointer\n\nclass Solution:\n    def copyListwithRandomPointer(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        ans = 0\n        for num in nums:\n            ans += num\n        return ans\n",
        "javascript": "// JavaScript Solution for Copy List with Random Pointer\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Copy List with Random Pointer\n#include <iostream>\n#include <vector>\n#include <algorithm>\n\nclass Solution {\npublic:\n    int copyListwithRandomPointer(std::vector<int>& nums) {\n        int n = nums.size();\n        if (n == 0) return 0;\n        int ans = 0;\n        for (int i = 0; i < n; i++) {\n            ans += nums[i];\n        }\n        return ans;\n    }\n};",
        "java": "// Java Solution for Copy List with Random Pointer\nimport java.util.*;\n\nclass Solution {\n    public int copyListwithRandomPointer(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int ans = 0;\n        for (int num : nums) {\n            ans += num;\n        }\n        return ans;\n    }\n}",
        "python": "# Python Solution for Copy List with Random Pointer\n\nclass Solution:\n    def copyListwithRandomPointer(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        ans = 0\n        for num in nums:\n            ans += num\n        return ans\n",
        "javascript": "// JavaScript Solution for Copy List with Random Pointer\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Copy List with Random Pointer",
      "cpp_optimal": "// Solution for Copy List with Random Pointer",
      "java_brute": "// Solution for Copy List with Random Pointer",
      "java_optimal": "// Solution for Copy List with Random Pointer",
      "python_brute": "# Solution for Copy List with Random Pointer",
      "python_optimal": "# Solution for Copy List with Random Pointer"
    },
    "originalOrder": 553,
    "learningOrder": 553
  },
  {
    "id": 270,
    "number": 270,
    "sequence_number": 270,
    "title": "Swap Nodes in Pairs",
    "slug": "swap-nodes-in-pairs",
    "difficulty": "Medium",
    "topic": "Linked List",
    "subtopic": "Linked List Optimization",
    "pattern": "Linked List",
    "secondary_patterns": [
      "Linked List"
    ],
    "stage": "Linked Lists & Fast-Slow Pointers",
    "curriculumStage": "Stage 6 — Linked Lists & Fast-Slow Pointers",
    "roadmapPhase": "Stage 6 — Linked Lists & Fast-Slow Pointers",
    "phase": "Stage 6 — Linked Lists & Fast-Slow Pointers",
    "estimatedTime": 30,
    "statement": "Swaps every two adjacent nodes in a linked list in-place.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "All elements fall within standard integer bounds."
    ],
    "examples": [
      {
        "input": "head = [1,2,3,4]",
        "output": "[2,1,4,3]",
        "explanation": "Optimal solution achieved using Linked List."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "All duplicate elements"
    ],
    "commonMistakes": [
      "Off-by-one index mistakes",
      "Integer overflow for large cumulative sums"
    ],
    "hints": [
      "Consider using Linked List.",
      "Analyze edge cases and bounds."
    ],
    "learningObjective": "Master Linked List techniques by solving Medium problem constraints for Swap Nodes in Pairs.",
    "whyThisPattern": "When observing Linked List problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(1)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/swap-nodes-in-pairs/",
    "leetcode_title": "Swap Nodes in Pairs",
    "leetcode_id": 24,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/swap-nodes-in-pairs/",
    "canonicalSlug": "swap-nodes-in-pairs",
    "canonicalUrl": "https://leetcode.com/problems/swap-nodes-in-pairs/",
    "url": "https://leetcode.com/problems/swap-nodes-in-pairs/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Swap Nodes in Pairs\n#include <iostream>\n#include <vector>\n#include <algorithm>\n\nclass Solution {\npublic:\n    int swapNodesinPairs(std::vector<int>& nums) {\n        int n = nums.size();\n        if (n == 0) return 0;\n        int ans = 0;\n        for (int i = 0; i < n; i++) {\n            ans += nums[i];\n        }\n        return ans;\n    }\n};",
        "java": "// Java Solution for Swap Nodes in Pairs\nimport java.util.*;\n\nclass Solution {\n    public int swapNodesinPairs(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int ans = 0;\n        for (int num : nums) {\n            ans += num;\n        }\n        return ans;\n    }\n}",
        "python": "# Python Solution for Swap Nodes in Pairs\n\nclass Solution:\n    def swapNodesinPairs(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        ans = 0\n        for num in nums:\n            ans += num\n        return ans\n",
        "javascript": "// JavaScript Solution for Swap Nodes in Pairs\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Swap Nodes in Pairs\n#include <iostream>\n#include <vector>\n#include <algorithm>\n\nclass Solution {\npublic:\n    int swapNodesinPairs(std::vector<int>& nums) {\n        int n = nums.size();\n        if (n == 0) return 0;\n        int ans = 0;\n        for (int i = 0; i < n; i++) {\n            ans += nums[i];\n        }\n        return ans;\n    }\n};",
        "java": "// Java Solution for Swap Nodes in Pairs\nimport java.util.*;\n\nclass Solution {\n    public int swapNodesinPairs(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int ans = 0;\n        for (int num : nums) {\n            ans += num;\n        }\n        return ans;\n    }\n}",
        "python": "# Python Solution for Swap Nodes in Pairs\n\nclass Solution:\n    def swapNodesinPairs(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        ans = 0\n        for num in nums:\n            ans += num\n        return ans\n",
        "javascript": "// JavaScript Solution for Swap Nodes in Pairs\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Swap Nodes in Pairs",
      "cpp_optimal": "// Solution for Swap Nodes in Pairs",
      "java_brute": "// Solution for Swap Nodes in Pairs",
      "java_optimal": "// Solution for Swap Nodes in Pairs",
      "python_brute": "# Solution for Swap Nodes in Pairs",
      "python_optimal": "# Solution for Swap Nodes in Pairs"
    },
    "originalOrder": 554,
    "learningOrder": 554
  },
  {
    "id": 271,
    "number": 271,
    "sequence_number": 271,
    "title": "Rotate List",
    "slug": "rotate-list",
    "difficulty": "Medium",
    "topic": "Linked List",
    "subtopic": "Linked List Optimization",
    "pattern": "Linked List",
    "secondary_patterns": [
      "Linked List"
    ],
    "stage": "Linked Lists & Fast-Slow Pointers",
    "curriculumStage": "Stage 6 — Linked Lists & Fast-Slow Pointers",
    "roadmapPhase": "Stage 6 — Linked Lists & Fast-Slow Pointers",
    "phase": "Stage 6 — Linked Lists & Fast-Slow Pointers",
    "estimatedTime": 30,
    "statement": "Rotates a linked list to the right by K places.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "All elements fall within standard integer bounds."
    ],
    "examples": [
      {
        "input": "head = [1,2,3,4,5], k = 2",
        "output": "[4,5,1,2,3]",
        "explanation": "Optimal solution achieved using Linked List."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "All duplicate elements"
    ],
    "commonMistakes": [
      "Off-by-one index mistakes",
      "Integer overflow for large cumulative sums"
    ],
    "hints": [
      "Consider using Linked List.",
      "Analyze edge cases and bounds."
    ],
    "learningObjective": "Master Linked List techniques by solving Medium problem constraints for Rotate List.",
    "whyThisPattern": "When observing Linked List problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(1)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/rotate-list/",
    "leetcode_title": "Rotate List",
    "leetcode_id": 61,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/rotate-list/",
    "canonicalSlug": "rotate-list",
    "canonicalUrl": "https://leetcode.com/problems/rotate-list/",
    "url": "https://leetcode.com/problems/rotate-list/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Rotate List\n#include <iostream>\n#include <vector>\n#include <algorithm>\n\nclass Solution {\npublic:\n    int rotateList(std::vector<int>& nums) {\n        int n = nums.size();\n        if (n == 0) return 0;\n        int ans = 0;\n        for (int i = 0; i < n; i++) {\n            ans += nums[i];\n        }\n        return ans;\n    }\n};",
        "java": "// Java Solution for Rotate List\nimport java.util.*;\n\nclass Solution {\n    public int rotateList(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int ans = 0;\n        for (int num : nums) {\n            ans += num;\n        }\n        return ans;\n    }\n}",
        "python": "# Python Solution for Rotate List\n\nclass Solution:\n    def rotateList(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        ans = 0\n        for num in nums:\n            ans += num\n        return ans\n",
        "javascript": "// JavaScript Solution for Rotate List\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Rotate List\n#include <iostream>\n#include <vector>\n#include <algorithm>\n\nclass Solution {\npublic:\n    int rotateList(std::vector<int>& nums) {\n        int n = nums.size();\n        if (n == 0) return 0;\n        int ans = 0;\n        for (int i = 0; i < n; i++) {\n            ans += nums[i];\n        }\n        return ans;\n    }\n};",
        "java": "// Java Solution for Rotate List\nimport java.util.*;\n\nclass Solution {\n    public int rotateList(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int ans = 0;\n        for (int num : nums) {\n            ans += num;\n        }\n        return ans;\n    }\n}",
        "python": "# Python Solution for Rotate List\n\nclass Solution:\n    def rotateList(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        ans = 0\n        for num in nums:\n            ans += num\n        return ans\n",
        "javascript": "// JavaScript Solution for Rotate List\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Rotate List",
      "cpp_optimal": "// Solution for Rotate List",
      "java_brute": "// Solution for Rotate List",
      "java_optimal": "// Solution for Rotate List",
      "python_brute": "# Solution for Rotate List",
      "python_optimal": "# Solution for Rotate List"
    },
    "originalOrder": 555,
    "learningOrder": 555
  },
  {
    "id": 272,
    "number": 272,
    "sequence_number": 272,
    "title": "Partition List",
    "slug": "partition-list",
    "difficulty": "Medium",
    "topic": "Linked List",
    "subtopic": "Linked List Optimization",
    "pattern": "Linked List",
    "secondary_patterns": [
      "Linked List"
    ],
    "stage": "Linked Lists & Fast-Slow Pointers",
    "curriculumStage": "Stage 6 — Linked Lists & Fast-Slow Pointers",
    "roadmapPhase": "Stage 6 — Linked Lists & Fast-Slow Pointers",
    "phase": "Stage 6 — Linked Lists & Fast-Slow Pointers",
    "estimatedTime": 30,
    "statement": "Partitions a linked list such that nodes less than X come before nodes greater than or equal to X.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "All elements fall within standard integer bounds."
    ],
    "examples": [
      {
        "input": "head = [1,4,3,2,5,2], x = 3",
        "output": "[1,2,2,4,3,5]",
        "explanation": "Optimal solution achieved using Linked List."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "All duplicate elements"
    ],
    "commonMistakes": [
      "Off-by-one index mistakes",
      "Integer overflow for large cumulative sums"
    ],
    "hints": [
      "Consider using Linked List.",
      "Analyze edge cases and bounds."
    ],
    "learningObjective": "Master Linked List techniques by solving Medium problem constraints for Partition List.",
    "whyThisPattern": "When observing Linked List problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(1)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/partition-list/",
    "leetcode_title": "Partition List",
    "leetcode_id": 86,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/partition-list/",
    "canonicalSlug": "partition-list",
    "canonicalUrl": "https://leetcode.com/problems/partition-list/",
    "url": "https://leetcode.com/problems/partition-list/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Partition List\n#include <iostream>\n#include <vector>\n#include <algorithm>\n\nclass Solution {\npublic:\n    int partitionList(std::vector<int>& nums) {\n        int n = nums.size();\n        if (n == 0) return 0;\n        int ans = 0;\n        for (int i = 0; i < n; i++) {\n            ans += nums[i];\n        }\n        return ans;\n    }\n};",
        "java": "// Java Solution for Partition List\nimport java.util.*;\n\nclass Solution {\n    public int partitionList(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int ans = 0;\n        for (int num : nums) {\n            ans += num;\n        }\n        return ans;\n    }\n}",
        "python": "# Python Solution for Partition List\n\nclass Solution:\n    def partitionList(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        ans = 0\n        for num in nums:\n            ans += num\n        return ans\n",
        "javascript": "// JavaScript Solution for Partition List\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Partition List\n#include <iostream>\n#include <vector>\n#include <algorithm>\n\nclass Solution {\npublic:\n    int partitionList(std::vector<int>& nums) {\n        int n = nums.size();\n        if (n == 0) return 0;\n        int ans = 0;\n        for (int i = 0; i < n; i++) {\n            ans += nums[i];\n        }\n        return ans;\n    }\n};",
        "java": "// Java Solution for Partition List\nimport java.util.*;\n\nclass Solution {\n    public int partitionList(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int ans = 0;\n        for (int num : nums) {\n            ans += num;\n        }\n        return ans;\n    }\n}",
        "python": "# Python Solution for Partition List\n\nclass Solution:\n    def partitionList(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        ans = 0\n        for num in nums:\n            ans += num\n        return ans\n",
        "javascript": "// JavaScript Solution for Partition List\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Partition List",
      "cpp_optimal": "// Solution for Partition List",
      "java_brute": "// Solution for Partition List",
      "java_optimal": "// Solution for Partition List",
      "python_brute": "# Solution for Partition List",
      "python_optimal": "# Solution for Partition List"
    },
    "originalOrder": 556,
    "learningOrder": 556
  },
  {
    "id": 273,
    "number": 273,
    "sequence_number": 273,
    "title": "Add Two Numbers",
    "slug": "add-two-numbers",
    "difficulty": "Medium",
    "topic": "Linked List",
    "subtopic": "Linked List Optimization",
    "pattern": "Linked List",
    "secondary_patterns": [
      "Linked List"
    ],
    "stage": "Linked Lists & Fast-Slow Pointers",
    "curriculumStage": "Stage 6 — Linked Lists & Fast-Slow Pointers",
    "roadmapPhase": "Stage 6 — Linked Lists & Fast-Slow Pointers",
    "phase": "Stage 6 — Linked Lists & Fast-Slow Pointers",
    "estimatedTime": 30,
    "statement": "Adds two non-empty linked lists representing non-negative integers in reverse digit order.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "All elements fall within standard integer bounds."
    ],
    "examples": [
      {
        "input": "l1 = [2,4,3], l2 = [5,6,4]",
        "output": "[7,0,8]",
        "explanation": "Optimal solution achieved using Linked List."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "All duplicate elements"
    ],
    "commonMistakes": [
      "Off-by-one index mistakes",
      "Integer overflow for large cumulative sums"
    ],
    "hints": [
      "Consider using Linked List.",
      "Analyze edge cases and bounds."
    ],
    "learningObjective": "Master Linked List techniques by solving Medium problem constraints for Add Two Numbers.",
    "whyThisPattern": "When observing Linked List problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(1)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/add-two-numbers/",
    "leetcode_title": "Add Two Numbers",
    "leetcode_id": 2,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/add-two-numbers/",
    "canonicalSlug": "add-two-numbers",
    "canonicalUrl": "https://leetcode.com/problems/add-two-numbers/",
    "url": "https://leetcode.com/problems/add-two-numbers/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Add Two Numbers\n#include <iostream>\n#include <vector>\n#include <algorithm>\n\nclass Solution {\npublic:\n    int addTwoNumbers(std::vector<int>& nums) {\n        int n = nums.size();\n        if (n == 0) return 0;\n        int ans = 0;\n        for (int i = 0; i < n; i++) {\n            ans += nums[i];\n        }\n        return ans;\n    }\n};",
        "java": "// Java Solution for Add Two Numbers\nimport java.util.*;\n\nclass Solution {\n    public int addTwoNumbers(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int ans = 0;\n        for (int num : nums) {\n            ans += num;\n        }\n        return ans;\n    }\n}",
        "python": "# Python Solution for Add Two Numbers\n\nclass Solution:\n    def addTwoNumbers(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        ans = 0\n        for num in nums:\n            ans += num\n        return ans\n",
        "javascript": "// JavaScript Solution for Add Two Numbers\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Add Two Numbers\n#include <iostream>\n#include <vector>\n#include <algorithm>\n\nclass Solution {\npublic:\n    int addTwoNumbers(std::vector<int>& nums) {\n        int n = nums.size();\n        if (n == 0) return 0;\n        int ans = 0;\n        for (int i = 0; i < n; i++) {\n            ans += nums[i];\n        }\n        return ans;\n    }\n};",
        "java": "// Java Solution for Add Two Numbers\nimport java.util.*;\n\nclass Solution {\n    public int addTwoNumbers(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int ans = 0;\n        for (int num : nums) {\n            ans += num;\n        }\n        return ans;\n    }\n}",
        "python": "# Python Solution for Add Two Numbers\n\nclass Solution:\n    def addTwoNumbers(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        ans = 0\n        for num in nums:\n            ans += num\n        return ans\n",
        "javascript": "// JavaScript Solution for Add Two Numbers\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Add Two Numbers",
      "cpp_optimal": "// Solution for Add Two Numbers",
      "java_brute": "// Solution for Add Two Numbers",
      "java_optimal": "// Solution for Add Two Numbers",
      "python_brute": "# Solution for Add Two Numbers",
      "python_optimal": "# Solution for Add Two Numbers"
    },
    "originalOrder": 557,
    "learningOrder": 557
  },
  {
    "id": 274,
    "number": 274,
    "sequence_number": 274,
    "title": "Sort List",
    "slug": "sort-list",
    "difficulty": "Medium",
    "topic": "Linked List",
    "subtopic": "Linked List Optimization",
    "pattern": "Linked List",
    "secondary_patterns": [
      "Linked List"
    ],
    "stage": "Linked Lists & Fast-Slow Pointers",
    "curriculumStage": "Stage 6 — Linked Lists & Fast-Slow Pointers",
    "roadmapPhase": "Stage 6 — Linked Lists & Fast-Slow Pointers",
    "phase": "Stage 6 — Linked Lists & Fast-Slow Pointers",
    "estimatedTime": 30,
    "statement": "Sorts a linked list in O(N log N) time complexity using Merge Sort.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "All elements fall within standard integer bounds."
    ],
    "examples": [
      {
        "input": "head = [4,2,1,3]",
        "output": "[1,2,3,4]",
        "explanation": "Optimal solution achieved using Linked List."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "All duplicate elements"
    ],
    "commonMistakes": [
      "Off-by-one index mistakes",
      "Integer overflow for large cumulative sums"
    ],
    "hints": [
      "Consider using Linked List.",
      "Analyze edge cases and bounds."
    ],
    "learningObjective": "Master Linked List techniques by solving Medium problem constraints for Sort List.",
    "whyThisPattern": "When observing Linked List problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(1)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/sort-list/",
    "leetcode_title": "Sort List",
    "leetcode_id": 148,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/sort-list/",
    "canonicalSlug": "sort-list",
    "canonicalUrl": "https://leetcode.com/problems/sort-list/",
    "url": "https://leetcode.com/problems/sort-list/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Sort List\n#include <iostream>\n#include <vector>\n#include <algorithm>\n\nclass Solution {\npublic:\n    int sortList(std::vector<int>& nums) {\n        int n = nums.size();\n        if (n == 0) return 0;\n        int ans = 0;\n        for (int i = 0; i < n; i++) {\n            ans += nums[i];\n        }\n        return ans;\n    }\n};",
        "java": "// Java Solution for Sort List\nimport java.util.*;\n\nclass Solution {\n    public int sortList(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int ans = 0;\n        for (int num : nums) {\n            ans += num;\n        }\n        return ans;\n    }\n}",
        "python": "# Python Solution for Sort List\n\nclass Solution:\n    def sortList(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        ans = 0\n        for num in nums:\n            ans += num\n        return ans\n",
        "javascript": "// JavaScript Solution for Sort List\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Sort List\n#include <iostream>\n#include <vector>\n#include <algorithm>\n\nclass Solution {\npublic:\n    int sortList(std::vector<int>& nums) {\n        int n = nums.size();\n        if (n == 0) return 0;\n        int ans = 0;\n        for (int i = 0; i < n; i++) {\n            ans += nums[i];\n        }\n        return ans;\n    }\n};",
        "java": "// Java Solution for Sort List\nimport java.util.*;\n\nclass Solution {\n    public int sortList(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int ans = 0;\n        for (int num : nums) {\n            ans += num;\n        }\n        return ans;\n    }\n}",
        "python": "# Python Solution for Sort List\n\nclass Solution:\n    def sortList(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        ans = 0\n        for num in nums:\n            ans += num\n        return ans\n",
        "javascript": "// JavaScript Solution for Sort List\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Sort List",
      "cpp_optimal": "// Solution for Sort List",
      "java_brute": "// Solution for Sort List",
      "java_optimal": "// Solution for Sort List",
      "python_brute": "# Solution for Sort List",
      "python_optimal": "# Solution for Sort List"
    },
    "originalOrder": 558,
    "learningOrder": 558
  },
  {
    "id": 275,
    "number": 275,
    "sequence_number": 275,
    "title": "Linked List Components",
    "slug": "linked-list-components",
    "difficulty": "Medium",
    "topic": "Linked List",
    "subtopic": "Linked List Optimization",
    "pattern": "HashSet Component Count",
    "secondary_patterns": [
      "HashSet Component Count"
    ],
    "stage": "Linked Lists & Fast-Slow Pointers",
    "curriculumStage": "Stage 6 — Linked Lists & Fast-Slow Pointers",
    "roadmapPhase": "Stage 6 — Linked Lists & Fast-Slow Pointers",
    "phase": "Stage 6 — Linked Lists & Fast-Slow Pointers",
    "estimatedTime": 30,
    "statement": "Given the constraints and input parameters for Linked List Components, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Linked List Components."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Linked List Components.",
      "Leverage the optimal Linked List pattern to reduce time complexity."
    ],
    "learningObjective": "Master Linked List techniques by solving Medium problem constraints for Linked List Components.",
    "whyThisPattern": "When observing Linked List problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/linked-list-components/",
    "leetcode_title": "Linked List Components",
    "leetcode_id": 817,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/linked-list-components/",
    "canonicalSlug": "linked-list-components",
    "canonicalUrl": "https://leetcode.com/problems/linked-list-components/",
    "url": "https://leetcode.com/problems/linked-list-components/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Linked List Components\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Linked List Components\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Linked List Components\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Linked List Components\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Linked List Components\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Linked List Components\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Linked List Components\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Linked List Components\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Linked List Components",
      "cpp_optimal": "// Solution for Linked List Components",
      "java_brute": "// Solution for Linked List Components",
      "java_optimal": "// Solution for Linked List Components",
      "python_brute": "# Solution for Linked List Components",
      "python_optimal": "# Solution for Linked List Components"
    },
    "originalOrder": 559,
    "learningOrder": 559
  },
  {
    "id": 276,
    "number": 276,
    "sequence_number": 276,
    "title": "Merge In Between Linked Lists",
    "slug": "merge-in-between-linked-lists",
    "difficulty": "Medium",
    "topic": "Linked List",
    "subtopic": "Linked List Optimization",
    "pattern": "Pointer Splice",
    "secondary_patterns": [
      "Pointer Splice"
    ],
    "stage": "Linked Lists & Fast-Slow Pointers",
    "curriculumStage": "Stage 6 — Linked Lists & Fast-Slow Pointers",
    "roadmapPhase": "Stage 6 — Linked Lists & Fast-Slow Pointers",
    "phase": "Stage 6 — Linked Lists & Fast-Slow Pointers",
    "estimatedTime": 30,
    "statement": "Given the constraints and input parameters for Merge In Between Linked Lists, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Merge In Between Linked Lists."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Merge In Between Linked Lists.",
      "Leverage the optimal Linked List pattern to reduce time complexity."
    ],
    "learningObjective": "Master Linked List techniques by solving Medium problem constraints for Merge In Between Linked Lists.",
    "whyThisPattern": "When observing Linked List problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/merge-in-between-linked-lists/",
    "leetcode_title": "Merge In Between Linked Lists",
    "leetcode_id": 1669,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/merge-in-between-linked-lists/",
    "canonicalSlug": "merge-in-between-linked-lists",
    "canonicalUrl": "https://leetcode.com/problems/merge-in-between-linked-lists/",
    "url": "https://leetcode.com/problems/merge-in-between-linked-lists/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Merge In Between Linked Lists\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Merge In Between Linked Lists\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Merge In Between Linked Lists\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Merge In Between Linked Lists\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Merge In Between Linked Lists\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Merge In Between Linked Lists\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Merge In Between Linked Lists\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Merge In Between Linked Lists\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Merge In Between Linked Lists",
      "cpp_optimal": "// Solution for Merge In Between Linked Lists",
      "java_brute": "// Solution for Merge In Between Linked Lists",
      "java_optimal": "// Solution for Merge In Between Linked Lists",
      "python_brute": "# Solution for Merge In Between Linked Lists",
      "python_optimal": "# Solution for Merge In Between Linked Lists"
    },
    "originalOrder": 560,
    "learningOrder": 560
  },
  {
    "id": 277,
    "number": 277,
    "sequence_number": 277,
    "title": "Maximum Twin Sum of a Linked List",
    "slug": "maximum-twin-sum-of-a-linked-list",
    "difficulty": "Medium",
    "topic": "Linked List",
    "subtopic": "Linked List Optimization",
    "pattern": "Fast & Slow Pointers",
    "secondary_patterns": [
      "Fast & Slow Pointers"
    ],
    "stage": "Linked Lists & Fast-Slow Pointers",
    "curriculumStage": "Stage 6 — Linked Lists & Fast-Slow Pointers",
    "roadmapPhase": "Stage 6 — Linked Lists & Fast-Slow Pointers",
    "phase": "Stage 6 — Linked Lists & Fast-Slow Pointers",
    "estimatedTime": 30,
    "statement": "Given the constraints and input parameters for Maximum Twin Sum of a Linked List, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Maximum Twin Sum of a Linked List."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Maximum Twin Sum of a Linked List.",
      "Leverage the optimal Linked List pattern to reduce time complexity."
    ],
    "learningObjective": "Master Linked List techniques by solving Medium problem constraints for Maximum Twin Sum of a Linked List.",
    "whyThisPattern": "When observing Linked List problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/maximum-twin-sum-of-a-linked-list/",
    "leetcode_title": "Maximum Twin Sum of a Linked List",
    "leetcode_id": 2130,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/maximum-twin-sum-of-a-linked-list/",
    "canonicalSlug": "maximum-twin-sum-of-a-linked-list",
    "canonicalUrl": "https://leetcode.com/problems/maximum-twin-sum-of-a-linked-list/",
    "url": "https://leetcode.com/problems/maximum-twin-sum-of-a-linked-list/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Maximum Twin Sum of a Linked List\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Maximum Twin Sum of a Linked List\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Maximum Twin Sum of a Linked List\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Maximum Twin Sum of a Linked List\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Maximum Twin Sum of a Linked List\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Maximum Twin Sum of a Linked List\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Maximum Twin Sum of a Linked List\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Maximum Twin Sum of a Linked List\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Maximum Twin Sum of a Linked List",
      "cpp_optimal": "// Solution for Maximum Twin Sum of a Linked List",
      "java_brute": "// Solution for Maximum Twin Sum of a Linked List",
      "java_optimal": "// Solution for Maximum Twin Sum of a Linked List",
      "python_brute": "# Solution for Maximum Twin Sum of a Linked List",
      "python_optimal": "# Solution for Maximum Twin Sum of a Linked List"
    },
    "originalOrder": 561,
    "learningOrder": 561
  },
  {
    "id": 278,
    "number": 278,
    "sequence_number": 278,
    "title": "Sort Colors",
    "slug": "sort-colors",
    "difficulty": "Medium",
    "topic": "Two Pointers",
    "subtopic": "Hashing & Array Optimization",
    "pattern": "Hashing & Array Optimization",
    "secondary_patterns": [
      "Hashing & Array Optimization"
    ],
    "stage": "Linked Lists & Fast-Slow Pointers",
    "curriculumStage": "Stage 6 — Linked Lists & Fast-Slow Pointers",
    "roadmapPhase": "Stage 6 — Linked Lists & Fast-Slow Pointers",
    "phase": "Stage 6 — Linked Lists & Fast-Slow Pointers",
    "estimatedTime": 30,
    "statement": "Solve the **Sort Colors Challenge** problem using the **Hashing & Array Optimization** technique. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Hashing & Array Optimization identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Hashing & Array Optimization. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Hashing & Array Optimization techniques by solving Medium problem constraints for Sort Colors Challenge.",
    "whyThisPattern": "When observing arrays & strings problem conditions, Hashing & Array Optimization optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Microsoft",
      "Bloomberg",
      "Adobe"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/sort-colors/",
    "leetcode_title": "Sort Colors",
    "leetcode_id": 75,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/sort-colors/",
    "canonicalSlug": "sort-colors",
    "canonicalUrl": "https://leetcode.com/problems/sort-colors/",
    "url": "https://leetcode.com/problems/sort-colors/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Sort Colors Challenge (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Sort Colors Challenge (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Sort Colors Challenge (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Sort Colors Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Sort Colors Challenge (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Sort Colors Challenge (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Sort Colors Challenge (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Sort Colors Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Sort Colors",
      "cpp_optimal": "// Solution for Sort Colors",
      "java_brute": "// Solution for Sort Colors",
      "java_optimal": "// Solution for Sort Colors",
      "python_brute": "# Solution for Sort Colors",
      "python_optimal": "# Solution for Sort Colors"
    },
    "originalOrder": 679,
    "learningOrder": 679
  },
  {
    "id": 279,
    "number": 279,
    "sequence_number": 279,
    "title": "Remove Duplicates from Sorted Array II",
    "slug": "remove-duplicates-from-sorted-array-ii",
    "difficulty": "Medium",
    "topic": "Two Pointers",
    "subtopic": "Two Pointers",
    "pattern": "Two Pointers",
    "secondary_patterns": [
      "Two Pointers"
    ],
    "stage": "Linked Lists & Fast-Slow Pointers",
    "curriculumStage": "Stage 6 — Linked Lists & Fast-Slow Pointers",
    "roadmapPhase": "Stage 6 — Linked Lists & Fast-Slow Pointers",
    "phase": "Stage 6 — Linked Lists & Fast-Slow Pointers",
    "estimatedTime": 30,
    "statement": "Solve the **Remove Duplicates from Sorted Array II Challenge** problem using the **Two Pointers** technique. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Two Pointers identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Two Pointers. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Two Pointers techniques by solving Medium problem constraints for Remove Duplicates from Sorted Array II Challenge.",
    "whyThisPattern": "When observing arrays & strings problem conditions, Two Pointers optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(1)",
    "companyRelevance": [
      "Google",
      "Microsoft",
      "Bloomberg"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/remove-duplicates-from-sorted-array-ii/",
    "leetcode_title": "Remove Duplicates from Sorted Array II",
    "leetcode_id": 80,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/remove-duplicates-from-sorted-array-ii/",
    "canonicalSlug": "remove-duplicates-from-sorted-array-ii",
    "canonicalUrl": "https://leetcode.com/problems/remove-duplicates-from-sorted-array-ii/",
    "url": "https://leetcode.com/problems/remove-duplicates-from-sorted-array-ii/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Remove Duplicates from Sorted Array II Challenge (Two Pointers)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Remove Duplicates from Sorted Array II Challenge (Two Pointers)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Remove Duplicates from Sorted Array II Challenge (Two Pointers)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Remove Duplicates from Sorted Array II Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Remove Duplicates from Sorted Array II Challenge (Two Pointers)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Remove Duplicates from Sorted Array II Challenge (Two Pointers)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Remove Duplicates from Sorted Array II Challenge (Two Pointers)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Remove Duplicates from Sorted Array II Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Remove Duplicates from Sorted Array II",
      "cpp_optimal": "// Solution for Remove Duplicates from Sorted Array II",
      "java_brute": "// Solution for Remove Duplicates from Sorted Array II",
      "java_optimal": "// Solution for Remove Duplicates from Sorted Array II",
      "python_brute": "# Solution for Remove Duplicates from Sorted Array II",
      "python_optimal": "# Solution for Remove Duplicates from Sorted Array II"
    },
    "originalOrder": 680,
    "learningOrder": 680
  },
  {
    "id": 280,
    "number": 280,
    "sequence_number": 280,
    "title": "Populating Next Right Pointers in Each Node",
    "slug": "populating-next-right-pointers-in-each-node",
    "difficulty": "Medium",
    "topic": "Two Pointers",
    "subtopic": "Two Pointers",
    "pattern": "Two Pointers",
    "secondary_patterns": [
      "Two Pointers"
    ],
    "stage": "Linked Lists & Fast-Slow Pointers",
    "curriculumStage": "Stage 6 — Linked Lists & Fast-Slow Pointers",
    "roadmapPhase": "Stage 6 — Linked Lists & Fast-Slow Pointers",
    "phase": "Stage 6 — Linked Lists & Fast-Slow Pointers",
    "estimatedTime": 30,
    "statement": "Solve the **Populating Next Right Pointers in Each Node Challenge** problem using the **Two Pointers** technique. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Two Pointers identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Two Pointers. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Two Pointers techniques by solving Medium problem constraints for Populating Next Right Pointers in Each Node Challenge.",
    "whyThisPattern": "When observing arrays & strings problem conditions, Two Pointers optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(1)",
    "companyRelevance": [
      "Google",
      "Microsoft",
      "Bloomberg"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/populating-next-right-pointers-in-each-node/",
    "leetcode_title": "Populating Next Right Pointers in Each Node",
    "leetcode_id": 116,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/populating-next-right-pointers-in-each-node/",
    "canonicalSlug": "populating-next-right-pointers-in-each-node",
    "canonicalUrl": "https://leetcode.com/problems/populating-next-right-pointers-in-each-node/",
    "url": "https://leetcode.com/problems/populating-next-right-pointers-in-each-node/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Populating Next Right Pointers in Each Node Challenge (Two Pointers)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Populating Next Right Pointers in Each Node Challenge (Two Pointers)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Populating Next Right Pointers in Each Node Challenge (Two Pointers)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Populating Next Right Pointers in Each Node Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Populating Next Right Pointers in Each Node Challenge (Two Pointers)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Populating Next Right Pointers in Each Node Challenge (Two Pointers)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Populating Next Right Pointers in Each Node Challenge (Two Pointers)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Populating Next Right Pointers in Each Node Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Populating Next Right Pointers in Each Node",
      "cpp_optimal": "// Solution for Populating Next Right Pointers in Each Node",
      "java_brute": "// Solution for Populating Next Right Pointers in Each Node",
      "java_optimal": "// Solution for Populating Next Right Pointers in Each Node",
      "python_brute": "# Solution for Populating Next Right Pointers in Each Node",
      "python_optimal": "# Solution for Populating Next Right Pointers in Each Node"
    },
    "originalOrder": 681,
    "learningOrder": 681
  },
  {
    "id": 281,
    "number": 281,
    "sequence_number": 281,
    "title": "Populating Next Right Pointers in Each Node II",
    "slug": "populating-next-right-pointers-in-each-node-ii",
    "difficulty": "Medium",
    "topic": "Two Pointers",
    "subtopic": "Two Pointers",
    "pattern": "Two Pointers",
    "secondary_patterns": [
      "Two Pointers"
    ],
    "stage": "Linked Lists & Fast-Slow Pointers",
    "curriculumStage": "Stage 6 — Linked Lists & Fast-Slow Pointers",
    "roadmapPhase": "Stage 6 — Linked Lists & Fast-Slow Pointers",
    "phase": "Stage 6 — Linked Lists & Fast-Slow Pointers",
    "estimatedTime": 30,
    "statement": "Solve the **Populating Next Right Pointers in Each Node II Optimization** problem using the **Two Pointers** technique. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Two Pointers identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Two Pointers. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Two Pointers techniques by solving Medium problem constraints for Populating Next Right Pointers in Each Node II Optimization.",
    "whyThisPattern": "When observing arrays & strings problem conditions, Two Pointers optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(1)",
    "companyRelevance": [
      "Apple",
      "Adobe",
      "Atlassian"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/populating-next-right-pointers-in-each-node-ii/",
    "leetcode_title": "Populating Next Right Pointers in Each Node II",
    "leetcode_id": 117,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/populating-next-right-pointers-in-each-node-ii/",
    "canonicalSlug": "populating-next-right-pointers-in-each-node-ii",
    "canonicalUrl": "https://leetcode.com/problems/populating-next-right-pointers-in-each-node-ii/",
    "url": "https://leetcode.com/problems/populating-next-right-pointers-in-each-node-ii/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Populating Next Right Pointers in Each Node II Optimization (Two Pointers)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Populating Next Right Pointers in Each Node II Optimization (Two Pointers)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Populating Next Right Pointers in Each Node II Optimization (Two Pointers)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Populating Next Right Pointers in Each Node II Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Populating Next Right Pointers in Each Node II Optimization (Two Pointers)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Populating Next Right Pointers in Each Node II Optimization (Two Pointers)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Populating Next Right Pointers in Each Node II Optimization (Two Pointers)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Populating Next Right Pointers in Each Node II Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Populating Next Right Pointers in Each Node II",
      "cpp_optimal": "// Solution for Populating Next Right Pointers in Each Node II",
      "java_brute": "// Solution for Populating Next Right Pointers in Each Node II",
      "java_optimal": "// Solution for Populating Next Right Pointers in Each Node II",
      "python_brute": "# Solution for Populating Next Right Pointers in Each Node II",
      "python_optimal": "# Solution for Populating Next Right Pointers in Each Node II"
    },
    "originalOrder": 682,
    "learningOrder": 682
  },
  {
    "id": 282,
    "number": 282,
    "sequence_number": 282,
    "title": "Palindrome Partitioning",
    "slug": "palindrome-partitioning",
    "difficulty": "Medium",
    "topic": "Two Pointers",
    "subtopic": "Two Pointers",
    "pattern": "Two Pointers",
    "secondary_patterns": [
      "Two Pointers"
    ],
    "stage": "Linked Lists & Fast-Slow Pointers",
    "curriculumStage": "Stage 6 — Linked Lists & Fast-Slow Pointers",
    "roadmapPhase": "Stage 6 — Linked Lists & Fast-Slow Pointers",
    "phase": "Stage 6 — Linked Lists & Fast-Slow Pointers",
    "estimatedTime": 30,
    "statement": "Solve the **Palindrome Partitioning Challenge** problem using the **Two Pointers** technique. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Two Pointers identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Two Pointers. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Two Pointers techniques by solving Medium problem constraints for Palindrome Partitioning Challenge.",
    "whyThisPattern": "When observing arrays & strings problem conditions, Two Pointers optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(1)",
    "companyRelevance": [
      "Amazon",
      "Microsoft",
      "Uber"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/palindrome-partitioning/",
    "leetcode_title": "Palindrome Partitioning",
    "leetcode_id": 131,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/palindrome-partitioning/",
    "canonicalSlug": "palindrome-partitioning",
    "canonicalUrl": "https://leetcode.com/problems/palindrome-partitioning/",
    "url": "https://leetcode.com/problems/palindrome-partitioning/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Palindrome Partitioning Challenge (Two Pointers)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Palindrome Partitioning Challenge (Two Pointers)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Palindrome Partitioning Challenge (Two Pointers)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Palindrome Partitioning Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Palindrome Partitioning Challenge (Two Pointers)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Palindrome Partitioning Challenge (Two Pointers)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Palindrome Partitioning Challenge (Two Pointers)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Palindrome Partitioning Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Palindrome Partitioning",
      "cpp_optimal": "// Solution for Palindrome Partitioning",
      "java_brute": "// Solution for Palindrome Partitioning",
      "java_optimal": "// Solution for Palindrome Partitioning",
      "python_brute": "# Solution for Palindrome Partitioning",
      "python_optimal": "# Solution for Palindrome Partitioning"
    },
    "originalOrder": 683,
    "learningOrder": 683
  },
  {
    "id": 283,
    "number": 283,
    "sequence_number": 283,
    "title": "Two Sum II - Input Array Is Sorted",
    "slug": "two-sum-ii-input-array-is-sorted",
    "difficulty": "Medium",
    "topic": "Two Pointers",
    "subtopic": "Two Pointers",
    "pattern": "Two Pointers",
    "secondary_patterns": [
      "Two Pointers"
    ],
    "stage": "Linked Lists & Fast-Slow Pointers",
    "curriculumStage": "Stage 6 — Linked Lists & Fast-Slow Pointers",
    "roadmapPhase": "Stage 6 — Linked Lists & Fast-Slow Pointers",
    "phase": "Stage 6 — Linked Lists & Fast-Slow Pointers",
    "estimatedTime": 30,
    "statement": "Solve the **Two Sum II - Input Array Is Sorted Challenge** problem using the **Two Pointers** technique. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Two Pointers identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Two Pointers. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Two Pointers techniques by solving Medium problem constraints for Two Sum II - Input Array Is Sorted Challenge.",
    "whyThisPattern": "When observing arrays & strings problem conditions, Two Pointers optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(1)",
    "companyRelevance": [
      "Amazon",
      "Microsoft",
      "Uber"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/two-sum-ii-input-array-is-sorted/",
    "leetcode_title": "Two Sum II - Input Array Is Sorted",
    "leetcode_id": 167,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/two-sum-ii-input-array-is-sorted/",
    "canonicalSlug": "two-sum-ii-input-array-is-sorted",
    "canonicalUrl": "https://leetcode.com/problems/two-sum-ii-input-array-is-sorted/",
    "url": "https://leetcode.com/problems/two-sum-ii-input-array-is-sorted/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Two Sum II - Input Array Is Sorted Challenge (Two Pointers)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Two Sum II - Input Array Is Sorted Challenge (Two Pointers)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Two Sum II - Input Array Is Sorted Challenge (Two Pointers)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Two Sum II - Input Array Is Sorted Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Two Sum II - Input Array Is Sorted Challenge (Two Pointers)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Two Sum II - Input Array Is Sorted Challenge (Two Pointers)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Two Sum II - Input Array Is Sorted Challenge (Two Pointers)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Two Sum II - Input Array Is Sorted Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Two Sum II - Input Array Is Sorted",
      "cpp_optimal": "// Solution for Two Sum II - Input Array Is Sorted",
      "java_brute": "// Solution for Two Sum II - Input Array Is Sorted",
      "java_optimal": "// Solution for Two Sum II - Input Array Is Sorted",
      "python_brute": "# Solution for Two Sum II - Input Array Is Sorted",
      "python_optimal": "# Solution for Two Sum II - Input Array Is Sorted"
    },
    "originalOrder": 684,
    "learningOrder": 684
  },
  {
    "id": 284,
    "number": 284,
    "sequence_number": 284,
    "title": "Kth Smallest Element in a Sorted Matrix",
    "slug": "kth-smallest-element-in-a-sorted-matrix",
    "difficulty": "Medium",
    "topic": "Two Pointers",
    "subtopic": "Two Pointers",
    "pattern": "Two Pointers",
    "secondary_patterns": [
      "Two Pointers"
    ],
    "stage": "Linked Lists & Fast-Slow Pointers",
    "curriculumStage": "Stage 6 — Linked Lists & Fast-Slow Pointers",
    "roadmapPhase": "Stage 6 — Linked Lists & Fast-Slow Pointers",
    "phase": "Stage 6 — Linked Lists & Fast-Slow Pointers",
    "estimatedTime": 30,
    "statement": "Solve the **Kth Smallest Element in a Sorted Matrix Optimization** problem using the **Two Pointers** technique. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Two Pointers identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Two Pointers. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Two Pointers techniques by solving Medium problem constraints for Kth Smallest Element in a Sorted Matrix Optimization.",
    "whyThisPattern": "When observing arrays & strings problem conditions, Two Pointers optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(1)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/kth-smallest-element-in-a-sorted-matrix/",
    "leetcode_title": "Kth Smallest Element in a Sorted Matrix",
    "leetcode_id": 378,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/kth-smallest-element-in-a-sorted-matrix/",
    "canonicalSlug": "kth-smallest-element-in-a-sorted-matrix",
    "canonicalUrl": "https://leetcode.com/problems/kth-smallest-element-in-a-sorted-matrix/",
    "url": "https://leetcode.com/problems/kth-smallest-element-in-a-sorted-matrix/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Kth Smallest Element in a Sorted Matrix Optimization (Two Pointers)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Kth Smallest Element in a Sorted Matrix Optimization (Two Pointers)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Kth Smallest Element in a Sorted Matrix Optimization (Two Pointers)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Kth Smallest Element in a Sorted Matrix Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Kth Smallest Element in a Sorted Matrix Optimization (Two Pointers)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Kth Smallest Element in a Sorted Matrix Optimization (Two Pointers)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Kth Smallest Element in a Sorted Matrix Optimization (Two Pointers)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Kth Smallest Element in a Sorted Matrix Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Kth Smallest Element in a Sorted Matrix",
      "cpp_optimal": "// Solution for Kth Smallest Element in a Sorted Matrix",
      "java_brute": "// Solution for Kth Smallest Element in a Sorted Matrix",
      "java_optimal": "// Solution for Kth Smallest Element in a Sorted Matrix",
      "python_brute": "# Solution for Kth Smallest Element in a Sorted Matrix",
      "python_optimal": "# Solution for Kth Smallest Element in a Sorted Matrix"
    },
    "originalOrder": 685,
    "learningOrder": 685
  },
  {
    "id": 285,
    "number": 285,
    "sequence_number": 285,
    "title": "4Sum II",
    "slug": "4sum-ii",
    "difficulty": "Medium",
    "topic": "Two Pointers",
    "subtopic": "Hashing & Array Optimization",
    "pattern": "Hashing & Array Optimization",
    "secondary_patterns": [
      "Hashing & Array Optimization"
    ],
    "stage": "Linked Lists & Fast-Slow Pointers",
    "curriculumStage": "Stage 6 — Linked Lists & Fast-Slow Pointers",
    "roadmapPhase": "Stage 6 — Linked Lists & Fast-Slow Pointers",
    "phase": "Stage 6 — Linked Lists & Fast-Slow Pointers",
    "estimatedTime": 30,
    "statement": "Solve the **4Sum II Optimization** problem using the **Hashing & Array Optimization** technique. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Hashing & Array Optimization identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Hashing & Array Optimization. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Hashing & Array Optimization techniques by solving Medium problem constraints for 4Sum II Optimization.",
    "whyThisPattern": "When observing arrays & strings problem conditions, Hashing & Array Optimization optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/4sum-ii/",
    "leetcode_title": "4Sum II",
    "leetcode_id": 454,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/4sum-ii/",
    "canonicalSlug": "4sum-ii",
    "canonicalUrl": "https://leetcode.com/problems/4sum-ii/",
    "url": "https://leetcode.com/problems/4sum-ii/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for 4Sum II Optimization (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for 4Sum II Optimization (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for 4Sum II Optimization (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for 4Sum II Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for 4Sum II Optimization (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for 4Sum II Optimization (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for 4Sum II Optimization (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for 4Sum II Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for 4Sum II",
      "cpp_optimal": "// Solution for 4Sum II",
      "java_brute": "// Solution for 4Sum II",
      "java_optimal": "// Solution for 4Sum II",
      "python_brute": "# Solution for 4Sum II",
      "python_optimal": "# Solution for 4Sum II"
    },
    "originalOrder": 686,
    "learningOrder": 686
  },
  {
    "id": 286,
    "number": 286,
    "sequence_number": 286,
    "title": "Design Skiplist",
    "slug": "design-skiplist",
    "difficulty": "Hard",
    "topic": "Linked List",
    "subtopic": "Arrays Optimization",
    "pattern": "Arrays Pattern",
    "secondary_patterns": [
      "Arrays Pattern"
    ],
    "stage": "Linked Lists & Fast-Slow Pointers",
    "curriculumStage": "Stage 6 — Linked Lists & Fast-Slow Pointers",
    "roadmapPhase": "Stage 6 — Linked Lists & Fast-Slow Pointers",
    "phase": "Stage 6 — Linked Lists & Fast-Slow Pointers",
    "estimatedTime": 45,
    "statement": "Solve the **Design Skiplist** problem using standard Arrays techniques. Given input constraints appropriate for Hard level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Arrays algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Arrays properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Arrays techniques by solving Hard problem constraints for Design Skiplist.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/design-skiplist/",
    "leetcode_title": "Design Skiplist",
    "leetcode_id": 1206,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/design-skiplist/",
    "canonicalSlug": "design-skiplist",
    "canonicalUrl": "https://leetcode.com/problems/design-skiplist/",
    "url": "https://leetcode.com/problems/design-skiplist/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Design Skiplist\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Design Skiplist\n};",
        "java": "// Java Solution for Design Skiplist\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Design Skiplist\n}",
        "python": "# Python Solution for Design Skiplist\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Design Skiplist\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Design Skiplist\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Design Skiplist\n};",
        "java": "// Optimal Java Solution for Design Skiplist\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Design Skiplist\n}",
        "python": "# Optimal Python Solution for Design Skiplist\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Design Skiplist\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Design Skiplist",
      "cpp_optimal": "// Solution for Design Skiplist",
      "java_brute": "// Solution for Design Skiplist",
      "java_optimal": "// Solution for Design Skiplist",
      "python_brute": "# Solution for Design Skiplist",
      "python_optimal": "# Solution for Design Skiplist"
    },
    "originalOrder": 752,
    "learningOrder": 752
  },
  {
    "id": 287,
    "number": 287,
    "sequence_number": 287,
    "title": "All O`one Data Structure",
    "slug": "all-oone-data-structure",
    "difficulty": "Hard",
    "topic": "Linked List",
    "subtopic": "Linked List Optimization",
    "pattern": "Doubly Linked List + HashMap",
    "secondary_patterns": [
      "Doubly Linked List + HashMap"
    ],
    "stage": "Linked Lists & Fast-Slow Pointers",
    "curriculumStage": "Stage 6 — Linked Lists & Fast-Slow Pointers",
    "roadmapPhase": "Stage 6 — Linked Lists & Fast-Slow Pointers",
    "phase": "Stage 6 — Linked Lists & Fast-Slow Pointers",
    "estimatedTime": 45,
    "statement": "Designs a data structure that supports inc(key), dec(key), getMaxKey(), and getMinKey() operations in O(1) time complexity.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= key.length <= 10",
      "At most 5 * 10^4 calls will be made."
    ],
    "examples": [
      {
        "input": "inc('hello'), inc('hello'), getMaxKey()",
        "output": "'hello'",
        "explanation": "Returns key with maximum count."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "All duplicate elements"
    ],
    "commonMistakes": [
      "Off-by-one index mistakes",
      "Integer overflow for large cumulative sums"
    ],
    "hints": [
      "Consider using Linked List.",
      "Analyze edge cases and bounds."
    ],
    "learningObjective": "Master Linked List techniques by solving Hard problem constraints for All O`one Data Structure.",
    "whyThisPattern": "When observing Linked List problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(1)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/all-oone-data-structure/",
    "leetcode_title": "All O`one Data Structure",
    "leetcode_id": 432,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/all-oone-data-structure/",
    "canonicalSlug": "all-oone-data-structure",
    "canonicalUrl": "https://leetcode.com/problems/all-oone-data-structure/",
    "url": "https://leetcode.com/problems/all-oone-data-structure/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ All O`one Data Structure Implementation\n#include <string>\n#include <unordered_map>\n#include <unordered_set>\n#include <list>\n\nclass AllOne {\n    struct Node {\n        int count;\n        std::unordered_set<std::string> keys;\n    };\n    std::list<Node> buckets;\n    std::unordered_map<std::string, std::list<Node>::iterator> map;\n\npublic:\n    AllOne() {}\n    \n    void inc(std::string key) {\n        if (!map.count(key)) {\n            if (buckets.empty() || buckets.front().count != 1) {\n                buckets.push_front({1, {key}});\n            } else {\n                buckets.front().keys.insert(key);\n            }\n            map[key] = buckets.begin();\n        } else {\n            auto cur = map[key];\n            auto nxt = std::next(cur);\n            if (nxt == buckets.end() || nxt->count != cur->count + 1) {\n                nxt = buckets.insert(nxt, {cur->count + 1, {key}});\n            } else {\n                nxt->keys.insert(key);\n            }\n            map[key] = nxt;\n            cur->keys.erase(key);\n            if (cur->keys.empty()) buckets.erase(cur);\n        }\n    }\n    \n    void dec(std::string key) {\n        auto cur = map[key];\n        if (cur->count == 1) {\n            map.erase(key);\n        } else {\n            auto prev = std::prev(cur);\n            if (cur == buckets.begin() || prev->count != cur->count - 1) {\n                prev = buckets.insert(cur, {cur->count - 1, {key}});\n            } else {\n                prev->keys.insert(key);\n            }\n            map[key] = prev;\n        }\n        cur->keys.erase(key);\n        if (cur->keys.empty()) buckets.erase(cur);\n    }\n    \n    std::string getMaxKey() {\n        return buckets.empty() ? \"\" : *buckets.back().keys.begin();\n    }\n    \n    std::string getMinKey() {\n        return buckets.empty() ? \"\" : *buckets.front().keys.begin();\n    }\n};",
        "java": "// Java All O`one Data Structure Implementation\nimport java.util.*;\n\nclass AllOne {\n    class Node {\n        int count;\n        Set<String> keys = new HashSet<>();\n        Node prev, next;\n        Node(int c) { count = c; }\n    }\n\n    private Map<String, Node> map = new HashMap<>();\n    private Node head = new Node(0), tail = new Node(0);\n\n    public AllOne() {\n        head.next = tail;\n        tail.prev = head;\n    }\n\n    public void inc(String key) {\n        if (map.containsKey(key)) {\n            Node node = map.get(key);\n            node.keys.remove(key);\n            if (node.next == tail || node.next.count != node.count + 1) {\n                Node newNode = new Node(node.count + 1);\n                insertAfter(node, newNode);\n            }\n            node.next.keys.add(key);\n            map.put(key, node.next);\n            if (node.keys.isEmpty()) removeNode(node);\n        } else {\n            if (head.next == tail || head.next.count != 1) {\n                insertAfter(head, new Node(1));\n            }\n            head.next.keys.add(key);\n            map.put(key, head.next);\n        }\n    }\n\n    private void insertAfter(Node prev, Node newNode) {\n        newNode.next = prev.next;\n        newNode.prev = prev;\n        prev.next.prev = newNode;\n        prev.next = newNode;\n    }\n\n    private void removeNode(Node node) {\n        node.prev.next = node.next;\n        node.next.prev = node.prev;\n    }\n\n    public String getMaxKey() {\n        return tail.prev == head ? \"\" : tail.prev.keys.iterator().next();\n    }\n\n    public String getMinKey() {\n        return head.next == tail ? \"\" : head.next.keys.iterator().next();\n    }\n}",
        "python": "# Python All O`one Data Structure Implementation\n\nclass AllOne:\n    def __init__(self):\n        self.map = {}\n\n    def inc(self, key: str) -> None:\n        self.map[key] = self.map.get(key, 0) + 1\n\n    def dec(self, key: str) -> None:\n        if key in self.map:\n            if self.map[key] == 1:\n                del self.map[key]\n            else:\n                self.map[key] -= 1\n\n    def getMaxKey(self) -> str:\n        if not self.map: return \"\"\n        return max(self.map, key=self.map.get)\n\n    def getMinKey(self) -> str:\n        if not self.map: return \"\"\n        return min(self.map, key=self.map.get)\n",
        "javascript": "// JavaScript All O`one Data Structure Implementation\nclass AllOne {\n    constructor() {\n        this.map = new Map();\n    }\n    inc(key) {\n        this.map.set(key, (this.map.get(key) || 0) + 1);\n    }\n    dec(key) {\n        if (this.map.has(key)) {\n            const val = this.map.get(key);\n            if (val === 1) this.map.delete(key);\n            else this.map.set(key, val - 1);\n        }\n    }\n    getMaxKey() {\n        let maxK = \"\", maxV = -1;\n        for (const [k, v] of this.map.entries()) {\n            if (v > maxV) { maxV = v; maxK = k; }\n        }\n        return maxK;\n    }\n    getMinKey() {\n        let minK = \"\", minV = Infinity;\n        for (const [k, v] of this.map.entries()) {\n            if (v < minV) { minV = v; minK = k; }\n        }\n        return minV === Infinity ? \"\" : minK;\n    }\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ All O`one Data Structure Implementation\n#include <string>\n#include <unordered_map>\n#include <unordered_set>\n#include <list>\n\nclass AllOne {\n    struct Node {\n        int count;\n        std::unordered_set<std::string> keys;\n    };\n    std::list<Node> buckets;\n    std::unordered_map<std::string, std::list<Node>::iterator> map;\n\npublic:\n    AllOne() {}\n    \n    void inc(std::string key) {\n        if (!map.count(key)) {\n            if (buckets.empty() || buckets.front().count != 1) {\n                buckets.push_front({1, {key}});\n            } else {\n                buckets.front().keys.insert(key);\n            }\n            map[key] = buckets.begin();\n        } else {\n            auto cur = map[key];\n            auto nxt = std::next(cur);\n            if (nxt == buckets.end() || nxt->count != cur->count + 1) {\n                nxt = buckets.insert(nxt, {cur->count + 1, {key}});\n            } else {\n                nxt->keys.insert(key);\n            }\n            map[key] = nxt;\n            cur->keys.erase(key);\n            if (cur->keys.empty()) buckets.erase(cur);\n        }\n    }\n    \n    void dec(std::string key) {\n        auto cur = map[key];\n        if (cur->count == 1) {\n            map.erase(key);\n        } else {\n            auto prev = std::prev(cur);\n            if (cur == buckets.begin() || prev->count != cur->count - 1) {\n                prev = buckets.insert(cur, {cur->count - 1, {key}});\n            } else {\n                prev->keys.insert(key);\n            }\n            map[key] = prev;\n        }\n        cur->keys.erase(key);\n        if (cur->keys.empty()) buckets.erase(cur);\n    }\n    \n    std::string getMaxKey() {\n        return buckets.empty() ? \"\" : *buckets.back().keys.begin();\n    }\n    \n    std::string getMinKey() {\n        return buckets.empty() ? \"\" : *buckets.front().keys.begin();\n    }\n};",
        "java": "// Java All O`one Data Structure Implementation\nimport java.util.*;\n\nclass AllOne {\n    class Node {\n        int count;\n        Set<String> keys = new HashSet<>();\n        Node prev, next;\n        Node(int c) { count = c; }\n    }\n\n    private Map<String, Node> map = new HashMap<>();\n    private Node head = new Node(0), tail = new Node(0);\n\n    public AllOne() {\n        head.next = tail;\n        tail.prev = head;\n    }\n\n    public void inc(String key) {\n        if (map.containsKey(key)) {\n            Node node = map.get(key);\n            node.keys.remove(key);\n            if (node.next == tail || node.next.count != node.count + 1) {\n                Node newNode = new Node(node.count + 1);\n                insertAfter(node, newNode);\n            }\n            node.next.keys.add(key);\n            map.put(key, node.next);\n            if (node.keys.isEmpty()) removeNode(node);\n        } else {\n            if (head.next == tail || head.next.count != 1) {\n                insertAfter(head, new Node(1));\n            }\n            head.next.keys.add(key);\n            map.put(key, head.next);\n        }\n    }\n\n    private void insertAfter(Node prev, Node newNode) {\n        newNode.next = prev.next;\n        newNode.prev = prev;\n        prev.next.prev = newNode;\n        prev.next = newNode;\n    }\n\n    private void removeNode(Node node) {\n        node.prev.next = node.next;\n        node.next.prev = node.prev;\n    }\n\n    public String getMaxKey() {\n        return tail.prev == head ? \"\" : tail.prev.keys.iterator().next();\n    }\n\n    public String getMinKey() {\n        return head.next == tail ? \"\" : head.next.keys.iterator().next();\n    }\n}",
        "python": "# Python All O`one Data Structure Implementation\n\nclass AllOne:\n    def __init__(self):\n        self.map = {}\n\n    def inc(self, key: str) -> None:\n        self.map[key] = self.map.get(key, 0) + 1\n\n    def dec(self, key: str) -> None:\n        if key in self.map:\n            if self.map[key] == 1:\n                del self.map[key]\n            else:\n                self.map[key] -= 1\n\n    def getMaxKey(self) -> str:\n        if not self.map: return \"\"\n        return max(self.map, key=self.map.get)\n\n    def getMinKey(self) -> str:\n        if not self.map: return \"\"\n        return min(self.map, key=self.map.get)\n",
        "javascript": "// JavaScript All O`one Data Structure Implementation\nclass AllOne {\n    constructor() {\n        this.map = new Map();\n    }\n    inc(key) {\n        this.map.set(key, (this.map.get(key) || 0) + 1);\n    }\n    dec(key) {\n        if (this.map.has(key)) {\n            const val = this.map.get(key);\n            if (val === 1) this.map.delete(key);\n            else this.map.set(key, val - 1);\n        }\n    }\n    getMaxKey() {\n        let maxK = \"\", maxV = -1;\n        for (const [k, v] of this.map.entries()) {\n            if (v > maxV) { maxV = v; maxK = k; }\n        }\n        return maxK;\n    }\n    getMinKey() {\n        let minK = \"\", minV = Infinity;\n        for (const [k, v] of this.map.entries()) {\n            if (v < minV) { minV = v; minK = k; }\n        }\n        return minV === Infinity ? \"\" : minK;\n    }\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for All O`one Data Structure",
      "cpp_optimal": "// Solution for All O`one Data Structure",
      "java_brute": "// Solution for All O`one Data Structure",
      "java_optimal": "// Solution for All O`one Data Structure",
      "python_brute": "# Solution for All O`one Data Structure",
      "python_optimal": "# Solution for All O`one Data Structure"
    },
    "originalOrder": 913,
    "learningOrder": 913
  },
  {
    "id": 288,
    "number": 288,
    "sequence_number": 288,
    "title": "LFU Cache",
    "slug": "lfu-cache",
    "difficulty": "Hard",
    "topic": "Linked List",
    "subtopic": "Hashing & Array Optimization",
    "pattern": "Hashing & Array Optimization",
    "secondary_patterns": [
      "Hashing & Array Optimization"
    ],
    "stage": "Linked Lists & Fast-Slow Pointers",
    "curriculumStage": "Stage 6 — Linked Lists & Fast-Slow Pointers",
    "roadmapPhase": "Stage 6 — Linked Lists & Fast-Slow Pointers",
    "phase": "Stage 6 — Linked Lists & Fast-Slow Pointers",
    "estimatedTime": 45,
    "statement": "Solve the **LFU Cache Optimization** problem using the **Hashing & Array Optimization** technique. Given input constraints appropriate for Hard level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^6",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Hashing & Array Optimization identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Hashing & Array Optimization. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Hashing & Array Optimization techniques by solving Hard problem constraints for LFU Cache Optimization.",
    "whyThisPattern": "When observing arrays & strings problem conditions, Hashing & Array Optimization optimizes performance down to expected O(N log N).",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "LinkedIn",
      "Amazon"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/lfu-cache/",
    "leetcode_title": "LFU Cache",
    "leetcode_id": 460,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/lfu-cache/",
    "canonicalSlug": "lfu-cache",
    "canonicalUrl": "https://leetcode.com/problems/lfu-cache/",
    "url": "https://leetcode.com/problems/lfu-cache/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for LFU Cache Optimization (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for LFU Cache Optimization (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for LFU Cache Optimization (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for LFU Cache Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for LFU Cache Optimization (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for LFU Cache Optimization (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for LFU Cache Optimization (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for LFU Cache Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for LFU Cache",
      "cpp_optimal": "// Solution for LFU Cache",
      "java_brute": "// Solution for LFU Cache",
      "java_optimal": "// Solution for LFU Cache",
      "python_brute": "# Solution for LFU Cache",
      "python_optimal": "# Solution for LFU Cache"
    },
    "originalOrder": 914,
    "learningOrder": 914
  },
  {
    "id": 289,
    "number": 289,
    "sequence_number": 289,
    "title": "Merge k Sorted Lists",
    "slug": "merge-k-sorted-lists",
    "difficulty": "Hard",
    "topic": "Linked List",
    "subtopic": "Linked List Optimization",
    "pattern": "Linked List",
    "secondary_patterns": [
      "Linked List"
    ],
    "stage": "Linked Lists & Fast-Slow Pointers",
    "curriculumStage": "Stage 6 — Linked Lists & Fast-Slow Pointers",
    "roadmapPhase": "Stage 6 — Linked Lists & Fast-Slow Pointers",
    "phase": "Stage 6 — Linked Lists & Fast-Slow Pointers",
    "estimatedTime": 45,
    "statement": "Merges K sorted linked lists into one single sorted list using a Min-Heap Priority Queue.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "All elements fall within standard integer bounds."
    ],
    "examples": [
      {
        "input": "lists = [[1,4,5],[1,3,4],[2,6]]",
        "output": "[1,1,2,3,4,4,5,6]",
        "explanation": "Optimal solution achieved using Linked List."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "All duplicate elements"
    ],
    "commonMistakes": [
      "Off-by-one index mistakes",
      "Integer overflow for large cumulative sums"
    ],
    "hints": [
      "Consider using Linked List.",
      "Analyze edge cases and bounds."
    ],
    "learningObjective": "Master Linked List techniques by solving Hard problem constraints for Merge k Sorted Lists.",
    "whyThisPattern": "When observing Linked List problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(1)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/merge-k-sorted-lists/",
    "leetcode_title": "Merge k Sorted Lists",
    "leetcode_id": 23,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/merge-k-sorted-lists/",
    "canonicalSlug": "merge-k-sorted-lists",
    "canonicalUrl": "https://leetcode.com/problems/merge-k-sorted-lists/",
    "url": "https://leetcode.com/problems/merge-k-sorted-lists/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Merge K Sorted Lists\n#include <iostream>\n#include <vector>\n#include <algorithm>\n\nclass Solution {\npublic:\n    int mergeKSortedLists(std::vector<int>& nums) {\n        int n = nums.size();\n        if (n == 0) return 0;\n        int ans = 0;\n        for (int i = 0; i < n; i++) {\n            ans += nums[i];\n        }\n        return ans;\n    }\n};",
        "java": "// Java Solution for Merge K Sorted Lists\nimport java.util.*;\n\nclass Solution {\n    public int mergeKSortedLists(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int ans = 0;\n        for (int num : nums) {\n            ans += num;\n        }\n        return ans;\n    }\n}",
        "python": "# Python Solution for Merge K Sorted Lists\n\nclass Solution:\n    def mergeKSortedLists(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        ans = 0\n        for num in nums:\n            ans += num\n        return ans\n",
        "javascript": "// JavaScript Solution for Merge K Sorted Lists\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Merge K Sorted Lists\n#include <iostream>\n#include <vector>\n#include <algorithm>\n\nclass Solution {\npublic:\n    int mergeKSortedLists(std::vector<int>& nums) {\n        int n = nums.size();\n        if (n == 0) return 0;\n        int ans = 0;\n        for (int i = 0; i < n; i++) {\n            ans += nums[i];\n        }\n        return ans;\n    }\n};",
        "java": "// Java Solution for Merge K Sorted Lists\nimport java.util.*;\n\nclass Solution {\n    public int mergeKSortedLists(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int ans = 0;\n        for (int num : nums) {\n            ans += num;\n        }\n        return ans;\n    }\n}",
        "python": "# Python Solution for Merge K Sorted Lists\n\nclass Solution:\n    def mergeKSortedLists(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        ans = 0\n        for num in nums:\n            ans += num\n        return ans\n",
        "javascript": "// JavaScript Solution for Merge K Sorted Lists\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Merge k Sorted Lists",
      "cpp_optimal": "// Solution for Merge k Sorted Lists",
      "java_brute": "// Solution for Merge k Sorted Lists",
      "java_optimal": "// Solution for Merge k Sorted Lists",
      "python_brute": "# Solution for Merge k Sorted Lists",
      "python_optimal": "# Solution for Merge k Sorted Lists"
    },
    "originalOrder": 915,
    "learningOrder": 915
  },
  {
    "id": 290,
    "number": 290,
    "sequence_number": 290,
    "title": "Reverse Nodes in k-Group",
    "slug": "reverse-nodes-in-k-group",
    "difficulty": "Hard",
    "topic": "Linked List",
    "subtopic": "Linked List Optimization",
    "pattern": "Grouped Pointer Reversal",
    "secondary_patterns": [
      "Grouped Pointer Reversal"
    ],
    "stage": "Linked Lists & Fast-Slow Pointers",
    "curriculumStage": "Stage 6 — Linked Lists & Fast-Slow Pointers",
    "roadmapPhase": "Stage 6 — Linked Lists & Fast-Slow Pointers",
    "phase": "Stage 6 — Linked Lists & Fast-Slow Pointers",
    "estimatedTime": 45,
    "statement": "Given the constraints and input parameters for Reverse Nodes in k-Group, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Reverse Nodes in k-Group."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Reverse Nodes in k-Group.",
      "Leverage the optimal Linked List pattern to reduce time complexity."
    ],
    "learningObjective": "Master Linked List techniques by solving Hard problem constraints for Reverse Nodes in k-Group.",
    "whyThisPattern": "When observing Linked List problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/reverse-nodes-in-k-group/",
    "leetcode_title": "Reverse Nodes in k-Group",
    "leetcode_id": 25,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/reverse-nodes-in-k-group/",
    "canonicalSlug": "reverse-nodes-in-k-group",
    "canonicalUrl": "https://leetcode.com/problems/reverse-nodes-in-k-group/",
    "url": "https://leetcode.com/problems/reverse-nodes-in-k-group/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Reverse Nodes in k-Group\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Reverse Nodes in k-Group\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Reverse Nodes in k-Group\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Reverse Nodes in k-Group\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Reverse Nodes in k-Group\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Reverse Nodes in k-Group\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Reverse Nodes in k-Group\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Reverse Nodes in k-Group\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Reverse Nodes in k-Group",
      "cpp_optimal": "// Solution for Reverse Nodes in k-Group",
      "java_brute": "// Solution for Reverse Nodes in k-Group",
      "java_optimal": "// Solution for Reverse Nodes in k-Group",
      "python_brute": "# Solution for Reverse Nodes in k-Group",
      "python_optimal": "# Solution for Reverse Nodes in k-Group"
    },
    "originalOrder": 916,
    "learningOrder": 916
  },
  {
    "id": 291,
    "number": 291,
    "sequence_number": 291,
    "title": "Largest Palindrome Product",
    "slug": "largest-palindrome-product",
    "difficulty": "Hard",
    "topic": "Two Pointers",
    "subtopic": "Two Pointers",
    "pattern": "Two Pointers",
    "secondary_patterns": [
      "Two Pointers"
    ],
    "stage": "Linked Lists & Fast-Slow Pointers",
    "curriculumStage": "Stage 6 — Linked Lists & Fast-Slow Pointers",
    "roadmapPhase": "Stage 6 — Linked Lists & Fast-Slow Pointers",
    "phase": "Stage 6 — Linked Lists & Fast-Slow Pointers",
    "estimatedTime": 45,
    "statement": "Solve the **Largest Palindrome Product Optimization** problem using the **Two Pointers** technique. Given input constraints appropriate for Hard level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^6",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Two Pointers identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Two Pointers. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Two Pointers techniques by solving Hard problem constraints for Largest Palindrome Product Optimization.",
    "whyThisPattern": "When observing arrays & strings problem conditions, Two Pointers optimizes performance down to expected O(N log N).",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(1)",
    "companyRelevance": [
      "Google",
      "LinkedIn",
      "Amazon"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/largest-palindrome-product/",
    "leetcode_title": "Largest Palindrome Product",
    "leetcode_id": 479,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/largest-palindrome-product/",
    "canonicalSlug": "largest-palindrome-product",
    "canonicalUrl": "https://leetcode.com/problems/largest-palindrome-product/",
    "url": "https://leetcode.com/problems/largest-palindrome-product/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Largest Palindrome Product Optimization (Two Pointers)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Largest Palindrome Product Optimization (Two Pointers)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Largest Palindrome Product Optimization (Two Pointers)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Largest Palindrome Product Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Largest Palindrome Product Optimization (Two Pointers)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Largest Palindrome Product Optimization (Two Pointers)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Largest Palindrome Product Optimization (Two Pointers)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Largest Palindrome Product Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Largest Palindrome Product",
      "cpp_optimal": "// Solution for Largest Palindrome Product",
      "java_brute": "// Solution for Largest Palindrome Product",
      "java_optimal": "// Solution for Largest Palindrome Product",
      "python_brute": "# Solution for Largest Palindrome Product",
      "python_optimal": "# Solution for Largest Palindrome Product"
    },
    "originalOrder": 982,
    "learningOrder": 982
  },
  {
    "id": 292,
    "number": 292,
    "sequence_number": 292,
    "title": "Three Equal Parts",
    "slug": "three-equal-parts",
    "difficulty": "Hard",
    "topic": "Two Pointers",
    "subtopic": "Two Pointers Optimization",
    "pattern": "Bit Triplet Matching",
    "secondary_patterns": [
      "Bit Triplet Matching"
    ],
    "stage": "Linked Lists & Fast-Slow Pointers",
    "curriculumStage": "Stage 6 — Linked Lists & Fast-Slow Pointers",
    "roadmapPhase": "Stage 6 — Linked Lists & Fast-Slow Pointers",
    "phase": "Stage 6 — Linked Lists & Fast-Slow Pointers",
    "estimatedTime": 45,
    "statement": "Given the constraints and input parameters for Three Equal Parts, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Three Equal Parts."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Three Equal Parts.",
      "Leverage the optimal Two Pointers pattern to reduce time complexity."
    ],
    "learningObjective": "Master Two Pointers techniques by solving Hard problem constraints for Three Equal Parts.",
    "whyThisPattern": "When observing Two Pointers problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/three-equal-parts/",
    "leetcode_title": "Three Equal Parts",
    "leetcode_id": 927,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/three-equal-parts/",
    "canonicalSlug": "three-equal-parts",
    "canonicalUrl": "https://leetcode.com/problems/three-equal-parts/",
    "url": "https://leetcode.com/problems/three-equal-parts/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Three Equal Parts\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Three Equal Parts\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Three Equal Parts\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Three Equal Parts\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Three Equal Parts\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Three Equal Parts\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Three Equal Parts\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Three Equal Parts\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Three Equal Parts",
      "cpp_optimal": "// Solution for Three Equal Parts",
      "java_brute": "// Solution for Three Equal Parts",
      "java_optimal": "// Solution for Three Equal Parts",
      "python_brute": "# Solution for Three Equal Parts",
      "python_optimal": "# Solution for Three Equal Parts"
    },
    "originalOrder": 983,
    "learningOrder": 983
  },
  {
    "id": 293,
    "number": 293,
    "sequence_number": 293,
    "title": "Get the Maximum Score",
    "slug": "get-the-maximum-score",
    "difficulty": "Hard",
    "topic": "Two Pointers",
    "subtopic": "Two Pointers Optimization",
    "pattern": "Two Array Intersection Max Sum",
    "secondary_patterns": [
      "Two Array Intersection Max Sum"
    ],
    "stage": "Linked Lists & Fast-Slow Pointers",
    "curriculumStage": "Stage 6 — Linked Lists & Fast-Slow Pointers",
    "roadmapPhase": "Stage 6 — Linked Lists & Fast-Slow Pointers",
    "phase": "Stage 6 — Linked Lists & Fast-Slow Pointers",
    "estimatedTime": 45,
    "statement": "Given the constraints and input parameters for Get the Maximum Score, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Get the Maximum Score."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Get the Maximum Score.",
      "Leverage the optimal Two Pointers pattern to reduce time complexity."
    ],
    "learningObjective": "Master Two Pointers techniques by solving Hard problem constraints for Get the Maximum Score.",
    "whyThisPattern": "When observing Two Pointers problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/get-the-maximum-score/",
    "leetcode_title": "Get the Maximum Score",
    "leetcode_id": 1537,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/get-the-maximum-score/",
    "canonicalSlug": "get-the-maximum-score",
    "canonicalUrl": "https://leetcode.com/problems/get-the-maximum-score/",
    "url": "https://leetcode.com/problems/get-the-maximum-score/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Get the Maximum Score\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Get the Maximum Score\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Get the Maximum Score\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Get the Maximum Score\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Get the Maximum Score\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Get the Maximum Score\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Get the Maximum Score\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Get the Maximum Score\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Get the Maximum Score",
      "cpp_optimal": "// Solution for Get the Maximum Score",
      "java_brute": "// Solution for Get the Maximum Score",
      "java_optimal": "// Solution for Get the Maximum Score",
      "python_brute": "# Solution for Get the Maximum Score",
      "python_optimal": "# Solution for Get the Maximum Score"
    },
    "originalOrder": 984,
    "learningOrder": 984
  },
  {
    "id": 294,
    "number": 294,
    "sequence_number": 294,
    "title": "Minimum Number of Moves to Make Palindrome",
    "slug": "minimum-number-of-moves-to-make-palindrome",
    "difficulty": "Hard",
    "topic": "Two Pointers",
    "subtopic": "Two Pointers Optimization",
    "pattern": "Greedy Boundary Swaps",
    "secondary_patterns": [
      "Greedy Boundary Swaps"
    ],
    "stage": "Linked Lists & Fast-Slow Pointers",
    "curriculumStage": "Stage 6 — Linked Lists & Fast-Slow Pointers",
    "roadmapPhase": "Stage 6 — Linked Lists & Fast-Slow Pointers",
    "phase": "Stage 6 — Linked Lists & Fast-Slow Pointers",
    "estimatedTime": 45,
    "statement": "Given the constraints and input parameters for Minimum Number of Moves to Make Palindrome, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Minimum Number of Moves to Make Palindrome."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Minimum Number of Moves to Make Palindrome.",
      "Leverage the optimal Two Pointers pattern to reduce time complexity."
    ],
    "learningObjective": "Master Two Pointers techniques by solving Hard problem constraints for Minimum Number of Moves to Make Palindrome.",
    "whyThisPattern": "When observing Two Pointers problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/minimum-number-of-moves-to-make-palindrome/",
    "leetcode_title": "Minimum Number of Moves to Make Palindrome",
    "leetcode_id": 2193,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/minimum-number-of-moves-to-make-palindrome/",
    "canonicalSlug": "minimum-number-of-moves-to-make-palindrome",
    "canonicalUrl": "https://leetcode.com/problems/minimum-number-of-moves-to-make-palindrome/",
    "url": "https://leetcode.com/problems/minimum-number-of-moves-to-make-palindrome/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Minimum Number of Moves to Make Palindrome\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Minimum Number of Moves to Make Palindrome\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Minimum Number of Moves to Make Palindrome\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Minimum Number of Moves to Make Palindrome\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Minimum Number of Moves to Make Palindrome\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Minimum Number of Moves to Make Palindrome\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Minimum Number of Moves to Make Palindrome\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Minimum Number of Moves to Make Palindrome\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Minimum Number of Moves to Make Palindrome",
      "cpp_optimal": "// Solution for Minimum Number of Moves to Make Palindrome",
      "java_brute": "// Solution for Minimum Number of Moves to Make Palindrome",
      "java_optimal": "// Solution for Minimum Number of Moves to Make Palindrome",
      "python_brute": "# Solution for Minimum Number of Moves to Make Palindrome",
      "python_optimal": "# Solution for Minimum Number of Moves to Make Palindrome"
    },
    "originalOrder": 985,
    "learningOrder": 985
  },
  {
    "id": 295,
    "number": 295,
    "sequence_number": 295,
    "title": "Sum of Subsequence Widths",
    "slug": "sum-of-subsequence-widths",
    "difficulty": "Hard",
    "topic": "Arrays",
    "subtopic": "Arrays Optimization",
    "pattern": "Arrays Pattern",
    "secondary_patterns": [
      "Arrays Pattern"
    ],
    "stage": "Linked Lists & Fast-Slow Pointers",
    "curriculumStage": "Stage 6 — Linked Lists & Fast-Slow Pointers",
    "roadmapPhase": "Stage 6 — Linked Lists & Fast-Slow Pointers",
    "phase": "Stage 6 — Linked Lists & Fast-Slow Pointers",
    "estimatedTime": 45,
    "statement": "Solve the **Sum of Subsequence Widths** problem using standard Arrays techniques. Given input constraints appropriate for Hard level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Arrays algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Arrays properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Arrays techniques by solving Hard problem constraints for Sum of Subsequence Widths.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/sum-of-subsequence-widths/",
    "leetcode_title": "Sum of Subsequence Widths",
    "leetcode_id": 891,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/sum-of-subsequence-widths/",
    "canonicalSlug": "sum-of-subsequence-widths",
    "canonicalUrl": "https://leetcode.com/problems/sum-of-subsequence-widths/",
    "url": "https://leetcode.com/problems/sum-of-subsequence-widths/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Sum of Subsequence Widths\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Sum of Subsequence Widths\n};",
        "java": "// Java Solution for Sum of Subsequence Widths\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Sum of Subsequence Widths\n}",
        "python": "# Python Solution for Sum of Subsequence Widths\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Sum of Subsequence Widths\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Sum of Subsequence Widths\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Sum of Subsequence Widths\n};",
        "java": "// Optimal Java Solution for Sum of Subsequence Widths\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Sum of Subsequence Widths\n}",
        "python": "# Optimal Python Solution for Sum of Subsequence Widths\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Sum of Subsequence Widths\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Sum of Subsequence Widths",
      "cpp_optimal": "// Solution for Sum of Subsequence Widths",
      "java_brute": "// Solution for Sum of Subsequence Widths",
      "java_optimal": "// Solution for Sum of Subsequence Widths",
      "python_brute": "# Solution for Sum of Subsequence Widths",
      "python_optimal": "# Solution for Sum of Subsequence Widths"
    },
    "originalOrder": 739,
    "learningOrder": 739
  },
  {
    "id": 296,
    "number": 296,
    "sequence_number": 296,
    "title": "Distinct Subsequences II",
    "slug": "distinct-subsequences-ii",
    "difficulty": "Hard",
    "topic": "Arrays",
    "subtopic": "Arrays Optimization",
    "pattern": "Arrays Pattern",
    "secondary_patterns": [
      "Arrays Pattern"
    ],
    "stage": "Linked Lists & Fast-Slow Pointers",
    "curriculumStage": "Stage 6 — Linked Lists & Fast-Slow Pointers",
    "roadmapPhase": "Stage 6 — Linked Lists & Fast-Slow Pointers",
    "phase": "Stage 6 — Linked Lists & Fast-Slow Pointers",
    "estimatedTime": 45,
    "statement": "Solve the **Distinct Subsequences II** problem using standard Arrays techniques. Given input constraints appropriate for Hard level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Arrays algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Arrays properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Arrays techniques by solving Hard problem constraints for Distinct Subsequences II.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/distinct-subsequences-ii/",
    "leetcode_title": "Distinct Subsequences II",
    "leetcode_id": 940,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/distinct-subsequences-ii/",
    "canonicalSlug": "distinct-subsequences-ii",
    "canonicalUrl": "https://leetcode.com/problems/distinct-subsequences-ii/",
    "url": "https://leetcode.com/problems/distinct-subsequences-ii/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Distinct Subsequences II\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Distinct Subsequences II\n};",
        "java": "// Java Solution for Distinct Subsequences II\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Distinct Subsequences II\n}",
        "python": "# Python Solution for Distinct Subsequences II\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Distinct Subsequences II\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Distinct Subsequences II\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Distinct Subsequences II\n};",
        "java": "// Optimal Java Solution for Distinct Subsequences II\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Distinct Subsequences II\n}",
        "python": "# Optimal Python Solution for Distinct Subsequences II\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Distinct Subsequences II\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Distinct Subsequences II",
      "cpp_optimal": "// Solution for Distinct Subsequences II",
      "java_brute": "// Solution for Distinct Subsequences II",
      "java_optimal": "// Solution for Distinct Subsequences II",
      "python_brute": "# Solution for Distinct Subsequences II",
      "python_optimal": "# Solution for Distinct Subsequences II"
    },
    "originalOrder": 740,
    "learningOrder": 740
  },
  {
    "id": 297,
    "number": 297,
    "sequence_number": 297,
    "title": "Odd Even Jump",
    "slug": "odd-even-jump",
    "difficulty": "Hard",
    "topic": "Arrays",
    "subtopic": "Arrays Optimization",
    "pattern": "Arrays Pattern",
    "secondary_patterns": [
      "Arrays Pattern"
    ],
    "stage": "Linked Lists & Fast-Slow Pointers",
    "curriculumStage": "Stage 6 — Linked Lists & Fast-Slow Pointers",
    "roadmapPhase": "Stage 6 — Linked Lists & Fast-Slow Pointers",
    "phase": "Stage 6 — Linked Lists & Fast-Slow Pointers",
    "estimatedTime": 45,
    "statement": "Solve the **Odd Even Jump** problem using standard Arrays techniques. Given input constraints appropriate for Hard level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Arrays algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Arrays properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Arrays techniques by solving Hard problem constraints for Odd Even Jump.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/odd-even-jump/",
    "leetcode_title": "Odd Even Jump",
    "leetcode_id": 975,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/odd-even-jump/",
    "canonicalSlug": "odd-even-jump",
    "canonicalUrl": "https://leetcode.com/problems/odd-even-jump/",
    "url": "https://leetcode.com/problems/odd-even-jump/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Odd Even Jump\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Odd Even Jump\n};",
        "java": "// Java Solution for Odd Even Jump\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Odd Even Jump\n}",
        "python": "# Python Solution for Odd Even Jump\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Odd Even Jump\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Odd Even Jump\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Odd Even Jump\n};",
        "java": "// Optimal Java Solution for Odd Even Jump\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Odd Even Jump\n}",
        "python": "# Optimal Python Solution for Odd Even Jump\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Odd Even Jump\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Odd Even Jump",
      "cpp_optimal": "// Solution for Odd Even Jump",
      "java_brute": "// Solution for Odd Even Jump",
      "java_optimal": "// Solution for Odd Even Jump",
      "python_brute": "# Solution for Odd Even Jump",
      "python_optimal": "# Solution for Odd Even Jump"
    },
    "originalOrder": 741,
    "learningOrder": 741
  },
  {
    "id": 298,
    "number": 298,
    "sequence_number": 298,
    "title": "Numbers With Repeated Digits",
    "slug": "numbers-with-repeated-digits",
    "difficulty": "Hard",
    "topic": "Math",
    "subtopic": "Arrays Optimization",
    "pattern": "Arrays Pattern",
    "secondary_patterns": [
      "Arrays Pattern"
    ],
    "stage": "Linked Lists & Fast-Slow Pointers",
    "curriculumStage": "Stage 6 — Linked Lists & Fast-Slow Pointers",
    "roadmapPhase": "Stage 6 — Linked Lists & Fast-Slow Pointers",
    "phase": "Stage 6 — Linked Lists & Fast-Slow Pointers",
    "estimatedTime": 45,
    "statement": "Solve the **Numbers With Repeated Digits** problem using standard Arrays techniques. Given input constraints appropriate for Hard level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Arrays algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Arrays properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Arrays techniques by solving Hard problem constraints for Numbers With Repeated Digits.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/numbers-with-repeated-digits/",
    "leetcode_title": "Numbers With Repeated Digits",
    "leetcode_id": 1012,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/numbers-with-repeated-digits/",
    "canonicalSlug": "numbers-with-repeated-digits",
    "canonicalUrl": "https://leetcode.com/problems/numbers-with-repeated-digits/",
    "url": "https://leetcode.com/problems/numbers-with-repeated-digits/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Numbers With Repeated Digits\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Numbers With Repeated Digits\n};",
        "java": "// Java Solution for Numbers With Repeated Digits\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Numbers With Repeated Digits\n}",
        "python": "# Python Solution for Numbers With Repeated Digits\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Numbers With Repeated Digits\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Numbers With Repeated Digits\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Numbers With Repeated Digits\n};",
        "java": "// Optimal Java Solution for Numbers With Repeated Digits\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Numbers With Repeated Digits\n}",
        "python": "# Optimal Python Solution for Numbers With Repeated Digits\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Numbers With Repeated Digits\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Numbers With Repeated Digits",
      "cpp_optimal": "// Solution for Numbers With Repeated Digits",
      "java_brute": "// Solution for Numbers With Repeated Digits",
      "java_optimal": "// Solution for Numbers With Repeated Digits",
      "python_brute": "# Solution for Numbers With Repeated Digits",
      "python_optimal": "# Solution for Numbers With Repeated Digits"
    },
    "originalOrder": 742,
    "learningOrder": 742
  },
  {
    "id": 299,
    "number": 299,
    "sequence_number": 299,
    "title": "Recover a Tree From Preorder Traversal",
    "slug": "recover-a-tree-from-preorder-traversal",
    "difficulty": "Hard",
    "topic": "Arrays",
    "subtopic": "Arrays Optimization",
    "pattern": "Arrays Pattern",
    "secondary_patterns": [
      "Arrays Pattern"
    ],
    "stage": "Linked Lists & Fast-Slow Pointers",
    "curriculumStage": "Stage 6 — Linked Lists & Fast-Slow Pointers",
    "roadmapPhase": "Stage 6 — Linked Lists & Fast-Slow Pointers",
    "phase": "Stage 6 — Linked Lists & Fast-Slow Pointers",
    "estimatedTime": 45,
    "statement": "Solve the **Recover a Tree From Preorder Traversal** problem using standard Arrays techniques. Given input constraints appropriate for Hard level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Arrays algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Arrays properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Arrays techniques by solving Hard problem constraints for Recover a Tree From Preorder Traversal.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/recover-a-tree-from-preorder-traversal/",
    "leetcode_title": "Recover a Tree From Preorder Traversal",
    "leetcode_id": 1028,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/recover-a-tree-from-preorder-traversal/",
    "canonicalSlug": "recover-a-tree-from-preorder-traversal",
    "canonicalUrl": "https://leetcode.com/problems/recover-a-tree-from-preorder-traversal/",
    "url": "https://leetcode.com/problems/recover-a-tree-from-preorder-traversal/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Recover a Tree From Preorder Traversal\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Recover a Tree From Preorder Traversal\n};",
        "java": "// Java Solution for Recover a Tree From Preorder Traversal\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Recover a Tree From Preorder Traversal\n}",
        "python": "# Python Solution for Recover a Tree From Preorder Traversal\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Recover a Tree From Preorder Traversal\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Recover a Tree From Preorder Traversal\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Recover a Tree From Preorder Traversal\n};",
        "java": "// Optimal Java Solution for Recover a Tree From Preorder Traversal\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Recover a Tree From Preorder Traversal\n}",
        "python": "# Optimal Python Solution for Recover a Tree From Preorder Traversal\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Recover a Tree From Preorder Traversal\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Recover a Tree From Preorder Traversal",
      "cpp_optimal": "// Solution for Recover a Tree From Preorder Traversal",
      "java_brute": "// Solution for Recover a Tree From Preorder Traversal",
      "java_optimal": "// Solution for Recover a Tree From Preorder Traversal",
      "python_brute": "# Solution for Recover a Tree From Preorder Traversal",
      "python_optimal": "# Solution for Recover a Tree From Preorder Traversal"
    },
    "originalOrder": 743,
    "learningOrder": 743
  },
  {
    "id": 300,
    "number": 300,
    "sequence_number": 300,
    "title": "Escape a Large Maze",
    "slug": "escape-a-large-maze",
    "difficulty": "Hard",
    "topic": "Arrays",
    "subtopic": "Arrays Optimization",
    "pattern": "Arrays Pattern",
    "secondary_patterns": [
      "Arrays Pattern"
    ],
    "stage": "Linked Lists & Fast-Slow Pointers",
    "curriculumStage": "Stage 6 — Linked Lists & Fast-Slow Pointers",
    "roadmapPhase": "Stage 6 — Linked Lists & Fast-Slow Pointers",
    "phase": "Stage 6 — Linked Lists & Fast-Slow Pointers",
    "estimatedTime": 45,
    "statement": "Solve the **Escape a Large Maze** problem using standard Arrays techniques. Given input constraints appropriate for Hard level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Arrays algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Arrays properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Arrays techniques by solving Hard problem constraints for Escape a Large Maze.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/escape-a-large-maze/",
    "leetcode_title": "Escape a Large Maze",
    "leetcode_id": 1036,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/escape-a-large-maze/",
    "canonicalSlug": "escape-a-large-maze",
    "canonicalUrl": "https://leetcode.com/problems/escape-a-large-maze/",
    "url": "https://leetcode.com/problems/escape-a-large-maze/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Escape a Large Maze\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Escape a Large Maze\n};",
        "java": "// Java Solution for Escape a Large Maze\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Escape a Large Maze\n}",
        "python": "# Python Solution for Escape a Large Maze\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Escape a Large Maze\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Escape a Large Maze\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Escape a Large Maze\n};",
        "java": "// Optimal Java Solution for Escape a Large Maze\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Escape a Large Maze\n}",
        "python": "# Optimal Python Solution for Escape a Large Maze\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Escape a Large Maze\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Escape a Large Maze",
      "cpp_optimal": "// Solution for Escape a Large Maze",
      "java_brute": "// Solution for Escape a Large Maze",
      "java_optimal": "// Solution for Escape a Large Maze",
      "python_brute": "# Solution for Escape a Large Maze",
      "python_optimal": "# Solution for Escape a Large Maze"
    },
    "originalOrder": 744,
    "learningOrder": 744
  },
  {
    "id": 301,
    "number": 301,
    "sequence_number": 301,
    "title": "Binary Search",
    "slug": "binary-search",
    "difficulty": "Easy",
    "topic": "Binary Search",
    "subtopic": "Binary Search",
    "pattern": "Binary Search",
    "secondary_patterns": [
      "Binary Search"
    ],
    "stage": "Binary Search & Search on Answer",
    "curriculumStage": "Stage 7 — Binary Search & Search on Answer",
    "roadmapPhase": "Stage 7 — Binary Search & Search on Answer",
    "phase": "Stage 7 — Binary Search & Search on Answer",
    "estimatedTime": 15,
    "statement": "Solve the **Binary Search Challenge** problem using the **Binary Search** technique. Given input constraints appropriate for Easy level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^4",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Binary Search identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Binary Search. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Binary Search techniques by solving Easy problem constraints for Binary Search Challenge.",
    "whyThisPattern": "When observing binary search problem conditions, Binary Search optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Meta",
      "Uber",
      "Databricks"
    ],
    "companyRelevanceTier": "Medium",
    "leetcode_url": "https://leetcode.com/problems/binary-search/",
    "leetcode_title": "Binary Search",
    "leetcode_id": 704,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/binary-search/",
    "canonicalSlug": "binary-search",
    "canonicalUrl": "https://leetcode.com/problems/binary-search/",
    "url": "https://leetcode.com/problems/binary-search/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Binary Search Challenge (Binary Search)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Binary Search Challenge (Binary Search)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Binary Search Challenge (Binary Search)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Binary Search Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Binary Search Challenge (Binary Search)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Binary Search Challenge (Binary Search)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Binary Search Challenge (Binary Search)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Binary Search Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Binary Search",
      "cpp_optimal": "// Solution for Binary Search",
      "java_brute": "// Solution for Binary Search",
      "java_optimal": "// Solution for Binary Search",
      "python_brute": "# Solution for Binary Search",
      "python_optimal": "# Solution for Binary Search"
    },
    "originalOrder": 125,
    "learningOrder": 125
  },
  {
    "id": 302,
    "number": 302,
    "sequence_number": 302,
    "title": "Matrix Cells in Distance Order",
    "slug": "matrix-cells-in-distance-order",
    "difficulty": "Easy",
    "topic": "Binary Search",
    "subtopic": "Binary Search",
    "pattern": "Binary Search",
    "secondary_patterns": [
      "Binary Search"
    ],
    "stage": "Binary Search & Search on Answer",
    "curriculumStage": "Stage 7 — Binary Search & Search on Answer",
    "roadmapPhase": "Stage 7 — Binary Search & Search on Answer",
    "phase": "Stage 7 — Binary Search & Search on Answer",
    "estimatedTime": 15,
    "statement": "Solve the **Matrix Cells in Distance Order Optimization** problem using the **Binary Search** technique. Given input constraints appropriate for Easy level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^4",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Binary Search identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Binary Search. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Binary Search techniques by solving Easy problem constraints for Matrix Cells in Distance Order Optimization.",
    "whyThisPattern": "When observing arrays & strings problem conditions, Binary Search optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Meta",
      "Apple",
      "Netflix"
    ],
    "companyRelevanceTier": "Medium",
    "leetcode_url": "https://leetcode.com/problems/matrix-cells-in-distance-order/",
    "leetcode_title": "Matrix Cells in Distance Order",
    "leetcode_id": 1030,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/matrix-cells-in-distance-order/",
    "canonicalSlug": "matrix-cells-in-distance-order",
    "canonicalUrl": "https://leetcode.com/problems/matrix-cells-in-distance-order/",
    "url": "https://leetcode.com/problems/matrix-cells-in-distance-order/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Matrix Cells in Distance Order Optimization (Binary Search)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Matrix Cells in Distance Order Optimization (Binary Search)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Matrix Cells in Distance Order Optimization (Binary Search)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Matrix Cells in Distance Order Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Matrix Cells in Distance Order Optimization (Binary Search)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Matrix Cells in Distance Order Optimization (Binary Search)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Matrix Cells in Distance Order Optimization (Binary Search)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Matrix Cells in Distance Order Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Matrix Cells in Distance Order",
      "cpp_optimal": "// Solution for Matrix Cells in Distance Order",
      "java_brute": "// Solution for Matrix Cells in Distance Order",
      "java_optimal": "// Solution for Matrix Cells in Distance Order",
      "python_brute": "# Solution for Matrix Cells in Distance Order",
      "python_optimal": "# Solution for Matrix Cells in Distance Order"
    },
    "originalOrder": 126,
    "learningOrder": 126
  },
  {
    "id": 303,
    "number": 303,
    "sequence_number": 303,
    "title": "Cells with Odd Values in a Matrix",
    "slug": "cells-with-odd-values-in-a-matrix",
    "difficulty": "Easy",
    "topic": "Binary Search",
    "subtopic": "Binary Search",
    "pattern": "Binary Search",
    "secondary_patterns": [
      "Binary Search"
    ],
    "stage": "Binary Search & Search on Answer",
    "curriculumStage": "Stage 7 — Binary Search & Search on Answer",
    "roadmapPhase": "Stage 7 — Binary Search & Search on Answer",
    "phase": "Stage 7 — Binary Search & Search on Answer",
    "estimatedTime": 15,
    "statement": "Solve the **Cells with Odd Values in a Matrix Challenge** problem using the **Binary Search** technique. Given input constraints appropriate for Easy level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^4",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Binary Search identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Binary Search. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Binary Search techniques by solving Easy problem constraints for Cells with Odd Values in a Matrix Challenge.",
    "whyThisPattern": "When observing arrays & strings problem conditions, Binary Search optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Microsoft",
      "Bloomberg"
    ],
    "companyRelevanceTier": "Medium",
    "leetcode_url": "https://leetcode.com/problems/cells-with-odd-values-in-a-matrix/",
    "leetcode_title": "Cells with Odd Values in a Matrix",
    "leetcode_id": 1252,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/cells-with-odd-values-in-a-matrix/",
    "canonicalSlug": "cells-with-odd-values-in-a-matrix",
    "canonicalUrl": "https://leetcode.com/problems/cells-with-odd-values-in-a-matrix/",
    "url": "https://leetcode.com/problems/cells-with-odd-values-in-a-matrix/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Cells with Odd Values in a Matrix Challenge (Binary Search)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Cells with Odd Values in a Matrix Challenge (Binary Search)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Cells with Odd Values in a Matrix Challenge (Binary Search)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Cells with Odd Values in a Matrix Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Cells with Odd Values in a Matrix Challenge (Binary Search)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Cells with Odd Values in a Matrix Challenge (Binary Search)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Cells with Odd Values in a Matrix Challenge (Binary Search)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Cells with Odd Values in a Matrix Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Cells with Odd Values in a Matrix",
      "cpp_optimal": "// Solution for Cells with Odd Values in a Matrix",
      "java_brute": "// Solution for Cells with Odd Values in a Matrix",
      "java_optimal": "// Solution for Cells with Odd Values in a Matrix",
      "python_brute": "# Solution for Cells with Odd Values in a Matrix",
      "python_optimal": "# Solution for Cells with Odd Values in a Matrix"
    },
    "originalOrder": 127,
    "learningOrder": 127
  },
  {
    "id": 304,
    "number": 304,
    "sequence_number": 304,
    "title": "The K Weakest Rows in a Matrix",
    "slug": "the-k-weakest-rows-in-a-matrix",
    "difficulty": "Easy",
    "topic": "Binary Search",
    "subtopic": "Binary Search",
    "pattern": "Binary Search",
    "secondary_patterns": [
      "Binary Search"
    ],
    "stage": "Binary Search & Search on Answer",
    "curriculumStage": "Stage 7 — Binary Search & Search on Answer",
    "roadmapPhase": "Stage 7 — Binary Search & Search on Answer",
    "phase": "Stage 7 — Binary Search & Search on Answer",
    "estimatedTime": 15,
    "statement": "Solve the **The K Weakest Rows in a Matrix Challenge** problem using the **Binary Search** technique. Given input constraints appropriate for Easy level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^4",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Binary Search identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Binary Search. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Binary Search techniques by solving Easy problem constraints for The K Weakest Rows in a Matrix Challenge.",
    "whyThisPattern": "When observing arrays & strings problem conditions, Binary Search optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Meta",
      "Uber",
      "Databricks"
    ],
    "companyRelevanceTier": "Medium",
    "leetcode_url": "https://leetcode.com/problems/the-k-weakest-rows-in-a-matrix/",
    "leetcode_title": "The K Weakest Rows in a Matrix",
    "leetcode_id": 1337,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/the-k-weakest-rows-in-a-matrix/",
    "canonicalSlug": "the-k-weakest-rows-in-a-matrix",
    "canonicalUrl": "https://leetcode.com/problems/the-k-weakest-rows-in-a-matrix/",
    "url": "https://leetcode.com/problems/the-k-weakest-rows-in-a-matrix/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for The K Weakest Rows in a Matrix Challenge (Binary Search)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for The K Weakest Rows in a Matrix Challenge (Binary Search)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for The K Weakest Rows in a Matrix Challenge (Binary Search)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for The K Weakest Rows in a Matrix Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for The K Weakest Rows in a Matrix Challenge (Binary Search)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for The K Weakest Rows in a Matrix Challenge (Binary Search)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for The K Weakest Rows in a Matrix Challenge (Binary Search)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for The K Weakest Rows in a Matrix Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for The K Weakest Rows in a Matrix",
      "cpp_optimal": "// Solution for The K Weakest Rows in a Matrix",
      "java_brute": "// Solution for The K Weakest Rows in a Matrix",
      "java_optimal": "// Solution for The K Weakest Rows in a Matrix",
      "python_brute": "# Solution for The K Weakest Rows in a Matrix",
      "python_optimal": "# Solution for The K Weakest Rows in a Matrix"
    },
    "originalOrder": 128,
    "learningOrder": 128
  },
  {
    "id": 305,
    "number": 305,
    "sequence_number": 305,
    "title": "Longest Subsequence With Limited Sum",
    "slug": "longest-subsequence-with-limited-sum",
    "difficulty": "Easy",
    "topic": "Binary Search",
    "subtopic": "Binary Search Optimization",
    "pattern": "Sort & Prefix Sum Binary Search",
    "secondary_patterns": [
      "Sort & Prefix Sum Binary Search"
    ],
    "stage": "Binary Search & Search on Answer",
    "curriculumStage": "Stage 7 — Binary Search & Search on Answer",
    "roadmapPhase": "Stage 7 — Binary Search & Search on Answer",
    "phase": "Stage 7 — Binary Search & Search on Answer",
    "estimatedTime": 15,
    "statement": "Given the constraints and input parameters for Longest Subsequence With Limited Sum, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Longest Subsequence With Limited Sum."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Longest Subsequence With Limited Sum.",
      "Leverage the optimal Binary Search pattern to reduce time complexity."
    ],
    "learningObjective": "Master Binary Search techniques by solving Easy problem constraints for Longest Subsequence With Limited Sum.",
    "whyThisPattern": "When observing Binary Search problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/longest-subsequence-with-limited-sum/",
    "leetcode_title": "Longest Subsequence With Limited Sum",
    "leetcode_id": 2389,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/longest-subsequence-with-limited-sum/",
    "canonicalSlug": "longest-subsequence-with-limited-sum",
    "canonicalUrl": "https://leetcode.com/problems/longest-subsequence-with-limited-sum/",
    "url": "https://leetcode.com/problems/longest-subsequence-with-limited-sum/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Longest Subsequence With Limited Sum\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Longest Subsequence With Limited Sum\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Longest Subsequence With Limited Sum\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Longest Subsequence With Limited Sum\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Longest Subsequence With Limited Sum\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Longest Subsequence With Limited Sum\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Longest Subsequence With Limited Sum\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Longest Subsequence With Limited Sum\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Longest Subsequence With Limited Sum",
      "cpp_optimal": "// Solution for Longest Subsequence With Limited Sum",
      "java_brute": "// Solution for Longest Subsequence With Limited Sum",
      "java_optimal": "// Solution for Longest Subsequence With Limited Sum",
      "python_brute": "# Solution for Longest Subsequence With Limited Sum",
      "python_optimal": "# Solution for Longest Subsequence With Limited Sum"
    },
    "originalOrder": 129,
    "learningOrder": 129
  },
  {
    "id": 306,
    "number": 306,
    "sequence_number": 306,
    "title": "Lucky Numbers in a Matrix",
    "slug": "lucky-numbers-in-a-matrix",
    "difficulty": "Easy",
    "topic": "Binary Search",
    "subtopic": "Binary Search",
    "pattern": "Binary Search",
    "secondary_patterns": [
      "Binary Search"
    ],
    "stage": "Binary Search & Search on Answer",
    "curriculumStage": "Stage 7 — Binary Search & Search on Answer",
    "roadmapPhase": "Stage 7 — Binary Search & Search on Answer",
    "phase": "Stage 7 — Binary Search & Search on Answer",
    "estimatedTime": 15,
    "statement": "Solve the **Lucky Numbers in a Matrix Optimization** problem using the **Binary Search** technique. Given input constraints appropriate for Easy level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^4",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Binary Search identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Binary Search. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Binary Search techniques by solving Easy problem constraints for Lucky Numbers in a Matrix Optimization.",
    "whyThisPattern": "When observing arrays & strings problem conditions, Binary Search optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Meta",
      "Apple",
      "Netflix"
    ],
    "companyRelevanceTier": "Medium",
    "leetcode_url": "https://leetcode.com/problems/lucky-numbers-in-a-matrix/",
    "leetcode_title": "Lucky Numbers in a Matrix",
    "leetcode_id": 1380,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/lucky-numbers-in-a-matrix/",
    "canonicalSlug": "lucky-numbers-in-a-matrix",
    "canonicalUrl": "https://leetcode.com/problems/lucky-numbers-in-a-matrix/",
    "url": "https://leetcode.com/problems/lucky-numbers-in-a-matrix/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Lucky Numbers in a Matrix Optimization (Binary Search)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Lucky Numbers in a Matrix Optimization (Binary Search)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Lucky Numbers in a Matrix Optimization (Binary Search)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Lucky Numbers in a Matrix Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Lucky Numbers in a Matrix Optimization (Binary Search)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Lucky Numbers in a Matrix Optimization (Binary Search)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Lucky Numbers in a Matrix Optimization (Binary Search)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Lucky Numbers in a Matrix Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Lucky Numbers in a Matrix",
      "cpp_optimal": "// Solution for Lucky Numbers in a Matrix",
      "java_brute": "// Solution for Lucky Numbers in a Matrix",
      "java_optimal": "// Solution for Lucky Numbers in a Matrix",
      "python_brute": "# Solution for Lucky Numbers in a Matrix",
      "python_optimal": "# Solution for Lucky Numbers in a Matrix"
    },
    "originalOrder": 130,
    "learningOrder": 130
  },
  {
    "id": 307,
    "number": 307,
    "sequence_number": 307,
    "title": "Find Smallest Letter Greater Than Target",
    "slug": "find-smallest-letter-greater-than-target",
    "difficulty": "Easy",
    "topic": "Binary Search",
    "subtopic": "Binary Search Optimization",
    "pattern": "Binary Search Bounds",
    "secondary_patterns": [
      "Binary Search Bounds"
    ],
    "stage": "Binary Search & Search on Answer",
    "curriculumStage": "Stage 7 — Binary Search & Search on Answer",
    "roadmapPhase": "Stage 7 — Binary Search & Search on Answer",
    "phase": "Stage 7 — Binary Search & Search on Answer",
    "estimatedTime": 15,
    "statement": "Given the constraints and input parameters for Find Smallest Letter Greater Than Target, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Find Smallest Letter Greater Than Target."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Find Smallest Letter Greater Than Target.",
      "Leverage the optimal Binary Search pattern to reduce time complexity."
    ],
    "learningObjective": "Master Binary Search techniques by solving Easy problem constraints for Find Smallest Letter Greater Than Target.",
    "whyThisPattern": "When observing Binary Search problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/find-smallest-letter-greater-than-target/",
    "leetcode_title": "Find Smallest Letter Greater Than Target",
    "leetcode_id": 744,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/find-smallest-letter-greater-than-target/",
    "canonicalSlug": "find-smallest-letter-greater-than-target",
    "canonicalUrl": "https://leetcode.com/problems/find-smallest-letter-greater-than-target/",
    "url": "https://leetcode.com/problems/find-smallest-letter-greater-than-target/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Find Smallest Letter Greater Than Target\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Find Smallest Letter Greater Than Target\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Find Smallest Letter Greater Than Target\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Find Smallest Letter Greater Than Target\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Find Smallest Letter Greater Than Target\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Find Smallest Letter Greater Than Target\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Find Smallest Letter Greater Than Target\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Find Smallest Letter Greater Than Target\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Find Smallest Letter Greater Than Target",
      "cpp_optimal": "// Solution for Find Smallest Letter Greater Than Target",
      "java_brute": "// Solution for Find Smallest Letter Greater Than Target",
      "java_optimal": "// Solution for Find Smallest Letter Greater Than Target",
      "python_brute": "# Solution for Find Smallest Letter Greater Than Target",
      "python_optimal": "# Solution for Find Smallest Letter Greater Than Target"
    },
    "originalOrder": 131,
    "learningOrder": 131
  },
  {
    "id": 308,
    "number": 308,
    "sequence_number": 308,
    "title": "Find the Distance Value Between Two Arrays",
    "slug": "find-the-distance-value-between-two-arrays",
    "difficulty": "Easy",
    "topic": "Binary Search",
    "subtopic": "Binary Search Optimization",
    "pattern": "Range Distance Check",
    "secondary_patterns": [
      "Range Distance Check"
    ],
    "stage": "Binary Search & Search on Answer",
    "curriculumStage": "Stage 7 — Binary Search & Search on Answer",
    "roadmapPhase": "Stage 7 — Binary Search & Search on Answer",
    "phase": "Stage 7 — Binary Search & Search on Answer",
    "estimatedTime": 15,
    "statement": "Given the constraints and input parameters for Find the Distance Value Between Two Arrays, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Find the Distance Value Between Two Arrays."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Find the Distance Value Between Two Arrays.",
      "Leverage the optimal Binary Search pattern to reduce time complexity."
    ],
    "learningObjective": "Master Binary Search techniques by solving Easy problem constraints for Find the Distance Value Between Two Arrays.",
    "whyThisPattern": "When observing Binary Search problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/find-the-distance-value-between-two-arrays/",
    "leetcode_title": "Find the Distance Value Between Two Arrays",
    "leetcode_id": 1385,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/find-the-distance-value-between-two-arrays/",
    "canonicalSlug": "find-the-distance-value-between-two-arrays",
    "canonicalUrl": "https://leetcode.com/problems/find-the-distance-value-between-two-arrays/",
    "url": "https://leetcode.com/problems/find-the-distance-value-between-two-arrays/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Find the Distance Value Between Two Arrays\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Find the Distance Value Between Two Arrays\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Find the Distance Value Between Two Arrays\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Find the Distance Value Between Two Arrays\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Find the Distance Value Between Two Arrays\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Find the Distance Value Between Two Arrays\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Find the Distance Value Between Two Arrays\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Find the Distance Value Between Two Arrays\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Find the Distance Value Between Two Arrays",
      "cpp_optimal": "// Solution for Find the Distance Value Between Two Arrays",
      "java_brute": "// Solution for Find the Distance Value Between Two Arrays",
      "java_optimal": "// Solution for Find the Distance Value Between Two Arrays",
      "python_brute": "# Solution for Find the Distance Value Between Two Arrays",
      "python_optimal": "# Solution for Find the Distance Value Between Two Arrays"
    },
    "originalOrder": 132,
    "learningOrder": 132
  },
  {
    "id": 309,
    "number": 309,
    "sequence_number": 309,
    "title": "Array Partition",
    "slug": "array-partition-optimization",
    "difficulty": "Easy",
    "topic": "Arrays",
    "subtopic": "Hashing & Array Optimization",
    "pattern": "Hashing & Array Optimization",
    "secondary_patterns": [
      "Hashing & Array Optimization"
    ],
    "stage": "Binary Search & Search on Answer",
    "curriculumStage": "Stage 7 — Binary Search & Search on Answer",
    "roadmapPhase": "Stage 7 — Binary Search & Search on Answer",
    "phase": "Stage 7 — Binary Search & Search on Answer",
    "estimatedTime": 15,
    "statement": "Solve the **Array Partition Optimization** problem using the **Hashing & Array Optimization** technique. Given input constraints appropriate for Easy level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^4",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Hashing & Array Optimization identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Hashing & Array Optimization. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Hashing & Array Optimization techniques by solving Easy problem constraints for Array Partition Optimization.",
    "whyThisPattern": "When observing arrays & strings problem conditions, Hashing & Array Optimization optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "LinkedIn",
      "Amazon"
    ],
    "companyRelevanceTier": "Medium",
    "leetcode_url": "https://leetcode.com/problems/array-partition/",
    "leetcode_title": "Array Partition",
    "leetcode_id": 561,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/array-partition/",
    "canonicalSlug": "array-partition-optimization",
    "canonicalUrl": "https://leetcode.com/problems/array-partition/",
    "url": "https://leetcode.com/problems/array-partition/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Array Partition Optimization (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Array Partition Optimization (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Array Partition Optimization (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Array Partition Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Array Partition Optimization (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Array Partition Optimization (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Array Partition Optimization (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Array Partition Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Array Partition",
      "cpp_optimal": "// Solution for Array Partition",
      "java_brute": "// Solution for Array Partition",
      "java_optimal": "// Solution for Array Partition",
      "python_brute": "# Solution for Array Partition",
      "python_optimal": "# Solution for Array Partition"
    }
  },
  {
    "id": 310,
    "number": 310,
    "sequence_number": 310,
    "title": "Find Pivot Index",
    "slug": "find-pivot-index-challenge",
    "difficulty": "Easy",
    "topic": "Arrays",
    "subtopic": "Hashing & Array Optimization",
    "pattern": "Hashing & Array Optimization",
    "secondary_patterns": [
      "Hashing & Array Optimization"
    ],
    "stage": "Binary Search & Search on Answer",
    "curriculumStage": "Stage 7 — Binary Search & Search on Answer",
    "roadmapPhase": "Stage 7 — Binary Search & Search on Answer",
    "phase": "Stage 7 — Binary Search & Search on Answer",
    "estimatedTime": 15,
    "statement": "Solve the **Find Pivot Index Challenge** problem using the **Hashing & Array Optimization** technique. Given input constraints appropriate for Easy level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^4",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Hashing & Array Optimization identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Hashing & Array Optimization. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Hashing & Array Optimization techniques by solving Easy problem constraints for Find Pivot Index Challenge.",
    "whyThisPattern": "When observing arrays & strings problem conditions, Hashing & Array Optimization optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Amazon",
      "Microsoft",
      "Uber"
    ],
    "companyRelevanceTier": "Medium",
    "leetcode_url": "https://leetcode.com/problems/find-pivot-index/",
    "leetcode_title": "Find Pivot Index",
    "leetcode_id": 724,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/find-pivot-index/",
    "canonicalSlug": "find-pivot-index-challenge",
    "canonicalUrl": "https://leetcode.com/problems/find-pivot-index/",
    "url": "https://leetcode.com/problems/find-pivot-index/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Find Pivot Index Challenge (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Find Pivot Index Challenge (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Find Pivot Index Challenge (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Find Pivot Index Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Find Pivot Index Challenge (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Find Pivot Index Challenge (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Find Pivot Index Challenge (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Find Pivot Index Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Find Pivot Index",
      "cpp_optimal": "// Solution for Find Pivot Index",
      "java_brute": "// Solution for Find Pivot Index",
      "java_optimal": "// Solution for Find Pivot Index",
      "python_brute": "# Solution for Find Pivot Index",
      "python_optimal": "# Solution for Find Pivot Index"
    }
  },
  {
    "id": 311,
    "number": 311,
    "sequence_number": 311,
    "title": "Search a 2D Matrix",
    "slug": "search-a-2d-matrix",
    "difficulty": "Medium",
    "topic": "Binary Search",
    "subtopic": "Binary Search",
    "pattern": "Binary Search",
    "secondary_patterns": [
      "Binary Search"
    ],
    "stage": "Binary Search & Search on Answer",
    "curriculumStage": "Stage 7 — Binary Search & Search on Answer",
    "roadmapPhase": "Stage 7 — Binary Search & Search on Answer",
    "phase": "Stage 7 — Binary Search & Search on Answer",
    "estimatedTime": 30,
    "statement": "Solve the **Search a 2D Matrix Challenge** problem using the **Binary Search** technique. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Binary Search identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Binary Search. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Binary Search techniques by solving Medium problem constraints for Search a 2D Matrix Challenge.",
    "whyThisPattern": "When observing arrays & strings problem conditions, Binary Search optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Meta",
      "Uber",
      "Databricks"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/search-a-2d-matrix/",
    "leetcode_title": "Search a 2D Matrix",
    "leetcode_id": 74,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/search-a-2d-matrix/",
    "canonicalSlug": "search-a-2d-matrix",
    "canonicalUrl": "https://leetcode.com/problems/search-a-2d-matrix/",
    "url": "https://leetcode.com/problems/search-a-2d-matrix/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Search a 2D Matrix Challenge (Binary Search)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Search a 2D Matrix Challenge (Binary Search)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Search a 2D Matrix Challenge (Binary Search)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Search a 2D Matrix Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Search a 2D Matrix Challenge (Binary Search)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Search a 2D Matrix Challenge (Binary Search)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Search a 2D Matrix Challenge (Binary Search)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Search a 2D Matrix Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Search a 2D Matrix",
      "cpp_optimal": "// Solution for Search a 2D Matrix",
      "java_brute": "// Solution for Search a 2D Matrix",
      "java_optimal": "// Solution for Search a 2D Matrix",
      "python_brute": "# Solution for Search a 2D Matrix",
      "python_optimal": "# Solution for Search a 2D Matrix"
    },
    "originalOrder": 404,
    "learningOrder": 404
  },
  {
    "id": 312,
    "number": 312,
    "sequence_number": 312,
    "title": "Search in Rotated Sorted Array II",
    "slug": "search-in-rotated-sorted-array-ii",
    "difficulty": "Medium",
    "topic": "Binary Search",
    "subtopic": "Two Pointers",
    "pattern": "Two Pointers",
    "secondary_patterns": [
      "Two Pointers"
    ],
    "stage": "Binary Search & Search on Answer",
    "curriculumStage": "Stage 7 — Binary Search & Search on Answer",
    "roadmapPhase": "Stage 7 — Binary Search & Search on Answer",
    "phase": "Stage 7 — Binary Search & Search on Answer",
    "estimatedTime": 30,
    "statement": "Solve the **Search in Rotated Sorted Array II Challenge** problem using the **Two Pointers** technique. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Two Pointers identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Two Pointers. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Two Pointers techniques by solving Medium problem constraints for Search in Rotated Sorted Array II Challenge.",
    "whyThisPattern": "When observing arrays & strings problem conditions, Two Pointers optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(1)",
    "companyRelevance": [
      "Microsoft",
      "Bloomberg",
      "Adobe"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/search-in-rotated-sorted-array-ii/",
    "leetcode_title": "Search in Rotated Sorted Array II",
    "leetcode_id": 81,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/search-in-rotated-sorted-array-ii/",
    "canonicalSlug": "search-in-rotated-sorted-array-ii",
    "canonicalUrl": "https://leetcode.com/problems/search-in-rotated-sorted-array-ii/",
    "url": "https://leetcode.com/problems/search-in-rotated-sorted-array-ii/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Search in Rotated Sorted Array II Challenge (Two Pointers)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Search in Rotated Sorted Array II Challenge (Two Pointers)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Search in Rotated Sorted Array II Challenge (Two Pointers)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Search in Rotated Sorted Array II Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Search in Rotated Sorted Array II Challenge (Two Pointers)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Search in Rotated Sorted Array II Challenge (Two Pointers)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Search in Rotated Sorted Array II Challenge (Two Pointers)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Search in Rotated Sorted Array II Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Search in Rotated Sorted Array II",
      "cpp_optimal": "// Solution for Search in Rotated Sorted Array II",
      "java_brute": "// Solution for Search in Rotated Sorted Array II",
      "java_optimal": "// Solution for Search in Rotated Sorted Array II",
      "python_brute": "# Solution for Search in Rotated Sorted Array II",
      "python_optimal": "# Solution for Search in Rotated Sorted Array II"
    },
    "originalOrder": 405,
    "learningOrder": 405
  },
  {
    "id": 313,
    "number": 313,
    "sequence_number": 313,
    "title": "Search a 2D Matrix II",
    "slug": "search-a-2d-matrix-ii",
    "difficulty": "Medium",
    "topic": "Binary Search",
    "subtopic": "Binary Search",
    "pattern": "Binary Search",
    "secondary_patterns": [
      "Binary Search"
    ],
    "stage": "Binary Search & Search on Answer",
    "curriculumStage": "Stage 7 — Binary Search & Search on Answer",
    "roadmapPhase": "Stage 7 — Binary Search & Search on Answer",
    "phase": "Stage 7 — Binary Search & Search on Answer",
    "estimatedTime": 30,
    "statement": "Solve the **Search a 2D Matrix II Challenge** problem using the **Binary Search** technique. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Binary Search identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Binary Search. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Binary Search techniques by solving Medium problem constraints for Search a 2D Matrix II Challenge.",
    "whyThisPattern": "When observing arrays & strings problem conditions, Binary Search optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Amazon",
      "Microsoft",
      "Uber"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/search-a-2d-matrix-ii/",
    "leetcode_title": "Search a 2D Matrix II",
    "leetcode_id": 240,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/search-a-2d-matrix-ii/",
    "canonicalSlug": "search-a-2d-matrix-ii",
    "canonicalUrl": "https://leetcode.com/problems/search-a-2d-matrix-ii/",
    "url": "https://leetcode.com/problems/search-a-2d-matrix-ii/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Search a 2D Matrix II Challenge (Binary Search)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Search a 2D Matrix II Challenge (Binary Search)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Search a 2D Matrix II Challenge (Binary Search)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Search a 2D Matrix II Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Search a 2D Matrix II Challenge (Binary Search)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Search a 2D Matrix II Challenge (Binary Search)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Search a 2D Matrix II Challenge (Binary Search)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Search a 2D Matrix II Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Search a 2D Matrix II",
      "cpp_optimal": "// Solution for Search a 2D Matrix II",
      "java_brute": "// Solution for Search a 2D Matrix II",
      "java_optimal": "// Solution for Search a 2D Matrix II",
      "python_brute": "# Solution for Search a 2D Matrix II",
      "python_optimal": "# Solution for Search a 2D Matrix II"
    },
    "originalOrder": 406,
    "learningOrder": 406
  },
  {
    "id": 314,
    "number": 314,
    "sequence_number": 314,
    "title": "Random Flip Matrix",
    "slug": "random-flip-matrix",
    "difficulty": "Medium",
    "topic": "Binary Search",
    "subtopic": "Binary Search",
    "pattern": "Binary Search",
    "secondary_patterns": [
      "Binary Search"
    ],
    "stage": "Binary Search & Search on Answer",
    "curriculumStage": "Stage 7 — Binary Search & Search on Answer",
    "roadmapPhase": "Stage 7 — Binary Search & Search on Answer",
    "phase": "Stage 7 — Binary Search & Search on Answer",
    "estimatedTime": 30,
    "statement": "Solve the **Random Flip Matrix Optimization** problem using the **Binary Search** technique. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Binary Search identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Binary Search. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Binary Search techniques by solving Medium problem constraints for Random Flip Matrix Optimization.",
    "whyThisPattern": "When observing arrays & strings problem conditions, Binary Search optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "LinkedIn",
      "Amazon"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/random-flip-matrix/",
    "leetcode_title": "Random Flip Matrix",
    "leetcode_id": 519,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/random-flip-matrix/",
    "canonicalSlug": "random-flip-matrix",
    "canonicalUrl": "https://leetcode.com/problems/random-flip-matrix/",
    "url": "https://leetcode.com/problems/random-flip-matrix/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Random Flip Matrix Optimization (Binary Search)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Random Flip Matrix Optimization (Binary Search)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Random Flip Matrix Optimization (Binary Search)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Random Flip Matrix Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Random Flip Matrix Optimization (Binary Search)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Random Flip Matrix Optimization (Binary Search)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Random Flip Matrix Optimization (Binary Search)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Random Flip Matrix Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Random Flip Matrix",
      "cpp_optimal": "// Solution for Random Flip Matrix",
      "java_brute": "// Solution for Random Flip Matrix",
      "java_optimal": "// Solution for Random Flip Matrix",
      "python_brute": "# Solution for Random Flip Matrix",
      "python_optimal": "# Solution for Random Flip Matrix"
    },
    "originalOrder": 407,
    "learningOrder": 407
  },
  {
    "id": 315,
    "number": 315,
    "sequence_number": 315,
    "title": "01 Matrix",
    "slug": "01-matrix",
    "difficulty": "Medium",
    "topic": "Binary Search",
    "subtopic": "Binary Search",
    "pattern": "Binary Search",
    "secondary_patterns": [
      "Binary Search"
    ],
    "stage": "Binary Search & Search on Answer",
    "curriculumStage": "Stage 7 — Binary Search & Search on Answer",
    "roadmapPhase": "Stage 7 — Binary Search & Search on Answer",
    "phase": "Stage 7 — Binary Search & Search on Answer",
    "estimatedTime": 30,
    "statement": "Solve the **01 Matrix Challenge** problem using the **Binary Search** technique. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Binary Search identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Binary Search. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Binary Search techniques by solving Medium problem constraints for 01 Matrix Challenge.",
    "whyThisPattern": "When observing arrays & strings problem conditions, Binary Search optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Amazon",
      "Microsoft",
      "Uber"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/01-matrix/",
    "leetcode_title": "01 Matrix",
    "leetcode_id": 542,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/01-matrix/",
    "canonicalSlug": "01-matrix",
    "canonicalUrl": "https://leetcode.com/problems/01-matrix/",
    "url": "https://leetcode.com/problems/01-matrix/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for 01 Matrix Challenge (Binary Search)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for 01 Matrix Challenge (Binary Search)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for 01 Matrix Challenge (Binary Search)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for 01 Matrix Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for 01 Matrix Challenge (Binary Search)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for 01 Matrix Challenge (Binary Search)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for 01 Matrix Challenge (Binary Search)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for 01 Matrix Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for 01 Matrix",
      "cpp_optimal": "// Solution for 01 Matrix",
      "java_brute": "// Solution for 01 Matrix",
      "java_optimal": "// Solution for 01 Matrix",
      "python_brute": "# Solution for 01 Matrix",
      "python_optimal": "# Solution for 01 Matrix"
    },
    "originalOrder": 408,
    "learningOrder": 408
  },
  {
    "id": 316,
    "number": 316,
    "sequence_number": 316,
    "title": "Pyramid Transition Matrix",
    "slug": "pyramid-transition-matrix",
    "difficulty": "Medium",
    "topic": "Binary Search",
    "subtopic": "Binary Search",
    "pattern": "Binary Search",
    "secondary_patterns": [
      "Binary Search"
    ],
    "stage": "Binary Search & Search on Answer",
    "curriculumStage": "Stage 7 — Binary Search & Search on Answer",
    "roadmapPhase": "Stage 7 — Binary Search & Search on Answer",
    "phase": "Stage 7 — Binary Search & Search on Answer",
    "estimatedTime": 30,
    "statement": "Solve the **Pyramid Transition Matrix Optimization** problem using the **Binary Search** technique. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Binary Search identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Binary Search. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Binary Search techniques by solving Medium problem constraints for Pyramid Transition Matrix Optimization.",
    "whyThisPattern": "When observing arrays & strings problem conditions, Binary Search optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "LinkedIn",
      "Amazon"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/pyramid-transition-matrix/",
    "leetcode_title": "Pyramid Transition Matrix",
    "leetcode_id": 756,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/pyramid-transition-matrix/",
    "canonicalSlug": "pyramid-transition-matrix",
    "canonicalUrl": "https://leetcode.com/problems/pyramid-transition-matrix/",
    "url": "https://leetcode.com/problems/pyramid-transition-matrix/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Pyramid Transition Matrix Optimization (Binary Search)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Pyramid Transition Matrix Optimization (Binary Search)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Pyramid Transition Matrix Optimization (Binary Search)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Pyramid Transition Matrix Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Pyramid Transition Matrix Optimization (Binary Search)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Pyramid Transition Matrix Optimization (Binary Search)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Pyramid Transition Matrix Optimization (Binary Search)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Pyramid Transition Matrix Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Pyramid Transition Matrix",
      "cpp_optimal": "// Solution for Pyramid Transition Matrix",
      "java_brute": "// Solution for Pyramid Transition Matrix",
      "java_optimal": "// Solution for Pyramid Transition Matrix",
      "python_brute": "# Solution for Pyramid Transition Matrix",
      "python_optimal": "# Solution for Pyramid Transition Matrix"
    },
    "originalOrder": 409,
    "learningOrder": 409
  },
  {
    "id": 317,
    "number": 317,
    "sequence_number": 317,
    "title": "Rotated Digits",
    "slug": "rotated-digits",
    "difficulty": "Medium",
    "topic": "Binary Search",
    "subtopic": "Binary Search",
    "pattern": "Binary Search",
    "secondary_patterns": [
      "Binary Search"
    ],
    "stage": "Binary Search & Search on Answer",
    "curriculumStage": "Stage 7 — Binary Search & Search on Answer",
    "roadmapPhase": "Stage 7 — Binary Search & Search on Answer",
    "phase": "Stage 7 — Binary Search & Search on Answer",
    "estimatedTime": 30,
    "statement": "Solve the **Rotated Digits Challenge** problem using the **Binary Search** technique. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Binary Search identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Binary Search. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Binary Search techniques by solving Medium problem constraints for Rotated Digits Challenge.",
    "whyThisPattern": "When observing arrays & strings problem conditions, Binary Search optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Amazon",
      "Microsoft",
      "Uber"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/rotated-digits/",
    "leetcode_title": "Rotated Digits",
    "leetcode_id": 788,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/rotated-digits/",
    "canonicalSlug": "rotated-digits",
    "canonicalUrl": "https://leetcode.com/problems/rotated-digits/",
    "url": "https://leetcode.com/problems/rotated-digits/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Rotated Digits Challenge (Binary Search)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Rotated Digits Challenge (Binary Search)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Rotated Digits Challenge (Binary Search)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Rotated Digits Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Rotated Digits Challenge (Binary Search)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Rotated Digits Challenge (Binary Search)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Rotated Digits Challenge (Binary Search)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Rotated Digits Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Rotated Digits",
      "cpp_optimal": "// Solution for Rotated Digits",
      "java_brute": "// Solution for Rotated Digits",
      "java_optimal": "// Solution for Rotated Digits",
      "python_brute": "# Solution for Rotated Digits",
      "python_optimal": "# Solution for Rotated Digits"
    },
    "originalOrder": 410,
    "learningOrder": 410
  },
  {
    "id": 318,
    "number": 318,
    "sequence_number": 318,
    "title": "Score After Flipping Matrix",
    "slug": "score-after-flipping-matrix",
    "difficulty": "Medium",
    "topic": "Binary Search",
    "subtopic": "Binary Search",
    "pattern": "Binary Search",
    "secondary_patterns": [
      "Binary Search"
    ],
    "stage": "Binary Search & Search on Answer",
    "curriculumStage": "Stage 7 — Binary Search & Search on Answer",
    "roadmapPhase": "Stage 7 — Binary Search & Search on Answer",
    "phase": "Stage 7 — Binary Search & Search on Answer",
    "estimatedTime": 30,
    "statement": "Solve the **Score After Flipping Matrix Challenge** problem using the **Binary Search** technique. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Binary Search identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Binary Search. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Binary Search techniques by solving Medium problem constraints for Score After Flipping Matrix Challenge.",
    "whyThisPattern": "When observing arrays & strings problem conditions, Binary Search optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Meta",
      "Uber",
      "Databricks"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/score-after-flipping-matrix/",
    "leetcode_title": "Score After Flipping Matrix",
    "leetcode_id": 861,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/score-after-flipping-matrix/",
    "canonicalSlug": "score-after-flipping-matrix",
    "canonicalUrl": "https://leetcode.com/problems/score-after-flipping-matrix/",
    "url": "https://leetcode.com/problems/score-after-flipping-matrix/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Score After Flipping Matrix Challenge (Binary Search)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Score After Flipping Matrix Challenge (Binary Search)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Score After Flipping Matrix Challenge (Binary Search)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Score After Flipping Matrix Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Score After Flipping Matrix Challenge (Binary Search)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Score After Flipping Matrix Challenge (Binary Search)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Score After Flipping Matrix Challenge (Binary Search)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Score After Flipping Matrix Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Score After Flipping Matrix",
      "cpp_optimal": "// Solution for Score After Flipping Matrix",
      "java_brute": "// Solution for Score After Flipping Matrix",
      "java_optimal": "// Solution for Score After Flipping Matrix",
      "python_brute": "# Solution for Score After Flipping Matrix",
      "python_optimal": "# Solution for Score After Flipping Matrix"
    },
    "originalOrder": 411,
    "learningOrder": 411
  },
  {
    "id": 319,
    "number": 319,
    "sequence_number": 319,
    "title": "Koko Eating Bananas",
    "slug": "koko-eating-bananas",
    "difficulty": "Medium",
    "topic": "Binary Search",
    "subtopic": "Hashing & Array Optimization",
    "pattern": "Hashing & Array Optimization",
    "secondary_patterns": [
      "Hashing & Array Optimization"
    ],
    "stage": "Binary Search & Search on Answer",
    "curriculumStage": "Stage 7 — Binary Search & Search on Answer",
    "roadmapPhase": "Stage 7 — Binary Search & Search on Answer",
    "phase": "Stage 7 — Binary Search & Search on Answer",
    "estimatedTime": 30,
    "statement": "Solve the **Koko Eating Bananas Optimization** problem using the **Hashing & Array Optimization** technique. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Hashing & Array Optimization identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Hashing & Array Optimization. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Hashing & Array Optimization techniques by solving Medium problem constraints for Koko Eating Bananas Optimization.",
    "whyThisPattern": "When observing arrays & strings problem conditions, Hashing & Array Optimization optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Apple",
      "Adobe",
      "Atlassian"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/koko-eating-bananas/",
    "leetcode_title": "Koko Eating Bananas",
    "leetcode_id": 875,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/koko-eating-bananas/",
    "canonicalSlug": "koko-eating-bananas",
    "canonicalUrl": "https://leetcode.com/problems/koko-eating-bananas/",
    "url": "https://leetcode.com/problems/koko-eating-bananas/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Koko Eating Bananas Optimization (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Koko Eating Bananas Optimization (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Koko Eating Bananas Optimization (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Koko Eating Bananas Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Koko Eating Bananas Optimization (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Koko Eating Bananas Optimization (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Koko Eating Bananas Optimization (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Koko Eating Bananas Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Koko Eating Bananas",
      "cpp_optimal": "// Solution for Koko Eating Bananas",
      "java_brute": "// Solution for Koko Eating Bananas",
      "java_optimal": "// Solution for Koko Eating Bananas",
      "python_brute": "# Solution for Koko Eating Bananas",
      "python_optimal": "# Solution for Koko Eating Bananas"
    },
    "originalOrder": 412,
    "learningOrder": 412
  },
  {
    "id": 320,
    "number": 320,
    "sequence_number": 320,
    "title": "Spiral Matrix III",
    "slug": "spiral-matrix-iii",
    "difficulty": "Medium",
    "topic": "Binary Search",
    "subtopic": "Binary Search",
    "pattern": "Binary Search",
    "secondary_patterns": [
      "Binary Search"
    ],
    "stage": "Binary Search & Search on Answer",
    "curriculumStage": "Stage 7 — Binary Search & Search on Answer",
    "roadmapPhase": "Stage 7 — Binary Search & Search on Answer",
    "phase": "Stage 7 — Binary Search & Search on Answer",
    "estimatedTime": 30,
    "statement": "Solve the **Spiral Matrix III Optimization** problem using the **Binary Search** technique. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Binary Search identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Binary Search. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Binary Search techniques by solving Medium problem constraints for Spiral Matrix III Optimization.",
    "whyThisPattern": "When observing arrays & strings problem conditions, Binary Search optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Meta",
      "Apple",
      "Netflix"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/spiral-matrix-iii/",
    "leetcode_title": "Spiral Matrix III",
    "leetcode_id": 885,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/spiral-matrix-iii/",
    "canonicalSlug": "spiral-matrix-iii",
    "canonicalUrl": "https://leetcode.com/problems/spiral-matrix-iii/",
    "url": "https://leetcode.com/problems/spiral-matrix-iii/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Spiral Matrix III Optimization (Binary Search)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Spiral Matrix III Optimization (Binary Search)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Spiral Matrix III Optimization (Binary Search)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Spiral Matrix III Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Spiral Matrix III Optimization (Binary Search)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Spiral Matrix III Optimization (Binary Search)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Spiral Matrix III Optimization (Binary Search)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Spiral Matrix III Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Spiral Matrix III",
      "cpp_optimal": "// Solution for Spiral Matrix III",
      "java_brute": "// Solution for Spiral Matrix III",
      "java_optimal": "// Solution for Spiral Matrix III",
      "python_brute": "# Solution for Spiral Matrix III",
      "python_optimal": "# Solution for Spiral Matrix III"
    },
    "originalOrder": 413,
    "learningOrder": 413
  },
  {
    "id": 321,
    "number": 321,
    "sequence_number": 321,
    "title": "Time Based Key-Value Store",
    "slug": "time-based-key-value-store",
    "difficulty": "Medium",
    "topic": "Binary Search",
    "subtopic": "Binary Search Optimization",
    "pattern": "Binary Search on Timestamps",
    "secondary_patterns": [
      "Binary Search on Timestamps"
    ],
    "stage": "Binary Search & Search on Answer",
    "curriculumStage": "Stage 7 — Binary Search & Search on Answer",
    "roadmapPhase": "Stage 7 — Binary Search & Search on Answer",
    "phase": "Stage 7 — Binary Search & Search on Answer",
    "estimatedTime": 30,
    "statement": "Designs a time-based key-value data structure that can store multiple values for the same key at different timestamps.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= key.length, value.length <= 100",
      "1 <= timestamp <= 10^7"
    ],
    "examples": [
      {
        "input": "set('foo', 'bar', 1), get('foo', 1)",
        "output": "'bar'",
        "explanation": "Returns value at timestamp 1."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "All duplicate elements"
    ],
    "commonMistakes": [
      "Off-by-one index mistakes",
      "Integer overflow for large cumulative sums"
    ],
    "hints": [
      "Consider using Heap.",
      "Analyze edge cases and bounds."
    ],
    "learningObjective": "Master Binary Search techniques by solving Medium problem constraints for Time Based Key-Value Store.",
    "whyThisPattern": "When observing Binary Search problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(log N) for get",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/time-based-key-value-store/",
    "leetcode_title": "Time Based Key-Value Store",
    "leetcode_id": 981,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/time-based-key-value-store/",
    "canonicalSlug": "time-based-key-value-store",
    "canonicalUrl": "https://leetcode.com/problems/time-based-key-value-store/",
    "url": "https://leetcode.com/problems/time-based-key-value-store/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Time Based Key-Value Store Implementation\n#include <string>\n#include <unordered_map>\n#include <vector>\n#include <algorithm>\n\nclass TimeMap {\n    std::unordered_map<std::string, std::vector<std::pair<int, std::string>>> map;\npublic:\n    TimeMap() {}\n    \n    void set(std::string key, std::string value, int timestamp) {\n        map[key].push_back({timestamp, value});\n    }\n    \n    std::string get(std::string key, int timestamp) {\n        if (!map.count(key)) return \"\";\n        const auto& vec = map[key];\n        int low = 0, high = vec.size() - 1;\n        std::string ans = \"\";\n        while (low <= high) {\n            int mid = low + (high - low) / 2;\n            if (vec[mid].first <= timestamp) {\n                ans = vec[mid].second;\n                low = mid + 1;\n            } else {\n                high = mid - 1;\n            }\n        }\n        return ans;\n    }\n};",
        "java": "// Java Time Based Key-Value Store Implementation\nimport java.util.*;\n\nclass TimeMap {\n    private class Pair {\n        int timestamp;\n        String value;\n        Pair(int t, String v) { timestamp = t; value = v; }\n    }\n\n    private Map<String, List<Pair>> map = new HashMap<>();\n\n    public TimeMap() {}\n\n    public void set(String key, String value, int timestamp) {\n        map.putIfAbsent(key, new ArrayList<>());\n        map.get(key).add(new Pair(timestamp, value));\n    }\n\n    public String get(String key, int timestamp) {\n        if (!map.containsKey(key)) return \"\";\n        List<Pair> list = map.get(key);\n        int low = 0, high = list.size() - 1;\n        String ans = \"\";\n        while (low <= high) {\n            int mid = low + (high - low) / 2;\n            if (list.get(mid).timestamp <= timestamp) {\n                ans = list.get(mid).value;\n                low = mid + 1;\n            } else {\n                high = mid - 1;\n            }\n        }\n        return ans;\n    }\n}",
        "python": "# Python Time Based Key-Value Store Implementation\nfrom collections import defaultdict\nimport bisect\n\nclass TimeMap:\n    def __init__(self):\n        self.map = defaultdict(list)\n\n    def set(self, key: str, value: str, timestamp: int) -> None:\n        self.map[key].append((timestamp, value))\n\n    def get(self, key: str, timestamp: int) -> str:\n        if key not in self.map:\n            return \"\"\n        values = self.map[key]\n        idx = bisect.bisect_right(values, (timestamp, chr(127)))\n        return values[idx - 1][1] if idx > 0 else \"\"\n",
        "javascript": "// JavaScript Time Based Key-Value Store Implementation\nclass TimeMap {\n    constructor() {\n        this.map = new Map();\n    }\n    set(key, value, timestamp) {\n        if (!this.map.has(key)) this.map.set(key, []);\n        this.map.get(key).push({ timestamp, value });\n    }\n    get(key, timestamp) {\n        if (!this.map.has(key)) return \"\";\n        const list = this.map.get(key);\n        let low = 0, high = list.length - 1, ans = \"\";\n        while (low <= high) {\n            const mid = Math.floor((low + high) / 2);\n            if (list[mid].timestamp <= timestamp) {\n                ans = list[mid].value;\n                low = mid + 1;\n            } else {\n                high = mid - 1;\n            }\n        }\n        return ans;\n    }\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Time Based Key-Value Store Implementation\n#include <string>\n#include <unordered_map>\n#include <vector>\n#include <algorithm>\n\nclass TimeMap {\n    std::unordered_map<std::string, std::vector<std::pair<int, std::string>>> map;\npublic:\n    TimeMap() {}\n    \n    void set(std::string key, std::string value, int timestamp) {\n        map[key].push_back({timestamp, value});\n    }\n    \n    std::string get(std::string key, int timestamp) {\n        if (!map.count(key)) return \"\";\n        const auto& vec = map[key];\n        int low = 0, high = vec.size() - 1;\n        std::string ans = \"\";\n        while (low <= high) {\n            int mid = low + (high - low) / 2;\n            if (vec[mid].first <= timestamp) {\n                ans = vec[mid].second;\n                low = mid + 1;\n            } else {\n                high = mid - 1;\n            }\n        }\n        return ans;\n    }\n};",
        "java": "// Java Time Based Key-Value Store Implementation\nimport java.util.*;\n\nclass TimeMap {\n    private class Pair {\n        int timestamp;\n        String value;\n        Pair(int t, String v) { timestamp = t; value = v; }\n    }\n\n    private Map<String, List<Pair>> map = new HashMap<>();\n\n    public TimeMap() {}\n\n    public void set(String key, String value, int timestamp) {\n        map.putIfAbsent(key, new ArrayList<>());\n        map.get(key).add(new Pair(timestamp, value));\n    }\n\n    public String get(String key, int timestamp) {\n        if (!map.containsKey(key)) return \"\";\n        List<Pair> list = map.get(key);\n        int low = 0, high = list.size() - 1;\n        String ans = \"\";\n        while (low <= high) {\n            int mid = low + (high - low) / 2;\n            if (list.get(mid).timestamp <= timestamp) {\n                ans = list.get(mid).value;\n                low = mid + 1;\n            } else {\n                high = mid - 1;\n            }\n        }\n        return ans;\n    }\n}",
        "python": "# Python Time Based Key-Value Store Implementation\nfrom collections import defaultdict\nimport bisect\n\nclass TimeMap:\n    def __init__(self):\n        self.map = defaultdict(list)\n\n    def set(self, key: str, value: str, timestamp: int) -> None:\n        self.map[key].append((timestamp, value))\n\n    def get(self, key: str, timestamp: int) -> str:\n        if key not in self.map:\n            return \"\"\n        values = self.map[key]\n        idx = bisect.bisect_right(values, (timestamp, chr(127)))\n        return values[idx - 1][1] if idx > 0 else \"\"\n",
        "javascript": "// JavaScript Time Based Key-Value Store Implementation\nclass TimeMap {\n    constructor() {\n        this.map = new Map();\n    }\n    set(key, value, timestamp) {\n        if (!this.map.has(key)) this.map.set(key, []);\n        this.map.get(key).push({ timestamp, value });\n    }\n    get(key, timestamp) {\n        if (!this.map.has(key)) return \"\";\n        const list = this.map.get(key);\n        let low = 0, high = list.length - 1, ans = \"\";\n        while (low <= high) {\n            const mid = Math.floor((low + high) / 2);\n            if (list[mid].timestamp <= timestamp) {\n                ans = list[mid].value;\n                low = mid + 1;\n            } else {\n                high = mid - 1;\n            }\n        }\n        return ans;\n    }\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Time Based Key-Value Store",
      "cpp_optimal": "// Solution for Time Based Key-Value Store",
      "java_brute": "// Solution for Time Based Key-Value Store",
      "java_optimal": "// Solution for Time Based Key-Value Store",
      "python_brute": "# Solution for Time Based Key-Value Store",
      "python_optimal": "# Solution for Time Based Key-Value Store"
    },
    "originalOrder": 414,
    "learningOrder": 414
  },
  {
    "id": 322,
    "number": 322,
    "sequence_number": 322,
    "title": "Peak Index in a Mountain Array",
    "slug": "peak-index-in-a-mountain-array",
    "difficulty": "Medium",
    "topic": "Binary Search",
    "subtopic": "Binary Search Optimization",
    "pattern": "Ternary / Binary Peak Search",
    "secondary_patterns": [
      "Ternary / Binary Peak Search"
    ],
    "stage": "Binary Search & Search on Answer",
    "curriculumStage": "Stage 7 — Binary Search & Search on Answer",
    "roadmapPhase": "Stage 7 — Binary Search & Search on Answer",
    "phase": "Stage 7 — Binary Search & Search on Answer",
    "estimatedTime": 30,
    "statement": "Given the constraints and input parameters for Peak Index in a Mountain Array, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Peak Index in a Mountain Array."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Peak Index in a Mountain Array.",
      "Leverage the optimal Binary Search pattern to reduce time complexity."
    ],
    "learningObjective": "Master Binary Search techniques by solving Medium problem constraints for Peak Index in a Mountain Array.",
    "whyThisPattern": "When observing Binary Search problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/peak-index-in-a-mountain-array/",
    "leetcode_title": "Peak Index in a Mountain Array",
    "leetcode_id": 852,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/peak-index-in-a-mountain-array/",
    "canonicalSlug": "peak-index-in-a-mountain-array",
    "canonicalUrl": "https://leetcode.com/problems/peak-index-in-a-mountain-array/",
    "url": "https://leetcode.com/problems/peak-index-in-a-mountain-array/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Peak Index in a Mountain Array\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Peak Index in a Mountain Array\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Peak Index in a Mountain Array\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Peak Index in a Mountain Array\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Peak Index in a Mountain Array\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Peak Index in a Mountain Array\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Peak Index in a Mountain Array\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Peak Index in a Mountain Array\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Peak Index in a Mountain Array",
      "cpp_optimal": "// Solution for Peak Index in a Mountain Array",
      "java_brute": "// Solution for Peak Index in a Mountain Array",
      "java_optimal": "// Solution for Peak Index in a Mountain Array",
      "python_brute": "# Solution for Peak Index in a Mountain Array",
      "python_optimal": "# Solution for Peak Index in a Mountain Array"
    },
    "originalOrder": 415,
    "learningOrder": 415
  },
  {
    "id": 323,
    "number": 323,
    "sequence_number": 323,
    "title": "My Calendar I",
    "slug": "my-calendar-i",
    "difficulty": "Medium",
    "topic": "Binary Search",
    "subtopic": "Binary Search Optimization",
    "pattern": "TreeMap Interval Booking",
    "secondary_patterns": [
      "TreeMap Interval Booking"
    ],
    "stage": "Binary Search & Search on Answer",
    "curriculumStage": "Stage 7 — Binary Search & Search on Answer",
    "roadmapPhase": "Stage 7 — Binary Search & Search on Answer",
    "phase": "Stage 7 — Binary Search & Search on Answer",
    "estimatedTime": 30,
    "statement": "Given the constraints and input parameters for My Calendar I, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for My Calendar I."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for My Calendar I.",
      "Leverage the optimal Binary Search pattern to reduce time complexity."
    ],
    "learningObjective": "Master Binary Search techniques by solving Medium problem constraints for My Calendar I.",
    "whyThisPattern": "When observing Binary Search problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/my-calendar-i/",
    "leetcode_title": "My Calendar I",
    "leetcode_id": 729,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/my-calendar-i/",
    "canonicalSlug": "my-calendar-i",
    "canonicalUrl": "https://leetcode.com/problems/my-calendar-i/",
    "url": "https://leetcode.com/problems/my-calendar-i/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for My Calendar I\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for My Calendar I\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for My Calendar I\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for My Calendar I\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for My Calendar I\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for My Calendar I\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for My Calendar I\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for My Calendar I\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for My Calendar I",
      "cpp_optimal": "// Solution for My Calendar I",
      "java_brute": "// Solution for My Calendar I",
      "java_optimal": "// Solution for My Calendar I",
      "python_brute": "# Solution for My Calendar I",
      "python_optimal": "# Solution for My Calendar I"
    },
    "originalOrder": 416,
    "learningOrder": 416
  },
  {
    "id": 324,
    "number": 324,
    "sequence_number": 324,
    "title": "My Calendar II",
    "slug": "my-calendar-ii",
    "difficulty": "Medium",
    "topic": "Binary Search",
    "subtopic": "Binary Search Optimization",
    "pattern": "Overlap List Booking",
    "secondary_patterns": [
      "Overlap List Booking"
    ],
    "stage": "Binary Search & Search on Answer",
    "curriculumStage": "Stage 7 — Binary Search & Search on Answer",
    "roadmapPhase": "Stage 7 — Binary Search & Search on Answer",
    "phase": "Stage 7 — Binary Search & Search on Answer",
    "estimatedTime": 30,
    "statement": "Given the constraints and input parameters for My Calendar II, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for My Calendar II."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for My Calendar II.",
      "Leverage the optimal Binary Search pattern to reduce time complexity."
    ],
    "learningObjective": "Master Binary Search techniques by solving Medium problem constraints for My Calendar II.",
    "whyThisPattern": "When observing Binary Search problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/my-calendar-ii/",
    "leetcode_title": "My Calendar II",
    "leetcode_id": 731,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/my-calendar-ii/",
    "canonicalSlug": "my-calendar-ii",
    "canonicalUrl": "https://leetcode.com/problems/my-calendar-ii/",
    "url": "https://leetcode.com/problems/my-calendar-ii/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for My Calendar II\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for My Calendar II\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for My Calendar II\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for My Calendar II\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for My Calendar II\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for My Calendar II\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for My Calendar II\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for My Calendar II\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for My Calendar II",
      "cpp_optimal": "// Solution for My Calendar II",
      "java_brute": "// Solution for My Calendar II",
      "java_optimal": "// Solution for My Calendar II",
      "python_brute": "# Solution for My Calendar II",
      "python_optimal": "# Solution for My Calendar II"
    },
    "originalOrder": 417,
    "learningOrder": 417
  },
  {
    "id": 325,
    "number": 325,
    "sequence_number": 325,
    "title": "Online Election",
    "slug": "online-election",
    "difficulty": "Medium",
    "topic": "Binary Search",
    "subtopic": "Binary Search Optimization",
    "pattern": "Leading Candidate Vector",
    "secondary_patterns": [
      "Leading Candidate Vector"
    ],
    "stage": "Binary Search & Search on Answer",
    "curriculumStage": "Stage 7 — Binary Search & Search on Answer",
    "roadmapPhase": "Stage 7 — Binary Search & Search on Answer",
    "phase": "Stage 7 — Binary Search & Search on Answer",
    "estimatedTime": 30,
    "statement": "Given the constraints and input parameters for Online Election, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Online Election."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Online Election.",
      "Leverage the optimal Binary Search pattern to reduce time complexity."
    ],
    "learningObjective": "Master Binary Search techniques by solving Medium problem constraints for Online Election.",
    "whyThisPattern": "When observing Binary Search problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/online-election/",
    "leetcode_title": "Online Election",
    "leetcode_id": 911,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/online-election/",
    "canonicalSlug": "online-election",
    "canonicalUrl": "https://leetcode.com/problems/online-election/",
    "url": "https://leetcode.com/problems/online-election/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Online Election\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Online Election\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Online Election\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Online Election\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Online Election\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Online Election\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Online Election\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Online Election\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Online Election",
      "cpp_optimal": "// Solution for Online Election",
      "java_brute": "// Solution for Online Election",
      "java_optimal": "// Solution for Online Election",
      "python_brute": "# Solution for Online Election",
      "python_optimal": "# Solution for Online Election"
    },
    "originalOrder": 418,
    "learningOrder": 418
  },
  {
    "id": 326,
    "number": 326,
    "sequence_number": 326,
    "title": "Minimum Absolute Sum Difference",
    "slug": "minimum-absolute-sum-difference",
    "difficulty": "Medium",
    "topic": "Binary Search",
    "subtopic": "Binary Search Optimization",
    "pattern": "Sorted Array Closest Search",
    "secondary_patterns": [
      "Sorted Array Closest Search"
    ],
    "stage": "Binary Search & Search on Answer",
    "curriculumStage": "Stage 7 — Binary Search & Search on Answer",
    "roadmapPhase": "Stage 7 — Binary Search & Search on Answer",
    "phase": "Stage 7 — Binary Search & Search on Answer",
    "estimatedTime": 30,
    "statement": "Given the constraints and input parameters for Minimum Absolute Sum Difference, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Minimum Absolute Sum Difference."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Minimum Absolute Sum Difference.",
      "Leverage the optimal Binary Search pattern to reduce time complexity."
    ],
    "learningObjective": "Master Binary Search techniques by solving Medium problem constraints for Minimum Absolute Sum Difference.",
    "whyThisPattern": "When observing Binary Search problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/minimum-absolute-sum-difference/",
    "leetcode_title": "Minimum Absolute Sum Difference",
    "leetcode_id": 1818,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/minimum-absolute-sum-difference/",
    "canonicalSlug": "minimum-absolute-sum-difference",
    "canonicalUrl": "https://leetcode.com/problems/minimum-absolute-sum-difference/",
    "url": "https://leetcode.com/problems/minimum-absolute-sum-difference/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Minimum Absolute Sum Difference\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Minimum Absolute Sum Difference\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Minimum Absolute Sum Difference\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Minimum Absolute Sum Difference\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Minimum Absolute Sum Difference\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Minimum Absolute Sum Difference\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Minimum Absolute Sum Difference\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Minimum Absolute Sum Difference\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Minimum Absolute Sum Difference",
      "cpp_optimal": "// Solution for Minimum Absolute Sum Difference",
      "java_brute": "// Solution for Minimum Absolute Sum Difference",
      "java_optimal": "// Solution for Minimum Absolute Sum Difference",
      "python_brute": "# Solution for Minimum Absolute Sum Difference",
      "python_optimal": "# Solution for Minimum Absolute Sum Difference"
    },
    "originalOrder": 419,
    "learningOrder": 419
  },
  {
    "id": 327,
    "number": 327,
    "sequence_number": 327,
    "title": "Minimum Speed to Arrive on Time",
    "slug": "minimum-speed-to-arrive-on-time",
    "difficulty": "Medium",
    "topic": "Binary Search",
    "subtopic": "Binary Search Optimization",
    "pattern": "Search on Speed Space",
    "secondary_patterns": [
      "Search on Speed Space"
    ],
    "stage": "Binary Search & Search on Answer",
    "curriculumStage": "Stage 7 — Binary Search & Search on Answer",
    "roadmapPhase": "Stage 7 — Binary Search & Search on Answer",
    "phase": "Stage 7 — Binary Search & Search on Answer",
    "estimatedTime": 30,
    "statement": "Given the constraints and input parameters for Minimum Speed to Arrive on Time, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Minimum Speed to Arrive on Time."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Minimum Speed to Arrive on Time.",
      "Leverage the optimal Binary Search pattern to reduce time complexity."
    ],
    "learningObjective": "Master Binary Search techniques by solving Medium problem constraints for Minimum Speed to Arrive on Time.",
    "whyThisPattern": "When observing Binary Search problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/minimum-speed-to-arrive-on-time/",
    "leetcode_title": "Minimum Speed to Arrive on Time",
    "leetcode_id": 1870,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/minimum-speed-to-arrive-on-time/",
    "canonicalSlug": "minimum-speed-to-arrive-on-time",
    "canonicalUrl": "https://leetcode.com/problems/minimum-speed-to-arrive-on-time/",
    "url": "https://leetcode.com/problems/minimum-speed-to-arrive-on-time/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Minimum Speed to Arrive on Time\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Minimum Speed to Arrive on Time\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Minimum Speed to Arrive on Time\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Minimum Speed to Arrive on Time\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Minimum Speed to Arrive on Time\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Minimum Speed to Arrive on Time\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Minimum Speed to Arrive on Time\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Minimum Speed to Arrive on Time\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Minimum Speed to Arrive on Time",
      "cpp_optimal": "// Solution for Minimum Speed to Arrive on Time",
      "java_brute": "// Solution for Minimum Speed to Arrive on Time",
      "java_optimal": "// Solution for Minimum Speed to Arrive on Time",
      "python_brute": "# Solution for Minimum Speed to Arrive on Time",
      "python_optimal": "# Solution for Minimum Speed to Arrive on Time"
    },
    "originalOrder": 420,
    "learningOrder": 420
  },
  {
    "id": 328,
    "number": 328,
    "sequence_number": 328,
    "title": "Maximum Value at a Given Index in a Bounded Array",
    "slug": "maximum-value-at-a-given-index-in-a-bounded-array",
    "difficulty": "Medium",
    "topic": "Binary Search",
    "subtopic": "Binary Search Optimization",
    "pattern": "Pyramid Sum Binary Search",
    "secondary_patterns": [
      "Pyramid Sum Binary Search"
    ],
    "stage": "Binary Search & Search on Answer",
    "curriculumStage": "Stage 7 — Binary Search & Search on Answer",
    "roadmapPhase": "Stage 7 — Binary Search & Search on Answer",
    "phase": "Stage 7 — Binary Search & Search on Answer",
    "estimatedTime": 30,
    "statement": "Given the constraints and input parameters for Maximum Value at a Given Index in a Bounded Array, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Maximum Value at a Given Index in a Bounded Array."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Maximum Value at a Given Index in a Bounded Array.",
      "Leverage the optimal Binary Search pattern to reduce time complexity."
    ],
    "learningObjective": "Master Binary Search techniques by solving Medium problem constraints for Maximum Value at a Given Index in a Bounded Array.",
    "whyThisPattern": "When observing Binary Search problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/maximum-value-at-a-given-index-in-a-bounded-array/",
    "leetcode_title": "Maximum Value at a Given Index in a Bounded Array",
    "leetcode_id": 1802,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/maximum-value-at-a-given-index-in-a-bounded-array/",
    "canonicalSlug": "maximum-value-at-a-given-index-in-a-bounded-array",
    "canonicalUrl": "https://leetcode.com/problems/maximum-value-at-a-given-index-in-a-bounded-array/",
    "url": "https://leetcode.com/problems/maximum-value-at-a-given-index-in-a-bounded-array/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Maximum Value at a Given Index in a Bounded Array\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Maximum Value at a Given Index in a Bounded Array\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Maximum Value at a Given Index in a Bounded Array\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Maximum Value at a Given Index in a Bounded Array\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Maximum Value at a Given Index in a Bounded Array\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Maximum Value at a Given Index in a Bounded Array\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Maximum Value at a Given Index in a Bounded Array\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Maximum Value at a Given Index in a Bounded Array\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Maximum Value at a Given Index in a Bounded Array",
      "cpp_optimal": "// Solution for Maximum Value at a Given Index in a Bounded Array",
      "java_brute": "// Solution for Maximum Value at a Given Index in a Bounded Array",
      "java_optimal": "// Solution for Maximum Value at a Given Index in a Bounded Array",
      "python_brute": "# Solution for Maximum Value at a Given Index in a Bounded Array",
      "python_optimal": "# Solution for Maximum Value at a Given Index in a Bounded Array"
    },
    "originalOrder": 421,
    "learningOrder": 421
  },
  {
    "id": 329,
    "number": 329,
    "sequence_number": 329,
    "title": "Minimum Limit of Balls in a Bag",
    "slug": "minimum-limit-of-balls-in-a-bag",
    "difficulty": "Medium",
    "topic": "Binary Search",
    "subtopic": "Binary Search Optimization",
    "pattern": "Penalty Binary Search",
    "secondary_patterns": [
      "Penalty Binary Search"
    ],
    "stage": "Binary Search & Search on Answer",
    "curriculumStage": "Stage 7 — Binary Search & Search on Answer",
    "roadmapPhase": "Stage 7 — Binary Search & Search on Answer",
    "phase": "Stage 7 — Binary Search & Search on Answer",
    "estimatedTime": 30,
    "statement": "Given the constraints and input parameters for Minimum Limit of Balls in a Bag, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Minimum Limit of Balls in a Bag."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Minimum Limit of Balls in a Bag.",
      "Leverage the optimal Binary Search pattern to reduce time complexity."
    ],
    "learningObjective": "Master Binary Search techniques by solving Medium problem constraints for Minimum Limit of Balls in a Bag.",
    "whyThisPattern": "When observing Binary Search problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/minimum-limit-of-balls-in-a-bag/",
    "leetcode_title": "Minimum Limit of Balls in a Bag",
    "leetcode_id": 1760,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/minimum-limit-of-balls-in-a-bag/",
    "canonicalSlug": "minimum-limit-of-balls-in-a-bag",
    "canonicalUrl": "https://leetcode.com/problems/minimum-limit-of-balls-in-a-bag/",
    "url": "https://leetcode.com/problems/minimum-limit-of-balls-in-a-bag/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Minimum Limit of Balls in a Bag\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Minimum Limit of Balls in a Bag\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Minimum Limit of Balls in a Bag\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Minimum Limit of Balls in a Bag\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Minimum Limit of Balls in a Bag\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Minimum Limit of Balls in a Bag\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Minimum Limit of Balls in a Bag\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Minimum Limit of Balls in a Bag\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Minimum Limit of Balls in a Bag",
      "cpp_optimal": "// Solution for Minimum Limit of Balls in a Bag",
      "java_brute": "// Solution for Minimum Limit of Balls in a Bag",
      "java_optimal": "// Solution for Minimum Limit of Balls in a Bag",
      "python_brute": "# Solution for Minimum Limit of Balls in a Bag",
      "python_optimal": "# Solution for Minimum Limit of Balls in a Bag"
    },
    "originalOrder": 422,
    "learningOrder": 422
  },
  {
    "id": 330,
    "number": 330,
    "sequence_number": 330,
    "title": "Sell Diminishing-Valued Colored Balls",
    "slug": "sell-diminishing-valued-colored-balls",
    "difficulty": "Medium",
    "topic": "Binary Search",
    "subtopic": "Binary Search Optimization",
    "pattern": "Value Threshold Sum",
    "secondary_patterns": [
      "Value Threshold Sum"
    ],
    "stage": "Binary Search & Search on Answer",
    "curriculumStage": "Stage 7 — Binary Search & Search on Answer",
    "roadmapPhase": "Stage 7 — Binary Search & Search on Answer",
    "phase": "Stage 7 — Binary Search & Search on Answer",
    "estimatedTime": 30,
    "statement": "Given the constraints and input parameters for Sell Diminishing-Valued Colored Balls, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Sell Diminishing-Valued Colored Balls."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Sell Diminishing-Valued Colored Balls.",
      "Leverage the optimal Binary Search pattern to reduce time complexity."
    ],
    "learningObjective": "Master Binary Search techniques by solving Medium problem constraints for Sell Diminishing-Valued Colored Balls.",
    "whyThisPattern": "When observing Binary Search problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/sell-diminishing-valued-colored-balls/",
    "leetcode_title": "Sell Diminishing-Valued Colored Balls",
    "leetcode_id": 1648,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/sell-diminishing-valued-colored-balls/",
    "canonicalSlug": "sell-diminishing-valued-colored-balls",
    "canonicalUrl": "https://leetcode.com/problems/sell-diminishing-valued-colored-balls/",
    "url": "https://leetcode.com/problems/sell-diminishing-valued-colored-balls/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Sell Diminishing-Valued Colored Balls\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Sell Diminishing-Valued Colored Balls\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Sell Diminishing-Valued Colored Balls\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Sell Diminishing-Valued Colored Balls\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Sell Diminishing-Valued Colored Balls\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Sell Diminishing-Valued Colored Balls\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Sell Diminishing-Valued Colored Balls\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Sell Diminishing-Valued Colored Balls\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Sell Diminishing-Valued Colored Balls",
      "cpp_optimal": "// Solution for Sell Diminishing-Valued Colored Balls",
      "java_brute": "// Solution for Sell Diminishing-Valued Colored Balls",
      "java_optimal": "// Solution for Sell Diminishing-Valued Colored Balls",
      "python_brute": "# Solution for Sell Diminishing-Valued Colored Balls",
      "python_optimal": "# Solution for Sell Diminishing-Valued Colored Balls"
    },
    "originalOrder": 423,
    "learningOrder": 423
  },
  {
    "id": 331,
    "number": 331,
    "sequence_number": 331,
    "title": "Magnetic Force Between Two Balls",
    "slug": "magnetic-force-between-two-balls",
    "difficulty": "Medium",
    "topic": "Binary Search",
    "subtopic": "Binary Search Optimization",
    "pattern": "Min Distance Search Space",
    "secondary_patterns": [
      "Min Distance Search Space"
    ],
    "stage": "Binary Search & Search on Answer",
    "curriculumStage": "Stage 7 — Binary Search & Search on Answer",
    "roadmapPhase": "Stage 7 — Binary Search & Search on Answer",
    "phase": "Stage 7 — Binary Search & Search on Answer",
    "estimatedTime": 30,
    "statement": "Given the constraints and input parameters for Magnetic Force Between Two Balls, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Magnetic Force Between Two Balls."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Magnetic Force Between Two Balls.",
      "Leverage the optimal Binary Search pattern to reduce time complexity."
    ],
    "learningObjective": "Master Binary Search techniques by solving Medium problem constraints for Magnetic Force Between Two Balls.",
    "whyThisPattern": "When observing Binary Search problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/magnetic-force-between-two-balls/",
    "leetcode_title": "Magnetic Force Between Two Balls",
    "leetcode_id": 1552,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/magnetic-force-between-two-balls/",
    "canonicalSlug": "magnetic-force-between-two-balls",
    "canonicalUrl": "https://leetcode.com/problems/magnetic-force-between-two-balls/",
    "url": "https://leetcode.com/problems/magnetic-force-between-two-balls/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Magnetic Force Between Two Balls\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Magnetic Force Between Two Balls\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Magnetic Force Between Two Balls\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Magnetic Force Between Two Balls\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Magnetic Force Between Two Balls\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Magnetic Force Between Two Balls\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Magnetic Force Between Two Balls\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Magnetic Force Between Two Balls\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Magnetic Force Between Two Balls",
      "cpp_optimal": "// Solution for Magnetic Force Between Two Balls",
      "java_brute": "// Solution for Magnetic Force Between Two Balls",
      "java_optimal": "// Solution for Magnetic Force Between Two Balls",
      "python_brute": "# Solution for Magnetic Force Between Two Balls",
      "python_optimal": "# Solution for Magnetic Force Between Two Balls"
    },
    "originalOrder": 424,
    "learningOrder": 424
  },
  {
    "id": 332,
    "number": 332,
    "sequence_number": 332,
    "title": "Minimum Number of Days to Make m Bouquets",
    "slug": "minimum-number-of-days-to-make-m-bouquets",
    "difficulty": "Medium",
    "topic": "Binary Search",
    "subtopic": "Binary Search Optimization",
    "pattern": "Day Space Binary Search",
    "secondary_patterns": [
      "Day Space Binary Search"
    ],
    "stage": "Binary Search & Search on Answer",
    "curriculumStage": "Stage 7 — Binary Search & Search on Answer",
    "roadmapPhase": "Stage 7 — Binary Search & Search on Answer",
    "phase": "Stage 7 — Binary Search & Search on Answer",
    "estimatedTime": 30,
    "statement": "Given the constraints and input parameters for Minimum Number of Days to Make m Bouquets, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Minimum Number of Days to Make m Bouquets."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Minimum Number of Days to Make m Bouquets.",
      "Leverage the optimal Binary Search pattern to reduce time complexity."
    ],
    "learningObjective": "Master Binary Search techniques by solving Medium problem constraints for Minimum Number of Days to Make m Bouquets.",
    "whyThisPattern": "When observing Binary Search problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/minimum-number-of-days-to-make-m-bouquets/",
    "leetcode_title": "Minimum Number of Days to Make m Bouquets",
    "leetcode_id": 1482,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/minimum-number-of-days-to-make-m-bouquets/",
    "canonicalSlug": "minimum-number-of-days-to-make-m-bouquets",
    "canonicalUrl": "https://leetcode.com/problems/minimum-number-of-days-to-make-m-bouquets/",
    "url": "https://leetcode.com/problems/minimum-number-of-days-to-make-m-bouquets/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Minimum Number of Days to Make m Bouquets\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Minimum Number of Days to Make m Bouquets\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Minimum Number of Days to Make m Bouquets\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Minimum Number of Days to Make m Bouquets\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Minimum Number of Days to Make m Bouquets\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Minimum Number of Days to Make m Bouquets\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Minimum Number of Days to Make m Bouquets\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Minimum Number of Days to Make m Bouquets\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Minimum Number of Days to Make m Bouquets",
      "cpp_optimal": "// Solution for Minimum Number of Days to Make m Bouquets",
      "java_brute": "// Solution for Minimum Number of Days to Make m Bouquets",
      "java_optimal": "// Solution for Minimum Number of Days to Make m Bouquets",
      "python_brute": "# Solution for Minimum Number of Days to Make m Bouquets",
      "python_optimal": "# Solution for Minimum Number of Days to Make m Bouquets"
    },
    "originalOrder": 425,
    "learningOrder": 425
  },
  {
    "id": 333,
    "number": 333,
    "sequence_number": 333,
    "title": "Find Peak Element",
    "slug": "find-peak-element",
    "difficulty": "Medium",
    "topic": "Binary Search",
    "subtopic": "Binary Search Optimization",
    "pattern": "Logarithmic Boundary Search",
    "secondary_patterns": [
      "Logarithmic Boundary Search"
    ],
    "stage": "Binary Search & Search on Answer",
    "curriculumStage": "Stage 7 — Binary Search & Search on Answer",
    "roadmapPhase": "Stage 7 — Binary Search & Search on Answer",
    "phase": "Stage 7 — Binary Search & Search on Answer",
    "estimatedTime": 30,
    "statement": "Given the constraints and input parameters for Find Peak Element, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Find Peak Element."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Find Peak Element.",
      "Leverage the optimal Binary Search pattern to reduce time complexity."
    ],
    "learningObjective": "Master Binary Search techniques by solving Medium problem constraints for Find Peak Element.",
    "whyThisPattern": "When observing Binary Search problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/find-peak-element/",
    "leetcode_title": "Find Peak Element",
    "leetcode_id": 162,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/find-peak-element/",
    "canonicalSlug": "find-peak-element",
    "canonicalUrl": "https://leetcode.com/problems/find-peak-element/",
    "url": "https://leetcode.com/problems/find-peak-element/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Find Peak Element\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Find Peak Element\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Find Peak Element\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Find Peak Element\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Find Peak Element\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Find Peak Element\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Find Peak Element\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Find Peak Element\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Find Peak Element",
      "cpp_optimal": "// Solution for Find Peak Element",
      "java_brute": "// Solution for Find Peak Element",
      "java_optimal": "// Solution for Find Peak Element",
      "python_brute": "# Solution for Find Peak Element",
      "python_optimal": "# Solution for Find Peak Element"
    },
    "originalOrder": 426,
    "learningOrder": 426
  },
  {
    "id": 334,
    "number": 334,
    "sequence_number": 334,
    "title": "Minimum Time to Complete Trips",
    "slug": "minimum-time-to-complete-trips",
    "difficulty": "Medium",
    "topic": "Binary Search",
    "subtopic": "Binary Search Optimization",
    "pattern": "Time Space Search",
    "secondary_patterns": [
      "Time Space Search"
    ],
    "stage": "Binary Search & Search on Answer",
    "curriculumStage": "Stage 7 — Binary Search & Search on Answer",
    "roadmapPhase": "Stage 7 — Binary Search & Search on Answer",
    "phase": "Stage 7 — Binary Search & Search on Answer",
    "estimatedTime": 30,
    "statement": "Given the constraints and input parameters for Minimum Time to Complete Trips, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Minimum Time to Complete Trips."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Minimum Time to Complete Trips.",
      "Leverage the optimal Binary Search pattern to reduce time complexity."
    ],
    "learningObjective": "Master Binary Search techniques by solving Medium problem constraints for Minimum Time to Complete Trips.",
    "whyThisPattern": "When observing Binary Search problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/minimum-time-to-complete-trips/",
    "leetcode_title": "Minimum Time to Complete Trips",
    "leetcode_id": 2187,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/minimum-time-to-complete-trips/",
    "canonicalSlug": "minimum-time-to-complete-trips",
    "canonicalUrl": "https://leetcode.com/problems/minimum-time-to-complete-trips/",
    "url": "https://leetcode.com/problems/minimum-time-to-complete-trips/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Minimum Time to Complete Trips\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Minimum Time to Complete Trips\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Minimum Time to Complete Trips\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Minimum Time to Complete Trips\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Minimum Time to Complete Trips\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Minimum Time to Complete Trips\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Minimum Time to Complete Trips\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Minimum Time to Complete Trips\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Minimum Time to Complete Trips",
      "cpp_optimal": "// Solution for Minimum Time to Complete Trips",
      "java_brute": "// Solution for Minimum Time to Complete Trips",
      "java_optimal": "// Solution for Minimum Time to Complete Trips",
      "python_brute": "# Solution for Minimum Time to Complete Trips",
      "python_optimal": "# Solution for Minimum Time to Complete Trips"
    },
    "originalOrder": 427,
    "learningOrder": 427
  },
  {
    "id": 335,
    "number": 335,
    "sequence_number": 335,
    "title": "Evaluate Reverse Polish Notation",
    "slug": "evaluate-reverse-polish-notation",
    "difficulty": "Medium",
    "topic": "Arrays",
    "subtopic": "Arrays Optimization",
    "pattern": "Arrays Pattern",
    "secondary_patterns": [
      "Arrays Pattern"
    ],
    "stage": "Binary Search & Search on Answer",
    "curriculumStage": "Stage 7 — Binary Search & Search on Answer",
    "roadmapPhase": "Stage 7 — Binary Search & Search on Answer",
    "phase": "Stage 7 — Binary Search & Search on Answer",
    "estimatedTime": 30,
    "statement": "Solve the **Evaluate Reverse Polish Notation** problem using standard Arrays techniques. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Arrays algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Arrays properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Arrays techniques by solving Medium problem constraints for Evaluate Reverse Polish Notation.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/evaluate-reverse-polish-notation/",
    "leetcode_title": "Evaluate Reverse Polish Notation",
    "leetcode_id": 150,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/evaluate-reverse-polish-notation/",
    "canonicalSlug": "evaluate-reverse-polish-notation",
    "canonicalUrl": "https://leetcode.com/problems/evaluate-reverse-polish-notation/",
    "url": "https://leetcode.com/problems/evaluate-reverse-polish-notation/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Evaluate Reverse Polish Notation\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Evaluate Reverse Polish Notation\n};",
        "java": "// Java Solution for Evaluate Reverse Polish Notation\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Evaluate Reverse Polish Notation\n}",
        "python": "# Python Solution for Evaluate Reverse Polish Notation\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Evaluate Reverse Polish Notation\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Evaluate Reverse Polish Notation\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Evaluate Reverse Polish Notation\n};",
        "java": "// Optimal Java Solution for Evaluate Reverse Polish Notation\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Evaluate Reverse Polish Notation\n}",
        "python": "# Optimal Python Solution for Evaluate Reverse Polish Notation\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Evaluate Reverse Polish Notation\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Evaluate Reverse Polish Notation",
      "cpp_optimal": "// Solution for Evaluate Reverse Polish Notation",
      "java_brute": "// Solution for Evaluate Reverse Polish Notation",
      "java_optimal": "// Solution for Evaluate Reverse Polish Notation",
      "python_brute": "# Solution for Evaluate Reverse Polish Notation",
      "python_optimal": "# Solution for Evaluate Reverse Polish Notation"
    },
    "originalOrder": 272,
    "learningOrder": 272
  },
  {
    "id": 336,
    "number": 336,
    "sequence_number": 336,
    "title": "Find Minimum in Rotated Sorted Array II",
    "slug": "find-minimum-in-rotated-sorted-array-ii",
    "difficulty": "Hard",
    "topic": "Binary Search",
    "subtopic": "Two Pointers",
    "pattern": "Two Pointers",
    "secondary_patterns": [
      "Two Pointers"
    ],
    "stage": "Binary Search & Search on Answer",
    "curriculumStage": "Stage 7 — Binary Search & Search on Answer",
    "roadmapPhase": "Stage 7 — Binary Search & Search on Answer",
    "phase": "Stage 7 — Binary Search & Search on Answer",
    "estimatedTime": 45,
    "statement": "Solve the **Find Minimum in Rotated Sorted Array II Optimization** problem using the **Two Pointers** technique. Given input constraints appropriate for Hard level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^6",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Two Pointers identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Two Pointers. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Two Pointers techniques by solving Hard problem constraints for Find Minimum in Rotated Sorted Array II Optimization.",
    "whyThisPattern": "When observing arrays & strings problem conditions, Two Pointers optimizes performance down to expected O(N log N).",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(1)",
    "companyRelevance": [
      "Meta",
      "Apple",
      "Netflix"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/find-minimum-in-rotated-sorted-array-ii/",
    "leetcode_title": "Find Minimum in Rotated Sorted Array II",
    "leetcode_id": 154,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/find-minimum-in-rotated-sorted-array-ii/",
    "canonicalSlug": "find-minimum-in-rotated-sorted-array-ii",
    "canonicalUrl": "https://leetcode.com/problems/find-minimum-in-rotated-sorted-array-ii/",
    "url": "https://leetcode.com/problems/find-minimum-in-rotated-sorted-array-ii/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Find Minimum in Rotated Sorted Array II Optimization (Two Pointers)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Find Minimum in Rotated Sorted Array II Optimization (Two Pointers)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Find Minimum in Rotated Sorted Array II Optimization (Two Pointers)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Find Minimum in Rotated Sorted Array II Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Find Minimum in Rotated Sorted Array II Optimization (Two Pointers)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Find Minimum in Rotated Sorted Array II Optimization (Two Pointers)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Find Minimum in Rotated Sorted Array II Optimization (Two Pointers)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Find Minimum in Rotated Sorted Array II Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Find Minimum in Rotated Sorted Array II",
      "cpp_optimal": "// Solution for Find Minimum in Rotated Sorted Array II",
      "java_brute": "// Solution for Find Minimum in Rotated Sorted Array II",
      "java_optimal": "// Solution for Find Minimum in Rotated Sorted Array II",
      "python_brute": "# Solution for Find Minimum in Rotated Sorted Array II",
      "python_optimal": "# Solution for Find Minimum in Rotated Sorted Array II"
    },
    "originalOrder": 788,
    "learningOrder": 788
  },
  {
    "id": 337,
    "number": 337,
    "sequence_number": 337,
    "title": "Longest Increasing Path in a Matrix",
    "slug": "longest-increasing-path-in-a-matrix",
    "difficulty": "Hard",
    "topic": "Binary Search",
    "subtopic": "Binary Search",
    "pattern": "Binary Search",
    "secondary_patterns": [
      "Binary Search"
    ],
    "stage": "Binary Search & Search on Answer",
    "curriculumStage": "Stage 7 — Binary Search & Search on Answer",
    "roadmapPhase": "Stage 7 — Binary Search & Search on Answer",
    "phase": "Stage 7 — Binary Search & Search on Answer",
    "estimatedTime": 45,
    "statement": "Solve the **Longest Increasing Path in a Matrix Challenge** problem using the **Binary Search** technique. Given input constraints appropriate for Hard level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^6",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Binary Search identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Binary Search. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Binary Search techniques by solving Hard problem constraints for Longest Increasing Path in a Matrix Challenge.",
    "whyThisPattern": "When observing arrays & strings problem conditions, Binary Search optimizes performance down to expected O(N log N).",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Meta",
      "Uber",
      "Databricks"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/longest-increasing-path-in-a-matrix/",
    "leetcode_title": "Longest Increasing Path in a Matrix",
    "leetcode_id": 329,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/longest-increasing-path-in-a-matrix/",
    "canonicalSlug": "longest-increasing-path-in-a-matrix",
    "canonicalUrl": "https://leetcode.com/problems/longest-increasing-path-in-a-matrix/",
    "url": "https://leetcode.com/problems/longest-increasing-path-in-a-matrix/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Longest Increasing Path in a Matrix Challenge (Binary Search)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Longest Increasing Path in a Matrix Challenge (Binary Search)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Longest Increasing Path in a Matrix Challenge (Binary Search)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Longest Increasing Path in a Matrix Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Longest Increasing Path in a Matrix Challenge (Binary Search)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Longest Increasing Path in a Matrix Challenge (Binary Search)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Longest Increasing Path in a Matrix Challenge (Binary Search)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Longest Increasing Path in a Matrix Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Longest Increasing Path in a Matrix",
      "cpp_optimal": "// Solution for Longest Increasing Path in a Matrix",
      "java_brute": "// Solution for Longest Increasing Path in a Matrix",
      "java_optimal": "// Solution for Longest Increasing Path in a Matrix",
      "python_brute": "# Solution for Longest Increasing Path in a Matrix",
      "python_optimal": "# Solution for Longest Increasing Path in a Matrix"
    },
    "originalOrder": 789,
    "learningOrder": 789
  },
  {
    "id": 338,
    "number": 338,
    "sequence_number": 338,
    "title": "Minimum Number of Flips to Convert Binary Matrix to Zero Matrix",
    "slug": "minimum-number-of-flips-to-convert-binary-matrix-to-zero-matrix",
    "difficulty": "Hard",
    "topic": "Binary Search",
    "subtopic": "Binary Search",
    "pattern": "Binary Search",
    "secondary_patterns": [
      "Binary Search"
    ],
    "stage": "Binary Search & Search on Answer",
    "curriculumStage": "Stage 7 — Binary Search & Search on Answer",
    "roadmapPhase": "Stage 7 — Binary Search & Search on Answer",
    "phase": "Stage 7 — Binary Search & Search on Answer",
    "estimatedTime": 45,
    "statement": "Solve the **Minimum Number of Flips to Convert Binary Matrix to Zero Matrix Challenge** problem using the **Binary Search** technique. Given input constraints appropriate for Hard level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^6",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Binary Search identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Binary Search. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Binary Search techniques by solving Hard problem constraints for Minimum Number of Flips to Convert Binary Matrix to Zero Matrix Challenge.",
    "whyThisPattern": "When observing arrays & strings problem conditions, Binary Search optimizes performance down to expected O(N log N).",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Amazon",
      "Microsoft",
      "Uber"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/minimum-number-of-flips-to-convert-binary-matrix-to-zero-matrix/",
    "leetcode_title": "Minimum Number of Flips to Convert Binary Matrix to Zero Matrix",
    "leetcode_id": 1284,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/minimum-number-of-flips-to-convert-binary-matrix-to-zero-matrix/",
    "canonicalSlug": "minimum-number-of-flips-to-convert-binary-matrix-to-zero-matrix",
    "canonicalUrl": "https://leetcode.com/problems/minimum-number-of-flips-to-convert-binary-matrix-to-zero-matrix/",
    "url": "https://leetcode.com/problems/minimum-number-of-flips-to-convert-binary-matrix-to-zero-matrix/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Minimum Number of Flips to Convert Binary Matrix to Zero Matrix Challenge (Binary Search)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Minimum Number of Flips to Convert Binary Matrix to Zero Matrix Challenge (Binary Search)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Minimum Number of Flips to Convert Binary Matrix to Zero Matrix Challenge (Binary Search)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Minimum Number of Flips to Convert Binary Matrix to Zero Matrix Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Minimum Number of Flips to Convert Binary Matrix to Zero Matrix Challenge (Binary Search)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Minimum Number of Flips to Convert Binary Matrix to Zero Matrix Challenge (Binary Search)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Minimum Number of Flips to Convert Binary Matrix to Zero Matrix Challenge (Binary Search)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Minimum Number of Flips to Convert Binary Matrix to Zero Matrix Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Minimum Number of Flips to Convert Binary Matrix to Zero Matrix",
      "cpp_optimal": "// Solution for Minimum Number of Flips to Convert Binary Matrix to Zero Matrix",
      "java_brute": "// Solution for Minimum Number of Flips to Convert Binary Matrix to Zero Matrix",
      "java_optimal": "// Solution for Minimum Number of Flips to Convert Binary Matrix to Zero Matrix",
      "python_brute": "# Solution for Minimum Number of Flips to Convert Binary Matrix to Zero Matrix",
      "python_optimal": "# Solution for Minimum Number of Flips to Convert Binary Matrix to Zero Matrix"
    },
    "originalOrder": 790,
    "learningOrder": 790
  },
  {
    "id": 339,
    "number": 339,
    "sequence_number": 339,
    "title": "Kth Smallest Number in Multiplication Table",
    "slug": "kth-smallest-number-in-multiplication-table",
    "difficulty": "Hard",
    "topic": "Binary Search",
    "subtopic": "Binary Search Optimization",
    "pattern": "Search on Answer Space",
    "secondary_patterns": [
      "Search on Answer Space"
    ],
    "stage": "Binary Search & Search on Answer",
    "curriculumStage": "Stage 7 — Binary Search & Search on Answer",
    "roadmapPhase": "Stage 7 — Binary Search & Search on Answer",
    "phase": "Stage 7 — Binary Search & Search on Answer",
    "estimatedTime": 45,
    "statement": "Given the constraints and input parameters for Kth Smallest Number in Multiplication Table, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Kth Smallest Number in Multiplication Table."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Kth Smallest Number in Multiplication Table.",
      "Leverage the optimal Binary Search pattern to reduce time complexity."
    ],
    "learningObjective": "Master Binary Search techniques by solving Hard problem constraints for Kth Smallest Number in Multiplication Table.",
    "whyThisPattern": "When observing Binary Search problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/kth-smallest-number-in-multiplication-table/",
    "leetcode_title": "Kth Smallest Number in Multiplication Table",
    "leetcode_id": 668,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/kth-smallest-number-in-multiplication-table/",
    "canonicalSlug": "kth-smallest-number-in-multiplication-table",
    "canonicalUrl": "https://leetcode.com/problems/kth-smallest-number-in-multiplication-table/",
    "url": "https://leetcode.com/problems/kth-smallest-number-in-multiplication-table/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Kth Smallest Number in Multiplication Table\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Kth Smallest Number in Multiplication Table\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Kth Smallest Number in Multiplication Table\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Kth Smallest Number in Multiplication Table\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Kth Smallest Number in Multiplication Table\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Kth Smallest Number in Multiplication Table\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Kth Smallest Number in Multiplication Table\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Kth Smallest Number in Multiplication Table\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Kth Smallest Number in Multiplication Table",
      "cpp_optimal": "// Solution for Kth Smallest Number in Multiplication Table",
      "java_brute": "// Solution for Kth Smallest Number in Multiplication Table",
      "java_optimal": "// Solution for Kth Smallest Number in Multiplication Table",
      "python_brute": "# Solution for Kth Smallest Number in Multiplication Table",
      "python_optimal": "# Solution for Kth Smallest Number in Multiplication Table"
    },
    "originalOrder": 791,
    "learningOrder": 791
  },
  {
    "id": 340,
    "number": 340,
    "sequence_number": 340,
    "title": "Max Sum of Rectangle No Larger Than K",
    "slug": "max-sum-of-rectangle-no-larger-than-k",
    "difficulty": "Hard",
    "topic": "Binary Search",
    "subtopic": "Binary Search Optimization",
    "pattern": "2D Prefix Sum + TreeSet",
    "secondary_patterns": [
      "2D Prefix Sum + TreeSet"
    ],
    "stage": "Binary Search & Search on Answer",
    "curriculumStage": "Stage 7 — Binary Search & Search on Answer",
    "roadmapPhase": "Stage 7 — Binary Search & Search on Answer",
    "phase": "Stage 7 — Binary Search & Search on Answer",
    "estimatedTime": 45,
    "statement": "Given the constraints and input parameters for Max Sum of Rectangle No Larger Than K, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Max Sum of Rectangle No Larger Than K."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Max Sum of Rectangle No Larger Than K.",
      "Leverage the optimal Binary Search pattern to reduce time complexity."
    ],
    "learningObjective": "Master Binary Search techniques by solving Hard problem constraints for Max Sum of Rectangle No Larger Than K.",
    "whyThisPattern": "When observing Binary Search problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/max-sum-of-rectangle-no-larger-than-k/",
    "leetcode_title": "Max Sum of Rectangle No Larger Than K",
    "leetcode_id": 363,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/max-sum-of-rectangle-no-larger-than-k/",
    "canonicalSlug": "max-sum-of-rectangle-no-larger-than-k",
    "canonicalUrl": "https://leetcode.com/problems/max-sum-of-rectangle-no-larger-than-k/",
    "url": "https://leetcode.com/problems/max-sum-of-rectangle-no-larger-than-k/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Max Sum of Rectangle No Larger Than K\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Max Sum of Rectangle No Larger Than K\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Max Sum of Rectangle No Larger Than K\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Max Sum of Rectangle No Larger Than K\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Max Sum of Rectangle No Larger Than K\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Max Sum of Rectangle No Larger Than K\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Max Sum of Rectangle No Larger Than K\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Max Sum of Rectangle No Larger Than K\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Max Sum of Rectangle No Larger Than K",
      "cpp_optimal": "// Solution for Max Sum of Rectangle No Larger Than K",
      "java_brute": "// Solution for Max Sum of Rectangle No Larger Than K",
      "java_optimal": "// Solution for Max Sum of Rectangle No Larger Than K",
      "python_brute": "# Solution for Max Sum of Rectangle No Larger Than K",
      "python_optimal": "# Solution for Max Sum of Rectangle No Larger Than K"
    },
    "originalOrder": 792,
    "learningOrder": 792
  },
  {
    "id": 341,
    "number": 341,
    "sequence_number": 341,
    "title": "Find K-th Smallest Pair Distance",
    "slug": "find-k-th-smallest-pair-distance",
    "difficulty": "Hard",
    "topic": "Binary Search",
    "subtopic": "Binary Search Optimization",
    "pattern": "Binary Search + Two Pointers",
    "secondary_patterns": [
      "Binary Search + Two Pointers"
    ],
    "stage": "Binary Search & Search on Answer",
    "curriculumStage": "Stage 7 — Binary Search & Search on Answer",
    "roadmapPhase": "Stage 7 — Binary Search & Search on Answer",
    "phase": "Stage 7 — Binary Search & Search on Answer",
    "estimatedTime": 45,
    "statement": "Given the constraints and input parameters for Find K-th Smallest Pair Distance, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Find K-th Smallest Pair Distance."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Find K-th Smallest Pair Distance.",
      "Leverage the optimal Binary Search pattern to reduce time complexity."
    ],
    "learningObjective": "Master Binary Search techniques by solving Hard problem constraints for Find K-th Smallest Pair Distance.",
    "whyThisPattern": "When observing Binary Search problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/find-k-th-smallest-pair-distance/",
    "leetcode_title": "Find K-th Smallest Pair Distance",
    "leetcode_id": 719,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/find-k-th-smallest-pair-distance/",
    "canonicalSlug": "find-k-th-smallest-pair-distance",
    "canonicalUrl": "https://leetcode.com/problems/find-k-th-smallest-pair-distance/",
    "url": "https://leetcode.com/problems/find-k-th-smallest-pair-distance/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Find K-th Smallest Pair Distance\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Find K-th Smallest Pair Distance\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Find K-th Smallest Pair Distance\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Find K-th Smallest Pair Distance\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Find K-th Smallest Pair Distance\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Find K-th Smallest Pair Distance\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Find K-th Smallest Pair Distance\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Find K-th Smallest Pair Distance\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Find K-th Smallest Pair Distance",
      "cpp_optimal": "// Solution for Find K-th Smallest Pair Distance",
      "java_brute": "// Solution for Find K-th Smallest Pair Distance",
      "java_optimal": "// Solution for Find K-th Smallest Pair Distance",
      "python_brute": "# Solution for Find K-th Smallest Pair Distance",
      "python_optimal": "# Solution for Find K-th Smallest Pair Distance"
    },
    "originalOrder": 793,
    "learningOrder": 793
  },
  {
    "id": 342,
    "number": 342,
    "sequence_number": 342,
    "title": "Kth Smallest Product of Two Sorted Arrays",
    "slug": "kth-smallest-product-of-two-sorted-arrays",
    "difficulty": "Hard",
    "topic": "Binary Search",
    "subtopic": "Binary Search Optimization",
    "pattern": "Double Binary Search Product",
    "secondary_patterns": [
      "Double Binary Search Product"
    ],
    "stage": "Binary Search & Search on Answer",
    "curriculumStage": "Stage 7 — Binary Search & Search on Answer",
    "roadmapPhase": "Stage 7 — Binary Search & Search on Answer",
    "phase": "Stage 7 — Binary Search & Search on Answer",
    "estimatedTime": 45,
    "statement": "Given the constraints and input parameters for Kth Smallest Product of Two Sorted Arrays, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Kth Smallest Product of Two Sorted Arrays."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Kth Smallest Product of Two Sorted Arrays.",
      "Leverage the optimal Binary Search pattern to reduce time complexity."
    ],
    "learningObjective": "Master Binary Search techniques by solving Hard problem constraints for Kth Smallest Product of Two Sorted Arrays.",
    "whyThisPattern": "When observing Binary Search problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/kth-smallest-product-of-two-sorted-arrays/",
    "leetcode_title": "Kth Smallest Product of Two Sorted Arrays",
    "leetcode_id": 2040,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/kth-smallest-product-of-two-sorted-arrays/",
    "canonicalSlug": "kth-smallest-product-of-two-sorted-arrays",
    "canonicalUrl": "https://leetcode.com/problems/kth-smallest-product-of-two-sorted-arrays/",
    "url": "https://leetcode.com/problems/kth-smallest-product-of-two-sorted-arrays/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Kth Smallest Product of Two Sorted Arrays\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Kth Smallest Product of Two Sorted Arrays\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Kth Smallest Product of Two Sorted Arrays\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Kth Smallest Product of Two Sorted Arrays\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Kth Smallest Product of Two Sorted Arrays\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Kth Smallest Product of Two Sorted Arrays\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Kth Smallest Product of Two Sorted Arrays\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Kth Smallest Product of Two Sorted Arrays\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Kth Smallest Product of Two Sorted Arrays",
      "cpp_optimal": "// Solution for Kth Smallest Product of Two Sorted Arrays",
      "java_brute": "// Solution for Kth Smallest Product of Two Sorted Arrays",
      "java_optimal": "// Solution for Kth Smallest Product of Two Sorted Arrays",
      "python_brute": "# Solution for Kth Smallest Product of Two Sorted Arrays",
      "python_optimal": "# Solution for Kth Smallest Product of Two Sorted Arrays"
    },
    "originalOrder": 794,
    "learningOrder": 794
  },
  {
    "id": 343,
    "number": 343,
    "sequence_number": 343,
    "title": "Minimum Cost to Make Array Equal",
    "slug": "minimum-cost-to-make-array-equal",
    "difficulty": "Hard",
    "topic": "Binary Search",
    "subtopic": "Binary Search Optimization",
    "pattern": "Weighted Median Convex Search",
    "secondary_patterns": [
      "Weighted Median Convex Search"
    ],
    "stage": "Binary Search & Search on Answer",
    "curriculumStage": "Stage 7 — Binary Search & Search on Answer",
    "roadmapPhase": "Stage 7 — Binary Search & Search on Answer",
    "phase": "Stage 7 — Binary Search & Search on Answer",
    "estimatedTime": 45,
    "statement": "Given the constraints and input parameters for Minimum Cost to Make Array Equal, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Minimum Cost to Make Array Equal."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Minimum Cost to Make Array Equal.",
      "Leverage the optimal Binary Search pattern to reduce time complexity."
    ],
    "learningObjective": "Master Binary Search techniques by solving Hard problem constraints for Minimum Cost to Make Array Equal.",
    "whyThisPattern": "When observing Binary Search problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/minimum-cost-to-make-array-equal/",
    "leetcode_title": "Minimum Cost to Make Array Equal",
    "leetcode_id": 2448,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/minimum-cost-to-make-array-equal/",
    "canonicalSlug": "minimum-cost-to-make-array-equal",
    "canonicalUrl": "https://leetcode.com/problems/minimum-cost-to-make-array-equal/",
    "url": "https://leetcode.com/problems/minimum-cost-to-make-array-equal/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Minimum Cost to Make Array Equal\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Minimum Cost to Make Array Equal\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Minimum Cost to Make Array Equal\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Minimum Cost to Make Array Equal\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Minimum Cost to Make Array Equal\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Minimum Cost to Make Array Equal\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Minimum Cost to Make Array Equal\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Minimum Cost to Make Array Equal\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Minimum Cost to Make Array Equal",
      "cpp_optimal": "// Solution for Minimum Cost to Make Array Equal",
      "java_brute": "// Solution for Minimum Cost to Make Array Equal",
      "java_optimal": "// Solution for Minimum Cost to Make Array Equal",
      "python_brute": "# Solution for Minimum Cost to Make Array Equal",
      "python_optimal": "# Solution for Minimum Cost to Make Array Equal"
    },
    "originalOrder": 795,
    "learningOrder": 795
  },
  {
    "id": 344,
    "number": 344,
    "sequence_number": 344,
    "title": "Longest Duplicate Substring",
    "slug": "longest-duplicate-substring",
    "difficulty": "Hard",
    "topic": "Arrays",
    "subtopic": "Arrays Optimization",
    "pattern": "Arrays Pattern",
    "secondary_patterns": [
      "Arrays Pattern"
    ],
    "stage": "Binary Search & Search on Answer",
    "curriculumStage": "Stage 7 — Binary Search & Search on Answer",
    "roadmapPhase": "Stage 7 — Binary Search & Search on Answer",
    "phase": "Stage 7 — Binary Search & Search on Answer",
    "estimatedTime": 45,
    "statement": "Solve the **Longest Duplicate Substring** problem using standard Arrays techniques. Given input constraints appropriate for Hard level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Arrays algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Arrays properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Arrays techniques by solving Hard problem constraints for Longest Duplicate Substring.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/longest-duplicate-substring/",
    "leetcode_title": "Longest Duplicate Substring",
    "leetcode_id": 1044,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/longest-duplicate-substring/",
    "canonicalSlug": "longest-duplicate-substring",
    "canonicalUrl": "https://leetcode.com/problems/longest-duplicate-substring/",
    "url": "https://leetcode.com/problems/longest-duplicate-substring/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Longest Duplicate Substring\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Longest Duplicate Substring\n};",
        "java": "// Java Solution for Longest Duplicate Substring\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Longest Duplicate Substring\n}",
        "python": "# Python Solution for Longest Duplicate Substring\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Longest Duplicate Substring\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Longest Duplicate Substring\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Longest Duplicate Substring\n};",
        "java": "// Optimal Java Solution for Longest Duplicate Substring\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Longest Duplicate Substring\n}",
        "python": "# Optimal Python Solution for Longest Duplicate Substring\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Longest Duplicate Substring\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Longest Duplicate Substring",
      "cpp_optimal": "// Solution for Longest Duplicate Substring",
      "java_brute": "// Solution for Longest Duplicate Substring",
      "java_optimal": "// Solution for Longest Duplicate Substring",
      "python_brute": "# Solution for Longest Duplicate Substring",
      "python_optimal": "# Solution for Longest Duplicate Substring"
    },
    "originalOrder": 745,
    "learningOrder": 745
  },
  {
    "id": 345,
    "number": 345,
    "sequence_number": 345,
    "title": "Find in Mountain Array",
    "slug": "find-in-mountain-array",
    "difficulty": "Hard",
    "topic": "Arrays",
    "subtopic": "Arrays Optimization",
    "pattern": "Arrays Pattern",
    "secondary_patterns": [
      "Arrays Pattern"
    ],
    "stage": "Binary Search & Search on Answer",
    "curriculumStage": "Stage 7 — Binary Search & Search on Answer",
    "roadmapPhase": "Stage 7 — Binary Search & Search on Answer",
    "phase": "Stage 7 — Binary Search & Search on Answer",
    "estimatedTime": 45,
    "statement": "Solve the **Find in Mountain Array** problem using standard Arrays techniques. Given input constraints appropriate for Hard level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Arrays algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Arrays properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Arrays techniques by solving Hard problem constraints for Find in Mountain Array.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/find-in-mountain-array/",
    "leetcode_title": "Find in Mountain Array",
    "leetcode_id": 1095,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/find-in-mountain-array/",
    "canonicalSlug": "find-in-mountain-array",
    "canonicalUrl": "https://leetcode.com/problems/find-in-mountain-array/",
    "url": "https://leetcode.com/problems/find-in-mountain-array/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Find in Mountain Array\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Find in Mountain Array\n};",
        "java": "// Java Solution for Find in Mountain Array\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Find in Mountain Array\n}",
        "python": "# Python Solution for Find in Mountain Array\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Find in Mountain Array\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Find in Mountain Array\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Find in Mountain Array\n};",
        "java": "// Optimal Java Solution for Find in Mountain Array\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Find in Mountain Array\n}",
        "python": "# Optimal Python Solution for Find in Mountain Array\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Find in Mountain Array\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Find in Mountain Array",
      "cpp_optimal": "// Solution for Find in Mountain Array",
      "java_brute": "// Solution for Find in Mountain Array",
      "java_optimal": "// Solution for Find in Mountain Array",
      "python_brute": "# Solution for Find in Mountain Array",
      "python_optimal": "# Solution for Find in Mountain Array"
    },
    "originalOrder": 746,
    "learningOrder": 746
  },
  {
    "id": 346,
    "number": 346,
    "sequence_number": 346,
    "title": "Brace Expansion II",
    "slug": "brace-expansion-ii",
    "difficulty": "Hard",
    "topic": "Arrays",
    "subtopic": "Arrays Optimization",
    "pattern": "Arrays Pattern",
    "secondary_patterns": [
      "Arrays Pattern"
    ],
    "stage": "Binary Search & Search on Answer",
    "curriculumStage": "Stage 7 — Binary Search & Search on Answer",
    "roadmapPhase": "Stage 7 — Binary Search & Search on Answer",
    "phase": "Stage 7 — Binary Search & Search on Answer",
    "estimatedTime": 45,
    "statement": "Solve the **Brace Expansion II** problem using standard Arrays techniques. Given input constraints appropriate for Hard level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Arrays algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Arrays properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Arrays techniques by solving Hard problem constraints for Brace Expansion II.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/brace-expansion-ii/",
    "leetcode_title": "Brace Expansion II",
    "leetcode_id": 1096,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/brace-expansion-ii/",
    "canonicalSlug": "brace-expansion-ii",
    "canonicalUrl": "https://leetcode.com/problems/brace-expansion-ii/",
    "url": "https://leetcode.com/problems/brace-expansion-ii/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Brace Expansion II\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Brace Expansion II\n};",
        "java": "// Java Solution for Brace Expansion II\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Brace Expansion II\n}",
        "python": "# Python Solution for Brace Expansion II\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Brace Expansion II\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Brace Expansion II\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Brace Expansion II\n};",
        "java": "// Optimal Java Solution for Brace Expansion II\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Brace Expansion II\n}",
        "python": "# Optimal Python Solution for Brace Expansion II\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Brace Expansion II\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Brace Expansion II",
      "cpp_optimal": "// Solution for Brace Expansion II",
      "java_brute": "// Solution for Brace Expansion II",
      "java_optimal": "// Solution for Brace Expansion II",
      "python_brute": "# Solution for Brace Expansion II",
      "python_optimal": "# Solution for Brace Expansion II"
    },
    "originalOrder": 747,
    "learningOrder": 747
  },
  {
    "id": 347,
    "number": 347,
    "sequence_number": 347,
    "title": "Parsing A Boolean Expression",
    "slug": "parsing-a-boolean-expression",
    "difficulty": "Hard",
    "topic": "Arrays",
    "subtopic": "Arrays Optimization",
    "pattern": "Arrays Pattern",
    "secondary_patterns": [
      "Arrays Pattern"
    ],
    "stage": "Binary Search & Search on Answer",
    "curriculumStage": "Stage 7 — Binary Search & Search on Answer",
    "roadmapPhase": "Stage 7 — Binary Search & Search on Answer",
    "phase": "Stage 7 — Binary Search & Search on Answer",
    "estimatedTime": 45,
    "statement": "Solve the **Parsing A Boolean Expression** problem using standard Arrays techniques. Given input constraints appropriate for Hard level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Arrays algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Arrays properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Arrays techniques by solving Hard problem constraints for Parsing A Boolean Expression.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/parsing-a-boolean-expression/",
    "leetcode_title": "Parsing A Boolean Expression",
    "leetcode_id": 1106,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/parsing-a-boolean-expression/",
    "canonicalSlug": "parsing-a-boolean-expression",
    "canonicalUrl": "https://leetcode.com/problems/parsing-a-boolean-expression/",
    "url": "https://leetcode.com/problems/parsing-a-boolean-expression/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Parsing A Boolean Expression\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Parsing A Boolean Expression\n};",
        "java": "// Java Solution for Parsing A Boolean Expression\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Parsing A Boolean Expression\n}",
        "python": "# Python Solution for Parsing A Boolean Expression\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Parsing A Boolean Expression\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Parsing A Boolean Expression\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Parsing A Boolean Expression\n};",
        "java": "// Optimal Java Solution for Parsing A Boolean Expression\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Parsing A Boolean Expression\n}",
        "python": "# Optimal Python Solution for Parsing A Boolean Expression\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Parsing A Boolean Expression\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Parsing A Boolean Expression",
      "cpp_optimal": "// Solution for Parsing A Boolean Expression",
      "java_brute": "// Solution for Parsing A Boolean Expression",
      "java_optimal": "// Solution for Parsing A Boolean Expression",
      "python_brute": "# Solution for Parsing A Boolean Expression",
      "python_optimal": "# Solution for Parsing A Boolean Expression"
    },
    "originalOrder": 748,
    "learningOrder": 748
  },
  {
    "id": 348,
    "number": 348,
    "sequence_number": 348,
    "title": "Smallest Sufficient Team",
    "slug": "smallest-sufficient-team",
    "difficulty": "Hard",
    "topic": "Arrays",
    "subtopic": "Arrays Optimization",
    "pattern": "Arrays Pattern",
    "secondary_patterns": [
      "Arrays Pattern"
    ],
    "stage": "Binary Search & Search on Answer",
    "curriculumStage": "Stage 7 — Binary Search & Search on Answer",
    "roadmapPhase": "Stage 7 — Binary Search & Search on Answer",
    "phase": "Stage 7 — Binary Search & Search on Answer",
    "estimatedTime": 45,
    "statement": "Solve the **Smallest Sufficient Team** problem using standard Arrays techniques. Given input constraints appropriate for Hard level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Arrays algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Arrays properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Arrays techniques by solving Hard problem constraints for Smallest Sufficient Team.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/smallest-sufficient-team/",
    "leetcode_title": "Smallest Sufficient Team",
    "leetcode_id": 1125,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/smallest-sufficient-team/",
    "canonicalSlug": "smallest-sufficient-team",
    "canonicalUrl": "https://leetcode.com/problems/smallest-sufficient-team/",
    "url": "https://leetcode.com/problems/smallest-sufficient-team/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Smallest Sufficient Team\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Smallest Sufficient Team\n};",
        "java": "// Java Solution for Smallest Sufficient Team\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Smallest Sufficient Team\n}",
        "python": "# Python Solution for Smallest Sufficient Team\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Smallest Sufficient Team\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Smallest Sufficient Team\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Smallest Sufficient Team\n};",
        "java": "// Optimal Java Solution for Smallest Sufficient Team\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Smallest Sufficient Team\n}",
        "python": "# Optimal Python Solution for Smallest Sufficient Team\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Smallest Sufficient Team\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Smallest Sufficient Team",
      "cpp_optimal": "// Solution for Smallest Sufficient Team",
      "java_brute": "// Solution for Smallest Sufficient Team",
      "java_optimal": "// Solution for Smallest Sufficient Team",
      "python_brute": "# Solution for Smallest Sufficient Team",
      "python_optimal": "# Solution for Smallest Sufficient Team"
    },
    "originalOrder": 749,
    "learningOrder": 749
  },
  {
    "id": 349,
    "number": 349,
    "sequence_number": 349,
    "title": "Longest Chunked Palindrome Decomposition",
    "slug": "longest-chunked-palindrome-decomposition",
    "difficulty": "Hard",
    "topic": "Arrays",
    "subtopic": "Arrays Optimization",
    "pattern": "Arrays Pattern",
    "secondary_patterns": [
      "Arrays Pattern"
    ],
    "stage": "Binary Search & Search on Answer",
    "curriculumStage": "Stage 7 — Binary Search & Search on Answer",
    "roadmapPhase": "Stage 7 — Binary Search & Search on Answer",
    "phase": "Stage 7 — Binary Search & Search on Answer",
    "estimatedTime": 45,
    "statement": "Solve the **Longest Chunked Palindrome Decomposition** problem using standard Arrays techniques. Given input constraints appropriate for Hard level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Arrays algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Arrays properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Arrays techniques by solving Hard problem constraints for Longest Chunked Palindrome Decomposition.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/longest-chunked-palindrome-decomposition/",
    "leetcode_title": "Longest Chunked Palindrome Decomposition",
    "leetcode_id": 1147,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/longest-chunked-palindrome-decomposition/",
    "canonicalSlug": "longest-chunked-palindrome-decomposition",
    "canonicalUrl": "https://leetcode.com/problems/longest-chunked-palindrome-decomposition/",
    "url": "https://leetcode.com/problems/longest-chunked-palindrome-decomposition/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Longest Chunked Palindrome Decomposition\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Longest Chunked Palindrome Decomposition\n};",
        "java": "// Java Solution for Longest Chunked Palindrome Decomposition\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Longest Chunked Palindrome Decomposition\n}",
        "python": "# Python Solution for Longest Chunked Palindrome Decomposition\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Longest Chunked Palindrome Decomposition\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Longest Chunked Palindrome Decomposition\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Longest Chunked Palindrome Decomposition\n};",
        "java": "// Optimal Java Solution for Longest Chunked Palindrome Decomposition\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Longest Chunked Palindrome Decomposition\n}",
        "python": "# Optimal Python Solution for Longest Chunked Palindrome Decomposition\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Longest Chunked Palindrome Decomposition\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Longest Chunked Palindrome Decomposition",
      "cpp_optimal": "// Solution for Longest Chunked Palindrome Decomposition",
      "java_brute": "// Solution for Longest Chunked Palindrome Decomposition",
      "java_optimal": "// Solution for Longest Chunked Palindrome Decomposition",
      "python_brute": "# Solution for Longest Chunked Palindrome Decomposition",
      "python_optimal": "# Solution for Longest Chunked Palindrome Decomposition"
    },
    "originalOrder": 750,
    "learningOrder": 750
  },
  {
    "id": 350,
    "number": 350,
    "sequence_number": 350,
    "title": "Make Array Strictly Increasing",
    "slug": "make-array-strictly-increasing",
    "difficulty": "Hard",
    "topic": "Arrays",
    "subtopic": "Arrays Optimization",
    "pattern": "Arrays Pattern",
    "secondary_patterns": [
      "Arrays Pattern"
    ],
    "stage": "Binary Search & Search on Answer",
    "curriculumStage": "Stage 7 — Binary Search & Search on Answer",
    "roadmapPhase": "Stage 7 — Binary Search & Search on Answer",
    "phase": "Stage 7 — Binary Search & Search on Answer",
    "estimatedTime": 45,
    "statement": "Solve the **Make Array Strictly Increasing** problem using standard Arrays techniques. Given input constraints appropriate for Hard level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Arrays algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Arrays properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Arrays techniques by solving Hard problem constraints for Make Array Strictly Increasing.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/make-array-strictly-increasing/",
    "leetcode_title": "Make Array Strictly Increasing",
    "leetcode_id": 1187,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/make-array-strictly-increasing/",
    "canonicalSlug": "make-array-strictly-increasing",
    "canonicalUrl": "https://leetcode.com/problems/make-array-strictly-increasing/",
    "url": "https://leetcode.com/problems/make-array-strictly-increasing/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Make Array Strictly Increasing\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Make Array Strictly Increasing\n};",
        "java": "// Java Solution for Make Array Strictly Increasing\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Make Array Strictly Increasing\n}",
        "python": "# Python Solution for Make Array Strictly Increasing\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Make Array Strictly Increasing\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Make Array Strictly Increasing\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Make Array Strictly Increasing\n};",
        "java": "// Optimal Java Solution for Make Array Strictly Increasing\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Make Array Strictly Increasing\n}",
        "python": "# Optimal Python Solution for Make Array Strictly Increasing\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Make Array Strictly Increasing\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Make Array Strictly Increasing",
      "cpp_optimal": "// Solution for Make Array Strictly Increasing",
      "java_brute": "// Solution for Make Array Strictly Increasing",
      "java_optimal": "// Solution for Make Array Strictly Increasing",
      "python_brute": "# Solution for Make Array Strictly Increasing",
      "python_optimal": "# Solution for Make Array Strictly Increasing"
    },
    "originalOrder": 751,
    "learningOrder": 751
  },
  {
    "id": 351,
    "number": 351,
    "sequence_number": 351,
    "title": "Subtree of Another Tree",
    "slug": "subtree-of-another-tree",
    "difficulty": "Easy",
    "topic": "Trees",
    "subtopic": "Tree Traversal & Recursion",
    "pattern": "Tree Traversal & Recursion",
    "secondary_patterns": [
      "Tree Traversal & Recursion"
    ],
    "stage": "Binary Trees & Tree Traversals",
    "curriculumStage": "Stage 8 — Binary Trees & Tree Traversals",
    "roadmapPhase": "Stage 8 — Binary Trees & Tree Traversals",
    "phase": "Stage 8 — Binary Trees & Tree Traversals",
    "estimatedTime": 15,
    "statement": "Solve the **Subtree of Another Tree Challenge** problem using the **Tree Traversal & Recursion** technique. Given input constraints appropriate for Easy level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^4",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Tree Traversal & Recursion identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Tree Traversal & Recursion. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Tree Traversal & Recursion techniques by solving Easy problem constraints for Subtree of Another Tree Challenge.",
    "whyThisPattern": "When observing binary trees problem conditions, Tree Traversal & Recursion optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Amazon",
      "Microsoft",
      "Uber"
    ],
    "companyRelevanceTier": "Medium",
    "leetcode_url": "https://leetcode.com/problems/subtree-of-another-tree/",
    "leetcode_title": "Subtree of Another Tree",
    "leetcode_id": 572,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/subtree-of-another-tree/",
    "canonicalSlug": "subtree-of-another-tree",
    "canonicalUrl": "https://leetcode.com/problems/subtree-of-another-tree/",
    "url": "https://leetcode.com/problems/subtree-of-another-tree/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Subtree of Another Tree Challenge (Tree Traversal & Recursion)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Subtree of Another Tree Challenge (Tree Traversal & Recursion)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Subtree of Another Tree Challenge (Tree Traversal & Recursion)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Subtree of Another Tree Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Subtree of Another Tree Challenge (Tree Traversal & Recursion)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Subtree of Another Tree Challenge (Tree Traversal & Recursion)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Subtree of Another Tree Challenge (Tree Traversal & Recursion)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Subtree of Another Tree Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Subtree of Another Tree",
      "cpp_optimal": "// Solution for Subtree of Another Tree",
      "java_brute": "// Solution for Subtree of Another Tree",
      "java_optimal": "// Solution for Subtree of Another Tree",
      "python_brute": "# Solution for Subtree of Another Tree",
      "python_optimal": "# Solution for Subtree of Another Tree"
    },
    "originalOrder": 216,
    "learningOrder": 216
  },
  {
    "id": 352,
    "number": 352,
    "sequence_number": 352,
    "title": "Binary Tree Inorder Traversal",
    "slug": "binary-tree-inorder-traversal",
    "difficulty": "Easy",
    "topic": "Trees",
    "subtopic": "Tree Traversal & Recursion",
    "pattern": "Tree Traversal & Recursion",
    "secondary_patterns": [
      "Tree Traversal & Recursion"
    ],
    "stage": "Binary Trees & Tree Traversals",
    "curriculumStage": "Stage 8 — Binary Trees & Tree Traversals",
    "roadmapPhase": "Stage 8 — Binary Trees & Tree Traversals",
    "phase": "Stage 8 — Binary Trees & Tree Traversals",
    "estimatedTime": 15,
    "statement": "Solve the **Binary Tree Inorder Traversal Challenge** problem using the **Tree Traversal & Recursion** technique. Given input constraints appropriate for Easy level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^4",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Tree Traversal & Recursion identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Tree Traversal & Recursion. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Tree Traversal & Recursion techniques by solving Easy problem constraints for Binary Tree Inorder Traversal Challenge.",
    "whyThisPattern": "When observing binary trees problem conditions, Tree Traversal & Recursion optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Microsoft",
      "Bloomberg"
    ],
    "companyRelevanceTier": "Medium",
    "leetcode_url": "https://leetcode.com/problems/binary-tree-inorder-traversal/",
    "leetcode_title": "Binary Tree Inorder Traversal",
    "leetcode_id": 94,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/binary-tree-inorder-traversal/",
    "canonicalSlug": "binary-tree-inorder-traversal",
    "canonicalUrl": "https://leetcode.com/problems/binary-tree-inorder-traversal/",
    "url": "https://leetcode.com/problems/binary-tree-inorder-traversal/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Binary Tree Inorder Traversal Challenge (Tree Traversal & Recursion)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Binary Tree Inorder Traversal Challenge (Tree Traversal & Recursion)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Binary Tree Inorder Traversal Challenge (Tree Traversal & Recursion)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Binary Tree Inorder Traversal Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Binary Tree Inorder Traversal Challenge (Tree Traversal & Recursion)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Binary Tree Inorder Traversal Challenge (Tree Traversal & Recursion)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Binary Tree Inorder Traversal Challenge (Tree Traversal & Recursion)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Binary Tree Inorder Traversal Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Binary Tree Inorder Traversal",
      "cpp_optimal": "// Solution for Binary Tree Inorder Traversal",
      "java_brute": "// Solution for Binary Tree Inorder Traversal",
      "java_optimal": "// Solution for Binary Tree Inorder Traversal",
      "python_brute": "# Solution for Binary Tree Inorder Traversal",
      "python_optimal": "# Solution for Binary Tree Inorder Traversal"
    },
    "originalOrder": 217,
    "learningOrder": 217
  },
  {
    "id": 353,
    "number": 353,
    "sequence_number": 353,
    "title": "Same Tree",
    "slug": "same-tree",
    "difficulty": "Easy",
    "topic": "Trees",
    "subtopic": "Tree Traversal & Recursion",
    "pattern": "Tree Traversal & Recursion",
    "secondary_patterns": [
      "Tree Traversal & Recursion"
    ],
    "stage": "Binary Trees & Tree Traversals",
    "curriculumStage": "Stage 8 — Binary Trees & Tree Traversals",
    "roadmapPhase": "Stage 8 — Binary Trees & Tree Traversals",
    "phase": "Stage 8 — Binary Trees & Tree Traversals",
    "estimatedTime": 15,
    "statement": "Solve the **Same Tree Optimization** problem using the **Tree Traversal & Recursion** technique. Given input constraints appropriate for Easy level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^4",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Tree Traversal & Recursion identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Tree Traversal & Recursion. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Tree Traversal & Recursion techniques by solving Easy problem constraints for Same Tree Optimization.",
    "whyThisPattern": "When observing binary trees problem conditions, Tree Traversal & Recursion optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "LinkedIn",
      "Amazon"
    ],
    "companyRelevanceTier": "Medium",
    "leetcode_url": "https://leetcode.com/problems/same-tree/",
    "leetcode_title": "Same Tree",
    "leetcode_id": 100,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/same-tree/",
    "canonicalSlug": "same-tree",
    "canonicalUrl": "https://leetcode.com/problems/same-tree/",
    "url": "https://leetcode.com/problems/same-tree/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Same Tree Optimization (Tree Traversal & Recursion)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Same Tree Optimization (Tree Traversal & Recursion)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Same Tree Optimization (Tree Traversal & Recursion)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Same Tree Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Same Tree Optimization (Tree Traversal & Recursion)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Same Tree Optimization (Tree Traversal & Recursion)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Same Tree Optimization (Tree Traversal & Recursion)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Same Tree Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Same Tree",
      "cpp_optimal": "// Solution for Same Tree",
      "java_brute": "// Solution for Same Tree",
      "java_optimal": "// Solution for Same Tree",
      "python_brute": "# Solution for Same Tree",
      "python_optimal": "# Solution for Same Tree"
    },
    "originalOrder": 218,
    "learningOrder": 218
  },
  {
    "id": 354,
    "number": 354,
    "sequence_number": 354,
    "title": "Symmetric Tree",
    "slug": "symmetric-tree",
    "difficulty": "Easy",
    "topic": "Trees",
    "subtopic": "Tree Traversal & Recursion",
    "pattern": "Tree Traversal & Recursion",
    "secondary_patterns": [
      "Tree Traversal & Recursion"
    ],
    "stage": "Binary Trees & Tree Traversals",
    "curriculumStage": "Stage 8 — Binary Trees & Tree Traversals",
    "roadmapPhase": "Stage 8 — Binary Trees & Tree Traversals",
    "phase": "Stage 8 — Binary Trees & Tree Traversals",
    "estimatedTime": 15,
    "statement": "Solve the **Symmetric Tree Optimization** problem using the **Tree Traversal & Recursion** technique. Given input constraints appropriate for Easy level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^4",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Tree Traversal & Recursion identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Tree Traversal & Recursion. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Tree Traversal & Recursion techniques by solving Easy problem constraints for Symmetric Tree Optimization.",
    "whyThisPattern": "When observing binary trees problem conditions, Tree Traversal & Recursion optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta"
    ],
    "companyRelevanceTier": "Medium",
    "leetcode_url": "https://leetcode.com/problems/symmetric-tree/",
    "leetcode_title": "Symmetric Tree",
    "leetcode_id": 101,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/symmetric-tree/",
    "canonicalSlug": "symmetric-tree",
    "canonicalUrl": "https://leetcode.com/problems/symmetric-tree/",
    "url": "https://leetcode.com/problems/symmetric-tree/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Symmetric Tree Optimization (Tree Traversal & Recursion)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Symmetric Tree Optimization (Tree Traversal & Recursion)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Symmetric Tree Optimization (Tree Traversal & Recursion)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Symmetric Tree Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Symmetric Tree Optimization (Tree Traversal & Recursion)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Symmetric Tree Optimization (Tree Traversal & Recursion)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Symmetric Tree Optimization (Tree Traversal & Recursion)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Symmetric Tree Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Symmetric Tree",
      "cpp_optimal": "// Solution for Symmetric Tree",
      "java_brute": "// Solution for Symmetric Tree",
      "java_optimal": "// Solution for Symmetric Tree",
      "python_brute": "# Solution for Symmetric Tree",
      "python_optimal": "# Solution for Symmetric Tree"
    },
    "originalOrder": 219,
    "learningOrder": 219
  },
  {
    "id": 355,
    "number": 355,
    "sequence_number": 355,
    "title": "Maximum Depth of Binary Tree",
    "slug": "maximum-depth-of-binary-tree",
    "difficulty": "Easy",
    "topic": "Trees",
    "subtopic": "Tree Traversal & Recursion",
    "pattern": "Tree Traversal & Recursion",
    "secondary_patterns": [
      "Tree Traversal & Recursion"
    ],
    "stage": "Binary Trees & Tree Traversals",
    "curriculumStage": "Stage 8 — Binary Trees & Tree Traversals",
    "roadmapPhase": "Stage 8 — Binary Trees & Tree Traversals",
    "phase": "Stage 8 — Binary Trees & Tree Traversals",
    "estimatedTime": 15,
    "statement": "Solve the **Maximum Depth of Binary Tree Challenge** problem using the **Tree Traversal & Recursion** technique. Given input constraints appropriate for Easy level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^4",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Tree Traversal & Recursion identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Tree Traversal & Recursion. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Tree Traversal & Recursion techniques by solving Easy problem constraints for Maximum Depth of Binary Tree Challenge.",
    "whyThisPattern": "When observing binary trees problem conditions, Tree Traversal & Recursion optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Amazon",
      "Microsoft",
      "Uber"
    ],
    "companyRelevanceTier": "Medium",
    "leetcode_url": "https://leetcode.com/problems/maximum-depth-of-binary-tree/",
    "leetcode_title": "Maximum Depth of Binary Tree",
    "leetcode_id": 104,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/maximum-depth-of-binary-tree/",
    "canonicalSlug": "maximum-depth-of-binary-tree",
    "canonicalUrl": "https://leetcode.com/problems/maximum-depth-of-binary-tree/",
    "url": "https://leetcode.com/problems/maximum-depth-of-binary-tree/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Maximum Depth of Binary Tree Challenge (Tree Traversal & Recursion)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Maximum Depth of Binary Tree Challenge (Tree Traversal & Recursion)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Maximum Depth of Binary Tree Challenge (Tree Traversal & Recursion)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Maximum Depth of Binary Tree Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Maximum Depth of Binary Tree Challenge (Tree Traversal & Recursion)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Maximum Depth of Binary Tree Challenge (Tree Traversal & Recursion)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Maximum Depth of Binary Tree Challenge (Tree Traversal & Recursion)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Maximum Depth of Binary Tree Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Maximum Depth of Binary Tree",
      "cpp_optimal": "// Solution for Maximum Depth of Binary Tree",
      "java_brute": "// Solution for Maximum Depth of Binary Tree",
      "java_optimal": "// Solution for Maximum Depth of Binary Tree",
      "python_brute": "# Solution for Maximum Depth of Binary Tree",
      "python_optimal": "# Solution for Maximum Depth of Binary Tree"
    },
    "originalOrder": 220,
    "learningOrder": 220
  },
  {
    "id": 356,
    "number": 356,
    "sequence_number": 356,
    "title": "N-ary Tree Preorder Traversal",
    "slug": "n-ary-tree-preorder-traversal",
    "difficulty": "Easy",
    "topic": "Trees",
    "subtopic": "Tree Traversal & Recursion",
    "pattern": "Tree Traversal & Recursion",
    "secondary_patterns": [
      "Tree Traversal & Recursion"
    ],
    "stage": "Binary Trees & Tree Traversals",
    "curriculumStage": "Stage 8 — Binary Trees & Tree Traversals",
    "roadmapPhase": "Stage 8 — Binary Trees & Tree Traversals",
    "phase": "Stage 8 — Binary Trees & Tree Traversals",
    "estimatedTime": 15,
    "statement": "Solve the **N-ary Tree Preorder Traversal Challenge** problem using the **Tree Traversal & Recursion** technique. Given input constraints appropriate for Easy level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^4",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Tree Traversal & Recursion identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Tree Traversal & Recursion. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Tree Traversal & Recursion techniques by solving Easy problem constraints for N-ary Tree Preorder Traversal Challenge.",
    "whyThisPattern": "When observing binary trees problem conditions, Tree Traversal & Recursion optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Meta",
      "Uber",
      "Databricks"
    ],
    "companyRelevanceTier": "Medium",
    "leetcode_url": "https://leetcode.com/problems/n-ary-tree-preorder-traversal/",
    "leetcode_title": "N-ary Tree Preorder Traversal",
    "leetcode_id": 589,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/n-ary-tree-preorder-traversal/",
    "canonicalSlug": "n-ary-tree-preorder-traversal",
    "canonicalUrl": "https://leetcode.com/problems/n-ary-tree-preorder-traversal/",
    "url": "https://leetcode.com/problems/n-ary-tree-preorder-traversal/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for N-ary Tree Preorder Traversal Challenge (Tree Traversal & Recursion)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for N-ary Tree Preorder Traversal Challenge (Tree Traversal & Recursion)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for N-ary Tree Preorder Traversal Challenge (Tree Traversal & Recursion)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for N-ary Tree Preorder Traversal Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for N-ary Tree Preorder Traversal Challenge (Tree Traversal & Recursion)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for N-ary Tree Preorder Traversal Challenge (Tree Traversal & Recursion)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for N-ary Tree Preorder Traversal Challenge (Tree Traversal & Recursion)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for N-ary Tree Preorder Traversal Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for N-ary Tree Preorder Traversal",
      "cpp_optimal": "// Solution for N-ary Tree Preorder Traversal",
      "java_brute": "// Solution for N-ary Tree Preorder Traversal",
      "java_optimal": "// Solution for N-ary Tree Preorder Traversal",
      "python_brute": "# Solution for N-ary Tree Preorder Traversal",
      "python_optimal": "# Solution for N-ary Tree Preorder Traversal"
    },
    "originalOrder": 221,
    "learningOrder": 221
  },
  {
    "id": 357,
    "number": 357,
    "sequence_number": 357,
    "title": "N-ary Tree Postorder Traversal",
    "slug": "n-ary-tree-postorder-traversal",
    "difficulty": "Easy",
    "topic": "Trees",
    "subtopic": "Tree Traversal & Recursion",
    "pattern": "Tree Traversal & Recursion",
    "secondary_patterns": [
      "Tree Traversal & Recursion"
    ],
    "stage": "Binary Trees & Tree Traversals",
    "curriculumStage": "Stage 8 — Binary Trees & Tree Traversals",
    "roadmapPhase": "Stage 8 — Binary Trees & Tree Traversals",
    "phase": "Stage 8 — Binary Trees & Tree Traversals",
    "estimatedTime": 15,
    "statement": "Solve the **N-ary Tree Postorder Traversal Optimization** problem using the **Tree Traversal & Recursion** technique. Given input constraints appropriate for Easy level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^4",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Tree Traversal & Recursion identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Tree Traversal & Recursion. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Tree Traversal & Recursion techniques by solving Easy problem constraints for N-ary Tree Postorder Traversal Optimization.",
    "whyThisPattern": "When observing binary trees problem conditions, Tree Traversal & Recursion optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "LinkedIn",
      "Amazon"
    ],
    "companyRelevanceTier": "Medium",
    "leetcode_url": "https://leetcode.com/problems/n-ary-tree-postorder-traversal/",
    "leetcode_title": "N-ary Tree Postorder Traversal",
    "leetcode_id": 590,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/n-ary-tree-postorder-traversal/",
    "canonicalSlug": "n-ary-tree-postorder-traversal",
    "canonicalUrl": "https://leetcode.com/problems/n-ary-tree-postorder-traversal/",
    "url": "https://leetcode.com/problems/n-ary-tree-postorder-traversal/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for N-ary Tree Postorder Traversal Optimization (Tree Traversal & Recursion)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for N-ary Tree Postorder Traversal Optimization (Tree Traversal & Recursion)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for N-ary Tree Postorder Traversal Optimization (Tree Traversal & Recursion)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for N-ary Tree Postorder Traversal Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for N-ary Tree Postorder Traversal Optimization (Tree Traversal & Recursion)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for N-ary Tree Postorder Traversal Optimization (Tree Traversal & Recursion)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for N-ary Tree Postorder Traversal Optimization (Tree Traversal & Recursion)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for N-ary Tree Postorder Traversal Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for N-ary Tree Postorder Traversal",
      "cpp_optimal": "// Solution for N-ary Tree Postorder Traversal",
      "java_brute": "// Solution for N-ary Tree Postorder Traversal",
      "java_optimal": "// Solution for N-ary Tree Postorder Traversal",
      "python_brute": "# Solution for N-ary Tree Postorder Traversal",
      "python_optimal": "# Solution for N-ary Tree Postorder Traversal"
    },
    "originalOrder": 222,
    "learningOrder": 222
  },
  {
    "id": 358,
    "number": 358,
    "sequence_number": 358,
    "title": "Merge Two Binary Trees",
    "slug": "merge-two-binary-trees",
    "difficulty": "Easy",
    "topic": "Trees",
    "subtopic": "Tree Traversal & Recursion",
    "pattern": "Tree Traversal & Recursion",
    "secondary_patterns": [
      "Tree Traversal & Recursion"
    ],
    "stage": "Binary Trees & Tree Traversals",
    "curriculumStage": "Stage 8 — Binary Trees & Tree Traversals",
    "roadmapPhase": "Stage 8 — Binary Trees & Tree Traversals",
    "phase": "Stage 8 — Binary Trees & Tree Traversals",
    "estimatedTime": 15,
    "statement": "Solve the **Merge Two Binary Trees Challenge** problem using the **Tree Traversal & Recursion** technique. Given input constraints appropriate for Easy level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^4",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Tree Traversal & Recursion identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Tree Traversal & Recursion. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Tree Traversal & Recursion techniques by solving Easy problem constraints for Merge Two Binary Trees Challenge.",
    "whyThisPattern": "When observing binary trees problem conditions, Tree Traversal & Recursion optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Meta",
      "Uber",
      "Databricks"
    ],
    "companyRelevanceTier": "Medium",
    "leetcode_url": "https://leetcode.com/problems/merge-two-binary-trees/",
    "leetcode_title": "Merge Two Binary Trees",
    "leetcode_id": 617,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/merge-two-binary-trees/",
    "canonicalSlug": "merge-two-binary-trees",
    "canonicalUrl": "https://leetcode.com/problems/merge-two-binary-trees/",
    "url": "https://leetcode.com/problems/merge-two-binary-trees/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Merge Two Binary Trees Challenge (Tree Traversal & Recursion)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Merge Two Binary Trees Challenge (Tree Traversal & Recursion)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Merge Two Binary Trees Challenge (Tree Traversal & Recursion)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Merge Two Binary Trees Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Merge Two Binary Trees Challenge (Tree Traversal & Recursion)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Merge Two Binary Trees Challenge (Tree Traversal & Recursion)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Merge Two Binary Trees Challenge (Tree Traversal & Recursion)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Merge Two Binary Trees Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Merge Two Binary Trees",
      "cpp_optimal": "// Solution for Merge Two Binary Trees",
      "java_brute": "// Solution for Merge Two Binary Trees",
      "java_optimal": "// Solution for Merge Two Binary Trees",
      "python_brute": "# Solution for Merge Two Binary Trees",
      "python_optimal": "# Solution for Merge Two Binary Trees"
    },
    "originalOrder": 223,
    "learningOrder": 223
  },
  {
    "id": 359,
    "number": 359,
    "sequence_number": 359,
    "title": "Average of Levels in Binary Tree",
    "slug": "average-of-levels-in-binary-tree",
    "difficulty": "Easy",
    "topic": "Trees",
    "subtopic": "Tree Traversal & Recursion",
    "pattern": "Tree Traversal & Recursion",
    "secondary_patterns": [
      "Tree Traversal & Recursion"
    ],
    "stage": "Binary Trees & Tree Traversals",
    "curriculumStage": "Stage 8 — Binary Trees & Tree Traversals",
    "roadmapPhase": "Stage 8 — Binary Trees & Tree Traversals",
    "phase": "Stage 8 — Binary Trees & Tree Traversals",
    "estimatedTime": 15,
    "statement": "Solve the **Average of Levels in Binary Tree Challenge** problem using the **Tree Traversal & Recursion** technique. Given input constraints appropriate for Easy level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^4",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Tree Traversal & Recursion identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Tree Traversal & Recursion. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Tree Traversal & Recursion techniques by solving Easy problem constraints for Average of Levels in Binary Tree Challenge.",
    "whyThisPattern": "When observing binary trees problem conditions, Tree Traversal & Recursion optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Amazon",
      "Microsoft",
      "Uber"
    ],
    "companyRelevanceTier": "Medium",
    "leetcode_url": "https://leetcode.com/problems/average-of-levels-in-binary-tree/",
    "leetcode_title": "Average of Levels in Binary Tree",
    "leetcode_id": 637,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/average-of-levels-in-binary-tree/",
    "canonicalSlug": "average-of-levels-in-binary-tree",
    "canonicalUrl": "https://leetcode.com/problems/average-of-levels-in-binary-tree/",
    "url": "https://leetcode.com/problems/average-of-levels-in-binary-tree/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Average of Levels in Binary Tree Challenge (Tree Traversal & Recursion)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Average of Levels in Binary Tree Challenge (Tree Traversal & Recursion)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Average of Levels in Binary Tree Challenge (Tree Traversal & Recursion)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Average of Levels in Binary Tree Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Average of Levels in Binary Tree Challenge (Tree Traversal & Recursion)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Average of Levels in Binary Tree Challenge (Tree Traversal & Recursion)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Average of Levels in Binary Tree Challenge (Tree Traversal & Recursion)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Average of Levels in Binary Tree Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Average of Levels in Binary Tree",
      "cpp_optimal": "// Solution for Average of Levels in Binary Tree",
      "java_brute": "// Solution for Average of Levels in Binary Tree",
      "java_optimal": "// Solution for Average of Levels in Binary Tree",
      "python_brute": "# Solution for Average of Levels in Binary Tree",
      "python_optimal": "# Solution for Average of Levels in Binary Tree"
    },
    "originalOrder": 224,
    "learningOrder": 224
  },
  {
    "id": 360,
    "number": 360,
    "sequence_number": 360,
    "title": "Second Minimum Node In a Binary Tree",
    "slug": "second-minimum-node-in-a-binary-tree",
    "difficulty": "Easy",
    "topic": "Trees",
    "subtopic": "Pointer Manipulation",
    "pattern": "Pointer Manipulation",
    "secondary_patterns": [
      "Pointer Manipulation"
    ],
    "stage": "Binary Trees & Tree Traversals",
    "curriculumStage": "Stage 8 — Binary Trees & Tree Traversals",
    "roadmapPhase": "Stage 8 — Binary Trees & Tree Traversals",
    "phase": "Stage 8 — Binary Trees & Tree Traversals",
    "estimatedTime": 15,
    "statement": "Solve the **Second Minimum Node In a Binary Tree Optimization** problem using the **Pointer Manipulation** technique. Given input constraints appropriate for Easy level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^4",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Pointer Manipulation identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Pointer Manipulation. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Pointer Manipulation techniques by solving Easy problem constraints for Second Minimum Node In a Binary Tree Optimization.",
    "whyThisPattern": "When observing binary trees problem conditions, Pointer Manipulation optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "LinkedIn",
      "Amazon"
    ],
    "companyRelevanceTier": "Medium",
    "leetcode_url": "https://leetcode.com/problems/second-minimum-node-in-a-binary-tree/",
    "leetcode_title": "Second Minimum Node In a Binary Tree",
    "leetcode_id": 671,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/second-minimum-node-in-a-binary-tree/",
    "canonicalSlug": "second-minimum-node-in-a-binary-tree",
    "canonicalUrl": "https://leetcode.com/problems/second-minimum-node-in-a-binary-tree/",
    "url": "https://leetcode.com/problems/second-minimum-node-in-a-binary-tree/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Second Minimum Node In a Binary Tree Optimization (Pointer Manipulation)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Second Minimum Node In a Binary Tree Optimization (Pointer Manipulation)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Second Minimum Node In a Binary Tree Optimization (Pointer Manipulation)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Second Minimum Node In a Binary Tree Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Second Minimum Node In a Binary Tree Optimization (Pointer Manipulation)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Second Minimum Node In a Binary Tree Optimization (Pointer Manipulation)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Second Minimum Node In a Binary Tree Optimization (Pointer Manipulation)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Second Minimum Node In a Binary Tree Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Second Minimum Node In a Binary Tree",
      "cpp_optimal": "// Solution for Second Minimum Node In a Binary Tree",
      "java_brute": "// Solution for Second Minimum Node In a Binary Tree",
      "java_optimal": "// Solution for Second Minimum Node In a Binary Tree",
      "python_brute": "# Solution for Second Minimum Node In a Binary Tree",
      "python_optimal": "# Solution for Second Minimum Node In a Binary Tree"
    },
    "originalOrder": 225,
    "learningOrder": 225
  },
  {
    "id": 361,
    "number": 361,
    "sequence_number": 361,
    "title": "Binary Tree Level Order Traversal",
    "slug": "binary-tree-level-order-traversal",
    "difficulty": "Medium",
    "topic": "Trees",
    "subtopic": "Tree Traversal & Recursion",
    "pattern": "Tree Traversal & Recursion",
    "secondary_patterns": [
      "Tree Traversal & Recursion"
    ],
    "stage": "Binary Trees & Tree Traversals",
    "curriculumStage": "Stage 8 — Binary Trees & Tree Traversals",
    "roadmapPhase": "Stage 8 — Binary Trees & Tree Traversals",
    "phase": "Stage 8 — Binary Trees & Tree Traversals",
    "estimatedTime": 30,
    "statement": "Solve the **Binary Tree Level Order Traversal Challenge** problem using the **Tree Traversal & Recursion** technique. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Tree Traversal & Recursion identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Tree Traversal & Recursion. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Tree Traversal & Recursion techniques by solving Medium problem constraints for Binary Tree Level Order Traversal Challenge.",
    "whyThisPattern": "When observing binary trees problem conditions, Tree Traversal & Recursion optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Meta",
      "Uber",
      "Databricks"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/binary-tree-level-order-traversal/",
    "leetcode_title": "Binary Tree Level Order Traversal",
    "leetcode_id": 102,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/binary-tree-level-order-traversal/",
    "canonicalSlug": "binary-tree-level-order-traversal",
    "canonicalUrl": "https://leetcode.com/problems/binary-tree-level-order-traversal/",
    "url": "https://leetcode.com/problems/binary-tree-level-order-traversal/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Binary Tree Level Order Traversal Challenge (Tree Traversal & Recursion)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Binary Tree Level Order Traversal Challenge (Tree Traversal & Recursion)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Binary Tree Level Order Traversal Challenge (Tree Traversal & Recursion)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Binary Tree Level Order Traversal Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Binary Tree Level Order Traversal Challenge (Tree Traversal & Recursion)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Binary Tree Level Order Traversal Challenge (Tree Traversal & Recursion)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Binary Tree Level Order Traversal Challenge (Tree Traversal & Recursion)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Binary Tree Level Order Traversal Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Binary Tree Level Order Traversal",
      "cpp_optimal": "// Solution for Binary Tree Level Order Traversal",
      "java_brute": "// Solution for Binary Tree Level Order Traversal",
      "java_optimal": "// Solution for Binary Tree Level Order Traversal",
      "python_brute": "# Solution for Binary Tree Level Order Traversal",
      "python_optimal": "# Solution for Binary Tree Level Order Traversal"
    },
    "originalOrder": 624,
    "learningOrder": 624
  },
  {
    "id": 362,
    "number": 362,
    "sequence_number": 362,
    "title": "Binary Tree Zigzag Level Order Traversal",
    "slug": "binary-tree-zigzag-level-order-traversal",
    "difficulty": "Medium",
    "topic": "Trees",
    "subtopic": "Tree Traversal & Recursion",
    "pattern": "Tree Traversal & Recursion",
    "secondary_patterns": [
      "Tree Traversal & Recursion"
    ],
    "stage": "Binary Trees & Tree Traversals",
    "curriculumStage": "Stage 8 — Binary Trees & Tree Traversals",
    "roadmapPhase": "Stage 8 — Binary Trees & Tree Traversals",
    "phase": "Stage 8 — Binary Trees & Tree Traversals",
    "estimatedTime": 30,
    "statement": "Solve the **Binary Tree Zigzag Level Order Traversal Challenge** problem using the **Tree Traversal & Recursion** technique. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Tree Traversal & Recursion identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Tree Traversal & Recursion. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Tree Traversal & Recursion techniques by solving Medium problem constraints for Binary Tree Zigzag Level Order Traversal Challenge.",
    "whyThisPattern": "When observing binary trees problem conditions, Tree Traversal & Recursion optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Amazon",
      "Microsoft",
      "Uber"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/binary-tree-zigzag-level-order-traversal/",
    "leetcode_title": "Binary Tree Zigzag Level Order Traversal",
    "leetcode_id": 103,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/binary-tree-zigzag-level-order-traversal/",
    "canonicalSlug": "binary-tree-zigzag-level-order-traversal",
    "canonicalUrl": "https://leetcode.com/problems/binary-tree-zigzag-level-order-traversal/",
    "url": "https://leetcode.com/problems/binary-tree-zigzag-level-order-traversal/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Binary Tree Zigzag Level Order Traversal Challenge (Tree Traversal & Recursion)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Binary Tree Zigzag Level Order Traversal Challenge (Tree Traversal & Recursion)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Binary Tree Zigzag Level Order Traversal Challenge (Tree Traversal & Recursion)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Binary Tree Zigzag Level Order Traversal Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Binary Tree Zigzag Level Order Traversal Challenge (Tree Traversal & Recursion)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Binary Tree Zigzag Level Order Traversal Challenge (Tree Traversal & Recursion)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Binary Tree Zigzag Level Order Traversal Challenge (Tree Traversal & Recursion)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Binary Tree Zigzag Level Order Traversal Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Binary Tree Zigzag Level Order Traversal",
      "cpp_optimal": "// Solution for Binary Tree Zigzag Level Order Traversal",
      "java_brute": "// Solution for Binary Tree Zigzag Level Order Traversal",
      "java_optimal": "// Solution for Binary Tree Zigzag Level Order Traversal",
      "python_brute": "# Solution for Binary Tree Zigzag Level Order Traversal",
      "python_optimal": "# Solution for Binary Tree Zigzag Level Order Traversal"
    },
    "originalOrder": 625,
    "learningOrder": 625
  },
  {
    "id": 363,
    "number": 363,
    "sequence_number": 363,
    "title": "Construct Binary Tree from Preorder and Inorder Traversal",
    "slug": "construct-binary-tree-from-preorder-and-inorder-traversal",
    "difficulty": "Medium",
    "topic": "Trees",
    "subtopic": "Tree Traversal & Recursion",
    "pattern": "Tree Traversal & Recursion",
    "secondary_patterns": [
      "Tree Traversal & Recursion"
    ],
    "stage": "Binary Trees & Tree Traversals",
    "curriculumStage": "Stage 8 — Binary Trees & Tree Traversals",
    "roadmapPhase": "Stage 8 — Binary Trees & Tree Traversals",
    "phase": "Stage 8 — Binary Trees & Tree Traversals",
    "estimatedTime": 30,
    "statement": "Solve the **Construct Binary Tree from Preorder and Inorder Traversal Challenge** problem using the **Tree Traversal & Recursion** technique. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Tree Traversal & Recursion identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Tree Traversal & Recursion. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Tree Traversal & Recursion techniques by solving Medium problem constraints for Construct Binary Tree from Preorder and Inorder Traversal Challenge.",
    "whyThisPattern": "When observing binary trees problem conditions, Tree Traversal & Recursion optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Microsoft",
      "Bloomberg"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/construct-binary-tree-from-preorder-and-inorder-traversal/",
    "leetcode_title": "Construct Binary Tree from Preorder and Inorder Traversal",
    "leetcode_id": 105,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/construct-binary-tree-from-preorder-and-inorder-traversal/",
    "canonicalSlug": "construct-binary-tree-from-preorder-and-inorder-traversal",
    "canonicalUrl": "https://leetcode.com/problems/construct-binary-tree-from-preorder-and-inorder-traversal/",
    "url": "https://leetcode.com/problems/construct-binary-tree-from-preorder-and-inorder-traversal/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Construct Binary Tree from Preorder and Inorder Traversal Challenge (Tree Traversal & Recursion)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Construct Binary Tree from Preorder and Inorder Traversal Challenge (Tree Traversal & Recursion)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Construct Binary Tree from Preorder and Inorder Traversal Challenge (Tree Traversal & Recursion)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Construct Binary Tree from Preorder and Inorder Traversal Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Construct Binary Tree from Preorder and Inorder Traversal Challenge (Tree Traversal & Recursion)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Construct Binary Tree from Preorder and Inorder Traversal Challenge (Tree Traversal & Recursion)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Construct Binary Tree from Preorder and Inorder Traversal Challenge (Tree Traversal & Recursion)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Construct Binary Tree from Preorder and Inorder Traversal Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Construct Binary Tree from Preorder and Inorder Traversal",
      "cpp_optimal": "// Solution for Construct Binary Tree from Preorder and Inorder Traversal",
      "java_brute": "// Solution for Construct Binary Tree from Preorder and Inorder Traversal",
      "java_optimal": "// Solution for Construct Binary Tree from Preorder and Inorder Traversal",
      "python_brute": "# Solution for Construct Binary Tree from Preorder and Inorder Traversal",
      "python_optimal": "# Solution for Construct Binary Tree from Preorder and Inorder Traversal"
    },
    "originalOrder": 626,
    "learningOrder": 626
  },
  {
    "id": 364,
    "number": 364,
    "sequence_number": 364,
    "title": "Construct Binary Tree from Inorder and Postorder Traversal",
    "slug": "construct-binary-tree-from-inorder-and-postorder-traversal",
    "difficulty": "Medium",
    "topic": "Trees",
    "subtopic": "Tree Traversal & Recursion",
    "pattern": "Tree Traversal & Recursion",
    "secondary_patterns": [
      "Tree Traversal & Recursion"
    ],
    "stage": "Binary Trees & Tree Traversals",
    "curriculumStage": "Stage 8 — Binary Trees & Tree Traversals",
    "roadmapPhase": "Stage 8 — Binary Trees & Tree Traversals",
    "phase": "Stage 8 — Binary Trees & Tree Traversals",
    "estimatedTime": 30,
    "statement": "Solve the **Construct Binary Tree from Inorder and Postorder Traversal Challenge** problem using the **Tree Traversal & Recursion** technique. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Tree Traversal & Recursion identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Tree Traversal & Recursion. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Tree Traversal & Recursion techniques by solving Medium problem constraints for Construct Binary Tree from Inorder and Postorder Traversal Challenge.",
    "whyThisPattern": "When observing binary trees problem conditions, Tree Traversal & Recursion optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Microsoft",
      "Bloomberg",
      "Adobe"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/construct-binary-tree-from-inorder-and-postorder-traversal/",
    "leetcode_title": "Construct Binary Tree from Inorder and Postorder Traversal",
    "leetcode_id": 106,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/construct-binary-tree-from-inorder-and-postorder-traversal/",
    "canonicalSlug": "construct-binary-tree-from-inorder-and-postorder-traversal",
    "canonicalUrl": "https://leetcode.com/problems/construct-binary-tree-from-inorder-and-postorder-traversal/",
    "url": "https://leetcode.com/problems/construct-binary-tree-from-inorder-and-postorder-traversal/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Construct Binary Tree from Inorder and Postorder Traversal Challenge (Tree Traversal & Recursion)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Construct Binary Tree from Inorder and Postorder Traversal Challenge (Tree Traversal & Recursion)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Construct Binary Tree from Inorder and Postorder Traversal Challenge (Tree Traversal & Recursion)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Construct Binary Tree from Inorder and Postorder Traversal Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Construct Binary Tree from Inorder and Postorder Traversal Challenge (Tree Traversal & Recursion)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Construct Binary Tree from Inorder and Postorder Traversal Challenge (Tree Traversal & Recursion)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Construct Binary Tree from Inorder and Postorder Traversal Challenge (Tree Traversal & Recursion)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Construct Binary Tree from Inorder and Postorder Traversal Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Construct Binary Tree from Inorder and Postorder Traversal",
      "cpp_optimal": "// Solution for Construct Binary Tree from Inorder and Postorder Traversal",
      "java_brute": "// Solution for Construct Binary Tree from Inorder and Postorder Traversal",
      "java_optimal": "// Solution for Construct Binary Tree from Inorder and Postorder Traversal",
      "python_brute": "# Solution for Construct Binary Tree from Inorder and Postorder Traversal",
      "python_optimal": "# Solution for Construct Binary Tree from Inorder and Postorder Traversal"
    },
    "originalOrder": 627,
    "learningOrder": 627
  },
  {
    "id": 365,
    "number": 365,
    "sequence_number": 365,
    "title": "Binary Tree Level Order Traversal II",
    "slug": "binary-tree-level-order-traversal-ii",
    "difficulty": "Medium",
    "topic": "Trees",
    "subtopic": "Tree Traversal & Recursion",
    "pattern": "Tree Traversal & Recursion",
    "secondary_patterns": [
      "Tree Traversal & Recursion"
    ],
    "stage": "Binary Trees & Tree Traversals",
    "curriculumStage": "Stage 8 — Binary Trees & Tree Traversals",
    "roadmapPhase": "Stage 8 — Binary Trees & Tree Traversals",
    "phase": "Stage 8 — Binary Trees & Tree Traversals",
    "estimatedTime": 30,
    "statement": "Solve the **Binary Tree Level Order Traversal II Challenge** problem using the **Tree Traversal & Recursion** technique. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Tree Traversal & Recursion identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Tree Traversal & Recursion. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Tree Traversal & Recursion techniques by solving Medium problem constraints for Binary Tree Level Order Traversal II Challenge.",
    "whyThisPattern": "When observing binary trees problem conditions, Tree Traversal & Recursion optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Amazon",
      "Microsoft",
      "Uber"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/binary-tree-level-order-traversal-ii/",
    "leetcode_title": "Binary Tree Level Order Traversal II",
    "leetcode_id": 107,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/binary-tree-level-order-traversal-ii/",
    "canonicalSlug": "binary-tree-level-order-traversal-ii",
    "canonicalUrl": "https://leetcode.com/problems/binary-tree-level-order-traversal-ii/",
    "url": "https://leetcode.com/problems/binary-tree-level-order-traversal-ii/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Binary Tree Level Order Traversal II Challenge (Tree Traversal & Recursion)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Binary Tree Level Order Traversal II Challenge (Tree Traversal & Recursion)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Binary Tree Level Order Traversal II Challenge (Tree Traversal & Recursion)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Binary Tree Level Order Traversal II Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Binary Tree Level Order Traversal II Challenge (Tree Traversal & Recursion)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Binary Tree Level Order Traversal II Challenge (Tree Traversal & Recursion)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Binary Tree Level Order Traversal II Challenge (Tree Traversal & Recursion)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Binary Tree Level Order Traversal II Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Binary Tree Level Order Traversal II",
      "cpp_optimal": "// Solution for Binary Tree Level Order Traversal II",
      "java_brute": "// Solution for Binary Tree Level Order Traversal II",
      "java_optimal": "// Solution for Binary Tree Level Order Traversal II",
      "python_brute": "# Solution for Binary Tree Level Order Traversal II",
      "python_optimal": "# Solution for Binary Tree Level Order Traversal II"
    },
    "originalOrder": 628,
    "learningOrder": 628
  },
  {
    "id": 366,
    "number": 366,
    "sequence_number": 366,
    "title": "Binary Tree Right Side View",
    "slug": "binary-tree-right-side-view",
    "difficulty": "Medium",
    "topic": "Trees",
    "subtopic": "Tree Traversal & Recursion",
    "pattern": "Tree Traversal & Recursion",
    "secondary_patterns": [
      "Tree Traversal & Recursion"
    ],
    "stage": "Binary Trees & Tree Traversals",
    "curriculumStage": "Stage 8 — Binary Trees & Tree Traversals",
    "roadmapPhase": "Stage 8 — Binary Trees & Tree Traversals",
    "phase": "Stage 8 — Binary Trees & Tree Traversals",
    "estimatedTime": 30,
    "statement": "Solve the **Binary Tree Right Side View Optimization** problem using the **Tree Traversal & Recursion** technique. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Tree Traversal & Recursion identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Tree Traversal & Recursion. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Tree Traversal & Recursion techniques by solving Medium problem constraints for Binary Tree Right Side View Optimization.",
    "whyThisPattern": "When observing binary trees problem conditions, Tree Traversal & Recursion optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Apple",
      "Adobe",
      "Atlassian"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/binary-tree-right-side-view/",
    "leetcode_title": "Binary Tree Right Side View",
    "leetcode_id": 199,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/binary-tree-right-side-view/",
    "canonicalSlug": "binary-tree-right-side-view",
    "canonicalUrl": "https://leetcode.com/problems/binary-tree-right-side-view/",
    "url": "https://leetcode.com/problems/binary-tree-right-side-view/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Binary Tree Right Side View Optimization (Tree Traversal & Recursion)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Binary Tree Right Side View Optimization (Tree Traversal & Recursion)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Binary Tree Right Side View Optimization (Tree Traversal & Recursion)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Binary Tree Right Side View Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Binary Tree Right Side View Optimization (Tree Traversal & Recursion)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Binary Tree Right Side View Optimization (Tree Traversal & Recursion)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Binary Tree Right Side View Optimization (Tree Traversal & Recursion)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Binary Tree Right Side View Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Binary Tree Right Side View",
      "cpp_optimal": "// Solution for Binary Tree Right Side View",
      "java_brute": "// Solution for Binary Tree Right Side View",
      "java_optimal": "// Solution for Binary Tree Right Side View",
      "python_brute": "# Solution for Binary Tree Right Side View",
      "python_optimal": "# Solution for Binary Tree Right Side View"
    },
    "originalOrder": 629,
    "learningOrder": 629
  },
  {
    "id": 367,
    "number": 367,
    "sequence_number": 367,
    "title": "Count Complete Tree Nodes",
    "slug": "count-complete-tree-nodes",
    "difficulty": "Medium",
    "topic": "Trees",
    "subtopic": "Pointer Manipulation",
    "pattern": "Pointer Manipulation",
    "secondary_patterns": [
      "Pointer Manipulation"
    ],
    "stage": "Binary Trees & Tree Traversals",
    "curriculumStage": "Stage 8 — Binary Trees & Tree Traversals",
    "roadmapPhase": "Stage 8 — Binary Trees & Tree Traversals",
    "phase": "Stage 8 — Binary Trees & Tree Traversals",
    "estimatedTime": 30,
    "statement": "Solve the **Count Complete Tree Nodes Challenge** problem using the **Pointer Manipulation** technique. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Pointer Manipulation identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Pointer Manipulation. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Pointer Manipulation techniques by solving Medium problem constraints for Count Complete Tree Nodes Challenge.",
    "whyThisPattern": "When observing binary trees problem conditions, Pointer Manipulation optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Microsoft",
      "Bloomberg",
      "Adobe"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/count-complete-tree-nodes/",
    "leetcode_title": "Count Complete Tree Nodes",
    "leetcode_id": 222,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/count-complete-tree-nodes/",
    "canonicalSlug": "count-complete-tree-nodes",
    "canonicalUrl": "https://leetcode.com/problems/count-complete-tree-nodes/",
    "url": "https://leetcode.com/problems/count-complete-tree-nodes/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Count Complete Tree Nodes Challenge (Pointer Manipulation)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Count Complete Tree Nodes Challenge (Pointer Manipulation)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Count Complete Tree Nodes Challenge (Pointer Manipulation)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Count Complete Tree Nodes Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Count Complete Tree Nodes Challenge (Pointer Manipulation)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Count Complete Tree Nodes Challenge (Pointer Manipulation)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Count Complete Tree Nodes Challenge (Pointer Manipulation)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Count Complete Tree Nodes Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Count Complete Tree Nodes",
      "cpp_optimal": "// Solution for Count Complete Tree Nodes",
      "java_brute": "// Solution for Count Complete Tree Nodes",
      "java_optimal": "// Solution for Count Complete Tree Nodes",
      "python_brute": "# Solution for Count Complete Tree Nodes",
      "python_optimal": "# Solution for Count Complete Tree Nodes"
    },
    "originalOrder": 630,
    "learningOrder": 630
  },
  {
    "id": 368,
    "number": 368,
    "sequence_number": 368,
    "title": "Lowest Common Ancestor of a Binary Tree",
    "slug": "lowest-common-ancestor-of-a-binary-tree",
    "difficulty": "Medium",
    "topic": "Trees",
    "subtopic": "Tree Traversal & Recursion",
    "pattern": "Tree Traversal & Recursion",
    "secondary_patterns": [
      "Tree Traversal & Recursion"
    ],
    "stage": "Binary Trees & Tree Traversals",
    "curriculumStage": "Stage 8 — Binary Trees & Tree Traversals",
    "roadmapPhase": "Stage 8 — Binary Trees & Tree Traversals",
    "phase": "Stage 8 — Binary Trees & Tree Traversals",
    "estimatedTime": 30,
    "statement": "Solve the **Lowest Common Ancestor of a Binary Tree Challenge** problem using the **Tree Traversal & Recursion** technique. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Tree Traversal & Recursion identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Tree Traversal & Recursion. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Tree Traversal & Recursion techniques by solving Medium problem constraints for Lowest Common Ancestor of a Binary Tree Challenge.",
    "whyThisPattern": "When observing binary trees problem conditions, Tree Traversal & Recursion optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Amazon",
      "Microsoft",
      "Uber"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/lowest-common-ancestor-of-a-binary-tree/",
    "leetcode_title": "Lowest Common Ancestor of a Binary Tree",
    "leetcode_id": 236,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/lowest-common-ancestor-of-a-binary-tree/",
    "canonicalSlug": "lowest-common-ancestor-of-a-binary-tree",
    "canonicalUrl": "https://leetcode.com/problems/lowest-common-ancestor-of-a-binary-tree/",
    "url": "https://leetcode.com/problems/lowest-common-ancestor-of-a-binary-tree/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Lowest Common Ancestor of a Binary Tree Challenge (Tree Traversal & Recursion)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Lowest Common Ancestor of a Binary Tree Challenge (Tree Traversal & Recursion)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Lowest Common Ancestor of a Binary Tree Challenge (Tree Traversal & Recursion)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Lowest Common Ancestor of a Binary Tree Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Lowest Common Ancestor of a Binary Tree Challenge (Tree Traversal & Recursion)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Lowest Common Ancestor of a Binary Tree Challenge (Tree Traversal & Recursion)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Lowest Common Ancestor of a Binary Tree Challenge (Tree Traversal & Recursion)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Lowest Common Ancestor of a Binary Tree Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Lowest Common Ancestor of a Binary Tree",
      "cpp_optimal": "// Solution for Lowest Common Ancestor of a Binary Tree",
      "java_brute": "// Solution for Lowest Common Ancestor of a Binary Tree",
      "java_optimal": "// Solution for Lowest Common Ancestor of a Binary Tree",
      "python_brute": "# Solution for Lowest Common Ancestor of a Binary Tree",
      "python_optimal": "# Solution for Lowest Common Ancestor of a Binary Tree"
    },
    "originalOrder": 631,
    "learningOrder": 631
  },
  {
    "id": 369,
    "number": 369,
    "sequence_number": 369,
    "title": "Minimum Height Trees",
    "slug": "minimum-height-trees",
    "difficulty": "Medium",
    "topic": "Trees",
    "subtopic": "Tree Traversal & Recursion",
    "pattern": "Tree Traversal & Recursion",
    "secondary_patterns": [
      "Tree Traversal & Recursion"
    ],
    "stage": "Binary Trees & Tree Traversals",
    "curriculumStage": "Stage 8 — Binary Trees & Tree Traversals",
    "roadmapPhase": "Stage 8 — Binary Trees & Tree Traversals",
    "phase": "Stage 8 — Binary Trees & Tree Traversals",
    "estimatedTime": 30,
    "statement": "Solve the **Minimum Height Trees Optimization** problem using the **Tree Traversal & Recursion** technique. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Tree Traversal & Recursion identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Tree Traversal & Recursion. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Tree Traversal & Recursion techniques by solving Medium problem constraints for Minimum Height Trees Optimization.",
    "whyThisPattern": "When observing binary trees problem conditions, Tree Traversal & Recursion optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "LinkedIn",
      "Amazon"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/minimum-height-trees/",
    "leetcode_title": "Minimum Height Trees",
    "leetcode_id": 310,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/minimum-height-trees/",
    "canonicalSlug": "minimum-height-trees",
    "canonicalUrl": "https://leetcode.com/problems/minimum-height-trees/",
    "url": "https://leetcode.com/problems/minimum-height-trees/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Minimum Height Trees Optimization (Tree Traversal & Recursion)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Minimum Height Trees Optimization (Tree Traversal & Recursion)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Minimum Height Trees Optimization (Tree Traversal & Recursion)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Minimum Height Trees Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Minimum Height Trees Optimization (Tree Traversal & Recursion)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Minimum Height Trees Optimization (Tree Traversal & Recursion)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Minimum Height Trees Optimization (Tree Traversal & Recursion)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Minimum Height Trees Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Minimum Height Trees",
      "cpp_optimal": "// Solution for Minimum Height Trees",
      "java_brute": "// Solution for Minimum Height Trees",
      "java_optimal": "// Solution for Minimum Height Trees",
      "python_brute": "# Solution for Minimum Height Trees",
      "python_optimal": "# Solution for Minimum Height Trees"
    },
    "originalOrder": 632,
    "learningOrder": 632
  },
  {
    "id": 370,
    "number": 370,
    "sequence_number": 370,
    "title": "Verify Preorder Serialization of a Binary Tree",
    "slug": "verify-preorder-serialization-of-a-binary-tree",
    "difficulty": "Medium",
    "topic": "Trees",
    "subtopic": "Tree Traversal & Recursion",
    "pattern": "Tree Traversal & Recursion",
    "secondary_patterns": [
      "Tree Traversal & Recursion"
    ],
    "stage": "Binary Trees & Tree Traversals",
    "curriculumStage": "Stage 8 — Binary Trees & Tree Traversals",
    "roadmapPhase": "Stage 8 — Binary Trees & Tree Traversals",
    "phase": "Stage 8 — Binary Trees & Tree Traversals",
    "estimatedTime": 30,
    "statement": "Solve the **Verify Preorder Serialization of a Binary Tree Optimization** problem using the **Tree Traversal & Recursion** technique. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Tree Traversal & Recursion identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Tree Traversal & Recursion. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Tree Traversal & Recursion techniques by solving Medium problem constraints for Verify Preorder Serialization of a Binary Tree Optimization.",
    "whyThisPattern": "When observing binary trees problem conditions, Tree Traversal & Recursion optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "LinkedIn",
      "Amazon"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/verify-preorder-serialization-of-a-binary-tree/",
    "leetcode_title": "Verify Preorder Serialization of a Binary Tree",
    "leetcode_id": 331,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/verify-preorder-serialization-of-a-binary-tree/",
    "canonicalSlug": "verify-preorder-serialization-of-a-binary-tree",
    "canonicalUrl": "https://leetcode.com/problems/verify-preorder-serialization-of-a-binary-tree/",
    "url": "https://leetcode.com/problems/verify-preorder-serialization-of-a-binary-tree/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Verify Preorder Serialization of a Binary Tree Optimization (Tree Traversal & Recursion)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Verify Preorder Serialization of a Binary Tree Optimization (Tree Traversal & Recursion)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Verify Preorder Serialization of a Binary Tree Optimization (Tree Traversal & Recursion)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Verify Preorder Serialization of a Binary Tree Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Verify Preorder Serialization of a Binary Tree Optimization (Tree Traversal & Recursion)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Verify Preorder Serialization of a Binary Tree Optimization (Tree Traversal & Recursion)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Verify Preorder Serialization of a Binary Tree Optimization (Tree Traversal & Recursion)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Verify Preorder Serialization of a Binary Tree Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Verify Preorder Serialization of a Binary Tree",
      "cpp_optimal": "// Solution for Verify Preorder Serialization of a Binary Tree",
      "java_brute": "// Solution for Verify Preorder Serialization of a Binary Tree",
      "java_optimal": "// Solution for Verify Preorder Serialization of a Binary Tree",
      "python_brute": "# Solution for Verify Preorder Serialization of a Binary Tree",
      "python_optimal": "# Solution for Verify Preorder Serialization of a Binary Tree"
    },
    "originalOrder": 633,
    "learningOrder": 633
  },
  {
    "id": 371,
    "number": 371,
    "sequence_number": 371,
    "title": "Construct Quad Tree",
    "slug": "construct-quad-tree",
    "difficulty": "Medium",
    "topic": "Trees",
    "subtopic": "Tree Traversal & Recursion",
    "pattern": "Tree Traversal & Recursion",
    "secondary_patterns": [
      "Tree Traversal & Recursion"
    ],
    "stage": "Binary Trees & Tree Traversals",
    "curriculumStage": "Stage 8 — Binary Trees & Tree Traversals",
    "roadmapPhase": "Stage 8 — Binary Trees & Tree Traversals",
    "phase": "Stage 8 — Binary Trees & Tree Traversals",
    "estimatedTime": 30,
    "statement": "Solve the **Construct Quad Tree Optimization** problem using the **Tree Traversal & Recursion** technique. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Tree Traversal & Recursion identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Tree Traversal & Recursion. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Tree Traversal & Recursion techniques by solving Medium problem constraints for Construct Quad Tree Optimization.",
    "whyThisPattern": "When observing binary trees problem conditions, Tree Traversal & Recursion optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Apple",
      "Adobe",
      "Atlassian"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/construct-quad-tree/",
    "leetcode_title": "Construct Quad Tree",
    "leetcode_id": 427,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/construct-quad-tree/",
    "canonicalSlug": "construct-quad-tree",
    "canonicalUrl": "https://leetcode.com/problems/construct-quad-tree/",
    "url": "https://leetcode.com/problems/construct-quad-tree/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Construct Quad Tree Optimization (Tree Traversal & Recursion)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Construct Quad Tree Optimization (Tree Traversal & Recursion)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Construct Quad Tree Optimization (Tree Traversal & Recursion)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Construct Quad Tree Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Construct Quad Tree Optimization (Tree Traversal & Recursion)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Construct Quad Tree Optimization (Tree Traversal & Recursion)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Construct Quad Tree Optimization (Tree Traversal & Recursion)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Construct Quad Tree Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Construct Quad Tree",
      "cpp_optimal": "// Solution for Construct Quad Tree",
      "java_brute": "// Solution for Construct Quad Tree",
      "java_optimal": "// Solution for Construct Quad Tree",
      "python_brute": "# Solution for Construct Quad Tree",
      "python_optimal": "# Solution for Construct Quad Tree"
    },
    "originalOrder": 634,
    "learningOrder": 634
  },
  {
    "id": 372,
    "number": 372,
    "sequence_number": 372,
    "title": "N-ary Tree Level Order Traversal",
    "slug": "n-ary-tree-level-order-traversal",
    "difficulty": "Medium",
    "topic": "Trees",
    "subtopic": "Tree Traversal & Recursion",
    "pattern": "Tree Traversal & Recursion",
    "secondary_patterns": [
      "Tree Traversal & Recursion"
    ],
    "stage": "Binary Trees & Tree Traversals",
    "curriculumStage": "Stage 8 — Binary Trees & Tree Traversals",
    "roadmapPhase": "Stage 8 — Binary Trees & Tree Traversals",
    "phase": "Stage 8 — Binary Trees & Tree Traversals",
    "estimatedTime": 30,
    "statement": "Solve the **N-ary Tree Level Order Traversal Challenge** problem using the **Tree Traversal & Recursion** technique. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Tree Traversal & Recursion identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Tree Traversal & Recursion. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Tree Traversal & Recursion techniques by solving Medium problem constraints for N-ary Tree Level Order Traversal Challenge.",
    "whyThisPattern": "When observing binary trees problem conditions, Tree Traversal & Recursion optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Microsoft",
      "Bloomberg",
      "Adobe"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/n-ary-tree-level-order-traversal/",
    "leetcode_title": "N-ary Tree Level Order Traversal",
    "leetcode_id": 429,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/n-ary-tree-level-order-traversal/",
    "canonicalSlug": "n-ary-tree-level-order-traversal",
    "canonicalUrl": "https://leetcode.com/problems/n-ary-tree-level-order-traversal/",
    "url": "https://leetcode.com/problems/n-ary-tree-level-order-traversal/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for N-ary Tree Level Order Traversal Challenge (Tree Traversal & Recursion)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for N-ary Tree Level Order Traversal Challenge (Tree Traversal & Recursion)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for N-ary Tree Level Order Traversal Challenge (Tree Traversal & Recursion)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for N-ary Tree Level Order Traversal Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for N-ary Tree Level Order Traversal Challenge (Tree Traversal & Recursion)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for N-ary Tree Level Order Traversal Challenge (Tree Traversal & Recursion)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for N-ary Tree Level Order Traversal Challenge (Tree Traversal & Recursion)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for N-ary Tree Level Order Traversal Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for N-ary Tree Level Order Traversal",
      "cpp_optimal": "// Solution for N-ary Tree Level Order Traversal",
      "java_brute": "// Solution for N-ary Tree Level Order Traversal",
      "java_optimal": "// Solution for N-ary Tree Level Order Traversal",
      "python_brute": "# Solution for N-ary Tree Level Order Traversal",
      "python_optimal": "# Solution for N-ary Tree Level Order Traversal"
    },
    "originalOrder": 635,
    "learningOrder": 635
  },
  {
    "id": 373,
    "number": 373,
    "sequence_number": 373,
    "title": "Most Frequent Subtree Sum",
    "slug": "most-frequent-subtree-sum",
    "difficulty": "Medium",
    "topic": "Trees",
    "subtopic": "Tree Traversal & Recursion",
    "pattern": "Tree Traversal & Recursion",
    "secondary_patterns": [
      "Tree Traversal & Recursion"
    ],
    "stage": "Binary Trees & Tree Traversals",
    "curriculumStage": "Stage 8 — Binary Trees & Tree Traversals",
    "roadmapPhase": "Stage 8 — Binary Trees & Tree Traversals",
    "phase": "Stage 8 — Binary Trees & Tree Traversals",
    "estimatedTime": 30,
    "statement": "Solve the **Most Frequent Subtree Sum Optimization** problem using the **Tree Traversal & Recursion** technique. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Tree Traversal & Recursion identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Tree Traversal & Recursion. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Tree Traversal & Recursion techniques by solving Medium problem constraints for Most Frequent Subtree Sum Optimization.",
    "whyThisPattern": "When observing binary trees problem conditions, Tree Traversal & Recursion optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "LinkedIn",
      "Amazon"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/most-frequent-subtree-sum/",
    "leetcode_title": "Most Frequent Subtree Sum",
    "leetcode_id": 508,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/most-frequent-subtree-sum/",
    "canonicalSlug": "most-frequent-subtree-sum",
    "canonicalUrl": "https://leetcode.com/problems/most-frequent-subtree-sum/",
    "url": "https://leetcode.com/problems/most-frequent-subtree-sum/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Most Frequent Subtree Sum Optimization (Tree Traversal & Recursion)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Most Frequent Subtree Sum Optimization (Tree Traversal & Recursion)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Most Frequent Subtree Sum Optimization (Tree Traversal & Recursion)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Most Frequent Subtree Sum Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Most Frequent Subtree Sum Optimization (Tree Traversal & Recursion)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Most Frequent Subtree Sum Optimization (Tree Traversal & Recursion)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Most Frequent Subtree Sum Optimization (Tree Traversal & Recursion)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Most Frequent Subtree Sum Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Most Frequent Subtree Sum",
      "cpp_optimal": "// Solution for Most Frequent Subtree Sum",
      "java_brute": "// Solution for Most Frequent Subtree Sum",
      "java_optimal": "// Solution for Most Frequent Subtree Sum",
      "python_brute": "# Solution for Most Frequent Subtree Sum",
      "python_optimal": "# Solution for Most Frequent Subtree Sum"
    },
    "originalOrder": 636,
    "learningOrder": 636
  },
  {
    "id": 374,
    "number": 374,
    "sequence_number": 374,
    "title": "Find Bottom Left Tree Value",
    "slug": "find-bottom-left-tree-value",
    "difficulty": "Medium",
    "topic": "Trees",
    "subtopic": "Tree Traversal & Recursion",
    "pattern": "Tree Traversal & Recursion",
    "secondary_patterns": [
      "Tree Traversal & Recursion"
    ],
    "stage": "Binary Trees & Tree Traversals",
    "curriculumStage": "Stage 8 — Binary Trees & Tree Traversals",
    "roadmapPhase": "Stage 8 — Binary Trees & Tree Traversals",
    "phase": "Stage 8 — Binary Trees & Tree Traversals",
    "estimatedTime": 30,
    "statement": "Solve the **Find Bottom Left Tree Value Optimization** problem using the **Tree Traversal & Recursion** technique. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Tree Traversal & Recursion identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Tree Traversal & Recursion. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Tree Traversal & Recursion techniques by solving Medium problem constraints for Find Bottom Left Tree Value Optimization.",
    "whyThisPattern": "When observing binary trees problem conditions, Tree Traversal & Recursion optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/find-bottom-left-tree-value/",
    "leetcode_title": "Find Bottom Left Tree Value",
    "leetcode_id": 513,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/find-bottom-left-tree-value/",
    "canonicalSlug": "find-bottom-left-tree-value",
    "canonicalUrl": "https://leetcode.com/problems/find-bottom-left-tree-value/",
    "url": "https://leetcode.com/problems/find-bottom-left-tree-value/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Find Bottom Left Tree Value Optimization (Tree Traversal & Recursion)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Find Bottom Left Tree Value Optimization (Tree Traversal & Recursion)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Find Bottom Left Tree Value Optimization (Tree Traversal & Recursion)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Find Bottom Left Tree Value Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Find Bottom Left Tree Value Optimization (Tree Traversal & Recursion)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Find Bottom Left Tree Value Optimization (Tree Traversal & Recursion)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Find Bottom Left Tree Value Optimization (Tree Traversal & Recursion)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Find Bottom Left Tree Value Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Find Bottom Left Tree Value",
      "cpp_optimal": "// Solution for Find Bottom Left Tree Value",
      "java_brute": "// Solution for Find Bottom Left Tree Value",
      "java_optimal": "// Solution for Find Bottom Left Tree Value",
      "python_brute": "# Solution for Find Bottom Left Tree Value",
      "python_optimal": "# Solution for Find Bottom Left Tree Value"
    },
    "originalOrder": 637,
    "learningOrder": 637
  },
  {
    "id": 375,
    "number": 375,
    "sequence_number": 375,
    "title": "Find Largest Value in Each Tree Row",
    "slug": "find-largest-value-in-each-tree-row",
    "difficulty": "Medium",
    "topic": "Trees",
    "subtopic": "Tree Traversal & Recursion",
    "pattern": "Tree Traversal & Recursion",
    "secondary_patterns": [
      "Tree Traversal & Recursion"
    ],
    "stage": "Binary Trees & Tree Traversals",
    "curriculumStage": "Stage 8 — Binary Trees & Tree Traversals",
    "roadmapPhase": "Stage 8 — Binary Trees & Tree Traversals",
    "phase": "Stage 8 — Binary Trees & Tree Traversals",
    "estimatedTime": 30,
    "statement": "Solve the **Find Largest Value in Each Tree Row Challenge** problem using the **Tree Traversal & Recursion** technique. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Tree Traversal & Recursion identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Tree Traversal & Recursion. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Tree Traversal & Recursion techniques by solving Medium problem constraints for Find Largest Value in Each Tree Row Challenge.",
    "whyThisPattern": "When observing binary trees problem conditions, Tree Traversal & Recursion optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Amazon",
      "Microsoft",
      "Uber"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/find-largest-value-in-each-tree-row/",
    "leetcode_title": "Find Largest Value in Each Tree Row",
    "leetcode_id": 515,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/find-largest-value-in-each-tree-row/",
    "canonicalSlug": "find-largest-value-in-each-tree-row",
    "canonicalUrl": "https://leetcode.com/problems/find-largest-value-in-each-tree-row/",
    "url": "https://leetcode.com/problems/find-largest-value-in-each-tree-row/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Find Largest Value in Each Tree Row Challenge (Tree Traversal & Recursion)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Find Largest Value in Each Tree Row Challenge (Tree Traversal & Recursion)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Find Largest Value in Each Tree Row Challenge (Tree Traversal & Recursion)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Find Largest Value in Each Tree Row Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Find Largest Value in Each Tree Row Challenge (Tree Traversal & Recursion)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Find Largest Value in Each Tree Row Challenge (Tree Traversal & Recursion)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Find Largest Value in Each Tree Row Challenge (Tree Traversal & Recursion)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Find Largest Value in Each Tree Row Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Find Largest Value in Each Tree Row",
      "cpp_optimal": "// Solution for Find Largest Value in Each Tree Row",
      "java_brute": "// Solution for Find Largest Value in Each Tree Row",
      "java_optimal": "// Solution for Find Largest Value in Each Tree Row",
      "python_brute": "# Solution for Find Largest Value in Each Tree Row",
      "python_optimal": "# Solution for Find Largest Value in Each Tree Row"
    },
    "originalOrder": 638,
    "learningOrder": 638
  },
  {
    "id": 376,
    "number": 376,
    "sequence_number": 376,
    "title": "Logical OR of Two Binary Grids Represented as Quad-Trees",
    "slug": "logical-or-of-two-binary-grids-represented-as-quad-trees",
    "difficulty": "Medium",
    "topic": "Trees",
    "subtopic": "Tree Traversal & Recursion",
    "pattern": "Tree Traversal & Recursion",
    "secondary_patterns": [
      "Tree Traversal & Recursion"
    ],
    "stage": "Binary Trees & Tree Traversals",
    "curriculumStage": "Stage 8 — Binary Trees & Tree Traversals",
    "roadmapPhase": "Stage 8 — Binary Trees & Tree Traversals",
    "phase": "Stage 8 — Binary Trees & Tree Traversals",
    "estimatedTime": 30,
    "statement": "Solve the **Logical OR of Two Binary Grids Represented as Quad-Trees Challenge** problem using the **Tree Traversal & Recursion** technique. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Tree Traversal & Recursion identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Tree Traversal & Recursion. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Tree Traversal & Recursion techniques by solving Medium problem constraints for Logical OR of Two Binary Grids Represented as Quad-Trees Challenge.",
    "whyThisPattern": "When observing binary trees problem conditions, Tree Traversal & Recursion optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Microsoft",
      "Bloomberg",
      "Adobe"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/logical-or-of-two-binary-grids-represented-as-quad-trees/",
    "leetcode_title": "Logical OR of Two Binary Grids Represented as Quad-Trees",
    "leetcode_id": 558,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/logical-or-of-two-binary-grids-represented-as-quad-trees/",
    "canonicalSlug": "logical-or-of-two-binary-grids-represented-as-quad-trees",
    "canonicalUrl": "https://leetcode.com/problems/logical-or-of-two-binary-grids-represented-as-quad-trees/",
    "url": "https://leetcode.com/problems/logical-or-of-two-binary-grids-represented-as-quad-trees/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Logical OR of Two Binary Grids Represented as Quad-Trees Challenge (Tree Traversal & Recursion)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Logical OR of Two Binary Grids Represented as Quad-Trees Challenge (Tree Traversal & Recursion)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Logical OR of Two Binary Grids Represented as Quad-Trees Challenge (Tree Traversal & Recursion)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Logical OR of Two Binary Grids Represented as Quad-Trees Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Logical OR of Two Binary Grids Represented as Quad-Trees Challenge (Tree Traversal & Recursion)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Logical OR of Two Binary Grids Represented as Quad-Trees Challenge (Tree Traversal & Recursion)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Logical OR of Two Binary Grids Represented as Quad-Trees Challenge (Tree Traversal & Recursion)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Logical OR of Two Binary Grids Represented as Quad-Trees Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Logical OR of Two Binary Grids Represented as Quad-Trees",
      "cpp_optimal": "// Solution for Logical OR of Two Binary Grids Represented as Quad-Trees",
      "java_brute": "// Solution for Logical OR of Two Binary Grids Represented as Quad-Trees",
      "java_optimal": "// Solution for Logical OR of Two Binary Grids Represented as Quad-Trees",
      "python_brute": "# Solution for Logical OR of Two Binary Grids Represented as Quad-Trees",
      "python_optimal": "# Solution for Logical OR of Two Binary Grids Represented as Quad-Trees"
    },
    "originalOrder": 639,
    "learningOrder": 639
  },
  {
    "id": 377,
    "number": 377,
    "sequence_number": 377,
    "title": "Tree Node",
    "slug": "tree-node",
    "difficulty": "Medium",
    "topic": "Trees",
    "subtopic": "Pointer Manipulation",
    "pattern": "Pointer Manipulation",
    "secondary_patterns": [
      "Pointer Manipulation"
    ],
    "stage": "Binary Trees & Tree Traversals",
    "curriculumStage": "Stage 8 — Binary Trees & Tree Traversals",
    "roadmapPhase": "Stage 8 — Binary Trees & Tree Traversals",
    "phase": "Stage 8 — Binary Trees & Tree Traversals",
    "estimatedTime": 30,
    "statement": "Solve the **Tree Node Optimization** problem using the **Pointer Manipulation** technique. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Pointer Manipulation identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Pointer Manipulation. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Pointer Manipulation techniques by solving Medium problem constraints for Tree Node Optimization.",
    "whyThisPattern": "When observing binary trees problem conditions, Pointer Manipulation optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/tree-node/",
    "leetcode_title": "Tree Node",
    "leetcode_id": 608,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/tree-node/",
    "canonicalSlug": "tree-node",
    "canonicalUrl": "https://leetcode.com/problems/tree-node/",
    "url": "https://leetcode.com/problems/tree-node/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Tree Node Optimization (Pointer Manipulation)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Tree Node Optimization (Pointer Manipulation)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Tree Node Optimization (Pointer Manipulation)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Tree Node Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Tree Node Optimization (Pointer Manipulation)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Tree Node Optimization (Pointer Manipulation)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Tree Node Optimization (Pointer Manipulation)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Tree Node Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Tree Node",
      "cpp_optimal": "// Solution for Tree Node",
      "java_brute": "// Solution for Tree Node",
      "java_optimal": "// Solution for Tree Node",
      "python_brute": "# Solution for Tree Node",
      "python_optimal": "# Solution for Tree Node"
    },
    "originalOrder": 640,
    "learningOrder": 640
  },
  {
    "id": 378,
    "number": 378,
    "sequence_number": 378,
    "title": "Add One Row to Tree",
    "slug": "add-one-row-to-tree",
    "difficulty": "Medium",
    "topic": "Trees",
    "subtopic": "Tree Traversal & Recursion",
    "pattern": "Tree Traversal & Recursion",
    "secondary_patterns": [
      "Tree Traversal & Recursion"
    ],
    "stage": "Binary Trees & Tree Traversals",
    "curriculumStage": "Stage 8 — Binary Trees & Tree Traversals",
    "roadmapPhase": "Stage 8 — Binary Trees & Tree Traversals",
    "phase": "Stage 8 — Binary Trees & Tree Traversals",
    "estimatedTime": 30,
    "statement": "Solve the **Add One Row to Tree Optimization** problem using the **Tree Traversal & Recursion** technique. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Tree Traversal & Recursion identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Tree Traversal & Recursion. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Tree Traversal & Recursion techniques by solving Medium problem constraints for Add One Row to Tree Optimization.",
    "whyThisPattern": "When observing binary trees problem conditions, Tree Traversal & Recursion optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Apple",
      "Adobe",
      "Atlassian"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/add-one-row-to-tree/",
    "leetcode_title": "Add One Row to Tree",
    "leetcode_id": 623,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/add-one-row-to-tree/",
    "canonicalSlug": "add-one-row-to-tree",
    "canonicalUrl": "https://leetcode.com/problems/add-one-row-to-tree/",
    "url": "https://leetcode.com/problems/add-one-row-to-tree/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Add One Row to Tree Optimization (Tree Traversal & Recursion)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Add One Row to Tree Optimization (Tree Traversal & Recursion)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Add One Row to Tree Optimization (Tree Traversal & Recursion)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Add One Row to Tree Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Add One Row to Tree Optimization (Tree Traversal & Recursion)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Add One Row to Tree Optimization (Tree Traversal & Recursion)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Add One Row to Tree Optimization (Tree Traversal & Recursion)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Add One Row to Tree Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Add One Row to Tree",
      "cpp_optimal": "// Solution for Add One Row to Tree",
      "java_brute": "// Solution for Add One Row to Tree",
      "java_optimal": "// Solution for Add One Row to Tree",
      "python_brute": "# Solution for Add One Row to Tree",
      "python_optimal": "# Solution for Add One Row to Tree"
    },
    "originalOrder": 641,
    "learningOrder": 641
  },
  {
    "id": 379,
    "number": 379,
    "sequence_number": 379,
    "title": "Find Duplicate Subtrees",
    "slug": "find-duplicate-subtrees",
    "difficulty": "Medium",
    "topic": "Trees",
    "subtopic": "Tree Traversal & Recursion",
    "pattern": "Tree Traversal & Recursion",
    "secondary_patterns": [
      "Tree Traversal & Recursion"
    ],
    "stage": "Binary Trees & Tree Traversals",
    "curriculumStage": "Stage 8 — Binary Trees & Tree Traversals",
    "roadmapPhase": "Stage 8 — Binary Trees & Tree Traversals",
    "phase": "Stage 8 — Binary Trees & Tree Traversals",
    "estimatedTime": 30,
    "statement": "Solve the **Find Duplicate Subtrees Optimization** problem using the **Tree Traversal & Recursion** technique. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Tree Traversal & Recursion identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Tree Traversal & Recursion. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Tree Traversal & Recursion techniques by solving Medium problem constraints for Find Duplicate Subtrees Optimization.",
    "whyThisPattern": "When observing binary trees problem conditions, Tree Traversal & Recursion optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Apple",
      "Adobe",
      "Atlassian"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/find-duplicate-subtrees/",
    "leetcode_title": "Find Duplicate Subtrees",
    "leetcode_id": 652,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/find-duplicate-subtrees/",
    "canonicalSlug": "find-duplicate-subtrees",
    "canonicalUrl": "https://leetcode.com/problems/find-duplicate-subtrees/",
    "url": "https://leetcode.com/problems/find-duplicate-subtrees/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Find Duplicate Subtrees Optimization (Tree Traversal & Recursion)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Find Duplicate Subtrees Optimization (Tree Traversal & Recursion)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Find Duplicate Subtrees Optimization (Tree Traversal & Recursion)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Find Duplicate Subtrees Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Find Duplicate Subtrees Optimization (Tree Traversal & Recursion)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Find Duplicate Subtrees Optimization (Tree Traversal & Recursion)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Find Duplicate Subtrees Optimization (Tree Traversal & Recursion)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Find Duplicate Subtrees Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Find Duplicate Subtrees",
      "cpp_optimal": "// Solution for Find Duplicate Subtrees",
      "java_brute": "// Solution for Find Duplicate Subtrees",
      "java_optimal": "// Solution for Find Duplicate Subtrees",
      "python_brute": "# Solution for Find Duplicate Subtrees",
      "python_optimal": "# Solution for Find Duplicate Subtrees"
    },
    "originalOrder": 642,
    "learningOrder": 642
  },
  {
    "id": 380,
    "number": 380,
    "sequence_number": 380,
    "title": "Maximum Binary Tree",
    "slug": "maximum-binary-tree",
    "difficulty": "Medium",
    "topic": "Trees",
    "subtopic": "Tree Traversal & Recursion",
    "pattern": "Tree Traversal & Recursion",
    "secondary_patterns": [
      "Tree Traversal & Recursion"
    ],
    "stage": "Binary Trees & Tree Traversals",
    "curriculumStage": "Stage 8 — Binary Trees & Tree Traversals",
    "roadmapPhase": "Stage 8 — Binary Trees & Tree Traversals",
    "phase": "Stage 8 — Binary Trees & Tree Traversals",
    "estimatedTime": 30,
    "statement": "Solve the **Maximum Binary Tree Challenge** problem using the **Tree Traversal & Recursion** technique. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Tree Traversal & Recursion identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Tree Traversal & Recursion. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Tree Traversal & Recursion techniques by solving Medium problem constraints for Maximum Binary Tree Challenge.",
    "whyThisPattern": "When observing binary trees problem conditions, Tree Traversal & Recursion optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Meta",
      "Uber",
      "Databricks"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/maximum-binary-tree/",
    "leetcode_title": "Maximum Binary Tree",
    "leetcode_id": 654,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/maximum-binary-tree/",
    "canonicalSlug": "maximum-binary-tree",
    "canonicalUrl": "https://leetcode.com/problems/maximum-binary-tree/",
    "url": "https://leetcode.com/problems/maximum-binary-tree/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Maximum Binary Tree Challenge (Tree Traversal & Recursion)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Maximum Binary Tree Challenge (Tree Traversal & Recursion)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Maximum Binary Tree Challenge (Tree Traversal & Recursion)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Maximum Binary Tree Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Maximum Binary Tree Challenge (Tree Traversal & Recursion)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Maximum Binary Tree Challenge (Tree Traversal & Recursion)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Maximum Binary Tree Challenge (Tree Traversal & Recursion)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Maximum Binary Tree Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Maximum Binary Tree",
      "cpp_optimal": "// Solution for Maximum Binary Tree",
      "java_brute": "// Solution for Maximum Binary Tree",
      "java_optimal": "// Solution for Maximum Binary Tree",
      "python_brute": "# Solution for Maximum Binary Tree",
      "python_optimal": "# Solution for Maximum Binary Tree"
    },
    "originalOrder": 643,
    "learningOrder": 643
  },
  {
    "id": 381,
    "number": 381,
    "sequence_number": 381,
    "title": "Print Binary Tree",
    "slug": "print-binary-tree",
    "difficulty": "Medium",
    "topic": "Trees",
    "subtopic": "Tree Traversal & Recursion",
    "pattern": "Tree Traversal & Recursion",
    "secondary_patterns": [
      "Tree Traversal & Recursion"
    ],
    "stage": "Binary Trees & Tree Traversals",
    "curriculumStage": "Stage 8 — Binary Trees & Tree Traversals",
    "roadmapPhase": "Stage 8 — Binary Trees & Tree Traversals",
    "phase": "Stage 8 — Binary Trees & Tree Traversals",
    "estimatedTime": 30,
    "statement": "Solve the **Print Binary Tree Optimization** problem using the **Tree Traversal & Recursion** technique. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Tree Traversal & Recursion identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Tree Traversal & Recursion. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Tree Traversal & Recursion techniques by solving Medium problem constraints for Print Binary Tree Optimization.",
    "whyThisPattern": "When observing binary trees problem conditions, Tree Traversal & Recursion optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/print-binary-tree/",
    "leetcode_title": "Print Binary Tree",
    "leetcode_id": 655,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/print-binary-tree/",
    "canonicalSlug": "print-binary-tree",
    "canonicalUrl": "https://leetcode.com/problems/print-binary-tree/",
    "url": "https://leetcode.com/problems/print-binary-tree/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Print Binary Tree Optimization (Tree Traversal & Recursion)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Print Binary Tree Optimization (Tree Traversal & Recursion)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Print Binary Tree Optimization (Tree Traversal & Recursion)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Print Binary Tree Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Print Binary Tree Optimization (Tree Traversal & Recursion)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Print Binary Tree Optimization (Tree Traversal & Recursion)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Print Binary Tree Optimization (Tree Traversal & Recursion)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Print Binary Tree Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Print Binary Tree",
      "cpp_optimal": "// Solution for Print Binary Tree",
      "java_brute": "// Solution for Print Binary Tree",
      "java_optimal": "// Solution for Print Binary Tree",
      "python_brute": "# Solution for Print Binary Tree",
      "python_optimal": "# Solution for Print Binary Tree"
    },
    "originalOrder": 644,
    "learningOrder": 644
  },
  {
    "id": 382,
    "number": 382,
    "sequence_number": 382,
    "title": "Maximum Width of Binary Tree",
    "slug": "maximum-width-of-binary-tree",
    "difficulty": "Medium",
    "topic": "Trees",
    "subtopic": "Tree Traversal & Recursion",
    "pattern": "Tree Traversal & Recursion",
    "secondary_patterns": [
      "Tree Traversal & Recursion"
    ],
    "stage": "Binary Trees & Tree Traversals",
    "curriculumStage": "Stage 8 — Binary Trees & Tree Traversals",
    "roadmapPhase": "Stage 8 — Binary Trees & Tree Traversals",
    "phase": "Stage 8 — Binary Trees & Tree Traversals",
    "estimatedTime": 30,
    "statement": "Solve the **Maximum Width of Binary Tree Optimization** problem using the **Tree Traversal & Recursion** technique. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Tree Traversal & Recursion identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Tree Traversal & Recursion. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Tree Traversal & Recursion techniques by solving Medium problem constraints for Maximum Width of Binary Tree Optimization.",
    "whyThisPattern": "When observing binary trees problem conditions, Tree Traversal & Recursion optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "LinkedIn",
      "Amazon"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/maximum-width-of-binary-tree/",
    "leetcode_title": "Maximum Width of Binary Tree",
    "leetcode_id": 662,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/maximum-width-of-binary-tree/",
    "canonicalSlug": "maximum-width-of-binary-tree",
    "canonicalUrl": "https://leetcode.com/problems/maximum-width-of-binary-tree/",
    "url": "https://leetcode.com/problems/maximum-width-of-binary-tree/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Maximum Width of Binary Tree Optimization (Tree Traversal & Recursion)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Maximum Width of Binary Tree Optimization (Tree Traversal & Recursion)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Maximum Width of Binary Tree Optimization (Tree Traversal & Recursion)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Maximum Width of Binary Tree Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Maximum Width of Binary Tree Optimization (Tree Traversal & Recursion)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Maximum Width of Binary Tree Optimization (Tree Traversal & Recursion)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Maximum Width of Binary Tree Optimization (Tree Traversal & Recursion)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Maximum Width of Binary Tree Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Maximum Width of Binary Tree",
      "cpp_optimal": "// Solution for Maximum Width of Binary Tree",
      "java_brute": "// Solution for Maximum Width of Binary Tree",
      "java_optimal": "// Solution for Maximum Width of Binary Tree",
      "python_brute": "# Solution for Maximum Width of Binary Tree",
      "python_optimal": "# Solution for Maximum Width of Binary Tree"
    },
    "originalOrder": 645,
    "learningOrder": 645
  },
  {
    "id": 383,
    "number": 383,
    "sequence_number": 383,
    "title": "Binary Tree Pruning",
    "slug": "binary-tree-pruning",
    "difficulty": "Medium",
    "topic": "Trees",
    "subtopic": "Tree Traversal & Recursion",
    "pattern": "Tree Traversal & Recursion",
    "secondary_patterns": [
      "Tree Traversal & Recursion"
    ],
    "stage": "Binary Trees & Tree Traversals",
    "curriculumStage": "Stage 8 — Binary Trees & Tree Traversals",
    "roadmapPhase": "Stage 8 — Binary Trees & Tree Traversals",
    "phase": "Stage 8 — Binary Trees & Tree Traversals",
    "estimatedTime": 30,
    "statement": "Solve the **Binary Tree Pruning Optimization** problem using the **Tree Traversal & Recursion** technique. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Tree Traversal & Recursion identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Tree Traversal & Recursion. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Tree Traversal & Recursion techniques by solving Medium problem constraints for Binary Tree Pruning Optimization.",
    "whyThisPattern": "When observing binary trees problem conditions, Tree Traversal & Recursion optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/binary-tree-pruning/",
    "leetcode_title": "Binary Tree Pruning",
    "leetcode_id": 814,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/binary-tree-pruning/",
    "canonicalSlug": "binary-tree-pruning",
    "canonicalUrl": "https://leetcode.com/problems/binary-tree-pruning/",
    "url": "https://leetcode.com/problems/binary-tree-pruning/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Binary Tree Pruning Optimization (Tree Traversal & Recursion)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Binary Tree Pruning Optimization (Tree Traversal & Recursion)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Binary Tree Pruning Optimization (Tree Traversal & Recursion)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Binary Tree Pruning Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Binary Tree Pruning Optimization (Tree Traversal & Recursion)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Binary Tree Pruning Optimization (Tree Traversal & Recursion)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Binary Tree Pruning Optimization (Tree Traversal & Recursion)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Binary Tree Pruning Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Binary Tree Pruning",
      "cpp_optimal": "// Solution for Binary Tree Pruning",
      "java_brute": "// Solution for Binary Tree Pruning",
      "java_optimal": "// Solution for Binary Tree Pruning",
      "python_brute": "# Solution for Binary Tree Pruning",
      "python_optimal": "# Solution for Binary Tree Pruning"
    },
    "originalOrder": 646,
    "learningOrder": 646
  },
  {
    "id": 384,
    "number": 384,
    "sequence_number": 384,
    "title": "Binary Trees With Factors",
    "slug": "binary-trees-with-factors",
    "difficulty": "Medium",
    "topic": "Trees",
    "subtopic": "Tree Traversal & Recursion",
    "pattern": "Tree Traversal & Recursion",
    "secondary_patterns": [
      "Tree Traversal & Recursion"
    ],
    "stage": "Binary Trees & Tree Traversals",
    "curriculumStage": "Stage 8 — Binary Trees & Tree Traversals",
    "roadmapPhase": "Stage 8 — Binary Trees & Tree Traversals",
    "phase": "Stage 8 — Binary Trees & Tree Traversals",
    "estimatedTime": 30,
    "statement": "Solve the **Binary Trees With Factors Challenge** problem using the **Tree Traversal & Recursion** technique. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Tree Traversal & Recursion identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Tree Traversal & Recursion. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Tree Traversal & Recursion techniques by solving Medium problem constraints for Binary Trees With Factors Challenge.",
    "whyThisPattern": "When observing binary trees problem conditions, Tree Traversal & Recursion optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Microsoft",
      "Bloomberg",
      "Adobe"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/binary-trees-with-factors/",
    "leetcode_title": "Binary Trees With Factors",
    "leetcode_id": 823,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/binary-trees-with-factors/",
    "canonicalSlug": "binary-trees-with-factors",
    "canonicalUrl": "https://leetcode.com/problems/binary-trees-with-factors/",
    "url": "https://leetcode.com/problems/binary-trees-with-factors/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Binary Trees With Factors Challenge (Tree Traversal & Recursion)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Binary Trees With Factors Challenge (Tree Traversal & Recursion)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Binary Trees With Factors Challenge (Tree Traversal & Recursion)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Binary Trees With Factors Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Binary Trees With Factors Challenge (Tree Traversal & Recursion)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Binary Trees With Factors Challenge (Tree Traversal & Recursion)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Binary Trees With Factors Challenge (Tree Traversal & Recursion)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Binary Trees With Factors Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Binary Trees With Factors",
      "cpp_optimal": "// Solution for Binary Trees With Factors",
      "java_brute": "// Solution for Binary Trees With Factors",
      "java_optimal": "// Solution for Binary Trees With Factors",
      "python_brute": "# Solution for Binary Trees With Factors",
      "python_optimal": "# Solution for Binary Trees With Factors"
    },
    "originalOrder": 647,
    "learningOrder": 647
  },
  {
    "id": 385,
    "number": 385,
    "sequence_number": 385,
    "title": "All Nodes Distance K in Binary Tree",
    "slug": "all-nodes-distance-k-in-binary-tree",
    "difficulty": "Medium",
    "topic": "Trees",
    "subtopic": "Pointer Manipulation",
    "pattern": "Pointer Manipulation",
    "secondary_patterns": [
      "Pointer Manipulation"
    ],
    "stage": "Binary Trees & Tree Traversals",
    "curriculumStage": "Stage 8 — Binary Trees & Tree Traversals",
    "roadmapPhase": "Stage 8 — Binary Trees & Tree Traversals",
    "phase": "Stage 8 — Binary Trees & Tree Traversals",
    "estimatedTime": 30,
    "statement": "Solve the **All Nodes Distance K in Binary Tree Optimization** problem using the **Pointer Manipulation** technique. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Pointer Manipulation identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Pointer Manipulation. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Pointer Manipulation techniques by solving Medium problem constraints for All Nodes Distance K in Binary Tree Optimization.",
    "whyThisPattern": "When observing binary trees problem conditions, Pointer Manipulation optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/all-nodes-distance-k-in-binary-tree/",
    "leetcode_title": "All Nodes Distance K in Binary Tree",
    "leetcode_id": 863,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/all-nodes-distance-k-in-binary-tree/",
    "canonicalSlug": "all-nodes-distance-k-in-binary-tree",
    "canonicalUrl": "https://leetcode.com/problems/all-nodes-distance-k-in-binary-tree/",
    "url": "https://leetcode.com/problems/all-nodes-distance-k-in-binary-tree/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for All Nodes Distance K in Binary Tree Optimization (Pointer Manipulation)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for All Nodes Distance K in Binary Tree Optimization (Pointer Manipulation)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for All Nodes Distance K in Binary Tree Optimization (Pointer Manipulation)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for All Nodes Distance K in Binary Tree Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for All Nodes Distance K in Binary Tree Optimization (Pointer Manipulation)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for All Nodes Distance K in Binary Tree Optimization (Pointer Manipulation)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for All Nodes Distance K in Binary Tree Optimization (Pointer Manipulation)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for All Nodes Distance K in Binary Tree Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for All Nodes Distance K in Binary Tree",
      "cpp_optimal": "// Solution for All Nodes Distance K in Binary Tree",
      "java_brute": "// Solution for All Nodes Distance K in Binary Tree",
      "java_optimal": "// Solution for All Nodes Distance K in Binary Tree",
      "python_brute": "# Solution for All Nodes Distance K in Binary Tree",
      "python_optimal": "# Solution for All Nodes Distance K in Binary Tree"
    },
    "originalOrder": 648,
    "learningOrder": 648
  },
  {
    "id": 386,
    "number": 386,
    "sequence_number": 386,
    "title": "Sum of Distances in Tree",
    "slug": "sum-of-distances-in-tree",
    "difficulty": "Hard",
    "topic": "Trees",
    "subtopic": "Trees Optimization",
    "pattern": "Rerooting DP Post-Order",
    "secondary_patterns": [
      "Rerooting DP Post-Order"
    ],
    "stage": "Binary Trees & Tree Traversals",
    "curriculumStage": "Stage 8 — Binary Trees & Tree Traversals",
    "roadmapPhase": "Stage 8 — Binary Trees & Tree Traversals",
    "phase": "Stage 8 — Binary Trees & Tree Traversals",
    "estimatedTime": 45,
    "statement": "Given the constraints and input parameters for Sum of Distances in Tree, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Sum of Distances in Tree."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Sum of Distances in Tree.",
      "Leverage the optimal Trees pattern to reduce time complexity."
    ],
    "learningObjective": "Master Trees techniques by solving Hard problem constraints for Sum of Distances in Tree.",
    "whyThisPattern": "When observing Trees problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/sum-of-distances-in-tree/",
    "leetcode_title": "Sum of Distances in Tree",
    "leetcode_id": 834,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/sum-of-distances-in-tree/",
    "canonicalSlug": "sum-of-distances-in-tree",
    "canonicalUrl": "https://leetcode.com/problems/sum-of-distances-in-tree/",
    "url": "https://leetcode.com/problems/sum-of-distances-in-tree/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Sum of Distances in Tree\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Sum of Distances in Tree\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Sum of Distances in Tree\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Sum of Distances in Tree\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Sum of Distances in Tree\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Sum of Distances in Tree\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Sum of Distances in Tree\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Sum of Distances in Tree\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Sum of Distances in Tree",
      "cpp_optimal": "// Solution for Sum of Distances in Tree",
      "java_brute": "// Solution for Sum of Distances in Tree",
      "java_optimal": "// Solution for Sum of Distances in Tree",
      "python_brute": "# Solution for Sum of Distances in Tree",
      "python_optimal": "# Solution for Sum of Distances in Tree"
    },
    "originalOrder": 965,
    "learningOrder": 965
  },
  {
    "id": 387,
    "number": 387,
    "sequence_number": 387,
    "title": "Binary Tree Cameras",
    "slug": "binary-tree-cameras",
    "difficulty": "Hard",
    "topic": "Trees",
    "subtopic": "Trees Optimization",
    "pattern": "Greedy DFS Post-Order",
    "secondary_patterns": [
      "Greedy DFS Post-Order"
    ],
    "stage": "Binary Trees & Tree Traversals",
    "curriculumStage": "Stage 8 — Binary Trees & Tree Traversals",
    "roadmapPhase": "Stage 8 — Binary Trees & Tree Traversals",
    "phase": "Stage 8 — Binary Trees & Tree Traversals",
    "estimatedTime": 45,
    "statement": "Given the constraints and input parameters for Binary Tree Cameras, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Binary Tree Cameras."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Binary Tree Cameras.",
      "Leverage the optimal Trees pattern to reduce time complexity."
    ],
    "learningObjective": "Master Trees techniques by solving Hard problem constraints for Binary Tree Cameras.",
    "whyThisPattern": "When observing Trees problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/binary-tree-cameras/",
    "leetcode_title": "Binary Tree Cameras",
    "leetcode_id": 968,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/binary-tree-cameras/",
    "canonicalSlug": "binary-tree-cameras",
    "canonicalUrl": "https://leetcode.com/problems/binary-tree-cameras/",
    "url": "https://leetcode.com/problems/binary-tree-cameras/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Binary Tree Cameras\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Binary Tree Cameras\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Binary Tree Cameras\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Binary Tree Cameras\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Binary Tree Cameras\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Binary Tree Cameras\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Binary Tree Cameras\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Binary Tree Cameras\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Binary Tree Cameras",
      "cpp_optimal": "// Solution for Binary Tree Cameras",
      "java_brute": "// Solution for Binary Tree Cameras",
      "java_optimal": "// Solution for Binary Tree Cameras",
      "python_brute": "# Solution for Binary Tree Cameras",
      "python_optimal": "# Solution for Binary Tree Cameras"
    },
    "originalOrder": 966,
    "learningOrder": 966
  },
  {
    "id": 388,
    "number": 388,
    "sequence_number": 388,
    "title": "Vertical Order Traversal of a Binary Tree",
    "slug": "vertical-order-traversal-of-a-binary-tree",
    "difficulty": "Hard",
    "topic": "Trees",
    "subtopic": "Trees Optimization",
    "pattern": "DFS Coordinate Map Sort",
    "secondary_patterns": [
      "DFS Coordinate Map Sort"
    ],
    "stage": "Binary Trees & Tree Traversals",
    "curriculumStage": "Stage 8 — Binary Trees & Tree Traversals",
    "roadmapPhase": "Stage 8 — Binary Trees & Tree Traversals",
    "phase": "Stage 8 — Binary Trees & Tree Traversals",
    "estimatedTime": 45,
    "statement": "Given the constraints and input parameters for Vertical Order Traversal of a Binary Tree, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Vertical Order Traversal of a Binary Tree."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Vertical Order Traversal of a Binary Tree.",
      "Leverage the optimal Trees pattern to reduce time complexity."
    ],
    "learningObjective": "Master Trees techniques by solving Hard problem constraints for Vertical Order Traversal of a Binary Tree.",
    "whyThisPattern": "When observing Trees problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/vertical-order-traversal-of-a-binary-tree/",
    "leetcode_title": "Vertical Order Traversal of a Binary Tree",
    "leetcode_id": 987,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/vertical-order-traversal-of-a-binary-tree/",
    "canonicalSlug": "vertical-order-traversal-of-a-binary-tree",
    "canonicalUrl": "https://leetcode.com/problems/vertical-order-traversal-of-a-binary-tree/",
    "url": "https://leetcode.com/problems/vertical-order-traversal-of-a-binary-tree/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Vertical Order Traversal of a Binary Tree\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Vertical Order Traversal of a Binary Tree\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Vertical Order Traversal of a Binary Tree\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Vertical Order Traversal of a Binary Tree\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Vertical Order Traversal of a Binary Tree\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Vertical Order Traversal of a Binary Tree\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Vertical Order Traversal of a Binary Tree\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Vertical Order Traversal of a Binary Tree\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Vertical Order Traversal of a Binary Tree",
      "cpp_optimal": "// Solution for Vertical Order Traversal of a Binary Tree",
      "java_brute": "// Solution for Vertical Order Traversal of a Binary Tree",
      "java_optimal": "// Solution for Vertical Order Traversal of a Binary Tree",
      "python_brute": "# Solution for Vertical Order Traversal of a Binary Tree",
      "python_optimal": "# Solution for Vertical Order Traversal of a Binary Tree"
    },
    "originalOrder": 967,
    "learningOrder": 967
  },
  {
    "id": 389,
    "number": 389,
    "sequence_number": 389,
    "title": "Frog Position After T Seconds",
    "slug": "frog-position-after-t-seconds",
    "difficulty": "Hard",
    "topic": "Trees",
    "subtopic": "Trees Optimization",
    "pattern": "Probability DFS Tree",
    "secondary_patterns": [
      "Probability DFS Tree"
    ],
    "stage": "Binary Trees & Tree Traversals",
    "curriculumStage": "Stage 8 — Binary Trees & Tree Traversals",
    "roadmapPhase": "Stage 8 — Binary Trees & Tree Traversals",
    "phase": "Stage 8 — Binary Trees & Tree Traversals",
    "estimatedTime": 45,
    "statement": "Given the constraints and input parameters for Frog Position After T Seconds, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Frog Position After T Seconds."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Frog Position After T Seconds.",
      "Leverage the optimal Trees pattern to reduce time complexity."
    ],
    "learningObjective": "Master Trees techniques by solving Hard problem constraints for Frog Position After T Seconds.",
    "whyThisPattern": "When observing Trees problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/frog-position-after-t-seconds/",
    "leetcode_title": "Frog Position After T Seconds",
    "leetcode_id": 1377,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/frog-position-after-t-seconds/",
    "canonicalSlug": "frog-position-after-t-seconds",
    "canonicalUrl": "https://leetcode.com/problems/frog-position-after-t-seconds/",
    "url": "https://leetcode.com/problems/frog-position-after-t-seconds/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Frog Position After T Seconds\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Frog Position After T Seconds\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Frog Position After T Seconds\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Frog Position After T Seconds\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Frog Position After T Seconds\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Frog Position After T Seconds\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Frog Position After T Seconds\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Frog Position After T Seconds\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Frog Position After T Seconds",
      "cpp_optimal": "// Solution for Frog Position After T Seconds",
      "java_brute": "// Solution for Frog Position After T Seconds",
      "java_optimal": "// Solution for Frog Position After T Seconds",
      "python_brute": "# Solution for Frog Position After T Seconds",
      "python_optimal": "# Solution for Frog Position After T Seconds"
    },
    "originalOrder": 968,
    "learningOrder": 968
  },
  {
    "id": 390,
    "number": 390,
    "sequence_number": 390,
    "title": "Kth Ancestor of a Tree Node",
    "slug": "kth-ancestor-of-a-tree-node",
    "difficulty": "Hard",
    "topic": "Trees",
    "subtopic": "Trees Optimization",
    "pattern": "Binary Lifting Ancestor Matrix",
    "secondary_patterns": [
      "Binary Lifting Ancestor Matrix"
    ],
    "stage": "Binary Trees & Tree Traversals",
    "curriculumStage": "Stage 8 — Binary Trees & Tree Traversals",
    "roadmapPhase": "Stage 8 — Binary Trees & Tree Traversals",
    "phase": "Stage 8 — Binary Trees & Tree Traversals",
    "estimatedTime": 45,
    "statement": "Given the constraints and input parameters for Kth Ancestor of a Tree Node, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Kth Ancestor of a Tree Node."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Kth Ancestor of a Tree Node.",
      "Leverage the optimal Trees pattern to reduce time complexity."
    ],
    "learningObjective": "Master Trees techniques by solving Hard problem constraints for Kth Ancestor of a Tree Node.",
    "whyThisPattern": "When observing Trees problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/kth-ancestor-of-a-tree-node/",
    "leetcode_title": "Kth Ancestor of a Tree Node",
    "leetcode_id": 1483,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/kth-ancestor-of-a-tree-node/",
    "canonicalSlug": "kth-ancestor-of-a-tree-node",
    "canonicalUrl": "https://leetcode.com/problems/kth-ancestor-of-a-tree-node/",
    "url": "https://leetcode.com/problems/kth-ancestor-of-a-tree-node/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Kth Ancestor of a Tree Node\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Kth Ancestor of a Tree Node\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Kth Ancestor of a Tree Node\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Kth Ancestor of a Tree Node\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Kth Ancestor of a Tree Node\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Kth Ancestor of a Tree Node\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Kth Ancestor of a Tree Node\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Kth Ancestor of a Tree Node\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Kth Ancestor of a Tree Node",
      "cpp_optimal": "// Solution for Kth Ancestor of a Tree Node",
      "java_brute": "// Solution for Kth Ancestor of a Tree Node",
      "java_optimal": "// Solution for Kth Ancestor of a Tree Node",
      "python_brute": "# Solution for Kth Ancestor of a Tree Node",
      "python_optimal": "# Solution for Kth Ancestor of a Tree Node"
    },
    "originalOrder": 969,
    "learningOrder": 969
  },
  {
    "id": 391,
    "number": 391,
    "sequence_number": 391,
    "title": "Binary Tree Maximum Path Sum",
    "slug": "binary-tree-maximum-path-sum",
    "difficulty": "Hard",
    "topic": "Trees",
    "subtopic": "Trees Optimization",
    "pattern": "Post-Order Tree Path Max",
    "secondary_patterns": [
      "Post-Order Tree Path Max"
    ],
    "stage": "Binary Trees & Tree Traversals",
    "curriculumStage": "Stage 8 — Binary Trees & Tree Traversals",
    "roadmapPhase": "Stage 8 — Binary Trees & Tree Traversals",
    "phase": "Stage 8 — Binary Trees & Tree Traversals",
    "estimatedTime": 45,
    "statement": "Given the constraints and input parameters for Binary Tree Maximum Path Sum, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Binary Tree Maximum Path Sum."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Binary Tree Maximum Path Sum.",
      "Leverage the optimal Trees pattern to reduce time complexity."
    ],
    "learningObjective": "Master Trees techniques by solving Hard problem constraints for Binary Tree Maximum Path Sum.",
    "whyThisPattern": "When observing Trees problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/binary-tree-maximum-path-sum/",
    "leetcode_title": "Binary Tree Maximum Path Sum",
    "leetcode_id": 124,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/binary-tree-maximum-path-sum/",
    "canonicalSlug": "binary-tree-maximum-path-sum",
    "canonicalUrl": "https://leetcode.com/problems/binary-tree-maximum-path-sum/",
    "url": "https://leetcode.com/problems/binary-tree-maximum-path-sum/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Binary Tree Maximum Path Sum\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Binary Tree Maximum Path Sum\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Binary Tree Maximum Path Sum\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Binary Tree Maximum Path Sum\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Binary Tree Maximum Path Sum\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Binary Tree Maximum Path Sum\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Binary Tree Maximum Path Sum\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Binary Tree Maximum Path Sum\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Binary Tree Maximum Path Sum",
      "cpp_optimal": "// Solution for Binary Tree Maximum Path Sum",
      "java_brute": "// Solution for Binary Tree Maximum Path Sum",
      "java_optimal": "// Solution for Binary Tree Maximum Path Sum",
      "python_brute": "# Solution for Binary Tree Maximum Path Sum",
      "python_optimal": "# Solution for Binary Tree Maximum Path Sum"
    },
    "originalOrder": 970,
    "learningOrder": 970
  },
  {
    "id": 392,
    "number": 392,
    "sequence_number": 392,
    "title": "Serialize and Deserialize Binary Tree",
    "slug": "serialize-and-deserialize-binary-tree",
    "difficulty": "Hard",
    "topic": "Trees",
    "subtopic": "Trees Optimization",
    "pattern": "Preorder Queue Traversal",
    "secondary_patterns": [
      "Preorder Queue Traversal"
    ],
    "stage": "Binary Trees & Tree Traversals",
    "curriculumStage": "Stage 8 — Binary Trees & Tree Traversals",
    "roadmapPhase": "Stage 8 — Binary Trees & Tree Traversals",
    "phase": "Stage 8 — Binary Trees & Tree Traversals",
    "estimatedTime": 45,
    "statement": "Given the constraints and input parameters for Serialize and Deserialize Binary Tree, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Serialize and Deserialize Binary Tree."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Serialize and Deserialize Binary Tree.",
      "Leverage the optimal Trees pattern to reduce time complexity."
    ],
    "learningObjective": "Master Trees techniques by solving Hard problem constraints for Serialize and Deserialize Binary Tree.",
    "whyThisPattern": "When observing Trees problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/serialize-and-deserialize-binary-tree/",
    "leetcode_title": "Serialize and Deserialize Binary Tree",
    "leetcode_id": 297,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/serialize-and-deserialize-binary-tree/",
    "canonicalSlug": "serialize-and-deserialize-binary-tree",
    "canonicalUrl": "https://leetcode.com/problems/serialize-and-deserialize-binary-tree/",
    "url": "https://leetcode.com/problems/serialize-and-deserialize-binary-tree/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Serialize and Deserialize Binary Tree\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Serialize and Deserialize Binary Tree\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Serialize and Deserialize Binary Tree\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Serialize and Deserialize Binary Tree\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Serialize and Deserialize Binary Tree\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Serialize and Deserialize Binary Tree\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Serialize and Deserialize Binary Tree\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Serialize and Deserialize Binary Tree\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Serialize and Deserialize Binary Tree",
      "cpp_optimal": "// Solution for Serialize and Deserialize Binary Tree",
      "java_brute": "// Solution for Serialize and Deserialize Binary Tree",
      "java_optimal": "// Solution for Serialize and Deserialize Binary Tree",
      "python_brute": "# Solution for Serialize and Deserialize Binary Tree",
      "python_optimal": "# Solution for Serialize and Deserialize Binary Tree"
    },
    "originalOrder": 971,
    "learningOrder": 971
  },
  {
    "id": 393,
    "number": 393,
    "sequence_number": 393,
    "title": "Create Components With Same Value",
    "slug": "create-components-with-same-value",
    "difficulty": "Hard",
    "topic": "Trees",
    "subtopic": "Trees Optimization",
    "pattern": "Tree Divisor BFS",
    "secondary_patterns": [
      "Tree Divisor BFS"
    ],
    "stage": "Binary Trees & Tree Traversals",
    "curriculumStage": "Stage 8 — Binary Trees & Tree Traversals",
    "roadmapPhase": "Stage 8 — Binary Trees & Tree Traversals",
    "phase": "Stage 8 — Binary Trees & Tree Traversals",
    "estimatedTime": 45,
    "statement": "Given the constraints and input parameters for Create Components With Same Value, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Create Components With Same Value."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Create Components With Same Value.",
      "Leverage the optimal Trees pattern to reduce time complexity."
    ],
    "learningObjective": "Master Trees techniques by solving Hard problem constraints for Create Components With Same Value.",
    "whyThisPattern": "When observing Trees problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/create-components-with-same-value/",
    "leetcode_title": "Create Components With Same Value",
    "leetcode_id": 2440,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/create-components-with-same-value/",
    "canonicalSlug": "create-components-with-same-value",
    "canonicalUrl": "https://leetcode.com/problems/create-components-with-same-value/",
    "url": "https://leetcode.com/problems/create-components-with-same-value/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Create Components With Same Value\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Create Components With Same Value\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Create Components With Same Value\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Create Components With Same Value\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Create Components With Same Value\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Create Components With Same Value\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Create Components With Same Value\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Create Components With Same Value\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Create Components With Same Value",
      "cpp_optimal": "// Solution for Create Components With Same Value",
      "java_brute": "// Solution for Create Components With Same Value",
      "java_optimal": "// Solution for Create Components With Same Value",
      "python_brute": "# Solution for Create Components With Same Value",
      "python_optimal": "# Solution for Create Components With Same Value"
    },
    "originalOrder": 972,
    "learningOrder": 972
  },
  {
    "id": 394,
    "number": 394,
    "sequence_number": 394,
    "title": "Count Paths That Can Form a Palindrome in a Tree",
    "slug": "count-paths-that-can-form-a-palindrome-in-a-tree",
    "difficulty": "Hard",
    "topic": "Trees",
    "subtopic": "Trees Optimization",
    "pattern": "Bitmask Path Parity DFS",
    "secondary_patterns": [
      "Bitmask Path Parity DFS"
    ],
    "stage": "Binary Trees & Tree Traversals",
    "curriculumStage": "Stage 8 — Binary Trees & Tree Traversals",
    "roadmapPhase": "Stage 8 — Binary Trees & Tree Traversals",
    "phase": "Stage 8 — Binary Trees & Tree Traversals",
    "estimatedTime": 45,
    "statement": "Given the constraints and input parameters for Count Paths That Can Form a Palindrome in a Tree, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Count Paths That Can Form a Palindrome in a Tree."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Count Paths That Can Form a Palindrome in a Tree.",
      "Leverage the optimal Trees pattern to reduce time complexity."
    ],
    "learningObjective": "Master Trees techniques by solving Hard problem constraints for Count Paths That Can Form a Palindrome in a Tree.",
    "whyThisPattern": "When observing Trees problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/count-paths-that-can-form-a-palindrome-in-a-tree/",
    "leetcode_title": "Count Paths That Can Form a Palindrome in a Tree",
    "leetcode_id": 2791,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/count-paths-that-can-form-a-palindrome-in-a-tree/",
    "canonicalSlug": "count-paths-that-can-form-a-palindrome-in-a-tree",
    "canonicalUrl": "https://leetcode.com/problems/count-paths-that-can-form-a-palindrome-in-a-tree/",
    "url": "https://leetcode.com/problems/count-paths-that-can-form-a-palindrome-in-a-tree/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Count Paths That Can Form a Palindrome in a Tree\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Count Paths That Can Form a Palindrome in a Tree\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Count Paths That Can Form a Palindrome in a Tree\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Count Paths That Can Form a Palindrome in a Tree\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Count Paths That Can Form a Palindrome in a Tree\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Count Paths That Can Form a Palindrome in a Tree\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Count Paths That Can Form a Palindrome in a Tree\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Count Paths That Can Form a Palindrome in a Tree\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Count Paths That Can Form a Palindrome in a Tree",
      "cpp_optimal": "// Solution for Count Paths That Can Form a Palindrome in a Tree",
      "java_brute": "// Solution for Count Paths That Can Form a Palindrome in a Tree",
      "java_optimal": "// Solution for Count Paths That Can Form a Palindrome in a Tree",
      "python_brute": "# Solution for Count Paths That Can Form a Palindrome in a Tree",
      "python_optimal": "# Solution for Count Paths That Can Form a Palindrome in a Tree"
    },
    "originalOrder": 973,
    "learningOrder": 973
  },
  {
    "id": 395,
    "number": 395,
    "sequence_number": 395,
    "title": "Minimum Moves to Reach Target with Rotations",
    "slug": "minimum-moves-to-reach-target-with-rotations",
    "difficulty": "Hard",
    "topic": "Arrays",
    "subtopic": "Arrays Optimization",
    "pattern": "Arrays Pattern",
    "secondary_patterns": [
      "Arrays Pattern"
    ],
    "stage": "Binary Trees & Tree Traversals",
    "curriculumStage": "Stage 8 — Binary Trees & Tree Traversals",
    "roadmapPhase": "Stage 8 — Binary Trees & Tree Traversals",
    "phase": "Stage 8 — Binary Trees & Tree Traversals",
    "estimatedTime": 45,
    "statement": "Solve the **Minimum Moves to Reach Target with Rotations** problem using standard Arrays techniques. Given input constraints appropriate for Hard level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Arrays algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Arrays properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Arrays techniques by solving Hard problem constraints for Minimum Moves to Reach Target with Rotations.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/minimum-moves-to-reach-target-with-rotations/",
    "leetcode_title": "Minimum Moves to Reach Target with Rotations",
    "leetcode_id": 1210,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/minimum-moves-to-reach-target-with-rotations/",
    "canonicalSlug": "minimum-moves-to-reach-target-with-rotations",
    "canonicalUrl": "https://leetcode.com/problems/minimum-moves-to-reach-target-with-rotations/",
    "url": "https://leetcode.com/problems/minimum-moves-to-reach-target-with-rotations/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Minimum Moves to Reach Target with Rotations\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Minimum Moves to Reach Target with Rotations\n};",
        "java": "// Java Solution for Minimum Moves to Reach Target with Rotations\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Minimum Moves to Reach Target with Rotations\n}",
        "python": "# Python Solution for Minimum Moves to Reach Target with Rotations\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Minimum Moves to Reach Target with Rotations\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Minimum Moves to Reach Target with Rotations\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Minimum Moves to Reach Target with Rotations\n};",
        "java": "// Optimal Java Solution for Minimum Moves to Reach Target with Rotations\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Minimum Moves to Reach Target with Rotations\n}",
        "python": "# Optimal Python Solution for Minimum Moves to Reach Target with Rotations\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Minimum Moves to Reach Target with Rotations\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Minimum Moves to Reach Target with Rotations",
      "cpp_optimal": "// Solution for Minimum Moves to Reach Target with Rotations",
      "java_brute": "// Solution for Minimum Moves to Reach Target with Rotations",
      "java_optimal": "// Solution for Minimum Moves to Reach Target with Rotations",
      "python_brute": "# Solution for Minimum Moves to Reach Target with Rotations",
      "python_optimal": "# Solution for Minimum Moves to Reach Target with Rotations"
    },
    "originalOrder": 753,
    "learningOrder": 753
  },
  {
    "id": 396,
    "number": 396,
    "sequence_number": 396,
    "title": "Count Vowels Permutation",
    "slug": "count-vowels-permutation",
    "difficulty": "Hard",
    "topic": "Arrays",
    "subtopic": "Arrays Optimization",
    "pattern": "Arrays Pattern",
    "secondary_patterns": [
      "Arrays Pattern"
    ],
    "stage": "Binary Trees & Tree Traversals",
    "curriculumStage": "Stage 8 — Binary Trees & Tree Traversals",
    "roadmapPhase": "Stage 8 — Binary Trees & Tree Traversals",
    "phase": "Stage 8 — Binary Trees & Tree Traversals",
    "estimatedTime": 45,
    "statement": "Solve the **Count Vowels Permutation** problem using standard Arrays techniques. Given input constraints appropriate for Hard level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Arrays algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Arrays properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Arrays techniques by solving Hard problem constraints for Count Vowels Permutation.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/count-vowels-permutation/",
    "leetcode_title": "Count Vowels Permutation",
    "leetcode_id": 1220,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/count-vowels-permutation/",
    "canonicalSlug": "count-vowels-permutation",
    "canonicalUrl": "https://leetcode.com/problems/count-vowels-permutation/",
    "url": "https://leetcode.com/problems/count-vowels-permutation/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Count Vowels Permutation\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Count Vowels Permutation\n};",
        "java": "// Java Solution for Count Vowels Permutation\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Count Vowels Permutation\n}",
        "python": "# Python Solution for Count Vowels Permutation\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Count Vowels Permutation\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Count Vowels Permutation\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Count Vowels Permutation\n};",
        "java": "// Optimal Java Solution for Count Vowels Permutation\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Count Vowels Permutation\n}",
        "python": "# Optimal Python Solution for Count Vowels Permutation\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Count Vowels Permutation\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Count Vowels Permutation",
      "cpp_optimal": "// Solution for Count Vowels Permutation",
      "java_brute": "// Solution for Count Vowels Permutation",
      "java_optimal": "// Solution for Count Vowels Permutation",
      "python_brute": "# Solution for Count Vowels Permutation",
      "python_optimal": "# Solution for Count Vowels Permutation"
    },
    "originalOrder": 754,
    "learningOrder": 754
  },
  {
    "id": 397,
    "number": 397,
    "sequence_number": 397,
    "title": "Maximum Profit in Job Scheduling",
    "slug": "maximum-profit-in-job-scheduling",
    "difficulty": "Hard",
    "topic": "Arrays",
    "subtopic": "Arrays Optimization",
    "pattern": "Arrays Pattern",
    "secondary_patterns": [
      "Arrays Pattern"
    ],
    "stage": "Binary Trees & Tree Traversals",
    "curriculumStage": "Stage 8 — Binary Trees & Tree Traversals",
    "roadmapPhase": "Stage 8 — Binary Trees & Tree Traversals",
    "phase": "Stage 8 — Binary Trees & Tree Traversals",
    "estimatedTime": 45,
    "statement": "Solve the **Maximum Profit in Job Scheduling** problem using standard Arrays techniques. Given input constraints appropriate for Hard level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Arrays algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Arrays properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Arrays techniques by solving Hard problem constraints for Maximum Profit in Job Scheduling.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/maximum-profit-in-job-scheduling/",
    "leetcode_title": "Maximum Profit in Job Scheduling",
    "leetcode_id": 1235,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/maximum-profit-in-job-scheduling/",
    "canonicalSlug": "maximum-profit-in-job-scheduling",
    "canonicalUrl": "https://leetcode.com/problems/maximum-profit-in-job-scheduling/",
    "url": "https://leetcode.com/problems/maximum-profit-in-job-scheduling/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Maximum Profit in Job Scheduling\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Maximum Profit in Job Scheduling\n};",
        "java": "// Java Solution for Maximum Profit in Job Scheduling\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Maximum Profit in Job Scheduling\n}",
        "python": "# Python Solution for Maximum Profit in Job Scheduling\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Maximum Profit in Job Scheduling\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Maximum Profit in Job Scheduling\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Maximum Profit in Job Scheduling\n};",
        "java": "// Optimal Java Solution for Maximum Profit in Job Scheduling\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Maximum Profit in Job Scheduling\n}",
        "python": "# Optimal Python Solution for Maximum Profit in Job Scheduling\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Maximum Profit in Job Scheduling\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Maximum Profit in Job Scheduling",
      "cpp_optimal": "// Solution for Maximum Profit in Job Scheduling",
      "java_brute": "// Solution for Maximum Profit in Job Scheduling",
      "java_optimal": "// Solution for Maximum Profit in Job Scheduling",
      "python_brute": "# Solution for Maximum Profit in Job Scheduling",
      "python_optimal": "# Solution for Maximum Profit in Job Scheduling"
    },
    "originalOrder": 755,
    "learningOrder": 755
  },
  {
    "id": 398,
    "number": 398,
    "sequence_number": 398,
    "title": "Check If It Is a Good Array",
    "slug": "check-if-it-is-a-good-array",
    "difficulty": "Hard",
    "topic": "Arrays",
    "subtopic": "Arrays Optimization",
    "pattern": "Arrays Pattern",
    "secondary_patterns": [
      "Arrays Pattern"
    ],
    "stage": "Binary Trees & Tree Traversals",
    "curriculumStage": "Stage 8 — Binary Trees & Tree Traversals",
    "roadmapPhase": "Stage 8 — Binary Trees & Tree Traversals",
    "phase": "Stage 8 — Binary Trees & Tree Traversals",
    "estimatedTime": 45,
    "statement": "Solve the **Check If It Is a Good Array** problem using standard Arrays techniques. Given input constraints appropriate for Hard level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Arrays algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Arrays properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Arrays techniques by solving Hard problem constraints for Check If It Is a Good Array.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/check-if-it-is-a-good-array/",
    "leetcode_title": "Check If It Is a Good Array",
    "leetcode_id": 1250,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/check-if-it-is-a-good-array/",
    "canonicalSlug": "check-if-it-is-a-good-array",
    "canonicalUrl": "https://leetcode.com/problems/check-if-it-is-a-good-array/",
    "url": "https://leetcode.com/problems/check-if-it-is-a-good-array/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Check If It Is a Good Array\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Check If It Is a Good Array\n};",
        "java": "// Java Solution for Check If It Is a Good Array\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Check If It Is a Good Array\n}",
        "python": "# Python Solution for Check If It Is a Good Array\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Check If It Is a Good Array\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Check If It Is a Good Array\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Check If It Is a Good Array\n};",
        "java": "// Optimal Java Solution for Check If It Is a Good Array\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Check If It Is a Good Array\n}",
        "python": "# Optimal Python Solution for Check If It Is a Good Array\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Check If It Is a Good Array\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Check If It Is a Good Array",
      "cpp_optimal": "// Solution for Check If It Is a Good Array",
      "java_brute": "// Solution for Check If It Is a Good Array",
      "java_optimal": "// Solution for Check If It Is a Good Array",
      "python_brute": "# Solution for Check If It Is a Good Array",
      "python_optimal": "# Solution for Check If It Is a Good Array"
    },
    "originalOrder": 756,
    "learningOrder": 756
  },
  {
    "id": 399,
    "number": 399,
    "sequence_number": 399,
    "title": "Maximum Score Words Formed by Letters",
    "slug": "maximum-score-words-formed-by-letters",
    "difficulty": "Hard",
    "topic": "Arrays",
    "subtopic": "Arrays Optimization",
    "pattern": "Arrays Pattern",
    "secondary_patterns": [
      "Arrays Pattern"
    ],
    "stage": "Binary Trees & Tree Traversals",
    "curriculumStage": "Stage 8 — Binary Trees & Tree Traversals",
    "roadmapPhase": "Stage 8 — Binary Trees & Tree Traversals",
    "phase": "Stage 8 — Binary Trees & Tree Traversals",
    "estimatedTime": 45,
    "statement": "Solve the **Maximum Score Words Formed by Letters** problem using standard Arrays techniques. Given input constraints appropriate for Hard level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Arrays algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Arrays properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Arrays techniques by solving Hard problem constraints for Maximum Score Words Formed by Letters.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/maximum-score-words-formed-by-letters/",
    "leetcode_title": "Maximum Score Words Formed by Letters",
    "leetcode_id": 1255,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/maximum-score-words-formed-by-letters/",
    "canonicalSlug": "maximum-score-words-formed-by-letters",
    "canonicalUrl": "https://leetcode.com/problems/maximum-score-words-formed-by-letters/",
    "url": "https://leetcode.com/problems/maximum-score-words-formed-by-letters/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Maximum Score Words Formed by Letters\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Maximum Score Words Formed by Letters\n};",
        "java": "// Java Solution for Maximum Score Words Formed by Letters\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Maximum Score Words Formed by Letters\n}",
        "python": "# Python Solution for Maximum Score Words Formed by Letters\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Maximum Score Words Formed by Letters\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Maximum Score Words Formed by Letters\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Maximum Score Words Formed by Letters\n};",
        "java": "// Optimal Java Solution for Maximum Score Words Formed by Letters\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Maximum Score Words Formed by Letters\n}",
        "python": "# Optimal Python Solution for Maximum Score Words Formed by Letters\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Maximum Score Words Formed by Letters\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Maximum Score Words Formed by Letters",
      "cpp_optimal": "// Solution for Maximum Score Words Formed by Letters",
      "java_brute": "// Solution for Maximum Score Words Formed by Letters",
      "java_optimal": "// Solution for Maximum Score Words Formed by Letters",
      "python_brute": "# Solution for Maximum Score Words Formed by Letters",
      "python_optimal": "# Solution for Maximum Score Words Formed by Letters"
    },
    "originalOrder": 757,
    "learningOrder": 757
  },
  {
    "id": 400,
    "number": 400,
    "sequence_number": 400,
    "title": "Minimum Moves to Move a Box to Their Target Location",
    "slug": "minimum-moves-to-move-a-box-to-their-target-location",
    "difficulty": "Hard",
    "topic": "Arrays",
    "subtopic": "Arrays Optimization",
    "pattern": "Arrays Pattern",
    "secondary_patterns": [
      "Arrays Pattern"
    ],
    "stage": "Binary Trees & Tree Traversals",
    "curriculumStage": "Stage 8 — Binary Trees & Tree Traversals",
    "roadmapPhase": "Stage 8 — Binary Trees & Tree Traversals",
    "phase": "Stage 8 — Binary Trees & Tree Traversals",
    "estimatedTime": 45,
    "statement": "Solve the **Minimum Moves to Move a Box to Their Target Location** problem using standard Arrays techniques. Given input constraints appropriate for Hard level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Arrays algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Arrays properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Arrays techniques by solving Hard problem constraints for Minimum Moves to Move a Box to Their Target Location.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/minimum-moves-to-move-a-box-to-their-target-location/",
    "leetcode_title": "Minimum Moves to Move a Box to Their Target Location",
    "leetcode_id": 1263,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/minimum-moves-to-move-a-box-to-their-target-location/",
    "canonicalSlug": "minimum-moves-to-move-a-box-to-their-target-location",
    "canonicalUrl": "https://leetcode.com/problems/minimum-moves-to-move-a-box-to-their-target-location/",
    "url": "https://leetcode.com/problems/minimum-moves-to-move-a-box-to-their-target-location/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Minimum Moves to Move a Box to Their Target Location\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Minimum Moves to Move a Box to Their Target Location\n};",
        "java": "// Java Solution for Minimum Moves to Move a Box to Their Target Location\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Minimum Moves to Move a Box to Their Target Location\n}",
        "python": "# Python Solution for Minimum Moves to Move a Box to Their Target Location\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Minimum Moves to Move a Box to Their Target Location\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Minimum Moves to Move a Box to Their Target Location\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Minimum Moves to Move a Box to Their Target Location\n};",
        "java": "// Optimal Java Solution for Minimum Moves to Move a Box to Their Target Location\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Minimum Moves to Move a Box to Their Target Location\n}",
        "python": "# Optimal Python Solution for Minimum Moves to Move a Box to Their Target Location\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Minimum Moves to Move a Box to Their Target Location\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Minimum Moves to Move a Box to Their Target Location",
      "cpp_optimal": "// Solution for Minimum Moves to Move a Box to Their Target Location",
      "java_brute": "// Solution for Minimum Moves to Move a Box to Their Target Location",
      "java_optimal": "// Solution for Minimum Moves to Move a Box to Their Target Location",
      "python_brute": "# Solution for Minimum Moves to Move a Box to Their Target Location",
      "python_optimal": "# Solution for Minimum Moves to Move a Box to Their Target Location"
    },
    "originalOrder": 758,
    "learningOrder": 758
  },
  {
    "id": 401,
    "number": 401,
    "sequence_number": 401,
    "title": "Range Sum of BST",
    "slug": "range-sum-of-bst",
    "difficulty": "Easy",
    "topic": "BST",
    "subtopic": "Hashing & Array Optimization",
    "pattern": "Hashing & Array Optimization",
    "secondary_patterns": [
      "Hashing & Array Optimization"
    ],
    "stage": "Binary Search Trees (BST) & Trie",
    "curriculumStage": "Stage 9 — Binary Search Trees (BST) & Trie",
    "roadmapPhase": "Stage 9 — Binary Search Trees (BST) & Trie",
    "phase": "Stage 9 — Binary Search Trees (BST) & Trie",
    "estimatedTime": 15,
    "statement": "Solve the **Range Sum of BST Challenge** problem using the **Hashing & Array Optimization** technique. Given input constraints appropriate for Easy level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^4",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Hashing & Array Optimization identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Hashing & Array Optimization. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Hashing & Array Optimization techniques by solving Easy problem constraints for Range Sum of BST Challenge.",
    "whyThisPattern": "When observing arrays & strings problem conditions, Hashing & Array Optimization optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Amazon",
      "Microsoft",
      "Uber"
    ],
    "companyRelevanceTier": "Medium",
    "leetcode_url": "https://leetcode.com/problems/range-sum-of-bst/",
    "leetcode_title": "Range Sum of BST",
    "leetcode_id": 938,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/range-sum-of-bst/",
    "canonicalSlug": "range-sum-of-bst",
    "canonicalUrl": "https://leetcode.com/problems/range-sum-of-bst/",
    "url": "https://leetcode.com/problems/range-sum-of-bst/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Range Sum of BST Challenge (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Range Sum of BST Challenge (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Range Sum of BST Challenge (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Range Sum of BST Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Range Sum of BST Challenge (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Range Sum of BST Challenge (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Range Sum of BST Challenge (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Range Sum of BST Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Range Sum of BST",
      "cpp_optimal": "// Solution for Range Sum of BST",
      "java_brute": "// Solution for Range Sum of BST",
      "java_optimal": "// Solution for Range Sum of BST",
      "python_brute": "# Solution for Range Sum of BST",
      "python_optimal": "# Solution for Range Sum of BST"
    },
    "originalOrder": 133,
    "learningOrder": 133
  },
  {
    "id": 402,
    "number": 402,
    "sequence_number": 402,
    "title": "Convert Sorted Array to Binary Search Tree",
    "slug": "convert-sorted-array-to-binary-search-tree",
    "difficulty": "Easy",
    "topic": "BST",
    "subtopic": "Two Pointers",
    "pattern": "Two Pointers",
    "secondary_patterns": [
      "Two Pointers"
    ],
    "stage": "Binary Search Trees (BST) & Trie",
    "curriculumStage": "Stage 9 — Binary Search Trees (BST) & Trie",
    "roadmapPhase": "Stage 9 — Binary Search Trees (BST) & Trie",
    "phase": "Stage 9 — Binary Search Trees (BST) & Trie",
    "estimatedTime": 15,
    "statement": "Solve the **Convert Sorted Array to Binary Search Tree Optimization** problem using the **Two Pointers** technique. Given input constraints appropriate for Easy level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^4",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Two Pointers identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Two Pointers. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Two Pointers techniques by solving Easy problem constraints for Convert Sorted Array to Binary Search Tree Optimization.",
    "whyThisPattern": "When observing binary search problem conditions, Two Pointers optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(1)",
    "companyRelevance": [
      "Meta",
      "Apple",
      "Netflix"
    ],
    "companyRelevanceTier": "Medium",
    "leetcode_url": "https://leetcode.com/problems/convert-sorted-array-to-binary-search-tree/",
    "leetcode_title": "Convert Sorted Array to Binary Search Tree",
    "leetcode_id": 108,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/convert-sorted-array-to-binary-search-tree/",
    "canonicalSlug": "convert-sorted-array-to-binary-search-tree",
    "canonicalUrl": "https://leetcode.com/problems/convert-sorted-array-to-binary-search-tree/",
    "url": "https://leetcode.com/problems/convert-sorted-array-to-binary-search-tree/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Convert Sorted Array to Binary Search Tree Optimization (Two Pointers)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Convert Sorted Array to Binary Search Tree Optimization (Two Pointers)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Convert Sorted Array to Binary Search Tree Optimization (Two Pointers)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Convert Sorted Array to Binary Search Tree Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Convert Sorted Array to Binary Search Tree Optimization (Two Pointers)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Convert Sorted Array to Binary Search Tree Optimization (Two Pointers)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Convert Sorted Array to Binary Search Tree Optimization (Two Pointers)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Convert Sorted Array to Binary Search Tree Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Convert Sorted Array to Binary Search Tree",
      "cpp_optimal": "// Solution for Convert Sorted Array to Binary Search Tree",
      "java_brute": "// Solution for Convert Sorted Array to Binary Search Tree",
      "java_optimal": "// Solution for Convert Sorted Array to Binary Search Tree",
      "python_brute": "# Solution for Convert Sorted Array to Binary Search Tree",
      "python_optimal": "# Solution for Convert Sorted Array to Binary Search Tree"
    },
    "originalOrder": 134,
    "learningOrder": 134
  },
  {
    "id": 403,
    "number": 403,
    "sequence_number": 403,
    "title": "Find Mode in Binary Search Tree",
    "slug": "find-mode-in-binary-search-tree",
    "difficulty": "Easy",
    "topic": "BST",
    "subtopic": "Binary Search",
    "pattern": "Binary Search",
    "secondary_patterns": [
      "Binary Search"
    ],
    "stage": "Binary Search Trees (BST) & Trie",
    "curriculumStage": "Stage 9 — Binary Search Trees (BST) & Trie",
    "roadmapPhase": "Stage 9 — Binary Search Trees (BST) & Trie",
    "phase": "Stage 9 — Binary Search Trees (BST) & Trie",
    "estimatedTime": 15,
    "statement": "Solve the **Find Mode in Binary Search Tree Optimization** problem using the **Binary Search** technique. Given input constraints appropriate for Easy level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^4",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Binary Search identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Binary Search. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Binary Search techniques by solving Easy problem constraints for Find Mode in Binary Search Tree Optimization.",
    "whyThisPattern": "When observing binary search problem conditions, Binary Search optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Meta",
      "Apple",
      "Netflix"
    ],
    "companyRelevanceTier": "Medium",
    "leetcode_url": "https://leetcode.com/problems/find-mode-in-binary-search-tree/",
    "leetcode_title": "Find Mode in Binary Search Tree",
    "leetcode_id": 501,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/find-mode-in-binary-search-tree/",
    "canonicalSlug": "find-mode-in-binary-search-tree",
    "canonicalUrl": "https://leetcode.com/problems/find-mode-in-binary-search-tree/",
    "url": "https://leetcode.com/problems/find-mode-in-binary-search-tree/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Find Mode in Binary Search Tree Optimization (Binary Search)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Find Mode in Binary Search Tree Optimization (Binary Search)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Find Mode in Binary Search Tree Optimization (Binary Search)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Find Mode in Binary Search Tree Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Find Mode in Binary Search Tree Optimization (Binary Search)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Find Mode in Binary Search Tree Optimization (Binary Search)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Find Mode in Binary Search Tree Optimization (Binary Search)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Find Mode in Binary Search Tree Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Find Mode in Binary Search Tree",
      "cpp_optimal": "// Solution for Find Mode in Binary Search Tree",
      "java_brute": "// Solution for Find Mode in Binary Search Tree",
      "java_optimal": "// Solution for Find Mode in Binary Search Tree",
      "python_brute": "# Solution for Find Mode in Binary Search Tree",
      "python_optimal": "# Solution for Find Mode in Binary Search Tree"
    },
    "originalOrder": 135,
    "learningOrder": 135
  },
  {
    "id": 404,
    "number": 404,
    "sequence_number": 404,
    "title": "Search in a Binary Search Tree",
    "slug": "search-in-a-binary-search-tree",
    "difficulty": "Easy",
    "topic": "BST",
    "subtopic": "Binary Search",
    "pattern": "Binary Search",
    "secondary_patterns": [
      "Binary Search"
    ],
    "stage": "Binary Search Trees (BST) & Trie",
    "curriculumStage": "Stage 9 — Binary Search Trees (BST) & Trie",
    "roadmapPhase": "Stage 9 — Binary Search Trees (BST) & Trie",
    "phase": "Stage 9 — Binary Search Trees (BST) & Trie",
    "estimatedTime": 15,
    "statement": "Solve the **Search in a Binary Search Tree Optimization** problem using the **Binary Search** technique. Given input constraints appropriate for Easy level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^4",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Binary Search identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Binary Search. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Binary Search techniques by solving Easy problem constraints for Search in a Binary Search Tree Optimization.",
    "whyThisPattern": "When observing binary search problem conditions, Binary Search optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Meta",
      "Apple",
      "Netflix"
    ],
    "companyRelevanceTier": "Medium",
    "leetcode_url": "https://leetcode.com/problems/search-in-a-binary-search-tree/",
    "leetcode_title": "Search in a Binary Search Tree",
    "leetcode_id": 700,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/search-in-a-binary-search-tree/",
    "canonicalSlug": "search-in-a-binary-search-tree",
    "canonicalUrl": "https://leetcode.com/problems/search-in-a-binary-search-tree/",
    "url": "https://leetcode.com/problems/search-in-a-binary-search-tree/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Search in a Binary Search Tree Optimization (Binary Search)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Search in a Binary Search Tree Optimization (Binary Search)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Search in a Binary Search Tree Optimization (Binary Search)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Search in a Binary Search Tree Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Search in a Binary Search Tree Optimization (Binary Search)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Search in a Binary Search Tree Optimization (Binary Search)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Search in a Binary Search Tree Optimization (Binary Search)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Search in a Binary Search Tree Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Search in a Binary Search Tree",
      "cpp_optimal": "// Solution for Search in a Binary Search Tree",
      "java_brute": "// Solution for Search in a Binary Search Tree",
      "java_optimal": "// Solution for Search in a Binary Search Tree",
      "python_brute": "# Solution for Search in a Binary Search Tree",
      "python_optimal": "# Solution for Search in a Binary Search Tree"
    },
    "originalOrder": 136,
    "learningOrder": 136
  },
  {
    "id": 405,
    "number": 405,
    "sequence_number": 405,
    "title": "Minimum Absolute Difference in BST",
    "slug": "minimum-absolute-difference-in-bst",
    "difficulty": "Easy",
    "topic": "BST",
    "subtopic": "Hashing & Array Optimization",
    "pattern": "Hashing & Array Optimization",
    "secondary_patterns": [
      "Hashing & Array Optimization"
    ],
    "stage": "Binary Search Trees (BST) & Trie",
    "curriculumStage": "Stage 9 — Binary Search Trees (BST) & Trie",
    "roadmapPhase": "Stage 9 — Binary Search Trees (BST) & Trie",
    "phase": "Stage 9 — Binary Search Trees (BST) & Trie",
    "estimatedTime": 15,
    "statement": "Solve the **Minimum Absolute Difference in BST Optimization** problem using the **Hashing & Array Optimization** technique. Given input constraints appropriate for Easy level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^4",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Hashing & Array Optimization identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Hashing & Array Optimization. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Hashing & Array Optimization techniques by solving Easy problem constraints for Minimum Absolute Difference in BST Optimization.",
    "whyThisPattern": "When observing arrays & strings problem conditions, Hashing & Array Optimization optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "LinkedIn",
      "Amazon"
    ],
    "companyRelevanceTier": "Medium",
    "leetcode_url": "https://leetcode.com/problems/minimum-absolute-difference-in-bst/",
    "leetcode_title": "Minimum Absolute Difference in BST",
    "leetcode_id": 530,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/minimum-absolute-difference-in-bst/",
    "canonicalSlug": "minimum-absolute-difference-in-bst",
    "canonicalUrl": "https://leetcode.com/problems/minimum-absolute-difference-in-bst/",
    "url": "https://leetcode.com/problems/minimum-absolute-difference-in-bst/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Minimum Absolute Difference in BST Optimization (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Minimum Absolute Difference in BST Optimization (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Minimum Absolute Difference in BST Optimization (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Minimum Absolute Difference in BST Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Minimum Absolute Difference in BST Optimization (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Minimum Absolute Difference in BST Optimization (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Minimum Absolute Difference in BST Optimization (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Minimum Absolute Difference in BST Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Minimum Absolute Difference in BST",
      "cpp_optimal": "// Solution for Minimum Absolute Difference in BST",
      "java_brute": "// Solution for Minimum Absolute Difference in BST",
      "java_optimal": "// Solution for Minimum Absolute Difference in BST",
      "python_brute": "# Solution for Minimum Absolute Difference in BST",
      "python_optimal": "# Solution for Minimum Absolute Difference in BST"
    },
    "originalOrder": 137,
    "learningOrder": 137
  },
  {
    "id": 406,
    "number": 406,
    "sequence_number": 406,
    "title": "Two Sum IV - Input is a BST",
    "slug": "two-sum-iv-input-is-a-bst",
    "difficulty": "Easy",
    "topic": "BST",
    "subtopic": "Two Pointers",
    "pattern": "Two Pointers",
    "secondary_patterns": [
      "Two Pointers"
    ],
    "stage": "Binary Search Trees (BST) & Trie",
    "curriculumStage": "Stage 9 — Binary Search Trees (BST) & Trie",
    "roadmapPhase": "Stage 9 — Binary Search Trees (BST) & Trie",
    "phase": "Stage 9 — Binary Search Trees (BST) & Trie",
    "estimatedTime": 15,
    "statement": "Solve the **Two Sum IV - Input is a BST Optimization** problem using the **Two Pointers** technique. Given input constraints appropriate for Easy level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^4",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Two Pointers identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Two Pointers. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Two Pointers techniques by solving Easy problem constraints for Two Sum IV - Input is a BST Optimization.",
    "whyThisPattern": "When observing arrays & strings problem conditions, Two Pointers optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(1)",
    "companyRelevance": [
      "Meta",
      "Apple",
      "Netflix"
    ],
    "companyRelevanceTier": "Medium",
    "leetcode_url": "https://leetcode.com/problems/two-sum-iv-input-is-a-bst/",
    "leetcode_title": "Two Sum IV - Input is a BST",
    "leetcode_id": 653,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/two-sum-iv-input-is-a-bst/",
    "canonicalSlug": "two-sum-iv-input-is-a-bst",
    "canonicalUrl": "https://leetcode.com/problems/two-sum-iv-input-is-a-bst/",
    "url": "https://leetcode.com/problems/two-sum-iv-input-is-a-bst/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Two Sum IV - Input is a BST Optimization (Two Pointers)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Two Sum IV - Input is a BST Optimization (Two Pointers)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Two Sum IV - Input is a BST Optimization (Two Pointers)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Two Sum IV - Input is a BST Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Two Sum IV - Input is a BST Optimization (Two Pointers)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Two Sum IV - Input is a BST Optimization (Two Pointers)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Two Sum IV - Input is a BST Optimization (Two Pointers)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Two Sum IV - Input is a BST Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Two Sum IV - Input is a BST",
      "cpp_optimal": "// Solution for Two Sum IV - Input is a BST",
      "java_brute": "// Solution for Two Sum IV - Input is a BST",
      "java_optimal": "// Solution for Two Sum IV - Input is a BST",
      "python_brute": "# Solution for Two Sum IV - Input is a BST",
      "python_optimal": "# Solution for Two Sum IV - Input is a BST"
    },
    "originalOrder": 138,
    "learningOrder": 138
  },
  {
    "id": 407,
    "number": 407,
    "sequence_number": 407,
    "title": "Count Binary Substrings",
    "slug": "count-binary-substrings",
    "difficulty": "Easy",
    "topic": "BST",
    "subtopic": "Sliding Window",
    "pattern": "Sliding Window",
    "secondary_patterns": [
      "Sliding Window"
    ],
    "stage": "Binary Search Trees (BST) & Trie",
    "curriculumStage": "Stage 9 — Binary Search Trees (BST) & Trie",
    "roadmapPhase": "Stage 9 — Binary Search Trees (BST) & Trie",
    "phase": "Stage 9 — Binary Search Trees (BST) & Trie",
    "estimatedTime": 15,
    "statement": "Solve the **Count Binary Substrings Optimization** problem using the **Sliding Window** technique. Given input constraints appropriate for Easy level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^4",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Sliding Window identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Sliding Window. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Sliding Window techniques by solving Easy problem constraints for Count Binary Substrings Optimization.",
    "whyThisPattern": "When observing arrays & strings problem conditions, Sliding Window optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Meta",
      "Apple",
      "Netflix"
    ],
    "companyRelevanceTier": "Medium",
    "leetcode_url": "https://leetcode.com/problems/count-binary-substrings/",
    "leetcode_title": "Count Binary Substrings",
    "leetcode_id": 696,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/count-binary-substrings/",
    "canonicalSlug": "count-binary-substrings",
    "canonicalUrl": "https://leetcode.com/problems/count-binary-substrings/",
    "url": "https://leetcode.com/problems/count-binary-substrings/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Count Binary Substrings Optimization (Sliding Window)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Count Binary Substrings Optimization (Sliding Window)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Count Binary Substrings Optimization (Sliding Window)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Count Binary Substrings Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Count Binary Substrings Optimization (Sliding Window)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Count Binary Substrings Optimization (Sliding Window)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Count Binary Substrings Optimization (Sliding Window)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Count Binary Substrings Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Count Binary Substrings",
      "cpp_optimal": "// Solution for Count Binary Substrings",
      "java_brute": "// Solution for Count Binary Substrings",
      "java_optimal": "// Solution for Count Binary Substrings",
      "python_brute": "# Solution for Count Binary Substrings",
      "python_optimal": "# Solution for Count Binary Substrings"
    },
    "originalOrder": 139,
    "learningOrder": 139
  },
  {
    "id": 408,
    "number": 408,
    "sequence_number": 408,
    "title": "Minimum Distance Between BST Nodes",
    "slug": "minimum-distance-between-bst-nodes",
    "difficulty": "Easy",
    "topic": "BST",
    "subtopic": "Pointer Manipulation",
    "pattern": "Pointer Manipulation",
    "secondary_patterns": [
      "Pointer Manipulation"
    ],
    "stage": "Binary Search Trees (BST) & Trie",
    "curriculumStage": "Stage 9 — Binary Search Trees (BST) & Trie",
    "roadmapPhase": "Stage 9 — Binary Search Trees (BST) & Trie",
    "phase": "Stage 9 — Binary Search Trees (BST) & Trie",
    "estimatedTime": 15,
    "statement": "Solve the **Minimum Distance Between BST Nodes Challenge** problem using the **Pointer Manipulation** technique. Given input constraints appropriate for Easy level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^4",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Pointer Manipulation identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Pointer Manipulation. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Pointer Manipulation techniques by solving Easy problem constraints for Minimum Distance Between BST Nodes Challenge.",
    "whyThisPattern": "When observing arrays & strings problem conditions, Pointer Manipulation optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Amazon",
      "Microsoft",
      "Uber"
    ],
    "companyRelevanceTier": "Medium",
    "leetcode_url": "https://leetcode.com/problems/minimum-distance-between-bst-nodes/",
    "leetcode_title": "Minimum Distance Between BST Nodes",
    "leetcode_id": 783,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/minimum-distance-between-bst-nodes/",
    "canonicalSlug": "minimum-distance-between-bst-nodes",
    "canonicalUrl": "https://leetcode.com/problems/minimum-distance-between-bst-nodes/",
    "url": "https://leetcode.com/problems/minimum-distance-between-bst-nodes/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Minimum Distance Between BST Nodes Challenge (Pointer Manipulation)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Minimum Distance Between BST Nodes Challenge (Pointer Manipulation)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Minimum Distance Between BST Nodes Challenge (Pointer Manipulation)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Minimum Distance Between BST Nodes Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Minimum Distance Between BST Nodes Challenge (Pointer Manipulation)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Minimum Distance Between BST Nodes Challenge (Pointer Manipulation)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Minimum Distance Between BST Nodes Challenge (Pointer Manipulation)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Minimum Distance Between BST Nodes Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Minimum Distance Between BST Nodes",
      "cpp_optimal": "// Solution for Minimum Distance Between BST Nodes",
      "java_brute": "// Solution for Minimum Distance Between BST Nodes",
      "java_optimal": "// Solution for Minimum Distance Between BST Nodes",
      "python_brute": "# Solution for Minimum Distance Between BST Nodes",
      "python_optimal": "# Solution for Minimum Distance Between BST Nodes"
    },
    "originalOrder": 140,
    "learningOrder": 140
  },
  {
    "id": 409,
    "number": 409,
    "sequence_number": 409,
    "title": "Big Countries",
    "slug": "big-countries",
    "difficulty": "Easy",
    "topic": "Trie",
    "subtopic": "Hashing & Array Optimization",
    "pattern": "Hashing & Array Optimization",
    "secondary_patterns": [
      "Hashing & Array Optimization"
    ],
    "stage": "Binary Search Trees (BST) & Trie",
    "curriculumStage": "Stage 9 — Binary Search Trees (BST) & Trie",
    "roadmapPhase": "Stage 9 — Binary Search Trees (BST) & Trie",
    "phase": "Stage 9 — Binary Search Trees (BST) & Trie",
    "estimatedTime": 15,
    "statement": "Solve the **Big Countries Optimization** problem using the **Hashing & Array Optimization** technique. Given input constraints appropriate for Easy level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^4",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Hashing & Array Optimization identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Hashing & Array Optimization. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Hashing & Array Optimization techniques by solving Easy problem constraints for Big Countries Optimization.",
    "whyThisPattern": "When observing trie data structure problem conditions, Hashing & Array Optimization optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "LinkedIn",
      "Amazon"
    ],
    "companyRelevanceTier": "Medium",
    "leetcode_url": "https://leetcode.com/problems/big-countries/",
    "leetcode_title": "Big Countries",
    "leetcode_id": 595,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/big-countries/",
    "canonicalSlug": "big-countries",
    "canonicalUrl": "https://leetcode.com/problems/big-countries/",
    "url": "https://leetcode.com/problems/big-countries/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Big Countries Optimization (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Big Countries Optimization (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Big Countries Optimization (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Big Countries Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Big Countries Optimization (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Big Countries Optimization (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Big Countries Optimization (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Big Countries Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Big Countries",
      "cpp_optimal": "// Solution for Big Countries",
      "java_brute": "// Solution for Big Countries",
      "java_optimal": "// Solution for Big Countries",
      "python_brute": "# Solution for Big Countries",
      "python_optimal": "# Solution for Big Countries"
    },
    "originalOrder": 240,
    "learningOrder": 240
  },
  {
    "id": 410,
    "number": 410,
    "sequence_number": 410,
    "title": "Balanced Binary Tree",
    "slug": "balanced-binary-tree",
    "difficulty": "Easy",
    "topic": "Trees",
    "subtopic": "Tree Traversal & Recursion",
    "pattern": "Tree Traversal & Recursion",
    "secondary_patterns": [
      "Tree Traversal & Recursion"
    ],
    "stage": "Binary Search Trees (BST) & Trie",
    "curriculumStage": "Stage 9 — Binary Search Trees (BST) & Trie",
    "roadmapPhase": "Stage 9 — Binary Search Trees (BST) & Trie",
    "phase": "Stage 9 — Binary Search Trees (BST) & Trie",
    "estimatedTime": 15,
    "statement": "Solve the **Balanced Binary Tree Challenge** problem using the **Tree Traversal & Recursion** technique. Given input constraints appropriate for Easy level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^4",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Tree Traversal & Recursion identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Tree Traversal & Recursion. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Tree Traversal & Recursion techniques by solving Easy problem constraints for Balanced Binary Tree Challenge.",
    "whyThisPattern": "When observing binary trees problem conditions, Tree Traversal & Recursion optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Microsoft",
      "Bloomberg",
      "Adobe"
    ],
    "companyRelevanceTier": "Medium",
    "leetcode_url": "https://leetcode.com/problems/balanced-binary-tree/",
    "leetcode_title": "Balanced Binary Tree",
    "leetcode_id": 110,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/balanced-binary-tree/",
    "canonicalSlug": "balanced-binary-tree",
    "canonicalUrl": "https://leetcode.com/problems/balanced-binary-tree/",
    "url": "https://leetcode.com/problems/balanced-binary-tree/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Balanced Binary Tree Challenge (Tree Traversal & Recursion)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Balanced Binary Tree Challenge (Tree Traversal & Recursion)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Balanced Binary Tree Challenge (Tree Traversal & Recursion)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Balanced Binary Tree Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Balanced Binary Tree Challenge (Tree Traversal & Recursion)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Balanced Binary Tree Challenge (Tree Traversal & Recursion)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Balanced Binary Tree Challenge (Tree Traversal & Recursion)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Balanced Binary Tree Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Balanced Binary Tree",
      "cpp_optimal": "// Solution for Balanced Binary Tree",
      "java_brute": "// Solution for Balanced Binary Tree",
      "java_optimal": "// Solution for Balanced Binary Tree",
      "python_brute": "# Solution for Balanced Binary Tree",
      "python_optimal": "# Solution for Balanced Binary Tree"
    },
    "originalOrder": 226,
    "learningOrder": 226
  },
  {
    "id": 411,
    "number": 411,
    "sequence_number": 411,
    "title": "Longest Substring Without Repeating Characters",
    "slug": "longest-substring-without-repeating-characters",
    "difficulty": "Medium",
    "topic": "BST",
    "subtopic": "BST Optimization",
    "pattern": "Sliding Window",
    "secondary_patterns": [
      "Sliding Window"
    ],
    "stage": "Binary Search Trees (BST) & Trie",
    "curriculumStage": "Stage 9 — Binary Search Trees (BST) & Trie",
    "roadmapPhase": "Stage 9 — Binary Search Trees (BST) & Trie",
    "phase": "Stage 9 — Binary Search Trees (BST) & Trie",
    "estimatedTime": 30,
    "statement": "Finds the length of the longest substring without repeating characters using a sliding window and set/map.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "All elements fall within standard integer bounds."
    ],
    "examples": [
      {
        "input": "s = 'abcabcbb'",
        "output": "3",
        "explanation": "Optimal solution achieved using Sliding Window."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "All duplicate elements"
    ],
    "commonMistakes": [
      "Off-by-one index mistakes",
      "Integer overflow for large cumulative sums"
    ],
    "hints": [
      "Consider using Sliding Window.",
      "Analyze edge cases and bounds."
    ],
    "learningObjective": "Master BST techniques by solving Medium problem constraints for Longest Substring Without Repeating Characters.",
    "whyThisPattern": "When observing BST problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(1)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/longest-substring-without-repeating-characters/",
    "leetcode_title": "Longest Substring Without Repeating Characters",
    "leetcode_id": 3,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/longest-substring-without-repeating-characters/",
    "canonicalSlug": "longest-substring-without-repeating-characters",
    "canonicalUrl": "https://leetcode.com/problems/longest-substring-without-repeating-characters/",
    "url": "https://leetcode.com/problems/longest-substring-without-repeating-characters/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Longest Substring Without Repeating Characters\n#include <iostream>\n#include <vector>\n#include <algorithm>\n\nclass Solution {\npublic:\n    int longestSubstringWithoutRepeatingCharacters(std::vector<int>& nums) {\n        int n = nums.size();\n        if (n == 0) return 0;\n        int ans = 0;\n        for (int i = 0; i < n; i++) {\n            ans += nums[i];\n        }\n        return ans;\n    }\n};",
        "java": "// Java Solution for Longest Substring Without Repeating Characters\nimport java.util.*;\n\nclass Solution {\n    public int longestSubstringWithoutRepeatingCharacters(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int ans = 0;\n        for (int num : nums) {\n            ans += num;\n        }\n        return ans;\n    }\n}",
        "python": "# Python Solution for Longest Substring Without Repeating Characters\n\nclass Solution:\n    def longestSubstringWithoutRepeatingCharacters(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        ans = 0\n        for num in nums:\n            ans += num\n        return ans\n",
        "javascript": "// JavaScript Solution for Longest Substring Without Repeating Characters\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Longest Substring Without Repeating Characters\n#include <iostream>\n#include <vector>\n#include <algorithm>\n\nclass Solution {\npublic:\n    int longestSubstringWithoutRepeatingCharacters(std::vector<int>& nums) {\n        int n = nums.size();\n        if (n == 0) return 0;\n        int ans = 0;\n        for (int i = 0; i < n; i++) {\n            ans += nums[i];\n        }\n        return ans;\n    }\n};",
        "java": "// Java Solution for Longest Substring Without Repeating Characters\nimport java.util.*;\n\nclass Solution {\n    public int longestSubstringWithoutRepeatingCharacters(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int ans = 0;\n        for (int num : nums) {\n            ans += num;\n        }\n        return ans;\n    }\n}",
        "python": "# Python Solution for Longest Substring Without Repeating Characters\n\nclass Solution:\n    def longestSubstringWithoutRepeatingCharacters(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        ans = 0\n        for num in nums:\n            ans += num\n        return ans\n",
        "javascript": "// JavaScript Solution for Longest Substring Without Repeating Characters\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Longest Substring Without Repeating Characters",
      "cpp_optimal": "// Solution for Longest Substring Without Repeating Characters",
      "java_brute": "// Solution for Longest Substring Without Repeating Characters",
      "java_optimal": "// Solution for Longest Substring Without Repeating Characters",
      "python_brute": "# Solution for Longest Substring Without Repeating Characters",
      "python_optimal": "# Solution for Longest Substring Without Repeating Characters"
    },
    "originalOrder": 431,
    "learningOrder": 431
  },
  {
    "id": 412,
    "number": 412,
    "sequence_number": 412,
    "title": "Longest Repeating Character Replacement",
    "slug": "longest-repeating-character-replacement",
    "difficulty": "Medium",
    "topic": "BST",
    "subtopic": "BST Optimization",
    "pattern": "Sliding Window",
    "secondary_patterns": [
      "Sliding Window"
    ],
    "stage": "Binary Search Trees (BST) & Trie",
    "curriculumStage": "Stage 9 — Binary Search Trees (BST) & Trie",
    "roadmapPhase": "Stage 9 — Binary Search Trees (BST) & Trie",
    "phase": "Stage 9 — Binary Search Trees (BST) & Trie",
    "estimatedTime": 30,
    "statement": "Finds the length of the longest substring containing same letters after at most K character replacements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "All elements fall within standard integer bounds."
    ],
    "examples": [
      {
        "input": "s = 'AABABBA', k = 1",
        "output": "4",
        "explanation": "Optimal solution achieved using Sliding Window."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "All duplicate elements"
    ],
    "commonMistakes": [
      "Off-by-one index mistakes",
      "Integer overflow for large cumulative sums"
    ],
    "hints": [
      "Consider using Sliding Window.",
      "Analyze edge cases and bounds."
    ],
    "learningObjective": "Master BST techniques by solving Medium problem constraints for Longest Repeating Character Replacement.",
    "whyThisPattern": "When observing BST problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(1)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/longest-repeating-character-replacement/",
    "leetcode_title": "Longest Repeating Character Replacement",
    "leetcode_id": 424,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/longest-repeating-character-replacement/",
    "canonicalSlug": "longest-repeating-character-replacement",
    "canonicalUrl": "https://leetcode.com/problems/longest-repeating-character-replacement/",
    "url": "https://leetcode.com/problems/longest-repeating-character-replacement/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Longest Repeating Character Replacement\n#include <iostream>\n#include <vector>\n#include <algorithm>\n\nclass Solution {\npublic:\n    int longestRepeatingCharacterReplacement(std::vector<int>& nums) {\n        int n = nums.size();\n        if (n == 0) return 0;\n        int ans = 0;\n        for (int i = 0; i < n; i++) {\n            ans += nums[i];\n        }\n        return ans;\n    }\n};",
        "java": "// Java Solution for Longest Repeating Character Replacement\nimport java.util.*;\n\nclass Solution {\n    public int longestRepeatingCharacterReplacement(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int ans = 0;\n        for (int num : nums) {\n            ans += num;\n        }\n        return ans;\n    }\n}",
        "python": "# Python Solution for Longest Repeating Character Replacement\n\nclass Solution:\n    def longestRepeatingCharacterReplacement(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        ans = 0\n        for num in nums:\n            ans += num\n        return ans\n",
        "javascript": "// JavaScript Solution for Longest Repeating Character Replacement\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Longest Repeating Character Replacement\n#include <iostream>\n#include <vector>\n#include <algorithm>\n\nclass Solution {\npublic:\n    int longestRepeatingCharacterReplacement(std::vector<int>& nums) {\n        int n = nums.size();\n        if (n == 0) return 0;\n        int ans = 0;\n        for (int i = 0; i < n; i++) {\n            ans += nums[i];\n        }\n        return ans;\n    }\n};",
        "java": "// Java Solution for Longest Repeating Character Replacement\nimport java.util.*;\n\nclass Solution {\n    public int longestRepeatingCharacterReplacement(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int ans = 0;\n        for (int num : nums) {\n            ans += num;\n        }\n        return ans;\n    }\n}",
        "python": "# Python Solution for Longest Repeating Character Replacement\n\nclass Solution:\n    def longestRepeatingCharacterReplacement(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        ans = 0\n        for num in nums:\n            ans += num\n        return ans\n",
        "javascript": "// JavaScript Solution for Longest Repeating Character Replacement\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Longest Repeating Character Replacement",
      "cpp_optimal": "// Solution for Longest Repeating Character Replacement",
      "java_brute": "// Solution for Longest Repeating Character Replacement",
      "java_optimal": "// Solution for Longest Repeating Character Replacement",
      "python_brute": "# Solution for Longest Repeating Character Replacement",
      "python_optimal": "# Solution for Longest Repeating Character Replacement"
    },
    "originalOrder": 432,
    "learningOrder": 432
  },
  {
    "id": 413,
    "number": 413,
    "sequence_number": 413,
    "title": "Unique Binary Search Trees II",
    "slug": "unique-binary-search-trees-ii",
    "difficulty": "Medium",
    "topic": "BST",
    "subtopic": "Binary Search",
    "pattern": "Binary Search",
    "secondary_patterns": [
      "Binary Search"
    ],
    "stage": "Binary Search Trees (BST) & Trie",
    "curriculumStage": "Stage 9 — Binary Search Trees (BST) & Trie",
    "roadmapPhase": "Stage 9 — Binary Search Trees (BST) & Trie",
    "phase": "Stage 9 — Binary Search Trees (BST) & Trie",
    "estimatedTime": 30,
    "statement": "Solve the **Unique Binary Search Trees II Challenge** problem using the **Binary Search** technique. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Binary Search identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Binary Search. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Binary Search techniques by solving Medium problem constraints for Unique Binary Search Trees II Challenge.",
    "whyThisPattern": "When observing binary search problem conditions, Binary Search optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Microsoft",
      "Bloomberg",
      "Adobe"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/unique-binary-search-trees-ii/",
    "leetcode_title": "Unique Binary Search Trees II",
    "leetcode_id": 95,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/unique-binary-search-trees-ii/",
    "canonicalSlug": "unique-binary-search-trees-ii",
    "canonicalUrl": "https://leetcode.com/problems/unique-binary-search-trees-ii/",
    "url": "https://leetcode.com/problems/unique-binary-search-trees-ii/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Unique Binary Search Trees II Challenge (Binary Search)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Unique Binary Search Trees II Challenge (Binary Search)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Unique Binary Search Trees II Challenge (Binary Search)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Unique Binary Search Trees II Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Unique Binary Search Trees II Challenge (Binary Search)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Unique Binary Search Trees II Challenge (Binary Search)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Unique Binary Search Trees II Challenge (Binary Search)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Unique Binary Search Trees II Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Unique Binary Search Trees II",
      "cpp_optimal": "// Solution for Unique Binary Search Trees II",
      "java_brute": "// Solution for Unique Binary Search Trees II",
      "java_optimal": "// Solution for Unique Binary Search Trees II",
      "python_brute": "# Solution for Unique Binary Search Trees II",
      "python_optimal": "# Solution for Unique Binary Search Trees II"
    },
    "originalOrder": 433,
    "learningOrder": 433
  },
  {
    "id": 414,
    "number": 414,
    "sequence_number": 414,
    "title": "Unique Binary Search Trees",
    "slug": "unique-binary-search-trees",
    "difficulty": "Medium",
    "topic": "BST",
    "subtopic": "Binary Search",
    "pattern": "Binary Search",
    "secondary_patterns": [
      "Binary Search"
    ],
    "stage": "Binary Search Trees (BST) & Trie",
    "curriculumStage": "Stage 9 — Binary Search Trees (BST) & Trie",
    "roadmapPhase": "Stage 9 — Binary Search Trees (BST) & Trie",
    "phase": "Stage 9 — Binary Search Trees (BST) & Trie",
    "estimatedTime": 30,
    "statement": "Solve the **Unique Binary Search Trees Challenge** problem using the **Binary Search** technique. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Binary Search identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Binary Search. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Binary Search techniques by solving Medium problem constraints for Unique Binary Search Trees Challenge.",
    "whyThisPattern": "When observing binary search problem conditions, Binary Search optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Amazon",
      "Microsoft",
      "Uber"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/unique-binary-search-trees/",
    "leetcode_title": "Unique Binary Search Trees",
    "leetcode_id": 96,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/unique-binary-search-trees/",
    "canonicalSlug": "unique-binary-search-trees",
    "canonicalUrl": "https://leetcode.com/problems/unique-binary-search-trees/",
    "url": "https://leetcode.com/problems/unique-binary-search-trees/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Unique Binary Search Trees Challenge (Binary Search)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Unique Binary Search Trees Challenge (Binary Search)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Unique Binary Search Trees Challenge (Binary Search)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Unique Binary Search Trees Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Unique Binary Search Trees Challenge (Binary Search)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Unique Binary Search Trees Challenge (Binary Search)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Unique Binary Search Trees Challenge (Binary Search)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Unique Binary Search Trees Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Unique Binary Search Trees",
      "cpp_optimal": "// Solution for Unique Binary Search Trees",
      "java_brute": "// Solution for Unique Binary Search Trees",
      "java_optimal": "// Solution for Unique Binary Search Trees",
      "python_brute": "# Solution for Unique Binary Search Trees",
      "python_optimal": "# Solution for Unique Binary Search Trees"
    },
    "originalOrder": 434,
    "learningOrder": 434
  },
  {
    "id": 415,
    "number": 415,
    "sequence_number": 415,
    "title": "Validate Binary Search Tree",
    "slug": "validate-binary-search-tree",
    "difficulty": "Medium",
    "topic": "BST",
    "subtopic": "Binary Search",
    "pattern": "Binary Search",
    "secondary_patterns": [
      "Binary Search"
    ],
    "stage": "Binary Search Trees (BST) & Trie",
    "curriculumStage": "Stage 9 — Binary Search Trees (BST) & Trie",
    "roadmapPhase": "Stage 9 — Binary Search Trees (BST) & Trie",
    "phase": "Stage 9 — Binary Search Trees (BST) & Trie",
    "estimatedTime": 30,
    "statement": "Solve the **Validate Binary Search Tree Challenge** problem using the **Binary Search** technique. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Binary Search identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Binary Search. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Binary Search techniques by solving Medium problem constraints for Validate Binary Search Tree Challenge.",
    "whyThisPattern": "When observing binary search problem conditions, Binary Search optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Microsoft",
      "Bloomberg",
      "Adobe"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/validate-binary-search-tree/",
    "leetcode_title": "Validate Binary Search Tree",
    "leetcode_id": 98,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/validate-binary-search-tree/",
    "canonicalSlug": "validate-binary-search-tree",
    "canonicalUrl": "https://leetcode.com/problems/validate-binary-search-tree/",
    "url": "https://leetcode.com/problems/validate-binary-search-tree/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Validate Binary Search Tree Challenge (Binary Search)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Validate Binary Search Tree Challenge (Binary Search)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Validate Binary Search Tree Challenge (Binary Search)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Validate Binary Search Tree Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Validate Binary Search Tree Challenge (Binary Search)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Validate Binary Search Tree Challenge (Binary Search)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Validate Binary Search Tree Challenge (Binary Search)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Validate Binary Search Tree Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Validate Binary Search Tree",
      "cpp_optimal": "// Solution for Validate Binary Search Tree",
      "java_brute": "// Solution for Validate Binary Search Tree",
      "java_optimal": "// Solution for Validate Binary Search Tree",
      "python_brute": "# Solution for Validate Binary Search Tree",
      "python_optimal": "# Solution for Validate Binary Search Tree"
    },
    "originalOrder": 435,
    "learningOrder": 435
  },
  {
    "id": 416,
    "number": 416,
    "sequence_number": 416,
    "title": "Recover Binary Search Tree",
    "slug": "recover-binary-search-tree",
    "difficulty": "Medium",
    "topic": "BST",
    "subtopic": "Binary Search",
    "pattern": "Binary Search",
    "secondary_patterns": [
      "Binary Search"
    ],
    "stage": "Binary Search Trees (BST) & Trie",
    "curriculumStage": "Stage 9 — Binary Search Trees (BST) & Trie",
    "roadmapPhase": "Stage 9 — Binary Search Trees (BST) & Trie",
    "phase": "Stage 9 — Binary Search Trees (BST) & Trie",
    "estimatedTime": 30,
    "statement": "Solve the **Recover Binary Search Tree Challenge** problem using the **Binary Search** technique. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Binary Search identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Binary Search. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Binary Search techniques by solving Medium problem constraints for Recover Binary Search Tree Challenge.",
    "whyThisPattern": "When observing binary search problem conditions, Binary Search optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Microsoft",
      "Bloomberg"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/recover-binary-search-tree/",
    "leetcode_title": "Recover Binary Search Tree",
    "leetcode_id": 99,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/recover-binary-search-tree/",
    "canonicalSlug": "recover-binary-search-tree",
    "canonicalUrl": "https://leetcode.com/problems/recover-binary-search-tree/",
    "url": "https://leetcode.com/problems/recover-binary-search-tree/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Recover Binary Search Tree Challenge (Binary Search)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Recover Binary Search Tree Challenge (Binary Search)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Recover Binary Search Tree Challenge (Binary Search)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Recover Binary Search Tree Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Recover Binary Search Tree Challenge (Binary Search)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Recover Binary Search Tree Challenge (Binary Search)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Recover Binary Search Tree Challenge (Binary Search)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Recover Binary Search Tree Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Recover Binary Search Tree",
      "cpp_optimal": "// Solution for Recover Binary Search Tree",
      "java_brute": "// Solution for Recover Binary Search Tree",
      "java_optimal": "// Solution for Recover Binary Search Tree",
      "python_brute": "# Solution for Recover Binary Search Tree",
      "python_optimal": "# Solution for Recover Binary Search Tree"
    },
    "originalOrder": 436,
    "learningOrder": 436
  },
  {
    "id": 417,
    "number": 417,
    "sequence_number": 417,
    "title": "Binary Search Tree Iterator",
    "slug": "binary-search-tree-iterator",
    "difficulty": "Medium",
    "topic": "BST",
    "subtopic": "Binary Search",
    "pattern": "Binary Search",
    "secondary_patterns": [
      "Binary Search"
    ],
    "stage": "Binary Search Trees (BST) & Trie",
    "curriculumStage": "Stage 9 — Binary Search Trees (BST) & Trie",
    "roadmapPhase": "Stage 9 — Binary Search Trees (BST) & Trie",
    "phase": "Stage 9 — Binary Search Trees (BST) & Trie",
    "estimatedTime": 30,
    "statement": "Solve the **Binary Search Tree Iterator Challenge** problem using the **Binary Search** technique. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Binary Search identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Binary Search. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Binary Search techniques by solving Medium problem constraints for Binary Search Tree Iterator Challenge.",
    "whyThisPattern": "When observing binary search problem conditions, Binary Search optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Microsoft",
      "Bloomberg",
      "Adobe"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/binary-search-tree-iterator/",
    "leetcode_title": "Binary Search Tree Iterator",
    "leetcode_id": 173,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/binary-search-tree-iterator/",
    "canonicalSlug": "binary-search-tree-iterator",
    "canonicalUrl": "https://leetcode.com/problems/binary-search-tree-iterator/",
    "url": "https://leetcode.com/problems/binary-search-tree-iterator/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Binary Search Tree Iterator Challenge (Binary Search)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Binary Search Tree Iterator Challenge (Binary Search)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Binary Search Tree Iterator Challenge (Binary Search)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Binary Search Tree Iterator Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Binary Search Tree Iterator Challenge (Binary Search)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Binary Search Tree Iterator Challenge (Binary Search)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Binary Search Tree Iterator Challenge (Binary Search)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Binary Search Tree Iterator Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Binary Search Tree Iterator",
      "cpp_optimal": "// Solution for Binary Search Tree Iterator",
      "java_brute": "// Solution for Binary Search Tree Iterator",
      "java_optimal": "// Solution for Binary Search Tree Iterator",
      "python_brute": "# Solution for Binary Search Tree Iterator",
      "python_optimal": "# Solution for Binary Search Tree Iterator"
    },
    "originalOrder": 437,
    "learningOrder": 437
  },
  {
    "id": 418,
    "number": 418,
    "sequence_number": 418,
    "title": "Lowest Common Ancestor of a Binary Search Tree",
    "slug": "lowest-common-ancestor-of-a-binary-search-tree",
    "difficulty": "Medium",
    "topic": "BST",
    "subtopic": "Binary Search",
    "pattern": "Binary Search",
    "secondary_patterns": [
      "Binary Search"
    ],
    "stage": "Binary Search Trees (BST) & Trie",
    "curriculumStage": "Stage 9 — Binary Search Trees (BST) & Trie",
    "roadmapPhase": "Stage 9 — Binary Search Trees (BST) & Trie",
    "phase": "Stage 9 — Binary Search Trees (BST) & Trie",
    "estimatedTime": 30,
    "statement": "Solve the **Lowest Common Ancestor of a Binary Search Tree Challenge** problem using the **Binary Search** technique. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Binary Search identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Binary Search. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Binary Search techniques by solving Medium problem constraints for Lowest Common Ancestor of a Binary Search Tree Challenge.",
    "whyThisPattern": "When observing binary search problem conditions, Binary Search optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Meta",
      "Uber",
      "Databricks"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/lowest-common-ancestor-of-a-binary-search-tree/",
    "leetcode_title": "Lowest Common Ancestor of a Binary Search Tree",
    "leetcode_id": 235,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/lowest-common-ancestor-of-a-binary-search-tree/",
    "canonicalSlug": "lowest-common-ancestor-of-a-binary-search-tree",
    "canonicalUrl": "https://leetcode.com/problems/lowest-common-ancestor-of-a-binary-search-tree/",
    "url": "https://leetcode.com/problems/lowest-common-ancestor-of-a-binary-search-tree/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Lowest Common Ancestor of a Binary Search Tree Challenge (Binary Search)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Lowest Common Ancestor of a Binary Search Tree Challenge (Binary Search)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Lowest Common Ancestor of a Binary Search Tree Challenge (Binary Search)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Lowest Common Ancestor of a Binary Search Tree Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Lowest Common Ancestor of a Binary Search Tree Challenge (Binary Search)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Lowest Common Ancestor of a Binary Search Tree Challenge (Binary Search)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Lowest Common Ancestor of a Binary Search Tree Challenge (Binary Search)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Lowest Common Ancestor of a Binary Search Tree Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Lowest Common Ancestor of a Binary Search Tree",
      "cpp_optimal": "// Solution for Lowest Common Ancestor of a Binary Search Tree",
      "java_brute": "// Solution for Lowest Common Ancestor of a Binary Search Tree",
      "java_optimal": "// Solution for Lowest Common Ancestor of a Binary Search Tree",
      "python_brute": "# Solution for Lowest Common Ancestor of a Binary Search Tree",
      "python_optimal": "# Solution for Lowest Common Ancestor of a Binary Search Tree"
    },
    "originalOrder": 438,
    "learningOrder": 438
  },
  {
    "id": 419,
    "number": 419,
    "sequence_number": 419,
    "title": "Trim a Binary Search Tree",
    "slug": "trim-a-binary-search-tree",
    "difficulty": "Medium",
    "topic": "BST",
    "subtopic": "Binary Search",
    "pattern": "Binary Search",
    "secondary_patterns": [
      "Binary Search"
    ],
    "stage": "Binary Search Trees (BST) & Trie",
    "curriculumStage": "Stage 9 — Binary Search Trees (BST) & Trie",
    "roadmapPhase": "Stage 9 — Binary Search Trees (BST) & Trie",
    "phase": "Stage 9 — Binary Search Trees (BST) & Trie",
    "estimatedTime": 30,
    "statement": "Solve the **Trim a Binary Search Tree Challenge** problem using the **Binary Search** technique. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Binary Search identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Binary Search. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Binary Search techniques by solving Medium problem constraints for Trim a Binary Search Tree Challenge.",
    "whyThisPattern": "When observing binary search problem conditions, Binary Search optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Microsoft",
      "Bloomberg"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/trim-a-binary-search-tree/",
    "leetcode_title": "Trim a Binary Search Tree",
    "leetcode_id": 669,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/trim-a-binary-search-tree/",
    "canonicalSlug": "trim-a-binary-search-tree",
    "canonicalUrl": "https://leetcode.com/problems/trim-a-binary-search-tree/",
    "url": "https://leetcode.com/problems/trim-a-binary-search-tree/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Trim a Binary Search Tree Challenge (Binary Search)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Trim a Binary Search Tree Challenge (Binary Search)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Trim a Binary Search Tree Challenge (Binary Search)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Trim a Binary Search Tree Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Trim a Binary Search Tree Challenge (Binary Search)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Trim a Binary Search Tree Challenge (Binary Search)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Trim a Binary Search Tree Challenge (Binary Search)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Trim a Binary Search Tree Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Trim a Binary Search Tree",
      "cpp_optimal": "// Solution for Trim a Binary Search Tree",
      "java_brute": "// Solution for Trim a Binary Search Tree",
      "java_optimal": "// Solution for Trim a Binary Search Tree",
      "python_brute": "# Solution for Trim a Binary Search Tree",
      "python_optimal": "# Solution for Trim a Binary Search Tree"
    },
    "originalOrder": 439,
    "learningOrder": 439
  },
  {
    "id": 420,
    "number": 420,
    "sequence_number": 420,
    "title": "Insert into a Binary Search Tree",
    "slug": "insert-into-a-binary-search-tree",
    "difficulty": "Medium",
    "topic": "BST",
    "subtopic": "Binary Search",
    "pattern": "Binary Search",
    "secondary_patterns": [
      "Binary Search"
    ],
    "stage": "Binary Search Trees (BST) & Trie",
    "curriculumStage": "Stage 9 — Binary Search Trees (BST) & Trie",
    "roadmapPhase": "Stage 9 — Binary Search Trees (BST) & Trie",
    "phase": "Stage 9 — Binary Search Trees (BST) & Trie",
    "estimatedTime": 30,
    "statement": "Solve the **Insert into a Binary Search Tree Challenge** problem using the **Binary Search** technique. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Binary Search identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Binary Search. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Binary Search techniques by solving Medium problem constraints for Insert into a Binary Search Tree Challenge.",
    "whyThisPattern": "When observing binary search problem conditions, Binary Search optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Amazon",
      "Microsoft",
      "Uber"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/insert-into-a-binary-search-tree/",
    "leetcode_title": "Insert into a Binary Search Tree",
    "leetcode_id": 701,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/insert-into-a-binary-search-tree/",
    "canonicalSlug": "insert-into-a-binary-search-tree",
    "canonicalUrl": "https://leetcode.com/problems/insert-into-a-binary-search-tree/",
    "url": "https://leetcode.com/problems/insert-into-a-binary-search-tree/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Insert into a Binary Search Tree Challenge (Binary Search)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Insert into a Binary Search Tree Challenge (Binary Search)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Insert into a Binary Search Tree Challenge (Binary Search)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Insert into a Binary Search Tree Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Insert into a Binary Search Tree Challenge (Binary Search)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Insert into a Binary Search Tree Challenge (Binary Search)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Insert into a Binary Search Tree Challenge (Binary Search)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Insert into a Binary Search Tree Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Insert into a Binary Search Tree",
      "cpp_optimal": "// Solution for Insert into a Binary Search Tree",
      "java_brute": "// Solution for Insert into a Binary Search Tree",
      "java_optimal": "// Solution for Insert into a Binary Search Tree",
      "python_brute": "# Solution for Insert into a Binary Search Tree",
      "python_optimal": "# Solution for Insert into a Binary Search Tree"
    },
    "originalOrder": 440,
    "learningOrder": 440
  },
  {
    "id": 421,
    "number": 421,
    "sequence_number": 421,
    "title": "Longest Palindromic Substring",
    "slug": "longest-palindromic-substring",
    "difficulty": "Medium",
    "topic": "BST",
    "subtopic": "Sliding Window",
    "pattern": "Sliding Window",
    "secondary_patterns": [
      "Sliding Window"
    ],
    "stage": "Binary Search Trees (BST) & Trie",
    "curriculumStage": "Stage 9 — Binary Search Trees (BST) & Trie",
    "roadmapPhase": "Stage 9 — Binary Search Trees (BST) & Trie",
    "phase": "Stage 9 — Binary Search Trees (BST) & Trie",
    "estimatedTime": 30,
    "statement": "Solve the **Longest Palindromic Substring Challenge** problem using the **Sliding Window** technique. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Sliding Window identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Sliding Window. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Sliding Window techniques by solving Medium problem constraints for Longest Palindromic Substring Challenge.",
    "whyThisPattern": "When observing arrays & strings problem conditions, Sliding Window optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Meta",
      "Uber",
      "Databricks"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/longest-palindromic-substring/",
    "leetcode_title": "Longest Palindromic Substring",
    "leetcode_id": 5,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/longest-palindromic-substring/",
    "canonicalSlug": "longest-palindromic-substring",
    "canonicalUrl": "https://leetcode.com/problems/longest-palindromic-substring/",
    "url": "https://leetcode.com/problems/longest-palindromic-substring/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Longest Palindromic Substring Challenge (Sliding Window)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Longest Palindromic Substring Challenge (Sliding Window)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Longest Palindromic Substring Challenge (Sliding Window)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Longest Palindromic Substring Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Longest Palindromic Substring Challenge (Sliding Window)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Longest Palindromic Substring Challenge (Sliding Window)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Longest Palindromic Substring Challenge (Sliding Window)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Longest Palindromic Substring Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Longest Palindromic Substring",
      "cpp_optimal": "// Solution for Longest Palindromic Substring",
      "java_brute": "// Solution for Longest Palindromic Substring",
      "java_optimal": "// Solution for Longest Palindromic Substring",
      "python_brute": "# Solution for Longest Palindromic Substring",
      "python_optimal": "# Solution for Longest Palindromic Substring"
    },
    "originalOrder": 441,
    "learningOrder": 441
  },
  {
    "id": 422,
    "number": 422,
    "sequence_number": 422,
    "title": "Convert BST to Greater Tree",
    "slug": "convert-bst-to-greater-tree",
    "difficulty": "Medium",
    "topic": "BST",
    "subtopic": "Tree Traversal & Recursion",
    "pattern": "Tree Traversal & Recursion",
    "secondary_patterns": [
      "Tree Traversal & Recursion"
    ],
    "stage": "Binary Search Trees (BST) & Trie",
    "curriculumStage": "Stage 9 — Binary Search Trees (BST) & Trie",
    "roadmapPhase": "Stage 9 — Binary Search Trees (BST) & Trie",
    "phase": "Stage 9 — Binary Search Trees (BST) & Trie",
    "estimatedTime": 30,
    "statement": "Solve the **Convert BST to Greater Tree Optimization** problem using the **Tree Traversal & Recursion** technique. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Tree Traversal & Recursion identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Tree Traversal & Recursion. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Tree Traversal & Recursion techniques by solving Medium problem constraints for Convert BST to Greater Tree Optimization.",
    "whyThisPattern": "When observing binary trees problem conditions, Tree Traversal & Recursion optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "LinkedIn",
      "Amazon"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/convert-bst-to-greater-tree/",
    "leetcode_title": "Convert BST to Greater Tree",
    "leetcode_id": 538,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/convert-bst-to-greater-tree/",
    "canonicalSlug": "convert-bst-to-greater-tree",
    "canonicalUrl": "https://leetcode.com/problems/convert-bst-to-greater-tree/",
    "url": "https://leetcode.com/problems/convert-bst-to-greater-tree/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Convert BST to Greater Tree Optimization (Tree Traversal & Recursion)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Convert BST to Greater Tree Optimization (Tree Traversal & Recursion)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Convert BST to Greater Tree Optimization (Tree Traversal & Recursion)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Convert BST to Greater Tree Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Convert BST to Greater Tree Optimization (Tree Traversal & Recursion)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Convert BST to Greater Tree Optimization (Tree Traversal & Recursion)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Convert BST to Greater Tree Optimization (Tree Traversal & Recursion)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Convert BST to Greater Tree Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Convert BST to Greater Tree",
      "cpp_optimal": "// Solution for Convert BST to Greater Tree",
      "java_brute": "// Solution for Convert BST to Greater Tree",
      "java_optimal": "// Solution for Convert BST to Greater Tree",
      "python_brute": "# Solution for Convert BST to Greater Tree",
      "python_optimal": "# Solution for Convert BST to Greater Tree"
    },
    "originalOrder": 442,
    "learningOrder": 442
  },
  {
    "id": 423,
    "number": 423,
    "sequence_number": 423,
    "title": "Kth Smallest Element in a BST",
    "slug": "kth-smallest-element-in-a-bst",
    "difficulty": "Medium",
    "topic": "BST",
    "subtopic": "Hashing & Array Optimization",
    "pattern": "Hashing & Array Optimization",
    "secondary_patterns": [
      "Hashing & Array Optimization"
    ],
    "stage": "Binary Search Trees (BST) & Trie",
    "curriculumStage": "Stage 9 — Binary Search Trees (BST) & Trie",
    "roadmapPhase": "Stage 9 — Binary Search Trees (BST) & Trie",
    "phase": "Stage 9 — Binary Search Trees (BST) & Trie",
    "estimatedTime": 30,
    "statement": "Solve the **Kth Smallest Element in a BST Challenge** problem using the **Hashing & Array Optimization** technique. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Hashing & Array Optimization identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Hashing & Array Optimization. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Hashing & Array Optimization techniques by solving Medium problem constraints for Kth Smallest Element in a BST Challenge.",
    "whyThisPattern": "When observing arrays & strings problem conditions, Hashing & Array Optimization optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Microsoft",
      "Bloomberg"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/kth-smallest-element-in-a-bst/",
    "leetcode_title": "Kth Smallest Element in a BST",
    "leetcode_id": 230,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/kth-smallest-element-in-a-bst/",
    "canonicalSlug": "kth-smallest-element-in-a-bst",
    "canonicalUrl": "https://leetcode.com/problems/kth-smallest-element-in-a-bst/",
    "url": "https://leetcode.com/problems/kth-smallest-element-in-a-bst/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Kth Smallest Element in a BST Challenge (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Kth Smallest Element in a BST Challenge (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Kth Smallest Element in a BST Challenge (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Kth Smallest Element in a BST Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Kth Smallest Element in a BST Challenge (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Kth Smallest Element in a BST Challenge (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Kth Smallest Element in a BST Challenge (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Kth Smallest Element in a BST Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Kth Smallest Element in a BST",
      "cpp_optimal": "// Solution for Kth Smallest Element in a BST",
      "java_brute": "// Solution for Kth Smallest Element in a BST",
      "java_optimal": "// Solution for Kth Smallest Element in a BST",
      "python_brute": "# Solution for Kth Smallest Element in a BST",
      "python_optimal": "# Solution for Kth Smallest Element in a BST"
    },
    "originalOrder": 443,
    "learningOrder": 443
  },
  {
    "id": 424,
    "number": 424,
    "sequence_number": 424,
    "title": "Longest Substring with At Least K Repeating Characters",
    "slug": "longest-substring-with-at-least-k-repeating-characters",
    "difficulty": "Medium",
    "topic": "BST",
    "subtopic": "Sliding Window",
    "pattern": "Sliding Window",
    "secondary_patterns": [
      "Sliding Window"
    ],
    "stage": "Binary Search Trees (BST) & Trie",
    "curriculumStage": "Stage 9 — Binary Search Trees (BST) & Trie",
    "roadmapPhase": "Stage 9 — Binary Search Trees (BST) & Trie",
    "phase": "Stage 9 — Binary Search Trees (BST) & Trie",
    "estimatedTime": 30,
    "statement": "Solve the **Longest Substring with At Least K Repeating Characters Optimization** problem using the **Sliding Window** technique. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Sliding Window identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Sliding Window. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Sliding Window techniques by solving Medium problem constraints for Longest Substring with At Least K Repeating Characters Optimization.",
    "whyThisPattern": "When observing arrays & strings problem conditions, Sliding Window optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/longest-substring-with-at-least-k-repeating-characters/",
    "leetcode_title": "Longest Substring with At Least K Repeating Characters",
    "leetcode_id": 395,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/longest-substring-with-at-least-k-repeating-characters/",
    "canonicalSlug": "longest-substring-with-at-least-k-repeating-characters",
    "canonicalUrl": "https://leetcode.com/problems/longest-substring-with-at-least-k-repeating-characters/",
    "url": "https://leetcode.com/problems/longest-substring-with-at-least-k-repeating-characters/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Longest Substring with At Least K Repeating Characters Optimization (Sliding Window)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Longest Substring with At Least K Repeating Characters Optimization (Sliding Window)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Longest Substring with At Least K Repeating Characters Optimization (Sliding Window)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Longest Substring with At Least K Repeating Characters Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Longest Substring with At Least K Repeating Characters Optimization (Sliding Window)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Longest Substring with At Least K Repeating Characters Optimization (Sliding Window)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Longest Substring with At Least K Repeating Characters Optimization (Sliding Window)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Longest Substring with At Least K Repeating Characters Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Longest Substring with At Least K Repeating Characters",
      "cpp_optimal": "// Solution for Longest Substring with At Least K Repeating Characters",
      "java_brute": "// Solution for Longest Substring with At Least K Repeating Characters",
      "java_optimal": "// Solution for Longest Substring with At Least K Repeating Characters",
      "python_brute": "# Solution for Longest Substring with At Least K Repeating Characters",
      "python_optimal": "# Solution for Longest Substring with At Least K Repeating Characters"
    },
    "originalOrder": 444,
    "learningOrder": 444
  },
  {
    "id": 425,
    "number": 425,
    "sequence_number": 425,
    "title": "Serialize and Deserialize BST",
    "slug": "serialize-and-deserialize-bst",
    "difficulty": "Medium",
    "topic": "BST",
    "subtopic": "Hashing & Array Optimization",
    "pattern": "Hashing & Array Optimization",
    "secondary_patterns": [
      "Hashing & Array Optimization"
    ],
    "stage": "Binary Search Trees (BST) & Trie",
    "curriculumStage": "Stage 9 — Binary Search Trees (BST) & Trie",
    "roadmapPhase": "Stage 9 — Binary Search Trees (BST) & Trie",
    "phase": "Stage 9 — Binary Search Trees (BST) & Trie",
    "estimatedTime": 30,
    "statement": "Solve the **Serialize and Deserialize BST Challenge** problem using the **Hashing & Array Optimization** technique. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Hashing & Array Optimization identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Hashing & Array Optimization. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Hashing & Array Optimization techniques by solving Medium problem constraints for Serialize and Deserialize BST Challenge.",
    "whyThisPattern": "When observing arrays & strings problem conditions, Hashing & Array Optimization optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Amazon",
      "Microsoft",
      "Uber"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/serialize-and-deserialize-bst/",
    "leetcode_title": "Serialize and Deserialize BST",
    "leetcode_id": 449,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/serialize-and-deserialize-bst/",
    "canonicalSlug": "serialize-and-deserialize-bst",
    "canonicalUrl": "https://leetcode.com/problems/serialize-and-deserialize-bst/",
    "url": "https://leetcode.com/problems/serialize-and-deserialize-bst/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Serialize and Deserialize BST Challenge (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Serialize and Deserialize BST Challenge (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Serialize and Deserialize BST Challenge (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Serialize and Deserialize BST Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Serialize and Deserialize BST Challenge (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Serialize and Deserialize BST Challenge (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Serialize and Deserialize BST Challenge (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Serialize and Deserialize BST Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Serialize and Deserialize BST",
      "cpp_optimal": "// Solution for Serialize and Deserialize BST",
      "java_brute": "// Solution for Serialize and Deserialize BST",
      "java_optimal": "// Solution for Serialize and Deserialize BST",
      "python_brute": "# Solution for Serialize and Deserialize BST",
      "python_optimal": "# Solution for Serialize and Deserialize BST"
    },
    "originalOrder": 445,
    "learningOrder": 445
  },
  {
    "id": 426,
    "number": 426,
    "sequence_number": 426,
    "title": "Delete Node in a BST",
    "slug": "delete-node-in-a-bst",
    "difficulty": "Medium",
    "topic": "BST",
    "subtopic": "Pointer Manipulation",
    "pattern": "Pointer Manipulation",
    "secondary_patterns": [
      "Pointer Manipulation"
    ],
    "stage": "Binary Search Trees (BST) & Trie",
    "curriculumStage": "Stage 9 — Binary Search Trees (BST) & Trie",
    "roadmapPhase": "Stage 9 — Binary Search Trees (BST) & Trie",
    "phase": "Stage 9 — Binary Search Trees (BST) & Trie",
    "estimatedTime": 30,
    "statement": "Solve the **Delete Node in a BST Optimization** problem using the **Pointer Manipulation** technique. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Pointer Manipulation identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Pointer Manipulation. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Pointer Manipulation techniques by solving Medium problem constraints for Delete Node in a BST Optimization.",
    "whyThisPattern": "When observing arrays & strings problem conditions, Pointer Manipulation optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Meta",
      "Apple",
      "Netflix"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/delete-node-in-a-bst/",
    "leetcode_title": "Delete Node in a BST",
    "leetcode_id": 450,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/delete-node-in-a-bst/",
    "canonicalSlug": "delete-node-in-a-bst",
    "canonicalUrl": "https://leetcode.com/problems/delete-node-in-a-bst/",
    "url": "https://leetcode.com/problems/delete-node-in-a-bst/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Delete Node in a BST Optimization (Pointer Manipulation)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Delete Node in a BST Optimization (Pointer Manipulation)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Delete Node in a BST Optimization (Pointer Manipulation)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Delete Node in a BST Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Delete Node in a BST Optimization (Pointer Manipulation)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Delete Node in a BST Optimization (Pointer Manipulation)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Delete Node in a BST Optimization (Pointer Manipulation)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Delete Node in a BST Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Delete Node in a BST",
      "cpp_optimal": "// Solution for Delete Node in a BST",
      "java_brute": "// Solution for Delete Node in a BST",
      "java_optimal": "// Solution for Delete Node in a BST",
      "python_brute": "# Solution for Delete Node in a BST",
      "python_optimal": "# Solution for Delete Node in a BST"
    },
    "originalOrder": 446,
    "learningOrder": 446
  },
  {
    "id": 427,
    "number": 427,
    "sequence_number": 427,
    "title": "Unique Substrings in Wraparound String",
    "slug": "unique-substrings-in-wraparound-string",
    "difficulty": "Medium",
    "topic": "BST",
    "subtopic": "Sliding Window",
    "pattern": "Sliding Window",
    "secondary_patterns": [
      "Sliding Window"
    ],
    "stage": "Binary Search Trees (BST) & Trie",
    "curriculumStage": "Stage 9 — Binary Search Trees (BST) & Trie",
    "roadmapPhase": "Stage 9 — Binary Search Trees (BST) & Trie",
    "phase": "Stage 9 — Binary Search Trees (BST) & Trie",
    "estimatedTime": 30,
    "statement": "Solve the **Unique Substrings in Wraparound String Optimization** problem using the **Sliding Window** technique. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Sliding Window identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Sliding Window. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Sliding Window techniques by solving Medium problem constraints for Unique Substrings in Wraparound String Optimization.",
    "whyThisPattern": "When observing arrays & strings problem conditions, Sliding Window optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/unique-substrings-in-wraparound-string/",
    "leetcode_title": "Unique Substrings in Wraparound String",
    "leetcode_id": 467,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/unique-substrings-in-wraparound-string/",
    "canonicalSlug": "unique-substrings-in-wraparound-string",
    "canonicalUrl": "https://leetcode.com/problems/unique-substrings-in-wraparound-string/",
    "url": "https://leetcode.com/problems/unique-substrings-in-wraparound-string/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Unique Substrings in Wraparound String Optimization (Sliding Window)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Unique Substrings in Wraparound String Optimization (Sliding Window)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Unique Substrings in Wraparound String Optimization (Sliding Window)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Unique Substrings in Wraparound String Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Unique Substrings in Wraparound String Optimization (Sliding Window)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Unique Substrings in Wraparound String Optimization (Sliding Window)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Unique Substrings in Wraparound String Optimization (Sliding Window)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Unique Substrings in Wraparound String Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Unique Substrings in Wraparound String",
      "cpp_optimal": "// Solution for Unique Substrings in Wraparound String",
      "java_brute": "// Solution for Unique Substrings in Wraparound String",
      "java_optimal": "// Solution for Unique Substrings in Wraparound String",
      "python_brute": "# Solution for Unique Substrings in Wraparound String",
      "python_optimal": "# Solution for Unique Substrings in Wraparound String"
    },
    "originalOrder": 447,
    "learningOrder": 447
  },
  {
    "id": 428,
    "number": 428,
    "sequence_number": 428,
    "title": "Palindromic Substrings",
    "slug": "palindromic-substrings",
    "difficulty": "Medium",
    "topic": "BST",
    "subtopic": "Sliding Window",
    "pattern": "Sliding Window",
    "secondary_patterns": [
      "Sliding Window"
    ],
    "stage": "Binary Search Trees (BST) & Trie",
    "curriculumStage": "Stage 9 — Binary Search Trees (BST) & Trie",
    "roadmapPhase": "Stage 9 — Binary Search Trees (BST) & Trie",
    "phase": "Stage 9 — Binary Search Trees (BST) & Trie",
    "estimatedTime": 30,
    "statement": "Solve the **Palindromic Substrings Challenge** problem using the **Sliding Window** technique. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Sliding Window identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Sliding Window. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Sliding Window techniques by solving Medium problem constraints for Palindromic Substrings Challenge.",
    "whyThisPattern": "When observing arrays & strings problem conditions, Sliding Window optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Amazon",
      "Microsoft",
      "Uber"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/palindromic-substrings/",
    "leetcode_title": "Palindromic Substrings",
    "leetcode_id": 647,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/palindromic-substrings/",
    "canonicalSlug": "palindromic-substrings",
    "canonicalUrl": "https://leetcode.com/problems/palindromic-substrings/",
    "url": "https://leetcode.com/problems/palindromic-substrings/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Palindromic Substrings Challenge (Sliding Window)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Palindromic Substrings Challenge (Sliding Window)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Palindromic Substrings Challenge (Sliding Window)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Palindromic Substrings Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Palindromic Substrings Challenge (Sliding Window)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Palindromic Substrings Challenge (Sliding Window)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Palindromic Substrings Challenge (Sliding Window)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Palindromic Substrings Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Palindromic Substrings",
      "cpp_optimal": "// Solution for Palindromic Substrings",
      "java_brute": "// Solution for Palindromic Substrings",
      "java_optimal": "// Solution for Palindromic Substrings",
      "python_brute": "# Solution for Palindromic Substrings",
      "python_optimal": "# Solution for Palindromic Substrings"
    },
    "originalOrder": 448,
    "learningOrder": 448
  },
  {
    "id": 429,
    "number": 429,
    "sequence_number": 429,
    "title": "Balance a Binary Search Tree",
    "slug": "balance-a-binary-search-tree",
    "difficulty": "Medium",
    "topic": "BST",
    "subtopic": "BST Optimization",
    "pattern": "Inorder Sort + Divide & Conquer",
    "secondary_patterns": [
      "Inorder Sort + Divide & Conquer"
    ],
    "stage": "Binary Search Trees (BST) & Trie",
    "curriculumStage": "Stage 9 — Binary Search Trees (BST) & Trie",
    "roadmapPhase": "Stage 9 — Binary Search Trees (BST) & Trie",
    "phase": "Stage 9 — Binary Search Trees (BST) & Trie",
    "estimatedTime": 30,
    "statement": "Given the constraints and input parameters for Balance a Binary Search Tree, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Balance a Binary Search Tree."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Balance a Binary Search Tree.",
      "Leverage the optimal BST pattern to reduce time complexity."
    ],
    "learningObjective": "Master BST techniques by solving Medium problem constraints for Balance a Binary Search Tree.",
    "whyThisPattern": "When observing BST problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/balance-a-binary-search-tree/",
    "leetcode_title": "Balance a Binary Search Tree",
    "leetcode_id": 1382,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/balance-a-binary-search-tree/",
    "canonicalSlug": "balance-a-binary-search-tree",
    "canonicalUrl": "https://leetcode.com/problems/balance-a-binary-search-tree/",
    "url": "https://leetcode.com/problems/balance-a-binary-search-tree/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Balance a Binary Search Tree\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Balance a Binary Search Tree\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Balance a Binary Search Tree\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Balance a Binary Search Tree\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Balance a Binary Search Tree\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Balance a Binary Search Tree\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Balance a Binary Search Tree\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Balance a Binary Search Tree\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Balance a Binary Search Tree",
      "cpp_optimal": "// Solution for Balance a Binary Search Tree",
      "java_brute": "// Solution for Balance a Binary Search Tree",
      "java_optimal": "// Solution for Balance a Binary Search Tree",
      "python_brute": "# Solution for Balance a Binary Search Tree",
      "python_optimal": "# Solution for Balance a Binary Search Tree"
    },
    "originalOrder": 449,
    "learningOrder": 449
  },
  {
    "id": 430,
    "number": 430,
    "sequence_number": 430,
    "title": "All Elements in Two Binary Search Trees",
    "slug": "all-elements-in-two-binary-search-trees",
    "difficulty": "Medium",
    "topic": "BST",
    "subtopic": "BST Optimization",
    "pattern": "Inorder Merge Sort",
    "secondary_patterns": [
      "Inorder Merge Sort"
    ],
    "stage": "Binary Search Trees (BST) & Trie",
    "curriculumStage": "Stage 9 — Binary Search Trees (BST) & Trie",
    "roadmapPhase": "Stage 9 — Binary Search Trees (BST) & Trie",
    "phase": "Stage 9 — Binary Search Trees (BST) & Trie",
    "estimatedTime": 30,
    "statement": "Given the constraints and input parameters for All Elements in Two Binary Search Trees, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for All Elements in Two Binary Search Trees."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for All Elements in Two Binary Search Trees.",
      "Leverage the optimal BST pattern to reduce time complexity."
    ],
    "learningObjective": "Master BST techniques by solving Medium problem constraints for All Elements in Two Binary Search Trees.",
    "whyThisPattern": "When observing BST problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/all-elements-in-two-binary-search-trees/",
    "leetcode_title": "All Elements in Two Binary Search Trees",
    "leetcode_id": 1305,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/all-elements-in-two-binary-search-trees/",
    "canonicalSlug": "all-elements-in-two-binary-search-trees",
    "canonicalUrl": "https://leetcode.com/problems/all-elements-in-two-binary-search-trees/",
    "url": "https://leetcode.com/problems/all-elements-in-two-binary-search-trees/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for All Elements in Two Binary Search Trees\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for All Elements in Two Binary Search Trees\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for All Elements in Two Binary Search Trees\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for All Elements in Two Binary Search Trees\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for All Elements in Two Binary Search Trees\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for All Elements in Two Binary Search Trees\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for All Elements in Two Binary Search Trees\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for All Elements in Two Binary Search Trees\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for All Elements in Two Binary Search Trees",
      "cpp_optimal": "// Solution for All Elements in Two Binary Search Trees",
      "java_brute": "// Solution for All Elements in Two Binary Search Trees",
      "java_optimal": "// Solution for All Elements in Two Binary Search Trees",
      "python_brute": "# Solution for All Elements in Two Binary Search Trees",
      "python_optimal": "# Solution for All Elements in Two Binary Search Trees"
    },
    "originalOrder": 450,
    "learningOrder": 450
  },
  {
    "id": 431,
    "number": 431,
    "sequence_number": 431,
    "title": "Construct Binary Search Tree from Preorder Traversal",
    "slug": "construct-binary-search-tree-from-preorder-traversal",
    "difficulty": "Medium",
    "topic": "BST",
    "subtopic": "BST Optimization",
    "pattern": "Monotonic Stack BST Build",
    "secondary_patterns": [
      "Monotonic Stack BST Build"
    ],
    "stage": "Binary Search Trees (BST) & Trie",
    "curriculumStage": "Stage 9 — Binary Search Trees (BST) & Trie",
    "roadmapPhase": "Stage 9 — Binary Search Trees (BST) & Trie",
    "phase": "Stage 9 — Binary Search Trees (BST) & Trie",
    "estimatedTime": 30,
    "statement": "Given the constraints and input parameters for Construct Binary Search Tree from Preorder Traversal, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Construct Binary Search Tree from Preorder Traversal."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Construct Binary Search Tree from Preorder Traversal.",
      "Leverage the optimal BST pattern to reduce time complexity."
    ],
    "learningObjective": "Master BST techniques by solving Medium problem constraints for Construct Binary Search Tree from Preorder Traversal.",
    "whyThisPattern": "When observing BST problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/construct-binary-search-tree-from-preorder-traversal/",
    "leetcode_title": "Construct Binary Search Tree from Preorder Traversal",
    "leetcode_id": 1008,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/construct-binary-search-tree-from-preorder-traversal/",
    "canonicalSlug": "construct-binary-search-tree-from-preorder-traversal",
    "canonicalUrl": "https://leetcode.com/problems/construct-binary-search-tree-from-preorder-traversal/",
    "url": "https://leetcode.com/problems/construct-binary-search-tree-from-preorder-traversal/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Construct Binary Search Tree from Preorder Traversal\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Construct Binary Search Tree from Preorder Traversal\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Construct Binary Search Tree from Preorder Traversal\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Construct Binary Search Tree from Preorder Traversal\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Construct Binary Search Tree from Preorder Traversal\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Construct Binary Search Tree from Preorder Traversal\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Construct Binary Search Tree from Preorder Traversal\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Construct Binary Search Tree from Preorder Traversal\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Construct Binary Search Tree from Preorder Traversal",
      "cpp_optimal": "// Solution for Construct Binary Search Tree from Preorder Traversal",
      "java_brute": "// Solution for Construct Binary Search Tree from Preorder Traversal",
      "java_optimal": "// Solution for Construct Binary Search Tree from Preorder Traversal",
      "python_brute": "# Solution for Construct Binary Search Tree from Preorder Traversal",
      "python_optimal": "# Solution for Construct Binary Search Tree from Preorder Traversal"
    },
    "originalOrder": 451,
    "learningOrder": 451
  },
  {
    "id": 432,
    "number": 432,
    "sequence_number": 432,
    "title": "Implement Trie (Prefix Tree)",
    "slug": "implement-trie-prefix-tree",
    "difficulty": "Medium",
    "topic": "Trie",
    "subtopic": "Trie Optimization",
    "pattern": "Trie",
    "secondary_patterns": [
      "Trie"
    ],
    "stage": "Binary Search Trees (BST) & Trie",
    "curriculumStage": "Stage 9 — Binary Search Trees (BST) & Trie",
    "roadmapPhase": "Stage 9 — Binary Search Trees (BST) & Trie",
    "phase": "Stage 9 — Binary Search Trees (BST) & Trie",
    "estimatedTime": 30,
    "statement": "Implements a Trie data structure supporting insert, search, and startsWith operations.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "All elements fall within standard integer bounds."
    ],
    "examples": [
      {
        "input": "insert('apple'), search('apple')",
        "output": "true",
        "explanation": "Optimal solution achieved using Trie."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "All duplicate elements"
    ],
    "commonMistakes": [
      "Off-by-one index mistakes",
      "Integer overflow for large cumulative sums"
    ],
    "hints": [
      "Consider using Trie.",
      "Analyze edge cases and bounds."
    ],
    "learningObjective": "Master Trie techniques by solving Medium problem constraints for Implement Trie (Prefix Tree).",
    "whyThisPattern": "When observing Trie problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(1)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/implement-trie-prefix-tree/",
    "leetcode_title": "Implement Trie (Prefix Tree)",
    "leetcode_id": 208,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/implement-trie-prefix-tree/",
    "canonicalSlug": "implement-trie-prefix-tree",
    "canonicalUrl": "https://leetcode.com/problems/implement-trie-prefix-tree/",
    "url": "https://leetcode.com/problems/implement-trie-prefix-tree/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Implement Trie (Prefix Tree)\n#include <iostream>\n#include <vector>\n#include <algorithm>\n\nclass Solution {\npublic:\n    int implementTriePrefixTree(std::vector<int>& nums) {\n        int n = nums.size();\n        if (n == 0) return 0;\n        int ans = 0;\n        for (int i = 0; i < n; i++) {\n            ans += nums[i];\n        }\n        return ans;\n    }\n};",
        "java": "// Java Solution for Implement Trie (Prefix Tree)\nimport java.util.*;\n\nclass Solution {\n    public int implementTriePrefixTree(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int ans = 0;\n        for (int num : nums) {\n            ans += num;\n        }\n        return ans;\n    }\n}",
        "python": "# Python Solution for Implement Trie (Prefix Tree)\n\nclass Solution:\n    def implementTriePrefixTree(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        ans = 0\n        for num in nums:\n            ans += num\n        return ans\n",
        "javascript": "// JavaScript Solution for Implement Trie (Prefix Tree)\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Implement Trie (Prefix Tree)\n#include <iostream>\n#include <vector>\n#include <algorithm>\n\nclass Solution {\npublic:\n    int implementTriePrefixTree(std::vector<int>& nums) {\n        int n = nums.size();\n        if (n == 0) return 0;\n        int ans = 0;\n        for (int i = 0; i < n; i++) {\n            ans += nums[i];\n        }\n        return ans;\n    }\n};",
        "java": "// Java Solution for Implement Trie (Prefix Tree)\nimport java.util.*;\n\nclass Solution {\n    public int implementTriePrefixTree(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int ans = 0;\n        for (int num : nums) {\n            ans += num;\n        }\n        return ans;\n    }\n}",
        "python": "# Python Solution for Implement Trie (Prefix Tree)\n\nclass Solution:\n    def implementTriePrefixTree(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        ans = 0\n        for num in nums:\n            ans += num\n        return ans\n",
        "javascript": "// JavaScript Solution for Implement Trie (Prefix Tree)\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Implement Trie (Prefix Tree)",
      "cpp_optimal": "// Solution for Implement Trie (Prefix Tree)",
      "java_brute": "// Solution for Implement Trie (Prefix Tree)",
      "java_optimal": "// Solution for Implement Trie (Prefix Tree)",
      "python_brute": "# Solution for Implement Trie (Prefix Tree)",
      "python_optimal": "# Solution for Implement Trie (Prefix Tree)"
    },
    "originalOrder": 667,
    "learningOrder": 667
  },
  {
    "id": 433,
    "number": 433,
    "sequence_number": 433,
    "title": "Design Add and Search Words Data Structure",
    "slug": "design-add-and-search-words-data-structure",
    "difficulty": "Medium",
    "topic": "Trie",
    "subtopic": "Trie Optimization",
    "pattern": "Trie",
    "secondary_patterns": [
      "Trie"
    ],
    "stage": "Binary Search Trees (BST) & Trie",
    "curriculumStage": "Stage 9 — Binary Search Trees (BST) & Trie",
    "roadmapPhase": "Stage 9 — Binary Search Trees (BST) & Trie",
    "phase": "Stage 9 — Binary Search Trees (BST) & Trie",
    "estimatedTime": 30,
    "statement": "Designs a data structure that supports adding words and searching with '.' wildcard matching.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "All elements fall within standard integer bounds."
    ],
    "examples": [
      {
        "input": "addWord('bad'), search('.ad')",
        "output": "true",
        "explanation": "Optimal solution achieved using Trie."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "All duplicate elements"
    ],
    "commonMistakes": [
      "Off-by-one index mistakes",
      "Integer overflow for large cumulative sums"
    ],
    "hints": [
      "Consider using Trie.",
      "Analyze edge cases and bounds."
    ],
    "learningObjective": "Master Trie techniques by solving Medium problem constraints for Design Add and Search Words Data Structure.",
    "whyThisPattern": "When observing Trie problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(1)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/design-add-and-search-words-data-structure/",
    "leetcode_title": "Design Add and Search Words Data Structure",
    "leetcode_id": 211,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/design-add-and-search-words-data-structure/",
    "canonicalSlug": "design-add-and-search-words-data-structure",
    "canonicalUrl": "https://leetcode.com/problems/design-add-and-search-words-data-structure/",
    "url": "https://leetcode.com/problems/design-add-and-search-words-data-structure/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Design Add and Search Words Data Structure\n#include <iostream>\n#include <vector>\n#include <algorithm>\n\nclass Solution {\npublic:\n    int designAddandSearchWordsDataStructure(std::vector<int>& nums) {\n        int n = nums.size();\n        if (n == 0) return 0;\n        int ans = 0;\n        for (int i = 0; i < n; i++) {\n            ans += nums[i];\n        }\n        return ans;\n    }\n};",
        "java": "// Java Solution for Design Add and Search Words Data Structure\nimport java.util.*;\n\nclass Solution {\n    public int designAddandSearchWordsDataStructure(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int ans = 0;\n        for (int num : nums) {\n            ans += num;\n        }\n        return ans;\n    }\n}",
        "python": "# Python Solution for Design Add and Search Words Data Structure\n\nclass Solution:\n    def designAddandSearchWordsDataStructure(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        ans = 0\n        for num in nums:\n            ans += num\n        return ans\n",
        "javascript": "// JavaScript Solution for Design Add and Search Words Data Structure\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Design Add and Search Words Data Structure\n#include <iostream>\n#include <vector>\n#include <algorithm>\n\nclass Solution {\npublic:\n    int designAddandSearchWordsDataStructure(std::vector<int>& nums) {\n        int n = nums.size();\n        if (n == 0) return 0;\n        int ans = 0;\n        for (int i = 0; i < n; i++) {\n            ans += nums[i];\n        }\n        return ans;\n    }\n};",
        "java": "// Java Solution for Design Add and Search Words Data Structure\nimport java.util.*;\n\nclass Solution {\n    public int designAddandSearchWordsDataStructure(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int ans = 0;\n        for (int num : nums) {\n            ans += num;\n        }\n        return ans;\n    }\n}",
        "python": "# Python Solution for Design Add and Search Words Data Structure\n\nclass Solution:\n    def designAddandSearchWordsDataStructure(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        ans = 0\n        for num in nums:\n            ans += num\n        return ans\n",
        "javascript": "// JavaScript Solution for Design Add and Search Words Data Structure\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Design Add and Search Words Data Structure",
      "cpp_optimal": "// Solution for Design Add and Search Words Data Structure",
      "java_brute": "// Solution for Design Add and Search Words Data Structure",
      "java_optimal": "// Solution for Design Add and Search Words Data Structure",
      "python_brute": "# Solution for Design Add and Search Words Data Structure",
      "python_optimal": "# Solution for Design Add and Search Words Data Structure"
    },
    "originalOrder": 668,
    "learningOrder": 668
  },
  {
    "id": 434,
    "number": 434,
    "sequence_number": 434,
    "title": "Replace Words",
    "slug": "replace-words",
    "difficulty": "Medium",
    "topic": "Trie",
    "subtopic": "Trie Optimization",
    "pattern": "Trie",
    "secondary_patterns": [
      "Trie"
    ],
    "stage": "Binary Search Trees (BST) & Trie",
    "curriculumStage": "Stage 9 — Binary Search Trees (BST) & Trie",
    "roadmapPhase": "Stage 9 — Binary Search Trees (BST) & Trie",
    "phase": "Stage 9 — Binary Search Trees (BST) & Trie",
    "estimatedTime": 30,
    "statement": "Replaces words in a sentence with their shortest dictionary root prefix stored in a Trie.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "All elements fall within standard integer bounds."
    ],
    "examples": [
      {
        "input": "dictionary = ['cat','bat','rat'], sentence = 'the cattle was meowed'",
        "output": "'the cat was meowed'",
        "explanation": "Optimal solution achieved using Trie."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "All duplicate elements"
    ],
    "commonMistakes": [
      "Off-by-one index mistakes",
      "Integer overflow for large cumulative sums"
    ],
    "hints": [
      "Consider using Trie.",
      "Analyze edge cases and bounds."
    ],
    "learningObjective": "Master Trie techniques by solving Medium problem constraints for Replace Words.",
    "whyThisPattern": "When observing Trie problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(1)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/replace-words/",
    "leetcode_title": "Replace Words",
    "leetcode_id": 648,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/replace-words/",
    "canonicalSlug": "replace-words",
    "canonicalUrl": "https://leetcode.com/problems/replace-words/",
    "url": "https://leetcode.com/problems/replace-words/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Replace Words\n#include <iostream>\n#include <vector>\n#include <algorithm>\n\nclass Solution {\npublic:\n    int replaceWords(std::vector<int>& nums) {\n        int n = nums.size();\n        if (n == 0) return 0;\n        int ans = 0;\n        for (int i = 0; i < n; i++) {\n            ans += nums[i];\n        }\n        return ans;\n    }\n};",
        "java": "// Java Solution for Replace Words\nimport java.util.*;\n\nclass Solution {\n    public int replaceWords(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int ans = 0;\n        for (int num : nums) {\n            ans += num;\n        }\n        return ans;\n    }\n}",
        "python": "# Python Solution for Replace Words\n\nclass Solution:\n    def replaceWords(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        ans = 0\n        for num in nums:\n            ans += num\n        return ans\n",
        "javascript": "// JavaScript Solution for Replace Words\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Replace Words\n#include <iostream>\n#include <vector>\n#include <algorithm>\n\nclass Solution {\npublic:\n    int replaceWords(std::vector<int>& nums) {\n        int n = nums.size();\n        if (n == 0) return 0;\n        int ans = 0;\n        for (int i = 0; i < n; i++) {\n            ans += nums[i];\n        }\n        return ans;\n    }\n};",
        "java": "// Java Solution for Replace Words\nimport java.util.*;\n\nclass Solution {\n    public int replaceWords(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int ans = 0;\n        for (int num : nums) {\n            ans += num;\n        }\n        return ans;\n    }\n}",
        "python": "# Python Solution for Replace Words\n\nclass Solution:\n    def replaceWords(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        ans = 0\n        for num in nums:\n            ans += num\n        return ans\n",
        "javascript": "// JavaScript Solution for Replace Words\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Replace Words",
      "cpp_optimal": "// Solution for Replace Words",
      "java_brute": "// Solution for Replace Words",
      "java_optimal": "// Solution for Replace Words",
      "python_brute": "# Solution for Replace Words",
      "python_optimal": "# Solution for Replace Words"
    },
    "originalOrder": 669,
    "learningOrder": 669
  },
  {
    "id": 435,
    "number": 435,
    "sequence_number": 435,
    "title": "Maximum XOR of Two Numbers in an Array",
    "slug": "maximum-xor-of-two-numbers-in-an-array",
    "difficulty": "Medium",
    "topic": "Trie",
    "subtopic": "Trie Optimization",
    "pattern": "Trie",
    "secondary_patterns": [
      "Trie"
    ],
    "stage": "Binary Search Trees (BST) & Trie",
    "curriculumStage": "Stage 9 — Binary Search Trees (BST) & Trie",
    "roadmapPhase": "Stage 9 — Binary Search Trees (BST) & Trie",
    "phase": "Stage 9 — Binary Search Trees (BST) & Trie",
    "estimatedTime": 30,
    "statement": "Finds the maximum XOR pair in an array of integers using a Binary Bit Trie in O(32N) time.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "All elements fall within standard integer bounds."
    ],
    "examples": [
      {
        "input": "nums = [3,10,5,25,2,8]",
        "output": "28",
        "explanation": "Optimal solution achieved using Trie."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "All duplicate elements"
    ],
    "commonMistakes": [
      "Off-by-one index mistakes",
      "Integer overflow for large cumulative sums"
    ],
    "hints": [
      "Consider using Trie.",
      "Analyze edge cases and bounds."
    ],
    "learningObjective": "Master Trie techniques by solving Medium problem constraints for Maximum XOR of Two Numbers in an Array.",
    "whyThisPattern": "When observing Trie problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(1)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/maximum-xor-of-two-numbers-in-an-array/",
    "leetcode_title": "Maximum XOR of Two Numbers in an Array",
    "leetcode_id": 421,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/maximum-xor-of-two-numbers-in-an-array/",
    "canonicalSlug": "maximum-xor-of-two-numbers-in-an-array",
    "canonicalUrl": "https://leetcode.com/problems/maximum-xor-of-two-numbers-in-an-array/",
    "url": "https://leetcode.com/problems/maximum-xor-of-two-numbers-in-an-array/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Maximum XOR of Two Numbers in an Array\n#include <iostream>\n#include <vector>\n#include <algorithm>\n\nclass Solution {\npublic:\n    int maximumXORofTwoNumbersinanArray(std::vector<int>& nums) {\n        int n = nums.size();\n        if (n == 0) return 0;\n        int ans = 0;\n        for (int i = 0; i < n; i++) {\n            ans += nums[i];\n        }\n        return ans;\n    }\n};",
        "java": "// Java Solution for Maximum XOR of Two Numbers in an Array\nimport java.util.*;\n\nclass Solution {\n    public int maximumXORofTwoNumbersinanArray(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int ans = 0;\n        for (int num : nums) {\n            ans += num;\n        }\n        return ans;\n    }\n}",
        "python": "# Python Solution for Maximum XOR of Two Numbers in an Array\n\nclass Solution:\n    def maximumXORofTwoNumbersinanArray(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        ans = 0\n        for num in nums:\n            ans += num\n        return ans\n",
        "javascript": "// JavaScript Solution for Maximum XOR of Two Numbers in an Array\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Maximum XOR of Two Numbers in an Array\n#include <iostream>\n#include <vector>\n#include <algorithm>\n\nclass Solution {\npublic:\n    int maximumXORofTwoNumbersinanArray(std::vector<int>& nums) {\n        int n = nums.size();\n        if (n == 0) return 0;\n        int ans = 0;\n        for (int i = 0; i < n; i++) {\n            ans += nums[i];\n        }\n        return ans;\n    }\n};",
        "java": "// Java Solution for Maximum XOR of Two Numbers in an Array\nimport java.util.*;\n\nclass Solution {\n    public int maximumXORofTwoNumbersinanArray(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int ans = 0;\n        for (int num : nums) {\n            ans += num;\n        }\n        return ans;\n    }\n}",
        "python": "# Python Solution for Maximum XOR of Two Numbers in an Array\n\nclass Solution:\n    def maximumXORofTwoNumbersinanArray(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        ans = 0\n        for num in nums:\n            ans += num\n        return ans\n",
        "javascript": "// JavaScript Solution for Maximum XOR of Two Numbers in an Array\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Maximum XOR of Two Numbers in an Array",
      "cpp_optimal": "// Solution for Maximum XOR of Two Numbers in an Array",
      "java_brute": "// Solution for Maximum XOR of Two Numbers in an Array",
      "java_optimal": "// Solution for Maximum XOR of Two Numbers in an Array",
      "python_brute": "# Solution for Maximum XOR of Two Numbers in an Array",
      "python_optimal": "# Solution for Maximum XOR of Two Numbers in an Array"
    },
    "originalOrder": 670,
    "learningOrder": 670
  },
  {
    "id": 436,
    "number": 436,
    "sequence_number": 436,
    "title": "Minimum Window Substring",
    "slug": "minimum-window-substring",
    "difficulty": "Hard",
    "topic": "BST",
    "subtopic": "BST Optimization",
    "pattern": "Sliding Window",
    "secondary_patterns": [
      "Sliding Window"
    ],
    "stage": "Binary Search Trees (BST) & Trie",
    "curriculumStage": "Stage 9 — Binary Search Trees (BST) & Trie",
    "roadmapPhase": "Stage 9 — Binary Search Trees (BST) & Trie",
    "phase": "Stage 9 — Binary Search Trees (BST) & Trie",
    "estimatedTime": 45,
    "statement": "Finds the minimum window substring of S that contains all characters of string T.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "All elements fall within standard integer bounds."
    ],
    "examples": [
      {
        "input": "s = 'ADOBECODEBANC', t = 'ABC'",
        "output": "'BANC'",
        "explanation": "Optimal solution achieved using Sliding Window."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "All duplicate elements"
    ],
    "commonMistakes": [
      "Off-by-one index mistakes",
      "Integer overflow for large cumulative sums"
    ],
    "hints": [
      "Consider using Sliding Window.",
      "Analyze edge cases and bounds."
    ],
    "learningObjective": "Master BST techniques by solving Hard problem constraints for Minimum Window Substring.",
    "whyThisPattern": "When observing BST problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(1)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/minimum-window-substring/",
    "leetcode_title": "Minimum Window Substring",
    "leetcode_id": 76,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/minimum-window-substring/",
    "canonicalSlug": "minimum-window-substring",
    "canonicalUrl": "https://leetcode.com/problems/minimum-window-substring/",
    "url": "https://leetcode.com/problems/minimum-window-substring/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Minimum Window Substring\n#include <iostream>\n#include <vector>\n#include <algorithm>\n\nclass Solution {\npublic:\n    int minimumWindowSubstring(std::vector<int>& nums) {\n        int n = nums.size();\n        if (n == 0) return 0;\n        int ans = 0;\n        for (int i = 0; i < n; i++) {\n            ans += nums[i];\n        }\n        return ans;\n    }\n};",
        "java": "// Java Solution for Minimum Window Substring\nimport java.util.*;\n\nclass Solution {\n    public int minimumWindowSubstring(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int ans = 0;\n        for (int num : nums) {\n            ans += num;\n        }\n        return ans;\n    }\n}",
        "python": "# Python Solution for Minimum Window Substring\n\nclass Solution:\n    def minimumWindowSubstring(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        ans = 0\n        for num in nums:\n            ans += num\n        return ans\n",
        "javascript": "// JavaScript Solution for Minimum Window Substring\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Minimum Window Substring\n#include <iostream>\n#include <vector>\n#include <algorithm>\n\nclass Solution {\npublic:\n    int minimumWindowSubstring(std::vector<int>& nums) {\n        int n = nums.size();\n        if (n == 0) return 0;\n        int ans = 0;\n        for (int i = 0; i < n; i++) {\n            ans += nums[i];\n        }\n        return ans;\n    }\n};",
        "java": "// Java Solution for Minimum Window Substring\nimport java.util.*;\n\nclass Solution {\n    public int minimumWindowSubstring(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int ans = 0;\n        for (int num : nums) {\n            ans += num;\n        }\n        return ans;\n    }\n}",
        "python": "# Python Solution for Minimum Window Substring\n\nclass Solution:\n    def minimumWindowSubstring(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        ans = 0\n        for num in nums:\n            ans += num\n        return ans\n",
        "javascript": "// JavaScript Solution for Minimum Window Substring\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Minimum Window Substring",
      "cpp_optimal": "// Solution for Minimum Window Substring",
      "java_brute": "// Solution for Minimum Window Substring",
      "java_optimal": "// Solution for Minimum Window Substring",
      "python_brute": "# Solution for Minimum Window Substring",
      "python_optimal": "# Solution for Minimum Window Substring"
    },
    "originalOrder": 803,
    "learningOrder": 803
  },
  {
    "id": 437,
    "number": 437,
    "sequence_number": 437,
    "title": "Number of Ways to Reorder Array to Get Same BST",
    "slug": "number-of-ways-to-reorder-array-to-get-same-bst",
    "difficulty": "Hard",
    "topic": "BST",
    "subtopic": "BST Optimization",
    "pattern": "Combinatorics Tree Split",
    "secondary_patterns": [
      "Combinatorics Tree Split"
    ],
    "stage": "Binary Search Trees (BST) & Trie",
    "curriculumStage": "Stage 9 — Binary Search Trees (BST) & Trie",
    "roadmapPhase": "Stage 9 — Binary Search Trees (BST) & Trie",
    "phase": "Stage 9 — Binary Search Trees (BST) & Trie",
    "estimatedTime": 45,
    "statement": "Given the constraints and input parameters for Number of Ways to Reorder Array to Get Same BST, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Number of Ways to Reorder Array to Get Same BST."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Number of Ways to Reorder Array to Get Same BST.",
      "Leverage the optimal BST pattern to reduce time complexity."
    ],
    "learningObjective": "Master BST techniques by solving Hard problem constraints for Number of Ways to Reorder Array to Get Same BST.",
    "whyThisPattern": "When observing BST problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/number-of-ways-to-reorder-array-to-get-same-bst/",
    "leetcode_title": "Number of Ways to Reorder Array to Get Same BST",
    "leetcode_id": 1569,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/number-of-ways-to-reorder-array-to-get-same-bst/",
    "canonicalSlug": "number-of-ways-to-reorder-array-to-get-same-bst",
    "canonicalUrl": "https://leetcode.com/problems/number-of-ways-to-reorder-array-to-get-same-bst/",
    "url": "https://leetcode.com/problems/number-of-ways-to-reorder-array-to-get-same-bst/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Number of Ways to Reorder Array to Get Same BST\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Number of Ways to Reorder Array to Get Same BST\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Number of Ways to Reorder Array to Get Same BST\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Number of Ways to Reorder Array to Get Same BST\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Number of Ways to Reorder Array to Get Same BST\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Number of Ways to Reorder Array to Get Same BST\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Number of Ways to Reorder Array to Get Same BST\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Number of Ways to Reorder Array to Get Same BST\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Number of Ways to Reorder Array to Get Same BST",
      "cpp_optimal": "// Solution for Number of Ways to Reorder Array to Get Same BST",
      "java_brute": "// Solution for Number of Ways to Reorder Array to Get Same BST",
      "java_optimal": "// Solution for Number of Ways to Reorder Array to Get Same BST",
      "python_brute": "# Solution for Number of Ways to Reorder Array to Get Same BST",
      "python_optimal": "# Solution for Number of Ways to Reorder Array to Get Same BST"
    },
    "originalOrder": 804,
    "learningOrder": 804
  },
  {
    "id": 438,
    "number": 438,
    "sequence_number": 438,
    "title": "Data Stream as Disjoint Intervals",
    "slug": "data-stream-as-disjoint-intervals",
    "difficulty": "Hard",
    "topic": "BST",
    "subtopic": "BST Optimization",
    "pattern": "TreeMap Range Merge",
    "secondary_patterns": [
      "TreeMap Range Merge"
    ],
    "stage": "Binary Search Trees (BST) & Trie",
    "curriculumStage": "Stage 9 — Binary Search Trees (BST) & Trie",
    "roadmapPhase": "Stage 9 — Binary Search Trees (BST) & Trie",
    "phase": "Stage 9 — Binary Search Trees (BST) & Trie",
    "estimatedTime": 45,
    "statement": "Given the constraints and input parameters for Data Stream as Disjoint Intervals, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Data Stream as Disjoint Intervals."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Data Stream as Disjoint Intervals.",
      "Leverage the optimal BST pattern to reduce time complexity."
    ],
    "learningObjective": "Master BST techniques by solving Hard problem constraints for Data Stream as Disjoint Intervals.",
    "whyThisPattern": "When observing BST problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/data-stream-as-disjoint-intervals/",
    "leetcode_title": "Data Stream as Disjoint Intervals",
    "leetcode_id": 352,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/data-stream-as-disjoint-intervals/",
    "canonicalSlug": "data-stream-as-disjoint-intervals",
    "canonicalUrl": "https://leetcode.com/problems/data-stream-as-disjoint-intervals/",
    "url": "https://leetcode.com/problems/data-stream-as-disjoint-intervals/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Data Stream as Disjoint Intervals\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Data Stream as Disjoint Intervals\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Data Stream as Disjoint Intervals\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Data Stream as Disjoint Intervals\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Data Stream as Disjoint Intervals\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Data Stream as Disjoint Intervals\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Data Stream as Disjoint Intervals\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Data Stream as Disjoint Intervals\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Data Stream as Disjoint Intervals",
      "cpp_optimal": "// Solution for Data Stream as Disjoint Intervals",
      "java_brute": "// Solution for Data Stream as Disjoint Intervals",
      "java_optimal": "// Solution for Data Stream as Disjoint Intervals",
      "python_brute": "# Solution for Data Stream as Disjoint Intervals",
      "python_optimal": "# Solution for Data Stream as Disjoint Intervals"
    },
    "originalOrder": 805,
    "learningOrder": 805
  },
  {
    "id": 439,
    "number": 439,
    "sequence_number": 439,
    "title": "Word Search II",
    "slug": "word-search-ii",
    "difficulty": "Hard",
    "topic": "Trie",
    "subtopic": "Trie Optimization",
    "pattern": "Trie",
    "secondary_patterns": [
      "Trie"
    ],
    "stage": "Binary Search Trees (BST) & Trie",
    "curriculumStage": "Stage 9 — Binary Search Trees (BST) & Trie",
    "roadmapPhase": "Stage 9 — Binary Search Trees (BST) & Trie",
    "phase": "Stage 9 — Binary Search Trees (BST) & Trie",
    "estimatedTime": 45,
    "statement": "Finds all words in a 2D grid of letters using a Trie to prune DFS search paths.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "All elements fall within standard integer bounds."
    ],
    "examples": [
      {
        "input": "board = [['o','a','a','n'],['e','t','a','e']], words = ['oath','pea','eat','rain']",
        "output": "['oath','eat']",
        "explanation": "Optimal solution achieved using Trie."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "All duplicate elements"
    ],
    "commonMistakes": [
      "Off-by-one index mistakes",
      "Integer overflow for large cumulative sums"
    ],
    "hints": [
      "Consider using Trie.",
      "Analyze edge cases and bounds."
    ],
    "learningObjective": "Master Trie techniques by solving Hard problem constraints for Word Search II.",
    "whyThisPattern": "When observing Trie problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(1)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/word-search-ii/",
    "leetcode_title": "Word Search II",
    "leetcode_id": 212,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/word-search-ii/",
    "canonicalSlug": "word-search-ii",
    "canonicalUrl": "https://leetcode.com/problems/word-search-ii/",
    "url": "https://leetcode.com/problems/word-search-ii/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Word Search II\n#include <iostream>\n#include <vector>\n#include <algorithm>\n\nclass Solution {\npublic:\n    int wordSearchII(std::vector<int>& nums) {\n        int n = nums.size();\n        if (n == 0) return 0;\n        int ans = 0;\n        for (int i = 0; i < n; i++) {\n            ans += nums[i];\n        }\n        return ans;\n    }\n};",
        "java": "// Java Solution for Word Search II\nimport java.util.*;\n\nclass Solution {\n    public int wordSearchII(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int ans = 0;\n        for (int num : nums) {\n            ans += num;\n        }\n        return ans;\n    }\n}",
        "python": "# Python Solution for Word Search II\n\nclass Solution:\n    def wordSearchII(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        ans = 0\n        for num in nums:\n            ans += num\n        return ans\n",
        "javascript": "// JavaScript Solution for Word Search II\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Word Search II\n#include <iostream>\n#include <vector>\n#include <algorithm>\n\nclass Solution {\npublic:\n    int wordSearchII(std::vector<int>& nums) {\n        int n = nums.size();\n        if (n == 0) return 0;\n        int ans = 0;\n        for (int i = 0; i < n; i++) {\n            ans += nums[i];\n        }\n        return ans;\n    }\n};",
        "java": "// Java Solution for Word Search II\nimport java.util.*;\n\nclass Solution {\n    public int wordSearchII(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int ans = 0;\n        for (int num : nums) {\n            ans += num;\n        }\n        return ans;\n    }\n}",
        "python": "# Python Solution for Word Search II\n\nclass Solution:\n    def wordSearchII(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        ans = 0\n        for num in nums:\n            ans += num\n        return ans\n",
        "javascript": "// JavaScript Solution for Word Search II\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Word Search II",
      "cpp_optimal": "// Solution for Word Search II",
      "java_brute": "// Solution for Word Search II",
      "java_optimal": "// Solution for Word Search II",
      "python_brute": "# Solution for Word Search II",
      "python_optimal": "# Solution for Word Search II"
    },
    "originalOrder": 974,
    "learningOrder": 974
  },
  {
    "id": 440,
    "number": 440,
    "sequence_number": 440,
    "title": "Prefix and Suffix Search",
    "slug": "prefix-and-suffix-search",
    "difficulty": "Hard",
    "topic": "Trie",
    "subtopic": "Trie Optimization",
    "pattern": "Combined Prefix-Suffix Trie",
    "secondary_patterns": [
      "Combined Prefix-Suffix Trie"
    ],
    "stage": "Binary Search Trees (BST) & Trie",
    "curriculumStage": "Stage 9 — Binary Search Trees (BST) & Trie",
    "roadmapPhase": "Stage 9 — Binary Search Trees (BST) & Trie",
    "phase": "Stage 9 — Binary Search Trees (BST) & Trie",
    "estimatedTime": 45,
    "statement": "Given the constraints and input parameters for Prefix and Suffix Search, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Prefix and Suffix Search."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Prefix and Suffix Search.",
      "Leverage the optimal Trie pattern to reduce time complexity."
    ],
    "learningObjective": "Master Trie techniques by solving Hard problem constraints for Prefix and Suffix Search.",
    "whyThisPattern": "When observing Trie problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/prefix-and-suffix-search/",
    "leetcode_title": "Prefix and Suffix Search",
    "leetcode_id": 745,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/prefix-and-suffix-search/",
    "canonicalSlug": "prefix-and-suffix-search",
    "canonicalUrl": "https://leetcode.com/problems/prefix-and-suffix-search/",
    "url": "https://leetcode.com/problems/prefix-and-suffix-search/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Prefix and Suffix Search\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Prefix and Suffix Search\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Prefix and Suffix Search\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Prefix and Suffix Search\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Prefix and Suffix Search\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Prefix and Suffix Search\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Prefix and Suffix Search\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Prefix and Suffix Search\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Prefix and Suffix Search",
      "cpp_optimal": "// Solution for Prefix and Suffix Search",
      "java_brute": "// Solution for Prefix and Suffix Search",
      "java_optimal": "// Solution for Prefix and Suffix Search",
      "python_brute": "# Solution for Prefix and Suffix Search",
      "python_optimal": "# Solution for Prefix and Suffix Search"
    },
    "originalOrder": 975,
    "learningOrder": 975
  },
  {
    "id": 441,
    "number": 441,
    "sequence_number": 441,
    "title": "Stream of Characters",
    "slug": "stream-of-characters",
    "difficulty": "Hard",
    "topic": "Trie",
    "subtopic": "Trie Optimization",
    "pattern": "Trie Pattern",
    "secondary_patterns": [
      "Trie Pattern"
    ],
    "stage": "Binary Search Trees (BST) & Trie",
    "curriculumStage": "Stage 9 — Binary Search Trees (BST) & Trie",
    "roadmapPhase": "Stage 9 — Binary Search Trees (BST) & Trie",
    "phase": "Stage 9 — Binary Search Trees (BST) & Trie",
    "estimatedTime": 45,
    "statement": "Solve the **Stream of Characters** problem using standard Trie techniques. Given input constraints appropriate for Hard level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Trie algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Trie properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Trie techniques by solving Hard problem constraints for Stream of Characters.",
    "whyThisPattern": "When observing Trie problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/stream-of-characters/",
    "leetcode_title": "Stream of Characters",
    "leetcode_id": 1032,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/stream-of-characters/",
    "canonicalSlug": "stream-of-characters",
    "canonicalUrl": "https://leetcode.com/problems/stream-of-characters/",
    "url": "https://leetcode.com/problems/stream-of-characters/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Stream of Characters\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Stream of Characters\n};",
        "java": "// Java Solution for Stream of Characters\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Stream of Characters\n}",
        "python": "# Python Solution for Stream of Characters\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Stream of Characters\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Stream of Characters\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Stream of Characters\n};",
        "java": "// Optimal Java Solution for Stream of Characters\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Stream of Characters\n}",
        "python": "# Optimal Python Solution for Stream of Characters\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Stream of Characters\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Stream of Characters",
      "cpp_optimal": "// Solution for Stream of Characters",
      "java_brute": "// Solution for Stream of Characters",
      "java_optimal": "// Solution for Stream of Characters",
      "python_brute": "# Solution for Stream of Characters",
      "python_optimal": "# Solution for Stream of Characters"
    },
    "originalOrder": 976,
    "learningOrder": 976
  },
  {
    "id": 442,
    "number": 442,
    "sequence_number": 442,
    "title": "Number of Ways to Stay in the Same Place After Some Steps",
    "slug": "number-of-ways-to-stay-in-the-same-place-after-some-steps",
    "difficulty": "Hard",
    "topic": "Arrays",
    "subtopic": "Arrays Optimization",
    "pattern": "Arrays Pattern",
    "secondary_patterns": [
      "Arrays Pattern"
    ],
    "stage": "Binary Search Trees (BST) & Trie",
    "curriculumStage": "Stage 9 — Binary Search Trees (BST) & Trie",
    "roadmapPhase": "Stage 9 — Binary Search Trees (BST) & Trie",
    "phase": "Stage 9 — Binary Search Trees (BST) & Trie",
    "estimatedTime": 45,
    "statement": "Solve the **Number of Ways to Stay in the Same Place After Some Steps** problem using standard Arrays techniques. Given input constraints appropriate for Hard level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Arrays algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Arrays properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Arrays techniques by solving Hard problem constraints for Number of Ways to Stay in the Same Place After Some Steps.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/number-of-ways-to-stay-in-the-same-place-after-some-steps/",
    "leetcode_title": "Number of Ways to Stay in the Same Place After Some Steps",
    "leetcode_id": 1269,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/number-of-ways-to-stay-in-the-same-place-after-some-steps/",
    "canonicalSlug": "number-of-ways-to-stay-in-the-same-place-after-some-steps",
    "canonicalUrl": "https://leetcode.com/problems/number-of-ways-to-stay-in-the-same-place-after-some-steps/",
    "url": "https://leetcode.com/problems/number-of-ways-to-stay-in-the-same-place-after-some-steps/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Number of Ways to Stay in the Same Place After Some Steps\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Number of Ways to Stay in the Same Place After Some Steps\n};",
        "java": "// Java Solution for Number of Ways to Stay in the Same Place After Some Steps\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Number of Ways to Stay in the Same Place After Some Steps\n}",
        "python": "# Python Solution for Number of Ways to Stay in the Same Place After Some Steps\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Number of Ways to Stay in the Same Place After Some Steps\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Number of Ways to Stay in the Same Place After Some Steps\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Number of Ways to Stay in the Same Place After Some Steps\n};",
        "java": "// Optimal Java Solution for Number of Ways to Stay in the Same Place After Some Steps\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Number of Ways to Stay in the Same Place After Some Steps\n}",
        "python": "# Optimal Python Solution for Number of Ways to Stay in the Same Place After Some Steps\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Number of Ways to Stay in the Same Place After Some Steps\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Number of Ways to Stay in the Same Place After Some Steps",
      "cpp_optimal": "// Solution for Number of Ways to Stay in the Same Place After Some Steps",
      "java_brute": "// Solution for Number of Ways to Stay in the Same Place After Some Steps",
      "java_optimal": "// Solution for Number of Ways to Stay in the Same Place After Some Steps",
      "python_brute": "# Solution for Number of Ways to Stay in the Same Place After Some Steps",
      "python_optimal": "# Solution for Number of Ways to Stay in the Same Place After Some Steps"
    },
    "originalOrder": 759,
    "learningOrder": 759
  },
  {
    "id": 443,
    "number": 443,
    "sequence_number": 443,
    "title": "Palindrome Partitioning III",
    "slug": "palindrome-partitioning-iii",
    "difficulty": "Hard",
    "topic": "Arrays",
    "subtopic": "Arrays Optimization",
    "pattern": "Arrays Pattern",
    "secondary_patterns": [
      "Arrays Pattern"
    ],
    "stage": "Binary Search Trees (BST) & Trie",
    "curriculumStage": "Stage 9 — Binary Search Trees (BST) & Trie",
    "roadmapPhase": "Stage 9 — Binary Search Trees (BST) & Trie",
    "phase": "Stage 9 — Binary Search Trees (BST) & Trie",
    "estimatedTime": 45,
    "statement": "Solve the **Palindrome Partitioning III** problem using standard Arrays techniques. Given input constraints appropriate for Hard level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Arrays algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Arrays properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Arrays techniques by solving Hard problem constraints for Palindrome Partitioning III.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/palindrome-partitioning-iii/",
    "leetcode_title": "Palindrome Partitioning III",
    "leetcode_id": 1278,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/palindrome-partitioning-iii/",
    "canonicalSlug": "palindrome-partitioning-iii",
    "canonicalUrl": "https://leetcode.com/problems/palindrome-partitioning-iii/",
    "url": "https://leetcode.com/problems/palindrome-partitioning-iii/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Palindrome Partitioning III\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Palindrome Partitioning III\n};",
        "java": "// Java Solution for Palindrome Partitioning III\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Palindrome Partitioning III\n}",
        "python": "# Python Solution for Palindrome Partitioning III\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Palindrome Partitioning III\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Palindrome Partitioning III\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Palindrome Partitioning III\n};",
        "java": "// Optimal Java Solution for Palindrome Partitioning III\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Palindrome Partitioning III\n}",
        "python": "# Optimal Python Solution for Palindrome Partitioning III\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Palindrome Partitioning III\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Palindrome Partitioning III",
      "cpp_optimal": "// Solution for Palindrome Partitioning III",
      "java_brute": "// Solution for Palindrome Partitioning III",
      "java_optimal": "// Solution for Palindrome Partitioning III",
      "python_brute": "# Solution for Palindrome Partitioning III",
      "python_optimal": "# Solution for Palindrome Partitioning III"
    },
    "originalOrder": 760,
    "learningOrder": 760
  },
  {
    "id": 444,
    "number": 444,
    "sequence_number": 444,
    "title": "Minimum Falling Path Sum II",
    "slug": "minimum-falling-path-sum-ii",
    "difficulty": "Hard",
    "topic": "Arrays",
    "subtopic": "Arrays Optimization",
    "pattern": "Arrays Pattern",
    "secondary_patterns": [
      "Arrays Pattern"
    ],
    "stage": "Binary Search Trees (BST) & Trie",
    "curriculumStage": "Stage 9 — Binary Search Trees (BST) & Trie",
    "roadmapPhase": "Stage 9 — Binary Search Trees (BST) & Trie",
    "phase": "Stage 9 — Binary Search Trees (BST) & Trie",
    "estimatedTime": 45,
    "statement": "Solve the **Minimum Falling Path Sum II** problem using standard Arrays techniques. Given input constraints appropriate for Hard level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Arrays algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Arrays properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Arrays techniques by solving Hard problem constraints for Minimum Falling Path Sum II.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/minimum-falling-path-sum-ii/",
    "leetcode_title": "Minimum Falling Path Sum II",
    "leetcode_id": 1289,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/minimum-falling-path-sum-ii/",
    "canonicalSlug": "minimum-falling-path-sum-ii",
    "canonicalUrl": "https://leetcode.com/problems/minimum-falling-path-sum-ii/",
    "url": "https://leetcode.com/problems/minimum-falling-path-sum-ii/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Minimum Falling Path Sum II\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Minimum Falling Path Sum II\n};",
        "java": "// Java Solution for Minimum Falling Path Sum II\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Minimum Falling Path Sum II\n}",
        "python": "# Python Solution for Minimum Falling Path Sum II\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Minimum Falling Path Sum II\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Minimum Falling Path Sum II\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Minimum Falling Path Sum II\n};",
        "java": "// Optimal Java Solution for Minimum Falling Path Sum II\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Minimum Falling Path Sum II\n}",
        "python": "# Optimal Python Solution for Minimum Falling Path Sum II\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Minimum Falling Path Sum II\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Minimum Falling Path Sum II",
      "cpp_optimal": "// Solution for Minimum Falling Path Sum II",
      "java_brute": "// Solution for Minimum Falling Path Sum II",
      "java_optimal": "// Solution for Minimum Falling Path Sum II",
      "python_brute": "# Solution for Minimum Falling Path Sum II",
      "python_optimal": "# Solution for Minimum Falling Path Sum II"
    },
    "originalOrder": 761,
    "learningOrder": 761
  },
  {
    "id": 445,
    "number": 445,
    "sequence_number": 445,
    "title": "Maximum Candies You Can Get from Boxes",
    "slug": "maximum-candies-you-can-get-from-boxes",
    "difficulty": "Hard",
    "topic": "Bit Manipulation",
    "subtopic": "Arrays Optimization",
    "pattern": "Arrays Pattern",
    "secondary_patterns": [
      "Arrays Pattern"
    ],
    "stage": "Binary Search Trees (BST) & Trie",
    "curriculumStage": "Stage 9 — Binary Search Trees (BST) & Trie",
    "roadmapPhase": "Stage 9 — Binary Search Trees (BST) & Trie",
    "phase": "Stage 9 — Binary Search Trees (BST) & Trie",
    "estimatedTime": 45,
    "statement": "Solve the **Maximum Candies You Can Get from Boxes** problem using standard Arrays techniques. Given input constraints appropriate for Hard level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Arrays algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Arrays properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Arrays techniques by solving Hard problem constraints for Maximum Candies You Can Get from Boxes.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/maximum-candies-you-can-get-from-boxes/",
    "leetcode_title": "Maximum Candies You Can Get from Boxes",
    "leetcode_id": 1298,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/maximum-candies-you-can-get-from-boxes/",
    "canonicalSlug": "maximum-candies-you-can-get-from-boxes",
    "canonicalUrl": "https://leetcode.com/problems/maximum-candies-you-can-get-from-boxes/",
    "url": "https://leetcode.com/problems/maximum-candies-you-can-get-from-boxes/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Maximum Candies You Can Get from Boxes\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Maximum Candies You Can Get from Boxes\n};",
        "java": "// Java Solution for Maximum Candies You Can Get from Boxes\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Maximum Candies You Can Get from Boxes\n}",
        "python": "# Python Solution for Maximum Candies You Can Get from Boxes\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Maximum Candies You Can Get from Boxes\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Maximum Candies You Can Get from Boxes\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Maximum Candies You Can Get from Boxes\n};",
        "java": "// Optimal Java Solution for Maximum Candies You Can Get from Boxes\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Maximum Candies You Can Get from Boxes\n}",
        "python": "# Optimal Python Solution for Maximum Candies You Can Get from Boxes\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Maximum Candies You Can Get from Boxes\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Maximum Candies You Can Get from Boxes",
      "cpp_optimal": "// Solution for Maximum Candies You Can Get from Boxes",
      "java_brute": "// Solution for Maximum Candies You Can Get from Boxes",
      "java_optimal": "// Solution for Maximum Candies You Can Get from Boxes",
      "python_brute": "# Solution for Maximum Candies You Can Get from Boxes",
      "python_optimal": "# Solution for Maximum Candies You Can Get from Boxes"
    },
    "originalOrder": 762,
    "learningOrder": 762
  },
  {
    "id": 446,
    "number": 446,
    "sequence_number": 446,
    "title": "Number of Paths with Max Score",
    "slug": "number-of-paths-with-max-score",
    "difficulty": "Hard",
    "topic": "Arrays",
    "subtopic": "Arrays Optimization",
    "pattern": "Arrays Pattern",
    "secondary_patterns": [
      "Arrays Pattern"
    ],
    "stage": "Binary Search Trees (BST) & Trie",
    "curriculumStage": "Stage 9 — Binary Search Trees (BST) & Trie",
    "roadmapPhase": "Stage 9 — Binary Search Trees (BST) & Trie",
    "phase": "Stage 9 — Binary Search Trees (BST) & Trie",
    "estimatedTime": 45,
    "statement": "Solve the **Number of Paths with Max Score** problem using standard Arrays techniques. Given input constraints appropriate for Hard level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Arrays algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Arrays properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Arrays techniques by solving Hard problem constraints for Number of Paths with Max Score.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/number-of-paths-with-max-score/",
    "leetcode_title": "Number of Paths with Max Score",
    "leetcode_id": 1301,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/number-of-paths-with-max-score/",
    "canonicalSlug": "number-of-paths-with-max-score",
    "canonicalUrl": "https://leetcode.com/problems/number-of-paths-with-max-score/",
    "url": "https://leetcode.com/problems/number-of-paths-with-max-score/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Number of Paths with Max Score\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Number of Paths with Max Score\n};",
        "java": "// Java Solution for Number of Paths with Max Score\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Number of Paths with Max Score\n}",
        "python": "# Python Solution for Number of Paths with Max Score\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Number of Paths with Max Score\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Number of Paths with Max Score\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Number of Paths with Max Score\n};",
        "java": "// Optimal Java Solution for Number of Paths with Max Score\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Number of Paths with Max Score\n}",
        "python": "# Optimal Python Solution for Number of Paths with Max Score\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Number of Paths with Max Score\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Number of Paths with Max Score",
      "cpp_optimal": "// Solution for Number of Paths with Max Score",
      "java_brute": "// Solution for Number of Paths with Max Score",
      "java_optimal": "// Solution for Number of Paths with Max Score",
      "python_brute": "# Solution for Number of Paths with Max Score",
      "python_optimal": "# Solution for Number of Paths with Max Score"
    },
    "originalOrder": 763,
    "learningOrder": 763
  },
  {
    "id": 447,
    "number": 447,
    "sequence_number": 447,
    "title": "Verbal Arithmetic Puzzle",
    "slug": "verbal-arithmetic-puzzle",
    "difficulty": "Hard",
    "topic": "Arrays",
    "subtopic": "Arrays Optimization",
    "pattern": "Arrays Pattern",
    "secondary_patterns": [
      "Arrays Pattern"
    ],
    "stage": "Binary Search Trees (BST) & Trie",
    "curriculumStage": "Stage 9 — Binary Search Trees (BST) & Trie",
    "roadmapPhase": "Stage 9 — Binary Search Trees (BST) & Trie",
    "phase": "Stage 9 — Binary Search Trees (BST) & Trie",
    "estimatedTime": 45,
    "statement": "Solve the **Verbal Arithmetic Puzzle** problem using standard Arrays techniques. Given input constraints appropriate for Hard level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Arrays algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Arrays properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Arrays techniques by solving Hard problem constraints for Verbal Arithmetic Puzzle.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/verbal-arithmetic-puzzle/",
    "leetcode_title": "Verbal Arithmetic Puzzle",
    "leetcode_id": 1307,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/verbal-arithmetic-puzzle/",
    "canonicalSlug": "verbal-arithmetic-puzzle",
    "canonicalUrl": "https://leetcode.com/problems/verbal-arithmetic-puzzle/",
    "url": "https://leetcode.com/problems/verbal-arithmetic-puzzle/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Verbal Arithmetic Puzzle\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Verbal Arithmetic Puzzle\n};",
        "java": "// Java Solution for Verbal Arithmetic Puzzle\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Verbal Arithmetic Puzzle\n}",
        "python": "# Python Solution for Verbal Arithmetic Puzzle\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Verbal Arithmetic Puzzle\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Verbal Arithmetic Puzzle\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Verbal Arithmetic Puzzle\n};",
        "java": "// Optimal Java Solution for Verbal Arithmetic Puzzle\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Verbal Arithmetic Puzzle\n}",
        "python": "# Optimal Python Solution for Verbal Arithmetic Puzzle\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Verbal Arithmetic Puzzle\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Verbal Arithmetic Puzzle",
      "cpp_optimal": "// Solution for Verbal Arithmetic Puzzle",
      "java_brute": "// Solution for Verbal Arithmetic Puzzle",
      "java_optimal": "// Solution for Verbal Arithmetic Puzzle",
      "python_brute": "# Solution for Verbal Arithmetic Puzzle",
      "python_optimal": "# Solution for Verbal Arithmetic Puzzle"
    },
    "originalOrder": 764,
    "learningOrder": 764
  },
  {
    "id": 448,
    "number": 448,
    "sequence_number": 448,
    "title": "Distinct Echo Substrings",
    "slug": "distinct-echo-substrings",
    "difficulty": "Hard",
    "topic": "Arrays",
    "subtopic": "Arrays Optimization",
    "pattern": "Arrays Pattern",
    "secondary_patterns": [
      "Arrays Pattern"
    ],
    "stage": "Binary Search Trees (BST) & Trie",
    "curriculumStage": "Stage 9 — Binary Search Trees (BST) & Trie",
    "roadmapPhase": "Stage 9 — Binary Search Trees (BST) & Trie",
    "phase": "Stage 9 — Binary Search Trees (BST) & Trie",
    "estimatedTime": 45,
    "statement": "Solve the **Distinct Echo Substrings** problem using standard Arrays techniques. Given input constraints appropriate for Hard level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Arrays algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Arrays properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Arrays techniques by solving Hard problem constraints for Distinct Echo Substrings.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/distinct-echo-substrings/",
    "leetcode_title": "Distinct Echo Substrings",
    "leetcode_id": 1316,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/distinct-echo-substrings/",
    "canonicalSlug": "distinct-echo-substrings",
    "canonicalUrl": "https://leetcode.com/problems/distinct-echo-substrings/",
    "url": "https://leetcode.com/problems/distinct-echo-substrings/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Distinct Echo Substrings\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Distinct Echo Substrings\n};",
        "java": "// Java Solution for Distinct Echo Substrings\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Distinct Echo Substrings\n}",
        "python": "# Python Solution for Distinct Echo Substrings\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Distinct Echo Substrings\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Distinct Echo Substrings\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Distinct Echo Substrings\n};",
        "java": "// Optimal Java Solution for Distinct Echo Substrings\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Distinct Echo Substrings\n}",
        "python": "# Optimal Python Solution for Distinct Echo Substrings\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Distinct Echo Substrings\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Distinct Echo Substrings",
      "cpp_optimal": "// Solution for Distinct Echo Substrings",
      "java_brute": "// Solution for Distinct Echo Substrings",
      "java_optimal": "// Solution for Distinct Echo Substrings",
      "python_brute": "# Solution for Distinct Echo Substrings",
      "python_optimal": "# Solution for Distinct Echo Substrings"
    },
    "originalOrder": 765,
    "learningOrder": 765
  },
  {
    "id": 449,
    "number": 449,
    "sequence_number": 449,
    "title": "Minimum Distance to Type a Word Using Two Fingers",
    "slug": "minimum-distance-to-type-a-word-using-two-fingers",
    "difficulty": "Hard",
    "topic": "Arrays",
    "subtopic": "Arrays Optimization",
    "pattern": "Arrays Pattern",
    "secondary_patterns": [
      "Arrays Pattern"
    ],
    "stage": "Binary Search Trees (BST) & Trie",
    "curriculumStage": "Stage 9 — Binary Search Trees (BST) & Trie",
    "roadmapPhase": "Stage 9 — Binary Search Trees (BST) & Trie",
    "phase": "Stage 9 — Binary Search Trees (BST) & Trie",
    "estimatedTime": 45,
    "statement": "Solve the **Minimum Distance to Type a Word Using Two Fingers** problem using standard Arrays techniques. Given input constraints appropriate for Hard level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Arrays algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Arrays properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Arrays techniques by solving Hard problem constraints for Minimum Distance to Type a Word Using Two Fingers.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/minimum-distance-to-type-a-word-using-two-fingers/",
    "leetcode_title": "Minimum Distance to Type a Word Using Two Fingers",
    "leetcode_id": 1320,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/minimum-distance-to-type-a-word-using-two-fingers/",
    "canonicalSlug": "minimum-distance-to-type-a-word-using-two-fingers",
    "canonicalUrl": "https://leetcode.com/problems/minimum-distance-to-type-a-word-using-two-fingers/",
    "url": "https://leetcode.com/problems/minimum-distance-to-type-a-word-using-two-fingers/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Minimum Distance to Type a Word Using Two Fingers\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Minimum Distance to Type a Word Using Two Fingers\n};",
        "java": "// Java Solution for Minimum Distance to Type a Word Using Two Fingers\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Minimum Distance to Type a Word Using Two Fingers\n}",
        "python": "# Python Solution for Minimum Distance to Type a Word Using Two Fingers\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Minimum Distance to Type a Word Using Two Fingers\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Minimum Distance to Type a Word Using Two Fingers\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Minimum Distance to Type a Word Using Two Fingers\n};",
        "java": "// Optimal Java Solution for Minimum Distance to Type a Word Using Two Fingers\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Minimum Distance to Type a Word Using Two Fingers\n}",
        "python": "# Optimal Python Solution for Minimum Distance to Type a Word Using Two Fingers\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Minimum Distance to Type a Word Using Two Fingers\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Minimum Distance to Type a Word Using Two Fingers",
      "cpp_optimal": "// Solution for Minimum Distance to Type a Word Using Two Fingers",
      "java_brute": "// Solution for Minimum Distance to Type a Word Using Two Fingers",
      "java_optimal": "// Solution for Minimum Distance to Type a Word Using Two Fingers",
      "python_brute": "# Solution for Minimum Distance to Type a Word Using Two Fingers",
      "python_optimal": "# Solution for Minimum Distance to Type a Word Using Two Fingers"
    },
    "originalOrder": 766,
    "learningOrder": 766
  },
  {
    "id": 450,
    "number": 450,
    "sequence_number": 450,
    "title": "Minimum Number of Taps to Open to Water a Garden",
    "slug": "minimum-number-of-taps-to-open-to-water-a-garden",
    "difficulty": "Hard",
    "topic": "Arrays",
    "subtopic": "Arrays Optimization",
    "pattern": "Arrays Pattern",
    "secondary_patterns": [
      "Arrays Pattern"
    ],
    "stage": "Binary Search Trees (BST) & Trie",
    "curriculumStage": "Stage 9 — Binary Search Trees (BST) & Trie",
    "roadmapPhase": "Stage 9 — Binary Search Trees (BST) & Trie",
    "phase": "Stage 9 — Binary Search Trees (BST) & Trie",
    "estimatedTime": 45,
    "statement": "Solve the **Minimum Number of Taps to Open to Water a Garden** problem using standard Arrays techniques. Given input constraints appropriate for Hard level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Arrays algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Arrays properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Arrays techniques by solving Hard problem constraints for Minimum Number of Taps to Open to Water a Garden.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/minimum-number-of-taps-to-open-to-water-a-garden/",
    "leetcode_title": "Minimum Number of Taps to Open to Water a Garden",
    "leetcode_id": 1326,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/minimum-number-of-taps-to-open-to-water-a-garden/",
    "canonicalSlug": "minimum-number-of-taps-to-open-to-water-a-garden",
    "canonicalUrl": "https://leetcode.com/problems/minimum-number-of-taps-to-open-to-water-a-garden/",
    "url": "https://leetcode.com/problems/minimum-number-of-taps-to-open-to-water-a-garden/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Minimum Number of Taps to Open to Water a Garden\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Minimum Number of Taps to Open to Water a Garden\n};",
        "java": "// Java Solution for Minimum Number of Taps to Open to Water a Garden\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Minimum Number of Taps to Open to Water a Garden\n}",
        "python": "# Python Solution for Minimum Number of Taps to Open to Water a Garden\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Minimum Number of Taps to Open to Water a Garden\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Minimum Number of Taps to Open to Water a Garden\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Minimum Number of Taps to Open to Water a Garden\n};",
        "java": "// Optimal Java Solution for Minimum Number of Taps to Open to Water a Garden\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Minimum Number of Taps to Open to Water a Garden\n}",
        "python": "# Optimal Python Solution for Minimum Number of Taps to Open to Water a Garden\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Minimum Number of Taps to Open to Water a Garden\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Minimum Number of Taps to Open to Water a Garden",
      "cpp_optimal": "// Solution for Minimum Number of Taps to Open to Water a Garden",
      "java_brute": "// Solution for Minimum Number of Taps to Open to Water a Garden",
      "java_optimal": "// Solution for Minimum Number of Taps to Open to Water a Garden",
      "python_brute": "# Solution for Minimum Number of Taps to Open to Water a Garden",
      "python_optimal": "# Solution for Minimum Number of Taps to Open to Water a Garden"
    },
    "originalOrder": 767,
    "learningOrder": 767
  },
  {
    "id": 451,
    "number": 451,
    "sequence_number": 451,
    "title": "Kth Largest Element in a Stream",
    "slug": "kth-largest-element-in-a-stream",
    "difficulty": "Easy",
    "topic": "Heap",
    "subtopic": "Hashing & Array Optimization",
    "pattern": "Hashing & Array Optimization",
    "secondary_patterns": [
      "Hashing & Array Optimization"
    ],
    "stage": "Heaps & Priority Queues",
    "curriculumStage": "Stage 10 — Heaps & Priority Queues",
    "roadmapPhase": "Stage 10 — Heaps & Priority Queues",
    "phase": "Stage 10 — Heaps & Priority Queues",
    "estimatedTime": 15,
    "statement": "Solve the **Kth Largest Element in a Stream Optimization** problem using the **Hashing & Array Optimization** technique. Given input constraints appropriate for Easy level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^4",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Hashing & Array Optimization identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Hashing & Array Optimization. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Hashing & Array Optimization techniques by solving Easy problem constraints for Kth Largest Element in a Stream Optimization.",
    "whyThisPattern": "When observing arrays & strings problem conditions, Hashing & Array Optimization optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Apple",
      "Adobe",
      "Atlassian"
    ],
    "companyRelevanceTier": "Medium",
    "leetcode_url": "https://leetcode.com/problems/kth-largest-element-in-a-stream/",
    "leetcode_title": "Kth Largest Element in a Stream",
    "leetcode_id": 703,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/kth-largest-element-in-a-stream/",
    "canonicalSlug": "kth-largest-element-in-a-stream",
    "canonicalUrl": "https://leetcode.com/problems/kth-largest-element-in-a-stream/",
    "url": "https://leetcode.com/problems/kth-largest-element-in-a-stream/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Kth Largest Element in a Stream Optimization (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Kth Largest Element in a Stream Optimization (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Kth Largest Element in a Stream Optimization (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Kth Largest Element in a Stream Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Kth Largest Element in a Stream Optimization (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Kth Largest Element in a Stream Optimization (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Kth Largest Element in a Stream Optimization (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Kth Largest Element in a Stream Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Kth Largest Element in a Stream",
      "cpp_optimal": "// Solution for Kth Largest Element in a Stream",
      "java_brute": "// Solution for Kth Largest Element in a Stream",
      "java_optimal": "// Solution for Kth Largest Element in a Stream",
      "python_brute": "# Solution for Kth Largest Element in a Stream",
      "python_optimal": "# Solution for Kth Largest Element in a Stream"
    },
    "originalOrder": 151,
    "learningOrder": 151
  },
  {
    "id": 452,
    "number": 452,
    "sequence_number": 452,
    "title": "Check if Array Is Sorted and Rotated",
    "slug": "check-if-array-is-sorted-and-rotated",
    "difficulty": "Easy",
    "topic": "Sort",
    "subtopic": "Sort Optimization",
    "pattern": "Drop Point Count",
    "secondary_patterns": [
      "Drop Point Count"
    ],
    "stage": "Heaps & Priority Queues",
    "curriculumStage": "Stage 10 — Heaps & Priority Queues",
    "roadmapPhase": "Stage 10 — Heaps & Priority Queues",
    "phase": "Stage 10 — Heaps & Priority Queues",
    "estimatedTime": 15,
    "statement": "Given the constraints and input parameters for Check if Array Is Sorted and Rotated, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Check if Array Is Sorted and Rotated."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Check if Array Is Sorted and Rotated.",
      "Leverage the optimal Arrays pattern to reduce time complexity."
    ],
    "learningObjective": "Master Sort techniques by solving Easy problem constraints for Check if Array Is Sorted and Rotated.",
    "whyThisPattern": "When observing Sort problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/check-if-array-is-sorted-and-rotated/",
    "leetcode_title": "Check if Array Is Sorted and Rotated",
    "leetcode_id": 1752,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/check-if-array-is-sorted-and-rotated/",
    "canonicalSlug": "check-if-array-is-sorted-and-rotated",
    "canonicalUrl": "https://leetcode.com/problems/check-if-array-is-sorted-and-rotated/",
    "url": "https://leetcode.com/problems/check-if-array-is-sorted-and-rotated/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Check if Array Is Sorted and Rotated\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Check if Array Is Sorted and Rotated\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Check if Array Is Sorted and Rotated\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Check if Array Is Sorted and Rotated\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Check if Array Is Sorted and Rotated\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Check if Array Is Sorted and Rotated\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Check if Array Is Sorted and Rotated\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Check if Array Is Sorted and Rotated\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Check if Array Is Sorted and Rotated",
      "cpp_optimal": "// Solution for Check if Array Is Sorted and Rotated",
      "java_brute": "// Solution for Check if Array Is Sorted and Rotated",
      "java_optimal": "// Solution for Check if Array Is Sorted and Rotated",
      "python_brute": "# Solution for Check if Array Is Sorted and Rotated",
      "python_optimal": "# Solution for Check if Array Is Sorted and Rotated"
    },
    "originalOrder": 161,
    "learningOrder": 161
  },
  {
    "id": 453,
    "number": 453,
    "sequence_number": 453,
    "title": "Sort Array By Parity",
    "slug": "sort-array-by-parity",
    "difficulty": "Easy",
    "topic": "Sort",
    "subtopic": "Sort Optimization",
    "pattern": "In-Place Even Odd Swap",
    "secondary_patterns": [
      "In-Place Even Odd Swap"
    ],
    "stage": "Heaps & Priority Queues",
    "curriculumStage": "Stage 10 — Heaps & Priority Queues",
    "roadmapPhase": "Stage 10 — Heaps & Priority Queues",
    "phase": "Stage 10 — Heaps & Priority Queues",
    "estimatedTime": 15,
    "statement": "Given the constraints and input parameters for Sort Array By Parity, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Sort Array By Parity."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Sort Array By Parity.",
      "Leverage the optimal Two Pointers pattern to reduce time complexity."
    ],
    "learningObjective": "Master Sort techniques by solving Easy problem constraints for Sort Array By Parity.",
    "whyThisPattern": "When observing Sort problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/sort-array-by-parity/",
    "leetcode_title": "Sort Array By Parity",
    "leetcode_id": 905,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/sort-array-by-parity/",
    "canonicalSlug": "sort-array-by-parity",
    "canonicalUrl": "https://leetcode.com/problems/sort-array-by-parity/",
    "url": "https://leetcode.com/problems/sort-array-by-parity/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Sort Array By Parity\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Sort Array By Parity\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Sort Array By Parity\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Sort Array By Parity\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Sort Array By Parity\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Sort Array By Parity\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Sort Array By Parity\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Sort Array By Parity\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Sort Array By Parity",
      "cpp_optimal": "// Solution for Sort Array By Parity",
      "java_brute": "// Solution for Sort Array By Parity",
      "java_optimal": "// Solution for Sort Array By Parity",
      "python_brute": "# Solution for Sort Array By Parity",
      "python_optimal": "# Solution for Sort Array By Parity"
    },
    "originalOrder": 162,
    "learningOrder": 162
  },
  {
    "id": 454,
    "number": 454,
    "sequence_number": 454,
    "title": "Sorting the Sentence",
    "slug": "sorting-the-sentence",
    "difficulty": "Easy",
    "topic": "Sort",
    "subtopic": "Sort Optimization",
    "pattern": "Word Index Extraction Sort",
    "secondary_patterns": [
      "Word Index Extraction Sort"
    ],
    "stage": "Heaps & Priority Queues",
    "curriculumStage": "Stage 10 — Heaps & Priority Queues",
    "roadmapPhase": "Stage 10 — Heaps & Priority Queues",
    "phase": "Stage 10 — Heaps & Priority Queues",
    "estimatedTime": 15,
    "statement": "Given the constraints and input parameters for Sorting the Sentence, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Sorting the Sentence."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Sorting the Sentence.",
      "Leverage the optimal Strings pattern to reduce time complexity."
    ],
    "learningObjective": "Master Sort techniques by solving Easy problem constraints for Sorting the Sentence.",
    "whyThisPattern": "When observing Sort problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/sorting-the-sentence/",
    "leetcode_title": "Sorting the Sentence",
    "leetcode_id": 1859,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/sorting-the-sentence/",
    "canonicalSlug": "sorting-the-sentence",
    "canonicalUrl": "https://leetcode.com/problems/sorting-the-sentence/",
    "url": "https://leetcode.com/problems/sorting-the-sentence/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Sorting the Sentence\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Sorting the Sentence\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Sorting the Sentence\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Sorting the Sentence\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Sorting the Sentence\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Sorting the Sentence\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Sorting the Sentence\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Sorting the Sentence\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Sorting the Sentence",
      "cpp_optimal": "// Solution for Sorting the Sentence",
      "java_brute": "// Solution for Sorting the Sentence",
      "java_optimal": "// Solution for Sorting the Sentence",
      "python_brute": "# Solution for Sorting the Sentence",
      "python_optimal": "# Solution for Sorting the Sentence"
    },
    "originalOrder": 163,
    "learningOrder": 163
  },
  {
    "id": 455,
    "number": 455,
    "sequence_number": 455,
    "title": "Reshape the Matrix",
    "slug": "reshape-the-matrix-optimization",
    "difficulty": "Easy",
    "topic": "Arrays",
    "subtopic": "Binary Search",
    "pattern": "Binary Search",
    "secondary_patterns": [
      "Binary Search"
    ],
    "stage": "Heaps & Priority Queues",
    "curriculumStage": "Stage 10 — Heaps & Priority Queues",
    "roadmapPhase": "Stage 10 — Heaps & Priority Queues",
    "phase": "Stage 10 — Heaps & Priority Queues",
    "estimatedTime": 15,
    "statement": "Solve the **Reshape the Matrix Optimization** problem using the **Binary Search** technique. Given input constraints appropriate for Easy level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^4",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Binary Search identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Binary Search. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Binary Search techniques by solving Easy problem constraints for Reshape the Matrix Optimization.",
    "whyThisPattern": "When observing arrays & strings problem conditions, Binary Search optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta"
    ],
    "companyRelevanceTier": "Medium",
    "leetcode_url": "https://leetcode.com/problems/reshape-the-matrix/",
    "leetcode_title": "Reshape the Matrix",
    "leetcode_id": 566,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/reshape-the-matrix/",
    "canonicalSlug": "reshape-the-matrix-optimization",
    "canonicalUrl": "https://leetcode.com/problems/reshape-the-matrix/",
    "url": "https://leetcode.com/problems/reshape-the-matrix/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Reshape the Matrix Optimization (Binary Search)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Reshape the Matrix Optimization (Binary Search)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Reshape the Matrix Optimization (Binary Search)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Reshape the Matrix Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Reshape the Matrix Optimization (Binary Search)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Reshape the Matrix Optimization (Binary Search)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Reshape the Matrix Optimization (Binary Search)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Reshape the Matrix Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Reshape the Matrix",
      "cpp_optimal": "// Solution for Reshape the Matrix",
      "java_brute": "// Solution for Reshape the Matrix",
      "java_optimal": "// Solution for Reshape the Matrix",
      "python_brute": "# Solution for Reshape the Matrix",
      "python_optimal": "# Solution for Reshape the Matrix"
    }
  },
  {
    "id": 456,
    "number": 456,
    "sequence_number": 456,
    "title": "Toeplitz Matrix",
    "slug": "toeplitz-matrix-optimization",
    "difficulty": "Easy",
    "topic": "Arrays",
    "subtopic": "Binary Search",
    "pattern": "Binary Search",
    "secondary_patterns": [
      "Binary Search"
    ],
    "stage": "Heaps & Priority Queues",
    "curriculumStage": "Stage 10 — Heaps & Priority Queues",
    "roadmapPhase": "Stage 10 — Heaps & Priority Queues",
    "phase": "Stage 10 — Heaps & Priority Queues",
    "estimatedTime": 15,
    "statement": "Solve the **Toeplitz Matrix Optimization** problem using the **Binary Search** technique. Given input constraints appropriate for Easy level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^4",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Binary Search identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Binary Search. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Binary Search techniques by solving Easy problem constraints for Toeplitz Matrix Optimization.",
    "whyThisPattern": "When observing arrays & strings problem conditions, Binary Search optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "LinkedIn",
      "Amazon"
    ],
    "companyRelevanceTier": "Medium",
    "leetcode_url": "https://leetcode.com/problems/toeplitz-matrix/",
    "leetcode_title": "Toeplitz Matrix",
    "leetcode_id": 766,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/toeplitz-matrix/",
    "canonicalSlug": "toeplitz-matrix-optimization",
    "canonicalUrl": "https://leetcode.com/problems/toeplitz-matrix/",
    "url": "https://leetcode.com/problems/toeplitz-matrix/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Toeplitz Matrix Optimization (Binary Search)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Toeplitz Matrix Optimization (Binary Search)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Toeplitz Matrix Optimization (Binary Search)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Toeplitz Matrix Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Toeplitz Matrix Optimization (Binary Search)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Toeplitz Matrix Optimization (Binary Search)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Toeplitz Matrix Optimization (Binary Search)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Toeplitz Matrix Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Toeplitz Matrix",
      "cpp_optimal": "// Solution for Toeplitz Matrix",
      "java_brute": "// Solution for Toeplitz Matrix",
      "java_optimal": "// Solution for Toeplitz Matrix",
      "python_brute": "# Solution for Toeplitz Matrix",
      "python_optimal": "# Solution for Toeplitz Matrix"
    }
  },
  {
    "id": 457,
    "number": 457,
    "sequence_number": 457,
    "title": "Transpose Matrix",
    "slug": "transpose-matrix-optimization",
    "difficulty": "Easy",
    "topic": "Arrays",
    "subtopic": "Binary Search",
    "pattern": "Binary Search",
    "secondary_patterns": [
      "Binary Search"
    ],
    "stage": "Heaps & Priority Queues",
    "curriculumStage": "Stage 10 — Heaps & Priority Queues",
    "roadmapPhase": "Stage 10 — Heaps & Priority Queues",
    "phase": "Stage 10 — Heaps & Priority Queues",
    "estimatedTime": 15,
    "statement": "Solve the **Transpose Matrix Optimization** problem using the **Binary Search** technique. Given input constraints appropriate for Easy level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^4",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Binary Search identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Binary Search. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Binary Search techniques by solving Easy problem constraints for Transpose Matrix Optimization.",
    "whyThisPattern": "When observing arrays & strings problem conditions, Binary Search optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "LinkedIn",
      "Amazon"
    ],
    "companyRelevanceTier": "Medium",
    "leetcode_url": "https://leetcode.com/problems/transpose-matrix/",
    "leetcode_title": "Transpose Matrix",
    "leetcode_id": 867,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/transpose-matrix/",
    "canonicalSlug": "transpose-matrix-optimization",
    "canonicalUrl": "https://leetcode.com/problems/transpose-matrix/",
    "url": "https://leetcode.com/problems/transpose-matrix/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Transpose Matrix Optimization (Binary Search)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Transpose Matrix Optimization (Binary Search)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Transpose Matrix Optimization (Binary Search)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Transpose Matrix Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Transpose Matrix Optimization (Binary Search)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Transpose Matrix Optimization (Binary Search)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Transpose Matrix Optimization (Binary Search)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Transpose Matrix Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Transpose Matrix",
      "cpp_optimal": "// Solution for Transpose Matrix",
      "java_brute": "// Solution for Transpose Matrix",
      "java_optimal": "// Solution for Transpose Matrix",
      "python_brute": "# Solution for Transpose Matrix",
      "python_optimal": "# Solution for Transpose Matrix"
    }
  },
  {
    "id": 458,
    "number": 458,
    "sequence_number": 458,
    "title": "Maximum Product of Three Numbers",
    "slug": "maximum-product-of-three-numbers",
    "difficulty": "Easy",
    "topic": "Arrays",
    "subtopic": "Arrays Optimization",
    "pattern": "Top 3 Max & Min 2",
    "secondary_patterns": [
      "Top 3 Max & Min 2"
    ],
    "stage": "Heaps & Priority Queues",
    "curriculumStage": "Stage 10 — Heaps & Priority Queues",
    "roadmapPhase": "Stage 10 — Heaps & Priority Queues",
    "phase": "Stage 10 — Heaps & Priority Queues",
    "estimatedTime": 15,
    "statement": "Given the constraints and input parameters for Maximum Product of Three Numbers, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Maximum Product of Three Numbers."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Maximum Product of Three Numbers.",
      "Leverage the optimal Arrays pattern to reduce time complexity."
    ],
    "learningObjective": "Master Arrays techniques by solving Easy problem constraints for Maximum Product of Three Numbers.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/maximum-product-of-three-numbers/",
    "leetcode_title": "Maximum Product of Three Numbers",
    "leetcode_id": 309,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/maximum-product-of-three-numbers/",
    "canonicalSlug": "maximum-product-of-three-numbers",
    "canonicalUrl": "https://leetcode.com/problems/maximum-product-of-three-numbers/",
    "url": "https://leetcode.com/problems/maximum-product-of-three-numbers/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Maximum Product of Three Numbers\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Maximum Product of Three Numbers\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Maximum Product of Three Numbers\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Maximum Product of Three Numbers\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Maximum Product of Three Numbers\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Maximum Product of Three Numbers\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Maximum Product of Three Numbers\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Maximum Product of Three Numbers\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Maximum Product of Three Numbers",
      "cpp_optimal": "// Solution for Maximum Product of Three Numbers",
      "java_brute": "// Solution for Maximum Product of Three Numbers",
      "java_optimal": "// Solution for Maximum Product of Three Numbers",
      "python_brute": "# Solution for Maximum Product of Three Numbers",
      "python_optimal": "# Solution for Maximum Product of Three Numbers"
    }
  },
  {
    "id": 459,
    "number": 459,
    "sequence_number": 459,
    "title": "Degree of an Array",
    "slug": "degree-of-an-array",
    "difficulty": "Easy",
    "topic": "Arrays",
    "subtopic": "Arrays Optimization",
    "pattern": "Frequency Map Range",
    "secondary_patterns": [
      "Frequency Map Range"
    ],
    "stage": "Heaps & Priority Queues",
    "curriculumStage": "Stage 10 — Heaps & Priority Queues",
    "roadmapPhase": "Stage 10 — Heaps & Priority Queues",
    "phase": "Stage 10 — Heaps & Priority Queues",
    "estimatedTime": 15,
    "statement": "Given the constraints and input parameters for Degree of an Array, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Degree of an Array."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Degree of an Array.",
      "Leverage the optimal Arrays pattern to reduce time complexity."
    ],
    "learningObjective": "Master Arrays techniques by solving Easy problem constraints for Degree of an Array.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/degree-of-an-array/",
    "leetcode_title": "Degree of an Array",
    "leetcode_id": 697,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/degree-of-an-array/",
    "canonicalSlug": "degree-of-an-array",
    "canonicalUrl": "https://leetcode.com/problems/degree-of-an-array/",
    "url": "https://leetcode.com/problems/degree-of-an-array/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Degree of an Array\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Degree of an Array\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Degree of an Array\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Degree of an Array\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Degree of an Array\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Degree of an Array\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Degree of an Array\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Degree of an Array\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Degree of an Array",
      "cpp_optimal": "// Solution for Degree of an Array",
      "java_brute": "// Solution for Degree of an Array",
      "java_optimal": "// Solution for Degree of an Array",
      "python_brute": "# Solution for Degree of an Array",
      "python_optimal": "# Solution for Degree of an Array"
    },
    "originalOrder": 102,
    "learningOrder": 102
  },
  {
    "id": 460,
    "number": 460,
    "sequence_number": 460,
    "title": "Flipping an Image",
    "slug": "flipping-an-image",
    "difficulty": "Easy",
    "topic": "Arrays",
    "subtopic": "Arrays Optimization",
    "pattern": "Two Pointer Invert Swap",
    "secondary_patterns": [
      "Two Pointer Invert Swap"
    ],
    "stage": "Heaps & Priority Queues",
    "curriculumStage": "Stage 10 — Heaps & Priority Queues",
    "roadmapPhase": "Stage 10 — Heaps & Priority Queues",
    "phase": "Stage 10 — Heaps & Priority Queues",
    "estimatedTime": 15,
    "statement": "Given the constraints and input parameters for Flipping an Image, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Flipping an Image."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Flipping an Image.",
      "Leverage the optimal Arrays pattern to reduce time complexity."
    ],
    "learningObjective": "Master Arrays techniques by solving Easy problem constraints for Flipping an Image.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/flipping-an-image/",
    "leetcode_title": "Flipping an Image",
    "leetcode_id": 832,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/flipping-an-image/",
    "canonicalSlug": "flipping-an-image",
    "canonicalUrl": "https://leetcode.com/problems/flipping-an-image/",
    "url": "https://leetcode.com/problems/flipping-an-image/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Flipping an Image\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Flipping an Image\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Flipping an Image\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Flipping an Image\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Flipping an Image\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Flipping an Image\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Flipping an Image\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Flipping an Image\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Flipping an Image",
      "cpp_optimal": "// Solution for Flipping an Image",
      "java_brute": "// Solution for Flipping an Image",
      "java_optimal": "// Solution for Flipping an Image",
      "python_brute": "# Solution for Flipping an Image",
      "python_optimal": "# Solution for Flipping an Image"
    },
    "originalOrder": 104,
    "learningOrder": 104
  },
  {
    "id": 461,
    "number": 461,
    "sequence_number": 461,
    "title": "Kth Largest Element in an Array",
    "slug": "kth-largest-element-in-an-array",
    "difficulty": "Medium",
    "topic": "Heap",
    "subtopic": "Hashing & Array Optimization",
    "pattern": "Hashing & Array Optimization",
    "secondary_patterns": [
      "Hashing & Array Optimization"
    ],
    "stage": "Heaps & Priority Queues",
    "curriculumStage": "Stage 10 — Heaps & Priority Queues",
    "roadmapPhase": "Stage 10 — Heaps & Priority Queues",
    "phase": "Stage 10 — Heaps & Priority Queues",
    "estimatedTime": 30,
    "statement": "Solve the **Kth Largest Element in an Array Challenge** problem using the **Hashing & Array Optimization** technique. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Hashing & Array Optimization identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Hashing & Array Optimization. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Hashing & Array Optimization techniques by solving Medium problem constraints for Kth Largest Element in an Array Challenge.",
    "whyThisPattern": "When observing arrays & strings problem conditions, Hashing & Array Optimization optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Meta",
      "Uber",
      "Databricks"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/kth-largest-element-in-an-array/",
    "leetcode_title": "Kth Largest Element in an Array",
    "leetcode_id": 215,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/kth-largest-element-in-an-array/",
    "canonicalSlug": "kth-largest-element-in-an-array",
    "canonicalUrl": "https://leetcode.com/problems/kth-largest-element-in-an-array/",
    "url": "https://leetcode.com/problems/kth-largest-element-in-an-array/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Kth Largest Element in an Array Challenge (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Kth Largest Element in an Array Challenge (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Kth Largest Element in an Array Challenge (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Kth Largest Element in an Array Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Kth Largest Element in an Array Challenge (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Kth Largest Element in an Array Challenge (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Kth Largest Element in an Array Challenge (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Kth Largest Element in an Array Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Kth Largest Element in an Array",
      "cpp_optimal": "// Solution for Kth Largest Element in an Array",
      "java_brute": "// Solution for Kth Largest Element in an Array",
      "java_optimal": "// Solution for Kth Largest Element in an Array",
      "python_brute": "# Solution for Kth Largest Element in an Array",
      "python_optimal": "# Solution for Kth Largest Element in an Array"
    },
    "originalOrder": 538,
    "learningOrder": 538
  },
  {
    "id": 462,
    "number": 462,
    "sequence_number": 462,
    "title": "Top K Frequent Elements",
    "slug": "top-k-frequent-elements",
    "difficulty": "Medium",
    "topic": "Heap",
    "subtopic": "Hashing & Array Optimization",
    "pattern": "Hashing & Array Optimization",
    "secondary_patterns": [
      "Hashing & Array Optimization"
    ],
    "stage": "Heaps & Priority Queues",
    "curriculumStage": "Stage 10 — Heaps & Priority Queues",
    "roadmapPhase": "Stage 10 — Heaps & Priority Queues",
    "phase": "Stage 10 — Heaps & Priority Queues",
    "estimatedTime": 30,
    "statement": "Solve the **Top K Frequent Elements Challenge** problem using the **Hashing & Array Optimization** technique. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Hashing & Array Optimization identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Hashing & Array Optimization. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Hashing & Array Optimization techniques by solving Medium problem constraints for Top K Frequent Elements Challenge.",
    "whyThisPattern": "When observing arrays & strings problem conditions, Hashing & Array Optimization optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Meta",
      "Uber",
      "Databricks"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/top-k-frequent-elements/",
    "leetcode_title": "Top K Frequent Elements",
    "leetcode_id": 347,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/top-k-frequent-elements/",
    "canonicalSlug": "top-k-frequent-elements",
    "canonicalUrl": "https://leetcode.com/problems/top-k-frequent-elements/",
    "url": "https://leetcode.com/problems/top-k-frequent-elements/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Top K Frequent Elements Challenge (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Top K Frequent Elements Challenge (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Top K Frequent Elements Challenge (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Top K Frequent Elements Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Top K Frequent Elements Challenge (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Top K Frequent Elements Challenge (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Top K Frequent Elements Challenge (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Top K Frequent Elements Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Top K Frequent Elements",
      "cpp_optimal": "// Solution for Top K Frequent Elements",
      "java_brute": "// Solution for Top K Frequent Elements",
      "java_optimal": "// Solution for Top K Frequent Elements",
      "python_brute": "# Solution for Top K Frequent Elements",
      "python_optimal": "# Solution for Top K Frequent Elements"
    },
    "originalOrder": 539,
    "learningOrder": 539
  },
  {
    "id": 463,
    "number": 463,
    "sequence_number": 463,
    "title": "Top K Frequent Words",
    "slug": "top-k-frequent-words",
    "difficulty": "Medium",
    "topic": "Heap",
    "subtopic": "Hashing & Array Optimization",
    "pattern": "Hashing & Array Optimization",
    "secondary_patterns": [
      "Hashing & Array Optimization"
    ],
    "stage": "Heaps & Priority Queues",
    "curriculumStage": "Stage 10 — Heaps & Priority Queues",
    "roadmapPhase": "Stage 10 — Heaps & Priority Queues",
    "phase": "Stage 10 — Heaps & Priority Queues",
    "estimatedTime": 30,
    "statement": "Solve the **Top K Frequent Words Challenge** problem using the **Hashing & Array Optimization** technique. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Hashing & Array Optimization identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Hashing & Array Optimization. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Hashing & Array Optimization techniques by solving Medium problem constraints for Top K Frequent Words Challenge.",
    "whyThisPattern": "When observing arrays & strings problem conditions, Hashing & Array Optimization optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Meta",
      "Uber",
      "Databricks"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/top-k-frequent-words/",
    "leetcode_title": "Top K Frequent Words",
    "leetcode_id": 692,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/top-k-frequent-words/",
    "canonicalSlug": "top-k-frequent-words",
    "canonicalUrl": "https://leetcode.com/problems/top-k-frequent-words/",
    "url": "https://leetcode.com/problems/top-k-frequent-words/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Top K Frequent Words Challenge (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Top K Frequent Words Challenge (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Top K Frequent Words Challenge (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Top K Frequent Words Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Top K Frequent Words Challenge (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Top K Frequent Words Challenge (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Top K Frequent Words Challenge (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Top K Frequent Words Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Top K Frequent Words",
      "cpp_optimal": "// Solution for Top K Frequent Words",
      "java_brute": "// Solution for Top K Frequent Words",
      "java_optimal": "// Solution for Top K Frequent Words",
      "python_brute": "# Solution for Top K Frequent Words",
      "python_optimal": "# Solution for Top K Frequent Words"
    },
    "originalOrder": 540,
    "learningOrder": 540
  },
  {
    "id": 464,
    "number": 464,
    "sequence_number": 464,
    "title": "Reorganize String",
    "slug": "reorganize-string",
    "difficulty": "Medium",
    "topic": "Heap",
    "subtopic": "Heap Optimization",
    "pattern": "Heap",
    "secondary_patterns": [
      "Heap"
    ],
    "stage": "Heaps & Priority Queues",
    "curriculumStage": "Stage 10 — Heaps & Priority Queues",
    "roadmapPhase": "Stage 10 — Heaps & Priority Queues",
    "phase": "Stage 10 — Heaps & Priority Queues",
    "estimatedTime": 30,
    "statement": "Rearranges characters of a string such that no two adjacent characters are identical using Max-Heap frequency tracking.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "All elements fall within standard integer bounds."
    ],
    "examples": [
      {
        "input": "s = 'aab'",
        "output": "'aba'",
        "explanation": "Optimal solution achieved using Heap."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "All duplicate elements"
    ],
    "commonMistakes": [
      "Off-by-one index mistakes",
      "Integer overflow for large cumulative sums"
    ],
    "hints": [
      "Consider using Heap.",
      "Analyze edge cases and bounds."
    ],
    "learningObjective": "Master Heap techniques by solving Medium problem constraints for Reorganize String.",
    "whyThisPattern": "When observing Heap problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(1)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/reorganize-string/",
    "leetcode_title": "Reorganize String",
    "leetcode_id": 767,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/reorganize-string/",
    "canonicalSlug": "reorganize-string",
    "canonicalUrl": "https://leetcode.com/problems/reorganize-string/",
    "url": "https://leetcode.com/problems/reorganize-string/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Reorganize String\n#include <iostream>\n#include <vector>\n#include <algorithm>\n\nclass Solution {\npublic:\n    int reorganizeString(std::vector<int>& nums) {\n        int n = nums.size();\n        if (n == 0) return 0;\n        int ans = 0;\n        for (int i = 0; i < n; i++) {\n            ans += nums[i];\n        }\n        return ans;\n    }\n};",
        "java": "// Java Solution for Reorganize String\nimport java.util.*;\n\nclass Solution {\n    public int reorganizeString(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int ans = 0;\n        for (int num : nums) {\n            ans += num;\n        }\n        return ans;\n    }\n}",
        "python": "# Python Solution for Reorganize String\n\nclass Solution:\n    def reorganizeString(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        ans = 0\n        for num in nums:\n            ans += num\n        return ans\n",
        "javascript": "// JavaScript Solution for Reorganize String\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Reorganize String\n#include <iostream>\n#include <vector>\n#include <algorithm>\n\nclass Solution {\npublic:\n    int reorganizeString(std::vector<int>& nums) {\n        int n = nums.size();\n        if (n == 0) return 0;\n        int ans = 0;\n        for (int i = 0; i < n; i++) {\n            ans += nums[i];\n        }\n        return ans;\n    }\n};",
        "java": "// Java Solution for Reorganize String\nimport java.util.*;\n\nclass Solution {\n    public int reorganizeString(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int ans = 0;\n        for (int num : nums) {\n            ans += num;\n        }\n        return ans;\n    }\n}",
        "python": "# Python Solution for Reorganize String\n\nclass Solution:\n    def reorganizeString(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        ans = 0\n        for num in nums:\n            ans += num\n        return ans\n",
        "javascript": "// JavaScript Solution for Reorganize String\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Reorganize String",
      "cpp_optimal": "// Solution for Reorganize String",
      "java_brute": "// Solution for Reorganize String",
      "java_optimal": "// Solution for Reorganize String",
      "python_brute": "# Solution for Reorganize String",
      "python_optimal": "# Solution for Reorganize String"
    },
    "originalOrder": 541,
    "learningOrder": 541
  },
  {
    "id": 465,
    "number": 465,
    "sequence_number": 465,
    "title": "K Closest Points to Origin",
    "slug": "k-closest-points-to-origin",
    "difficulty": "Medium",
    "topic": "Heap",
    "subtopic": "Heap Optimization",
    "pattern": "Heap",
    "secondary_patterns": [
      "Heap"
    ],
    "stage": "Heaps & Priority Queues",
    "curriculumStage": "Stage 10 — Heaps & Priority Queues",
    "roadmapPhase": "Stage 10 — Heaps & Priority Queues",
    "phase": "Stage 10 — Heaps & Priority Queues",
    "estimatedTime": 30,
    "statement": "Finds the K closest 2D points to the origin (0, 0) using Euclidean distance and Max-Heap.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "All elements fall within standard integer bounds."
    ],
    "examples": [
      {
        "input": "points = [[1,3],[-2,2]], k = 1",
        "output": "[[-2,2]]",
        "explanation": "Optimal solution achieved using Heap."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "All duplicate elements"
    ],
    "commonMistakes": [
      "Off-by-one index mistakes",
      "Integer overflow for large cumulative sums"
    ],
    "hints": [
      "Consider using Heap.",
      "Analyze edge cases and bounds."
    ],
    "learningObjective": "Master Heap techniques by solving Medium problem constraints for K Closest Points to Origin.",
    "whyThisPattern": "When observing Heap problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(1)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/k-closest-points-to-origin/",
    "leetcode_title": "K Closest Points to Origin",
    "leetcode_id": 973,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/k-closest-points-to-origin/",
    "canonicalSlug": "k-closest-points-to-origin",
    "canonicalUrl": "https://leetcode.com/problems/k-closest-points-to-origin/",
    "url": "https://leetcode.com/problems/k-closest-points-to-origin/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for K Closest Points to Origin\n#include <iostream>\n#include <vector>\n#include <algorithm>\n\nclass Solution {\npublic:\n    int kClosestPointstoOrigin(std::vector<int>& nums) {\n        int n = nums.size();\n        if (n == 0) return 0;\n        int ans = 0;\n        for (int i = 0; i < n; i++) {\n            ans += nums[i];\n        }\n        return ans;\n    }\n};",
        "java": "// Java Solution for K Closest Points to Origin\nimport java.util.*;\n\nclass Solution {\n    public int kClosestPointstoOrigin(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int ans = 0;\n        for (int num : nums) {\n            ans += num;\n        }\n        return ans;\n    }\n}",
        "python": "# Python Solution for K Closest Points to Origin\n\nclass Solution:\n    def kClosestPointstoOrigin(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        ans = 0\n        for num in nums:\n            ans += num\n        return ans\n",
        "javascript": "// JavaScript Solution for K Closest Points to Origin\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for K Closest Points to Origin\n#include <iostream>\n#include <vector>\n#include <algorithm>\n\nclass Solution {\npublic:\n    int kClosestPointstoOrigin(std::vector<int>& nums) {\n        int n = nums.size();\n        if (n == 0) return 0;\n        int ans = 0;\n        for (int i = 0; i < n; i++) {\n            ans += nums[i];\n        }\n        return ans;\n    }\n};",
        "java": "// Java Solution for K Closest Points to Origin\nimport java.util.*;\n\nclass Solution {\n    public int kClosestPointstoOrigin(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int ans = 0;\n        for (int num : nums) {\n            ans += num;\n        }\n        return ans;\n    }\n}",
        "python": "# Python Solution for K Closest Points to Origin\n\nclass Solution:\n    def kClosestPointstoOrigin(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        ans = 0\n        for num in nums:\n            ans += num\n        return ans\n",
        "javascript": "// JavaScript Solution for K Closest Points to Origin\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for K Closest Points to Origin",
      "cpp_optimal": "// Solution for K Closest Points to Origin",
      "java_brute": "// Solution for K Closest Points to Origin",
      "java_optimal": "// Solution for K Closest Points to Origin",
      "python_brute": "# Solution for K Closest Points to Origin",
      "python_optimal": "# Solution for K Closest Points to Origin"
    },
    "originalOrder": 542,
    "learningOrder": 542
  },
  {
    "id": 466,
    "number": 466,
    "sequence_number": 466,
    "title": "Find K Pairs with Smallest Sums",
    "slug": "find-k-pairs-with-smallest-sums",
    "difficulty": "Medium",
    "topic": "Heap",
    "subtopic": "Heap Optimization",
    "pattern": "Min-Heap Priority Queue",
    "secondary_patterns": [
      "Min-Heap Priority Queue"
    ],
    "stage": "Heaps & Priority Queues",
    "curriculumStage": "Stage 10 — Heaps & Priority Queues",
    "roadmapPhase": "Stage 10 — Heaps & Priority Queues",
    "phase": "Stage 10 — Heaps & Priority Queues",
    "estimatedTime": 30,
    "statement": "Finds K pairs (u, v) with the smallest sums from two non-decreasingly sorted arrays nums1 and nums2.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= nums1.length, nums2.length <= 10^5",
      "1 <= k <= 10^4"
    ],
    "examples": [
      {
        "input": "nums1 = [1,7,11], nums2 = [2,4,6], k = 3",
        "output": "[[1,2],[1,4],[1,6]]",
        "explanation": "First 3 pairs with smallest sums."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "All duplicate elements"
    ],
    "commonMistakes": [
      "Off-by-one index mistakes",
      "Integer overflow for large cumulative sums"
    ],
    "hints": [
      "Consider using Heap.",
      "Analyze edge cases and bounds."
    ],
    "learningObjective": "Master Heap techniques by solving Medium problem constraints for Find K Pairs with Smallest Sums.",
    "whyThisPattern": "When observing Heap problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(K log K)",
    "spaceComplexity": "O(K)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/find-k-pairs-with-smallest-sums/",
    "leetcode_title": "Find K Pairs with Smallest Sums",
    "leetcode_id": 373,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/find-k-pairs-with-smallest-sums/",
    "canonicalSlug": "find-k-pairs-with-smallest-sums",
    "canonicalUrl": "https://leetcode.com/problems/find-k-pairs-with-smallest-sums/",
    "url": "https://leetcode.com/problems/find-k-pairs-with-smallest-sums/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Find K Pairs with Smallest Sums\n#include <vector>\n#include <queue>\n\nstd::vector<std::vector<int>> kSmallestPairs(std::vector<int>& nums1, std::vector<int>& nums2, int k) {\n    std::vector<std::vector<int>> result;\n    if (nums1.empty() || nums2.empty() || k == 0) return result;\n    \n    using Element = std::tuple<int, int, int>; // sum, i, j\n    std::priority_queue<Element, std::vector<Element>, std::greater<Element>> pq;\n    \n    for (int i = 0; i < std::min((int)nums1.size(), k); i++) {\n        pq.push({nums1[i] + nums2[0], i, 0});\n    }\n    \n    while (!pq.empty() && result.size() < k) {\n        auto [sum, i, j] = pq.top(); pq.pop();\n        result.push_back({nums1[i], nums2[j]});\n        if (j + 1 < nums2.size()) {\n            pq.push({nums1[i] + nums2[j + 1], i, j + 1});\n        }\n    }\n    return result;\n}",
        "java": "// Java Find K Pairs with Smallest Sums\nimport java.util.*;\n\npublic class Solution {\n    public List<List<Integer>> kSmallestPairs(int[] nums1, int[] nums2, int k) {\n        List<List<Integer>> result = new ArrayList<>();\n        if (nums1.length == 0 || nums2.length == 0 || k == 0) return result;\n        \n        PriorityQueue<int[]> pq = new PriorityQueue<>(Comparator.comparingInt(a -> a[0]));\n        for (int i = 0; i < Math.min(nums1.length, k); i++) {\n            pq.offer(new int[]{nums1[i] + nums2[0], i, 0});\n        }\n        \n        while (!pq.isEmpty() && result.size() < k) {\n            int[] curr = pq.poll();\n            int i = curr[1], j = curr[2];\n            result.add(Arrays.asList(nums1[i], nums2[j]));\n            if (j + 1 < nums2.length) {\n                pq.offer(new int[]{nums1[i] + nums2[j + 1], i, j + 1});\n            }\n        }\n        return result;\n    }\n}",
        "python": "# Python Find K Pairs with Smallest Sums\nimport heapq\n\ndef k_smallest_pairs(nums1: list[int], nums2: list[int], k: int) -> list[list[int]]:\n    if not nums1 or not nums2 or k == 0:\n        return []\n    \n    pq = [(nums1[i] + nums2[0], i, 0) for i in range(min(len(nums1), k))]\n    heapq.heapify(pq)\n    result = []\n    \n    while pq and len(result) < k:\n        val, i, j = heapq.heappop(pq)\n        result.append([nums1[i], nums2[j]])\n        if j + 1 < len(nums2):\n            heapq.heappush(pq, (nums1[i] + nums2[j + 1], i, j + 1))\n            \n    return result\n",
        "javascript": "// JavaScript Find K Pairs with Smallest Sums\nfunction kSmallestPairs(nums1, nums2, k) {\n    const result = [];\n    if (!nums1.length || !nums2.length || !k) return result;\n    // Simple priority queue approach using sorted array\n    const pairs = [];\n    for (let i = 0; i < Math.min(nums1.length, k); i++) {\n        for (let j = 0; j < Math.min(nums2.length, k); j++) {\n            pairs.push([nums1[i], nums2[j]]);\n        }\n    }\n    pairs.sort((a, b) => (a[0] + a[1]) - (b[0] + b[1]));\n    return pairs.slice(0, k);\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Find K Pairs with Smallest Sums\n#include <vector>\n#include <queue>\n\nstd::vector<std::vector<int>> kSmallestPairs(std::vector<int>& nums1, std::vector<int>& nums2, int k) {\n    std::vector<std::vector<int>> result;\n    if (nums1.empty() || nums2.empty() || k == 0) return result;\n    \n    using Element = std::tuple<int, int, int>; // sum, i, j\n    std::priority_queue<Element, std::vector<Element>, std::greater<Element>> pq;\n    \n    for (int i = 0; i < std::min((int)nums1.size(), k); i++) {\n        pq.push({nums1[i] + nums2[0], i, 0});\n    }\n    \n    while (!pq.empty() && result.size() < k) {\n        auto [sum, i, j] = pq.top(); pq.pop();\n        result.push_back({nums1[i], nums2[j]});\n        if (j + 1 < nums2.size()) {\n            pq.push({nums1[i] + nums2[j + 1], i, j + 1});\n        }\n    }\n    return result;\n}",
        "java": "// Java Find K Pairs with Smallest Sums\nimport java.util.*;\n\npublic class Solution {\n    public List<List<Integer>> kSmallestPairs(int[] nums1, int[] nums2, int k) {\n        List<List<Integer>> result = new ArrayList<>();\n        if (nums1.length == 0 || nums2.length == 0 || k == 0) return result;\n        \n        PriorityQueue<int[]> pq = new PriorityQueue<>(Comparator.comparingInt(a -> a[0]));\n        for (int i = 0; i < Math.min(nums1.length, k); i++) {\n            pq.offer(new int[]{nums1[i] + nums2[0], i, 0});\n        }\n        \n        while (!pq.isEmpty() && result.size() < k) {\n            int[] curr = pq.poll();\n            int i = curr[1], j = curr[2];\n            result.add(Arrays.asList(nums1[i], nums2[j]));\n            if (j + 1 < nums2.length) {\n                pq.offer(new int[]{nums1[i] + nums2[j + 1], i, j + 1});\n            }\n        }\n        return result;\n    }\n}",
        "python": "# Python Find K Pairs with Smallest Sums\nimport heapq\n\ndef k_smallest_pairs(nums1: list[int], nums2: list[int], k: int) -> list[list[int]]:\n    if not nums1 or not nums2 or k == 0:\n        return []\n    \n    pq = [(nums1[i] + nums2[0], i, 0) for i in range(min(len(nums1), k))]\n    heapq.heapify(pq)\n    result = []\n    \n    while pq and len(result) < k:\n        val, i, j = heapq.heappop(pq)\n        result.append([nums1[i], nums2[j]])\n        if j + 1 < len(nums2):\n            heapq.heappush(pq, (nums1[i] + nums2[j + 1], i, j + 1))\n            \n    return result\n",
        "javascript": "// JavaScript Find K Pairs with Smallest Sums\nfunction kSmallestPairs(nums1, nums2, k) {\n    const result = [];\n    if (!nums1.length || !nums2.length || !k) return result;\n    // Simple priority queue approach using sorted array\n    const pairs = [];\n    for (let i = 0; i < Math.min(nums1.length, k); i++) {\n        for (let j = 0; j < Math.min(nums2.length, k); j++) {\n            pairs.push([nums1[i], nums2[j]]);\n        }\n    }\n    pairs.sort((a, b) => (a[0] + a[1]) - (b[0] + b[1]));\n    return pairs.slice(0, k);\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Find K Pairs with Smallest Sums",
      "cpp_optimal": "// Solution for Find K Pairs with Smallest Sums",
      "java_brute": "// Solution for Find K Pairs with Smallest Sums",
      "java_optimal": "// Solution for Find K Pairs with Smallest Sums",
      "python_brute": "# Solution for Find K Pairs with Smallest Sums",
      "python_optimal": "# Solution for Find K Pairs with Smallest Sums"
    },
    "originalOrder": 543,
    "learningOrder": 543
  },
  {
    "id": 467,
    "number": 467,
    "sequence_number": 467,
    "title": "Ugly Number II",
    "slug": "ugly-number-ii",
    "difficulty": "Medium",
    "topic": "Heap",
    "subtopic": "Heap Optimization",
    "pattern": "Min-Heap / Dynamic Programming 3-Pointers",
    "secondary_patterns": [
      "Min-Heap / Dynamic Programming 3-Pointers"
    ],
    "stage": "Heaps & Priority Queues",
    "curriculumStage": "Stage 10 — Heaps & Priority Queues",
    "roadmapPhase": "Stage 10 — Heaps & Priority Queues",
    "phase": "Stage 10 — Heaps & Priority Queues",
    "estimatedTime": 30,
    "statement": "Finds the Nth ugly number whose prime factors are limited to 2, 3, and 5.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= n <= 1690"
    ],
    "examples": [
      {
        "input": "n = 10",
        "output": "12",
        "explanation": "[1, 2, 3, 4, 5, 6, 8, 9, 10, 12] is sequence of first 10 ugly numbers."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "All duplicate elements"
    ],
    "commonMistakes": [
      "Off-by-one index mistakes",
      "Integer overflow for large cumulative sums"
    ],
    "hints": [
      "Consider using Heap.",
      "Analyze edge cases and bounds."
    ],
    "learningObjective": "Master Heap techniques by solving Medium problem constraints for Ugly Number II.",
    "whyThisPattern": "When observing Heap problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/ugly-number-ii/",
    "leetcode_title": "Ugly Number II",
    "leetcode_id": 264,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/ugly-number-ii/",
    "canonicalSlug": "ugly-number-ii",
    "canonicalUrl": "https://leetcode.com/problems/ugly-number-ii/",
    "url": "https://leetcode.com/problems/ugly-number-ii/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Ugly Number II Implementation\n#include <vector>\n#include <algorithm>\n\nint nthUglyNumber(int n) {\n    std::vector<int> dp(n);\n    dp[0] = 1;\n    int p2 = 0, p3 = 0, p5 = 0;\n    \n    for (int i = 1; i < n; i++) {\n        int nextUgly = std::min({dp[p2] * 2, dp[p3] * 3, dp[p5] * 5});\n        dp[i] = nextUgly;\n        if (nextUgly == dp[p2] * 2) p2++;\n        if (nextUgly == dp[p3] * 3) p3++;\n        if (nextUgly == dp[p5] * 5) p5++;\n    }\n    return dp[n - 1];\n}",
        "java": "// Java Ugly Number II Implementation\npublic class Solution {\n    public int nthUglyNumber(int n) {\n        int[] dp = new int[n];\n        dp[0] = 1;\n        int p2 = 0, p3 = 0, p5 = 0;\n        \n        for (int i = 1; i < n; i++) {\n            int nextUgly = Math.min(dp[p2] * 2, Math.min(dp[p3] * 3, dp[p5] * 5));\n            dp[i] = nextUgly;\n            if (nextUgly == dp[p2] * 2) p2++;\n            if (nextUgly == dp[p3] * 3) p3++;\n            if (nextUgly == dp[p5] * 5) p5++;\n        }\n        return dp[n - 1];\n    }\n}",
        "python": "# Python Ugly Number II Implementation\n\ndef nth_ugly_number(n: int) -> int:\n    dp = [0] * n\n    dp[0] = 1\n    p2 = p3 = p5 = 0\n    \n    for i in range(1, n):\n        next_ugly = min(dp[p2] * 2, dp[p3] * 3, dp[p5] * 5)\n        dp[i] = next_ugly\n        if next_ugly == dp[p2] * 2: p2 += 1\n        if next_ugly == dp[p3] * 3: p3 += 1\n        if next_ugly == dp[p5] * 5: p5 += 1\n        \n    return dp[-1]\n",
        "javascript": "// JavaScript Ugly Number II Implementation\nfunction nthUglyNumber(n) {\n    const dp = new Array(n);\n    dp[0] = 1;\n    let p2 = 0, p3 = 0, p5 = 0;\n    for (let i = 1; i < n; i++) {\n        const nextUgly = Math.min(dp[p2] * 2, dp[p3] * 3, dp[p5] * 5);\n        dp[i] = nextUgly;\n        if (nextUgly === dp[p2] * 2) p2++;\n        if (nextUgly === dp[p3] * 3) p3++;\n        if (nextUgly === dp[p5] * 5) p5++;\n    }\n    return dp[n - 1];\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Ugly Number II Implementation\n#include <vector>\n#include <algorithm>\n\nint nthUglyNumber(int n) {\n    std::vector<int> dp(n);\n    dp[0] = 1;\n    int p2 = 0, p3 = 0, p5 = 0;\n    \n    for (int i = 1; i < n; i++) {\n        int nextUgly = std::min({dp[p2] * 2, dp[p3] * 3, dp[p5] * 5});\n        dp[i] = nextUgly;\n        if (nextUgly == dp[p2] * 2) p2++;\n        if (nextUgly == dp[p3] * 3) p3++;\n        if (nextUgly == dp[p5] * 5) p5++;\n    }\n    return dp[n - 1];\n}",
        "java": "// Java Ugly Number II Implementation\npublic class Solution {\n    public int nthUglyNumber(int n) {\n        int[] dp = new int[n];\n        dp[0] = 1;\n        int p2 = 0, p3 = 0, p5 = 0;\n        \n        for (int i = 1; i < n; i++) {\n            int nextUgly = Math.min(dp[p2] * 2, Math.min(dp[p3] * 3, dp[p5] * 5));\n            dp[i] = nextUgly;\n            if (nextUgly == dp[p2] * 2) p2++;\n            if (nextUgly == dp[p3] * 3) p3++;\n            if (nextUgly == dp[p5] * 5) p5++;\n        }\n        return dp[n - 1];\n    }\n}",
        "python": "# Python Ugly Number II Implementation\n\ndef nth_ugly_number(n: int) -> int:\n    dp = [0] * n\n    dp[0] = 1\n    p2 = p3 = p5 = 0\n    \n    for i in range(1, n):\n        next_ugly = min(dp[p2] * 2, dp[p3] * 3, dp[p5] * 5)\n        dp[i] = next_ugly\n        if next_ugly == dp[p2] * 2: p2 += 1\n        if next_ugly == dp[p3] * 3: p3 += 1\n        if next_ugly == dp[p5] * 5: p5 += 1\n        \n    return dp[-1]\n",
        "javascript": "// JavaScript Ugly Number II Implementation\nfunction nthUglyNumber(n) {\n    const dp = new Array(n);\n    dp[0] = 1;\n    let p2 = 0, p3 = 0, p5 = 0;\n    for (let i = 1; i < n; i++) {\n        const nextUgly = Math.min(dp[p2] * 2, dp[p3] * 3, dp[p5] * 5);\n        dp[i] = nextUgly;\n        if (nextUgly === dp[p2] * 2) p2++;\n        if (nextUgly === dp[p3] * 3) p3++;\n        if (nextUgly === dp[p5] * 5) p5++;\n    }\n    return dp[n - 1];\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Ugly Number II",
      "cpp_optimal": "// Solution for Ugly Number II",
      "java_brute": "// Solution for Ugly Number II",
      "java_optimal": "// Solution for Ugly Number II",
      "python_brute": "# Solution for Ugly Number II",
      "python_optimal": "# Solution for Ugly Number II"
    },
    "originalOrder": 544,
    "learningOrder": 544
  },
  {
    "id": 468,
    "number": 468,
    "sequence_number": 468,
    "title": "Design Twitter",
    "slug": "design-twitter",
    "difficulty": "Medium",
    "topic": "Heap",
    "subtopic": "Heap Optimization",
    "pattern": "Min-Heap / Object Design",
    "secondary_patterns": [
      "Min-Heap / Object Design"
    ],
    "stage": "Heaps & Priority Queues",
    "curriculumStage": "Stage 10 — Heaps & Priority Queues",
    "roadmapPhase": "Stage 10 — Heaps & Priority Queues",
    "phase": "Stage 10 — Heaps & Priority Queues",
    "estimatedTime": 30,
    "statement": "Designs a simplified version of Twitter supporting postTweet, getNewsFeed, follow, and unfollow operations.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= userId, followeeId <= 500",
      "At most 3 * 10^4 calls made."
    ],
    "examples": [
      {
        "input": "postTweet(1, 5), getNewsFeed(1)",
        "output": "[5]",
        "explanation": "Returns 10 most recent tweet IDs."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "All duplicate elements"
    ],
    "commonMistakes": [
      "Off-by-one index mistakes",
      "Integer overflow for large cumulative sums"
    ],
    "hints": [
      "Consider using Linked List.",
      "Analyze edge cases and bounds."
    ],
    "learningObjective": "Master Heap techniques by solving Medium problem constraints for Design Twitter.",
    "whyThisPattern": "When observing Heap problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log K) for newsfeed",
    "spaceComplexity": "O(U + T)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/design-twitter/",
    "leetcode_title": "Design Twitter",
    "leetcode_id": 355,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/design-twitter/",
    "canonicalSlug": "design-twitter",
    "canonicalUrl": "https://leetcode.com/problems/design-twitter/",
    "url": "https://leetcode.com/problems/design-twitter/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Design Twitter Implementation\n#include <vector>\n#include <unordered_map>\n#include <unordered_set>\n#include <queue>\n\nclass Twitter {\n    struct Tweet {\n        int id;\n        int time;\n    };\n    int timestamp = 0;\n    std::unordered_map<int, std::vector<Tweet>> userTweets;\n    std::unordered_map<int, std::unordered_set<int>> follows;\n\npublic:\n    Twitter() {}\n    \n    void postTweet(int userId, int tweetId) {\n        userTweets[userId].push_back({tweetId, timestamp++});\n    }\n    \n    std::vector<int> getNewsFeed(int userId) {\n        follows[userId].insert(userId);\n        using Element = std::pair<int, int>; // time, tweetId\n        std::priority_queue<Element> maxHeap;\n        \n        for (int followee : follows[userId]) {\n            const auto& tweets = userTweets[followee];\n            for (int i = (int)tweets.size() - 1; i >= 0 && i >= (int)tweets.size() - 10; i--) {\n                maxHeap.push({tweets[i].time, tweets[i].id});\n            }\n        }\n        \n        std::vector<int> res;\n        while (!maxHeap.empty() && res.size() < 10) {\n            res.push_back(maxHeap.top().second);\n            maxHeap.pop();\n        }\n        return res;\n    }\n    \n    void follow(int followerId, int followeeId) {\n        follows[followerId].insert(followeeId);\n    }\n    \n    void unfollow(int followerId, int followeeId) {\n        if (followerId != followeeId) {\n            follows[followerId].erase(followeeId);\n        }\n    }\n};",
        "java": "// Java Design Twitter Implementation\nimport java.util.*;\n\nclass Twitter {\n    private static int timestamp = 0;\n    private class Tweet {\n        int id, time;\n        Tweet(int id, int time) { this.id = id; this.time = time; }\n    }\n\n    private Map<Integer, List<Tweet>> tweets = new HashMap<>();\n    private Map<Integer, Set<Integer>> follows = new HashMap<>();\n\n    public Twitter() {}\n\n    public void postTweet(int userId, int tweetId) {\n        tweets.putIfAbsent(userId, new ArrayList<>());\n        tweets.get(userId).add(new Tweet(tweetId, timestamp++));\n    }\n\n    public List<Integer> getNewsFeed(int userId) {\n        follows.putIfAbsent(userId, new HashSet<>());\n        follows.get(userId).add(userId);\n        \n        PriorityQueue<Tweet> maxHeap = new PriorityQueue<>((a, b) -> b.time - a.time);\n        for (int f : follows.get(userId)) {\n            List<Tweet> list = tweets.getOrDefault(f, new ArrayList<>());\n            for (int i = list.size() - 1; i >= 0 && i >= list.size() - 10; i--) {\n                maxHeap.offer(list.get(i));\n            }\n        }\n        \n        List<Integer> res = new ArrayList<>();\n        while (!maxHeap.isEmpty() && res.size() < 10) {\n            res.add(maxHeap.poll().id);\n        }\n        return res;\n    }\n\n    public void follow(int followerId, int followeeId) {\n        follows.putIfAbsent(followerId, new HashSet<>());\n        follows.get(followerId).add(followeeId);\n    }\n\n    public void unfollow(int followerId, int followeeId) {\n        if (followerId != followeeId && follows.containsKey(followerId)) {\n            follows.get(followerId).remove(followeeId);\n        }\n    }\n}",
        "python": "# Python Design Twitter Implementation\nfrom collections import defaultdict\nimport heapq\n\nclass Twitter:\n    def __init__(self):\n        self.time = 0\n        self.tweets = defaultdict(list)\n        self.follows = defaultdict(set)\n\n    def postTweet(self, userId: int, tweetId: int) -> None:\n        self.tweets[userId].append((self.time, tweetId))\n        self.time += 1\n\n    def getNewsFeed(self, userId: int) -> list[int]:\n        self.follows[userId].add(userId)\n        heap = []\n        for followee in self.follows[userId]:\n            for t, tid in self.tweets[followee][-10:]:\n                heapq.heappush(heap, (-t, tid))\n        res = []\n        while heap and len(res) < 10:\n            res.append(heapq.heappop(heap)[1])\n        return res\n\n    def follow(self, followerId: int, followeeId: int) -> None:\n        self.follows[followerId].add(followeeId)\n\n    def unfollow(self, followerId: int, followeeId: int) -> None:\n        if followerId != followeeId:\n            self.follows[followerId].discard(followeeId)\n",
        "javascript": "// JavaScript Design Twitter Implementation\nclass Twitter {\n    constructor() {\n        this.time = 0;\n        this.tweets = new Map();\n        this.follows = new Map();\n    }\n    postTweet(userId, tweetId) {\n        if (!this.tweets.has(userId)) this.tweets.set(userId, []);\n        this.tweets.get(userId).push({ id: tweetId, time: this.time++ });\n    }\n    getNewsFeed(userId) {\n        if (!this.follows.has(userId)) this.follows.set(userId, new Set());\n        this.follows.get(userId).add(userId);\n        const feed = [];\n        for (const f of this.follows.get(userId)) {\n            const list = this.tweets.get(f) || [];\n            for (let i = list.length - 1; i >= 0 && i >= list.length - 10; i--) {\n                feed.push(list[i]);\n            }\n        }\n        feed.sort((a, b) => b.time - a.time);\n        return feed.slice(0, 10).map(t => t.id);\n    }\n    follow(followerId, followeeId) {\n        if (!this.follows.has(followerId)) this.follows.set(followerId, new Set());\n        this.follows.get(followerId).add(followeeId);\n    }\n    unfollow(followerId, followeeId) {\n        if (followerId !== followeeId && this.follows.has(followerId)) {\n            this.follows.get(followerId).delete(followeeId);\n        }\n    }\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Design Twitter Implementation\n#include <vector>\n#include <unordered_map>\n#include <unordered_set>\n#include <queue>\n\nclass Twitter {\n    struct Tweet {\n        int id;\n        int time;\n    };\n    int timestamp = 0;\n    std::unordered_map<int, std::vector<Tweet>> userTweets;\n    std::unordered_map<int, std::unordered_set<int>> follows;\n\npublic:\n    Twitter() {}\n    \n    void postTweet(int userId, int tweetId) {\n        userTweets[userId].push_back({tweetId, timestamp++});\n    }\n    \n    std::vector<int> getNewsFeed(int userId) {\n        follows[userId].insert(userId);\n        using Element = std::pair<int, int>; // time, tweetId\n        std::priority_queue<Element> maxHeap;\n        \n        for (int followee : follows[userId]) {\n            const auto& tweets = userTweets[followee];\n            for (int i = (int)tweets.size() - 1; i >= 0 && i >= (int)tweets.size() - 10; i--) {\n                maxHeap.push({tweets[i].time, tweets[i].id});\n            }\n        }\n        \n        std::vector<int> res;\n        while (!maxHeap.empty() && res.size() < 10) {\n            res.push_back(maxHeap.top().second);\n            maxHeap.pop();\n        }\n        return res;\n    }\n    \n    void follow(int followerId, int followeeId) {\n        follows[followerId].insert(followeeId);\n    }\n    \n    void unfollow(int followerId, int followeeId) {\n        if (followerId != followeeId) {\n            follows[followerId].erase(followeeId);\n        }\n    }\n};",
        "java": "// Java Design Twitter Implementation\nimport java.util.*;\n\nclass Twitter {\n    private static int timestamp = 0;\n    private class Tweet {\n        int id, time;\n        Tweet(int id, int time) { this.id = id; this.time = time; }\n    }\n\n    private Map<Integer, List<Tweet>> tweets = new HashMap<>();\n    private Map<Integer, Set<Integer>> follows = new HashMap<>();\n\n    public Twitter() {}\n\n    public void postTweet(int userId, int tweetId) {\n        tweets.putIfAbsent(userId, new ArrayList<>());\n        tweets.get(userId).add(new Tweet(tweetId, timestamp++));\n    }\n\n    public List<Integer> getNewsFeed(int userId) {\n        follows.putIfAbsent(userId, new HashSet<>());\n        follows.get(userId).add(userId);\n        \n        PriorityQueue<Tweet> maxHeap = new PriorityQueue<>((a, b) -> b.time - a.time);\n        for (int f : follows.get(userId)) {\n            List<Tweet> list = tweets.getOrDefault(f, new ArrayList<>());\n            for (int i = list.size() - 1; i >= 0 && i >= list.size() - 10; i--) {\n                maxHeap.offer(list.get(i));\n            }\n        }\n        \n        List<Integer> res = new ArrayList<>();\n        while (!maxHeap.isEmpty() && res.size() < 10) {\n            res.add(maxHeap.poll().id);\n        }\n        return res;\n    }\n\n    public void follow(int followerId, int followeeId) {\n        follows.putIfAbsent(followerId, new HashSet<>());\n        follows.get(followerId).add(followeeId);\n    }\n\n    public void unfollow(int followerId, int followeeId) {\n        if (followerId != followeeId && follows.containsKey(followerId)) {\n            follows.get(followerId).remove(followeeId);\n        }\n    }\n}",
        "python": "# Python Design Twitter Implementation\nfrom collections import defaultdict\nimport heapq\n\nclass Twitter:\n    def __init__(self):\n        self.time = 0\n        self.tweets = defaultdict(list)\n        self.follows = defaultdict(set)\n\n    def postTweet(self, userId: int, tweetId: int) -> None:\n        self.tweets[userId].append((self.time, tweetId))\n        self.time += 1\n\n    def getNewsFeed(self, userId: int) -> list[int]:\n        self.follows[userId].add(userId)\n        heap = []\n        for followee in self.follows[userId]:\n            for t, tid in self.tweets[followee][-10:]:\n                heapq.heappush(heap, (-t, tid))\n        res = []\n        while heap and len(res) < 10:\n            res.append(heapq.heappop(heap)[1])\n        return res\n\n    def follow(self, followerId: int, followeeId: int) -> None:\n        self.follows[followerId].add(followeeId)\n\n    def unfollow(self, followerId: int, followeeId: int) -> None:\n        if followerId != followeeId:\n            self.follows[followerId].discard(followeeId)\n",
        "javascript": "// JavaScript Design Twitter Implementation\nclass Twitter {\n    constructor() {\n        this.time = 0;\n        this.tweets = new Map();\n        this.follows = new Map();\n    }\n    postTweet(userId, tweetId) {\n        if (!this.tweets.has(userId)) this.tweets.set(userId, []);\n        this.tweets.get(userId).push({ id: tweetId, time: this.time++ });\n    }\n    getNewsFeed(userId) {\n        if (!this.follows.has(userId)) this.follows.set(userId, new Set());\n        this.follows.get(userId).add(userId);\n        const feed = [];\n        for (const f of this.follows.get(userId)) {\n            const list = this.tweets.get(f) || [];\n            for (let i = list.length - 1; i >= 0 && i >= list.length - 10; i--) {\n                feed.push(list[i]);\n            }\n        }\n        feed.sort((a, b) => b.time - a.time);\n        return feed.slice(0, 10).map(t => t.id);\n    }\n    follow(followerId, followeeId) {\n        if (!this.follows.has(followerId)) this.follows.set(followerId, new Set());\n        this.follows.get(followerId).add(followeeId);\n    }\n    unfollow(followerId, followeeId) {\n        if (followerId !== followeeId && this.follows.has(followerId)) {\n            this.follows.get(followerId).delete(followeeId);\n        }\n    }\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Design Twitter",
      "cpp_optimal": "// Solution for Design Twitter",
      "java_brute": "// Solution for Design Twitter",
      "java_optimal": "// Solution for Design Twitter",
      "python_brute": "# Solution for Design Twitter",
      "python_optimal": "# Solution for Design Twitter"
    },
    "originalOrder": 545,
    "learningOrder": 545
  },
  {
    "id": 469,
    "number": 469,
    "sequence_number": 469,
    "title": "Maximum Number of Eaten Apples",
    "slug": "maximum-number-of-eaten-apples",
    "difficulty": "Medium",
    "topic": "Heap",
    "subtopic": "Heap Optimization",
    "pattern": "Min-Heap Expiration Date",
    "secondary_patterns": [
      "Min-Heap Expiration Date"
    ],
    "stage": "Heaps & Priority Queues",
    "curriculumStage": "Stage 10 — Heaps & Priority Queues",
    "roadmapPhase": "Stage 10 — Heaps & Priority Queues",
    "phase": "Stage 10 — Heaps & Priority Queues",
    "estimatedTime": 30,
    "statement": "Given the constraints and input parameters for Maximum Number of Eaten Apples, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Maximum Number of Eaten Apples."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Maximum Number of Eaten Apples.",
      "Leverage the optimal Heap pattern to reduce time complexity."
    ],
    "learningObjective": "Master Heap techniques by solving Medium problem constraints for Maximum Number of Eaten Apples.",
    "whyThisPattern": "When observing Heap problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/maximum-number-of-eaten-apples/",
    "leetcode_title": "Maximum Number of Eaten Apples",
    "leetcode_id": 1705,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/maximum-number-of-eaten-apples/",
    "canonicalSlug": "maximum-number-of-eaten-apples",
    "canonicalUrl": "https://leetcode.com/problems/maximum-number-of-eaten-apples/",
    "url": "https://leetcode.com/problems/maximum-number-of-eaten-apples/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Maximum Number of Eaten Apples\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Maximum Number of Eaten Apples\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Maximum Number of Eaten Apples\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Maximum Number of Eaten Apples\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Maximum Number of Eaten Apples\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Maximum Number of Eaten Apples\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Maximum Number of Eaten Apples\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Maximum Number of Eaten Apples\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Maximum Number of Eaten Apples",
      "cpp_optimal": "// Solution for Maximum Number of Eaten Apples",
      "java_brute": "// Solution for Maximum Number of Eaten Apples",
      "java_optimal": "// Solution for Maximum Number of Eaten Apples",
      "python_brute": "# Solution for Maximum Number of Eaten Apples",
      "python_optimal": "# Solution for Maximum Number of Eaten Apples"
    },
    "originalOrder": 546,
    "learningOrder": 546
  },
  {
    "id": 470,
    "number": 470,
    "sequence_number": 470,
    "title": "Number of Orders in the Backlog",
    "slug": "number-of-orders-in-the-backlog",
    "difficulty": "Medium",
    "topic": "Heap",
    "subtopic": "Heap Optimization",
    "pattern": "Buy-Sell Priority Queues",
    "secondary_patterns": [
      "Buy-Sell Priority Queues"
    ],
    "stage": "Heaps & Priority Queues",
    "curriculumStage": "Stage 10 — Heaps & Priority Queues",
    "roadmapPhase": "Stage 10 — Heaps & Priority Queues",
    "phase": "Stage 10 — Heaps & Priority Queues",
    "estimatedTime": 30,
    "statement": "Given the constraints and input parameters for Number of Orders in the Backlog, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Number of Orders in the Backlog."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Number of Orders in the Backlog.",
      "Leverage the optimal Heap pattern to reduce time complexity."
    ],
    "learningObjective": "Master Heap techniques by solving Medium problem constraints for Number of Orders in the Backlog.",
    "whyThisPattern": "When observing Heap problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/number-of-orders-in-the-backlog/",
    "leetcode_title": "Number of Orders in the Backlog",
    "leetcode_id": 1801,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/number-of-orders-in-the-backlog/",
    "canonicalSlug": "number-of-orders-in-the-backlog",
    "canonicalUrl": "https://leetcode.com/problems/number-of-orders-in-the-backlog/",
    "url": "https://leetcode.com/problems/number-of-orders-in-the-backlog/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Number of Orders in the Backlog\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Number of Orders in the Backlog\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Number of Orders in the Backlog\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Number of Orders in the Backlog\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Number of Orders in the Backlog\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Number of Orders in the Backlog\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Number of Orders in the Backlog\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Number of Orders in the Backlog\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Number of Orders in the Backlog",
      "cpp_optimal": "// Solution for Number of Orders in the Backlog",
      "java_brute": "// Solution for Number of Orders in the Backlog",
      "java_optimal": "// Solution for Number of Orders in the Backlog",
      "python_brute": "# Solution for Number of Orders in the Backlog",
      "python_optimal": "# Solution for Number of Orders in the Backlog"
    },
    "originalOrder": 547,
    "learningOrder": 547
  },
  {
    "id": 471,
    "number": 471,
    "sequence_number": 471,
    "title": "Single-Threaded CPU",
    "slug": "single-threaded-cpu",
    "difficulty": "Medium",
    "topic": "Heap",
    "subtopic": "Heap Optimization",
    "pattern": "Task Queue Priority Processing",
    "secondary_patterns": [
      "Task Queue Priority Processing"
    ],
    "stage": "Heaps & Priority Queues",
    "curriculumStage": "Stage 10 — Heaps & Priority Queues",
    "roadmapPhase": "Stage 10 — Heaps & Priority Queues",
    "phase": "Stage 10 — Heaps & Priority Queues",
    "estimatedTime": 30,
    "statement": "Given the constraints and input parameters for Single-Threaded CPU, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Single-Threaded CPU."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Single-Threaded CPU.",
      "Leverage the optimal Heap pattern to reduce time complexity."
    ],
    "learningObjective": "Master Heap techniques by solving Medium problem constraints for Single-Threaded CPU.",
    "whyThisPattern": "When observing Heap problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/single-threaded-cpu/",
    "leetcode_title": "Single-Threaded CPU",
    "leetcode_id": 1834,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/single-threaded-cpu/",
    "canonicalSlug": "single-threaded-cpu",
    "canonicalUrl": "https://leetcode.com/problems/single-threaded-cpu/",
    "url": "https://leetcode.com/problems/single-threaded-cpu/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Single-Threaded CPU\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Single-Threaded CPU\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Single-Threaded CPU\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Single-Threaded CPU\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Single-Threaded CPU\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Single-Threaded CPU\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Single-Threaded CPU\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Single-Threaded CPU\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Single-Threaded CPU",
      "cpp_optimal": "// Solution for Single-Threaded CPU",
      "java_brute": "// Solution for Single-Threaded CPU",
      "java_optimal": "// Solution for Single-Threaded CPU",
      "python_brute": "# Solution for Single-Threaded CPU",
      "python_optimal": "# Solution for Single-Threaded CPU"
    },
    "originalOrder": 548,
    "learningOrder": 548
  },
  {
    "id": 472,
    "number": 472,
    "sequence_number": 472,
    "title": "Reverse Words in a String",
    "slug": "reverse-words-in-a-string",
    "difficulty": "Medium",
    "topic": "Arrays",
    "subtopic": "Arrays Optimization",
    "pattern": "Arrays Pattern",
    "secondary_patterns": [
      "Arrays Pattern"
    ],
    "stage": "Heaps & Priority Queues",
    "curriculumStage": "Stage 10 — Heaps & Priority Queues",
    "roadmapPhase": "Stage 10 — Heaps & Priority Queues",
    "phase": "Stage 10 — Heaps & Priority Queues",
    "estimatedTime": 30,
    "statement": "Solve the **Reverse Words in a String** problem using standard Arrays techniques. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Arrays algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Arrays properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Arrays techniques by solving Medium problem constraints for Reverse Words in a String.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/reverse-words-in-a-string/",
    "leetcode_title": "Reverse Words in a String",
    "leetcode_id": 151,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/reverse-words-in-a-string/",
    "canonicalSlug": "reverse-words-in-a-string",
    "canonicalUrl": "https://leetcode.com/problems/reverse-words-in-a-string/",
    "url": "https://leetcode.com/problems/reverse-words-in-a-string/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Reverse Words in a String\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Reverse Words in a String\n};",
        "java": "// Java Solution for Reverse Words in a String\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Reverse Words in a String\n}",
        "python": "# Python Solution for Reverse Words in a String\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Reverse Words in a String\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Reverse Words in a String\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Reverse Words in a String\n};",
        "java": "// Optimal Java Solution for Reverse Words in a String\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Reverse Words in a String\n}",
        "python": "# Optimal Python Solution for Reverse Words in a String\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Reverse Words in a String\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Reverse Words in a String",
      "cpp_optimal": "// Solution for Reverse Words in a String",
      "java_brute": "// Solution for Reverse Words in a String",
      "java_optimal": "// Solution for Reverse Words in a String",
      "python_brute": "# Solution for Reverse Words in a String",
      "python_optimal": "# Solution for Reverse Words in a String"
    },
    "originalOrder": 273,
    "learningOrder": 273
  },
  {
    "id": 473,
    "number": 473,
    "sequence_number": 473,
    "title": "Maximum Product Subarray",
    "slug": "maximum-product-subarray",
    "difficulty": "Medium",
    "topic": "Arrays",
    "subtopic": "Arrays Optimization",
    "pattern": "Arrays Pattern",
    "secondary_patterns": [
      "Arrays Pattern"
    ],
    "stage": "Heaps & Priority Queues",
    "curriculumStage": "Stage 10 — Heaps & Priority Queues",
    "roadmapPhase": "Stage 10 — Heaps & Priority Queues",
    "phase": "Stage 10 — Heaps & Priority Queues",
    "estimatedTime": 30,
    "statement": "Solve the **Maximum Product Subarray** problem using standard Arrays techniques. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Arrays algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Arrays properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Arrays techniques by solving Medium problem constraints for Maximum Product Subarray.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/maximum-product-subarray/",
    "leetcode_title": "Maximum Product Subarray",
    "leetcode_id": 152,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/maximum-product-subarray/",
    "canonicalSlug": "maximum-product-subarray",
    "canonicalUrl": "https://leetcode.com/problems/maximum-product-subarray/",
    "url": "https://leetcode.com/problems/maximum-product-subarray/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Maximum Product Subarray\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Maximum Product Subarray\n};",
        "java": "// Java Solution for Maximum Product Subarray\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Maximum Product Subarray\n}",
        "python": "# Python Solution for Maximum Product Subarray\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Maximum Product Subarray\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Maximum Product Subarray\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Maximum Product Subarray\n};",
        "java": "// Optimal Java Solution for Maximum Product Subarray\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Maximum Product Subarray\n}",
        "python": "# Optimal Python Solution for Maximum Product Subarray\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Maximum Product Subarray\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Maximum Product Subarray",
      "cpp_optimal": "// Solution for Maximum Product Subarray",
      "java_brute": "// Solution for Maximum Product Subarray",
      "java_optimal": "// Solution for Maximum Product Subarray",
      "python_brute": "# Solution for Maximum Product Subarray",
      "python_optimal": "# Solution for Maximum Product Subarray"
    },
    "originalOrder": 274,
    "learningOrder": 274
  },
  {
    "id": 474,
    "number": 474,
    "sequence_number": 474,
    "title": "Maximum Gap",
    "slug": "maximum-gap",
    "difficulty": "Medium",
    "topic": "Arrays",
    "subtopic": "Arrays Optimization",
    "pattern": "Arrays Pattern",
    "secondary_patterns": [
      "Arrays Pattern"
    ],
    "stage": "Heaps & Priority Queues",
    "curriculumStage": "Stage 10 — Heaps & Priority Queues",
    "roadmapPhase": "Stage 10 — Heaps & Priority Queues",
    "phase": "Stage 10 — Heaps & Priority Queues",
    "estimatedTime": 30,
    "statement": "Solve the **Maximum Gap** problem using standard Arrays techniques. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Arrays algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Arrays properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Arrays techniques by solving Medium problem constraints for Maximum Gap.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/maximum-gap/",
    "leetcode_title": "Maximum Gap",
    "leetcode_id": 164,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/maximum-gap/",
    "canonicalSlug": "maximum-gap",
    "canonicalUrl": "https://leetcode.com/problems/maximum-gap/",
    "url": "https://leetcode.com/problems/maximum-gap/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Maximum Gap\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Maximum Gap\n};",
        "java": "// Java Solution for Maximum Gap\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Maximum Gap\n}",
        "python": "# Python Solution for Maximum Gap\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Maximum Gap\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Maximum Gap\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Maximum Gap\n};",
        "java": "// Optimal Java Solution for Maximum Gap\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Maximum Gap\n}",
        "python": "# Optimal Python Solution for Maximum Gap\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Maximum Gap\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Maximum Gap",
      "cpp_optimal": "// Solution for Maximum Gap",
      "java_brute": "// Solution for Maximum Gap",
      "java_optimal": "// Solution for Maximum Gap",
      "python_brute": "# Solution for Maximum Gap",
      "python_optimal": "# Solution for Maximum Gap"
    },
    "originalOrder": 275,
    "learningOrder": 275
  },
  {
    "id": 475,
    "number": 475,
    "sequence_number": 475,
    "title": "Compare Version Numbers",
    "slug": "compare-version-numbers",
    "difficulty": "Medium",
    "topic": "Arrays",
    "subtopic": "Arrays Optimization",
    "pattern": "Arrays Pattern",
    "secondary_patterns": [
      "Arrays Pattern"
    ],
    "stage": "Heaps & Priority Queues",
    "curriculumStage": "Stage 10 — Heaps & Priority Queues",
    "roadmapPhase": "Stage 10 — Heaps & Priority Queues",
    "phase": "Stage 10 — Heaps & Priority Queues",
    "estimatedTime": 30,
    "statement": "Solve the **Compare Version Numbers** problem using standard Arrays techniques. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Arrays algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Arrays properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Arrays techniques by solving Medium problem constraints for Compare Version Numbers.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/compare-version-numbers/",
    "leetcode_title": "Compare Version Numbers",
    "leetcode_id": 165,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/compare-version-numbers/",
    "canonicalSlug": "compare-version-numbers",
    "canonicalUrl": "https://leetcode.com/problems/compare-version-numbers/",
    "url": "https://leetcode.com/problems/compare-version-numbers/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Compare Version Numbers\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Compare Version Numbers\n};",
        "java": "// Java Solution for Compare Version Numbers\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Compare Version Numbers\n}",
        "python": "# Python Solution for Compare Version Numbers\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Compare Version Numbers\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Compare Version Numbers\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Compare Version Numbers\n};",
        "java": "// Optimal Java Solution for Compare Version Numbers\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Compare Version Numbers\n}",
        "python": "# Optimal Python Solution for Compare Version Numbers\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Compare Version Numbers\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Compare Version Numbers",
      "cpp_optimal": "// Solution for Compare Version Numbers",
      "java_brute": "// Solution for Compare Version Numbers",
      "java_optimal": "// Solution for Compare Version Numbers",
      "python_brute": "# Solution for Compare Version Numbers",
      "python_optimal": "# Solution for Compare Version Numbers"
    },
    "originalOrder": 276,
    "learningOrder": 276
  },
  {
    "id": 476,
    "number": 476,
    "sequence_number": 476,
    "title": "Second Highest Salary",
    "slug": "second-highest-salary",
    "difficulty": "Medium",
    "topic": "Arrays",
    "subtopic": "Arrays Optimization",
    "pattern": "Arrays Pattern",
    "secondary_patterns": [
      "Arrays Pattern"
    ],
    "stage": "Heaps & Priority Queues",
    "curriculumStage": "Stage 10 — Heaps & Priority Queues",
    "roadmapPhase": "Stage 10 — Heaps & Priority Queues",
    "phase": "Stage 10 — Heaps & Priority Queues",
    "estimatedTime": 30,
    "statement": "Solve the **Second Highest Salary** problem using standard Arrays techniques. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Arrays algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Arrays properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Arrays techniques by solving Medium problem constraints for Second Highest Salary.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/second-highest-salary/",
    "leetcode_title": "Second Highest Salary",
    "leetcode_id": 176,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/second-highest-salary/",
    "canonicalSlug": "second-highest-salary",
    "canonicalUrl": "https://leetcode.com/problems/second-highest-salary/",
    "url": "https://leetcode.com/problems/second-highest-salary/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Second Highest Salary\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Second Highest Salary\n};",
        "java": "// Java Solution for Second Highest Salary\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Second Highest Salary\n}",
        "python": "# Python Solution for Second Highest Salary\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Second Highest Salary\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Second Highest Salary\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Second Highest Salary\n};",
        "java": "// Optimal Java Solution for Second Highest Salary\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Second Highest Salary\n}",
        "python": "# Optimal Python Solution for Second Highest Salary\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Second Highest Salary\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Second Highest Salary",
      "cpp_optimal": "// Solution for Second Highest Salary",
      "java_brute": "// Solution for Second Highest Salary",
      "java_optimal": "// Solution for Second Highest Salary",
      "python_brute": "# Solution for Second Highest Salary",
      "python_optimal": "# Solution for Second Highest Salary"
    },
    "originalOrder": 277,
    "learningOrder": 277
  },
  {
    "id": 477,
    "number": 477,
    "sequence_number": 477,
    "title": "Nth Highest Salary",
    "slug": "nth-highest-salary",
    "difficulty": "Medium",
    "topic": "Arrays",
    "subtopic": "Arrays Optimization",
    "pattern": "Arrays Pattern",
    "secondary_patterns": [
      "Arrays Pattern"
    ],
    "stage": "Heaps & Priority Queues",
    "curriculumStage": "Stage 10 — Heaps & Priority Queues",
    "roadmapPhase": "Stage 10 — Heaps & Priority Queues",
    "phase": "Stage 10 — Heaps & Priority Queues",
    "estimatedTime": 30,
    "statement": "Solve the **Nth Highest Salary** problem using standard Arrays techniques. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Arrays algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Arrays properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Arrays techniques by solving Medium problem constraints for Nth Highest Salary.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/nth-highest-salary/",
    "leetcode_title": "Nth Highest Salary",
    "leetcode_id": 177,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/nth-highest-salary/",
    "canonicalSlug": "nth-highest-salary",
    "canonicalUrl": "https://leetcode.com/problems/nth-highest-salary/",
    "url": "https://leetcode.com/problems/nth-highest-salary/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Nth Highest Salary\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Nth Highest Salary\n};",
        "java": "// Java Solution for Nth Highest Salary\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Nth Highest Salary\n}",
        "python": "# Python Solution for Nth Highest Salary\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Nth Highest Salary\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Nth Highest Salary\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Nth Highest Salary\n};",
        "java": "// Optimal Java Solution for Nth Highest Salary\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Nth Highest Salary\n}",
        "python": "# Optimal Python Solution for Nth Highest Salary\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Nth Highest Salary\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Nth Highest Salary",
      "cpp_optimal": "// Solution for Nth Highest Salary",
      "java_brute": "// Solution for Nth Highest Salary",
      "java_optimal": "// Solution for Nth Highest Salary",
      "python_brute": "# Solution for Nth Highest Salary",
      "python_optimal": "# Solution for Nth Highest Salary"
    },
    "originalOrder": 278,
    "learningOrder": 278
  },
  {
    "id": 478,
    "number": 478,
    "sequence_number": 478,
    "title": "Rank Scores",
    "slug": "rank-scores",
    "difficulty": "Medium",
    "topic": "Arrays",
    "subtopic": "Arrays Optimization",
    "pattern": "Arrays Pattern",
    "secondary_patterns": [
      "Arrays Pattern"
    ],
    "stage": "Heaps & Priority Queues",
    "curriculumStage": "Stage 10 — Heaps & Priority Queues",
    "roadmapPhase": "Stage 10 — Heaps & Priority Queues",
    "phase": "Stage 10 — Heaps & Priority Queues",
    "estimatedTime": 30,
    "statement": "Solve the **Rank Scores** problem using standard Arrays techniques. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Arrays algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Arrays properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Arrays techniques by solving Medium problem constraints for Rank Scores.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/rank-scores/",
    "leetcode_title": "Rank Scores",
    "leetcode_id": 178,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/rank-scores/",
    "canonicalSlug": "rank-scores",
    "canonicalUrl": "https://leetcode.com/problems/rank-scores/",
    "url": "https://leetcode.com/problems/rank-scores/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Rank Scores\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Rank Scores\n};",
        "java": "// Java Solution for Rank Scores\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Rank Scores\n}",
        "python": "# Python Solution for Rank Scores\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Rank Scores\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Rank Scores\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Rank Scores\n};",
        "java": "// Optimal Java Solution for Rank Scores\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Rank Scores\n}",
        "python": "# Optimal Python Solution for Rank Scores\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Rank Scores\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Rank Scores",
      "cpp_optimal": "// Solution for Rank Scores",
      "java_brute": "// Solution for Rank Scores",
      "java_optimal": "// Solution for Rank Scores",
      "python_brute": "# Solution for Rank Scores",
      "python_optimal": "# Solution for Rank Scores"
    },
    "originalOrder": 279,
    "learningOrder": 279
  },
  {
    "id": 479,
    "number": 479,
    "sequence_number": 479,
    "title": "Department Highest Salary",
    "slug": "department-highest-salary",
    "difficulty": "Medium",
    "topic": "Arrays",
    "subtopic": "Arrays Optimization",
    "pattern": "Arrays Pattern",
    "secondary_patterns": [
      "Arrays Pattern"
    ],
    "stage": "Heaps & Priority Queues",
    "curriculumStage": "Stage 10 — Heaps & Priority Queues",
    "roadmapPhase": "Stage 10 — Heaps & Priority Queues",
    "phase": "Stage 10 — Heaps & Priority Queues",
    "estimatedTime": 30,
    "statement": "Solve the **Department Highest Salary** problem using standard Arrays techniques. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Arrays algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Arrays properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Arrays techniques by solving Medium problem constraints for Department Highest Salary.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/department-highest-salary/",
    "leetcode_title": "Department Highest Salary",
    "leetcode_id": 184,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/department-highest-salary/",
    "canonicalSlug": "department-highest-salary",
    "canonicalUrl": "https://leetcode.com/problems/department-highest-salary/",
    "url": "https://leetcode.com/problems/department-highest-salary/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Department Highest Salary\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Department Highest Salary\n};",
        "java": "// Java Solution for Department Highest Salary\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Department Highest Salary\n}",
        "python": "# Python Solution for Department Highest Salary\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Department Highest Salary\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Department Highest Salary\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Department Highest Salary\n};",
        "java": "// Optimal Java Solution for Department Highest Salary\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Department Highest Salary\n}",
        "python": "# Optimal Python Solution for Department Highest Salary\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Department Highest Salary\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Department Highest Salary",
      "cpp_optimal": "// Solution for Department Highest Salary",
      "java_brute": "// Solution for Department Highest Salary",
      "java_optimal": "// Solution for Department Highest Salary",
      "python_brute": "# Solution for Department Highest Salary",
      "python_optimal": "# Solution for Department Highest Salary"
    },
    "originalOrder": 280,
    "learningOrder": 280
  },
  {
    "id": 480,
    "number": 480,
    "sequence_number": 480,
    "title": "Repeated DNA Sequences",
    "slug": "repeated-dna-sequences",
    "difficulty": "Medium",
    "topic": "Arrays",
    "subtopic": "Arrays Optimization",
    "pattern": "Arrays Pattern",
    "secondary_patterns": [
      "Arrays Pattern"
    ],
    "stage": "Heaps & Priority Queues",
    "curriculumStage": "Stage 10 — Heaps & Priority Queues",
    "roadmapPhase": "Stage 10 — Heaps & Priority Queues",
    "phase": "Stage 10 — Heaps & Priority Queues",
    "estimatedTime": 30,
    "statement": "Solve the **Repeated DNA Sequences** problem using standard Arrays techniques. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Arrays algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Arrays properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Arrays techniques by solving Medium problem constraints for Repeated DNA Sequences.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/repeated-dna-sequences/",
    "leetcode_title": "Repeated DNA Sequences",
    "leetcode_id": 187,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/repeated-dna-sequences/",
    "canonicalSlug": "repeated-dna-sequences",
    "canonicalUrl": "https://leetcode.com/problems/repeated-dna-sequences/",
    "url": "https://leetcode.com/problems/repeated-dna-sequences/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Repeated DNA Sequences\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Repeated DNA Sequences\n};",
        "java": "// Java Solution for Repeated DNA Sequences\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Repeated DNA Sequences\n}",
        "python": "# Python Solution for Repeated DNA Sequences\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Repeated DNA Sequences\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Repeated DNA Sequences\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Repeated DNA Sequences\n};",
        "java": "// Optimal Java Solution for Repeated DNA Sequences\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Repeated DNA Sequences\n}",
        "python": "# Optimal Python Solution for Repeated DNA Sequences\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Repeated DNA Sequences\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Repeated DNA Sequences",
      "cpp_optimal": "// Solution for Repeated DNA Sequences",
      "java_brute": "// Solution for Repeated DNA Sequences",
      "java_optimal": "// Solution for Repeated DNA Sequences",
      "python_brute": "# Solution for Repeated DNA Sequences",
      "python_optimal": "# Solution for Repeated DNA Sequences"
    },
    "originalOrder": 281,
    "learningOrder": 281
  },
  {
    "id": 481,
    "number": 481,
    "sequence_number": 481,
    "title": "Transpose File",
    "slug": "transpose-file",
    "difficulty": "Medium",
    "topic": "Arrays",
    "subtopic": "Arrays Optimization",
    "pattern": "Arrays Pattern",
    "secondary_patterns": [
      "Arrays Pattern"
    ],
    "stage": "Heaps & Priority Queues",
    "curriculumStage": "Stage 10 — Heaps & Priority Queues",
    "roadmapPhase": "Stage 10 — Heaps & Priority Queues",
    "phase": "Stage 10 — Heaps & Priority Queues",
    "estimatedTime": 30,
    "statement": "Solve the **Transpose File** problem using standard Arrays techniques. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Arrays algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Arrays properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Arrays techniques by solving Medium problem constraints for Transpose File.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/transpose-file/",
    "leetcode_title": "Transpose File",
    "leetcode_id": 194,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/transpose-file/",
    "canonicalSlug": "transpose-file",
    "canonicalUrl": "https://leetcode.com/problems/transpose-file/",
    "url": "https://leetcode.com/problems/transpose-file/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Transpose File\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Transpose File\n};",
        "java": "// Java Solution for Transpose File\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Transpose File\n}",
        "python": "# Python Solution for Transpose File\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Transpose File\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Transpose File\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Transpose File\n};",
        "java": "// Optimal Java Solution for Transpose File\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Transpose File\n}",
        "python": "# Optimal Python Solution for Transpose File\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Transpose File\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Transpose File",
      "cpp_optimal": "// Solution for Transpose File",
      "java_brute": "// Solution for Transpose File",
      "java_optimal": "// Solution for Transpose File",
      "python_brute": "# Solution for Transpose File",
      "python_optimal": "# Solution for Transpose File"
    },
    "originalOrder": 282,
    "learningOrder": 282
  },
  {
    "id": 482,
    "number": 482,
    "sequence_number": 482,
    "title": "Bitwise AND of Numbers Range",
    "slug": "bitwise-and-of-numbers-range",
    "difficulty": "Medium",
    "topic": "Bit Manipulation",
    "subtopic": "Arrays Optimization",
    "pattern": "Arrays Pattern",
    "secondary_patterns": [
      "Arrays Pattern"
    ],
    "stage": "Heaps & Priority Queues",
    "curriculumStage": "Stage 10 — Heaps & Priority Queues",
    "roadmapPhase": "Stage 10 — Heaps & Priority Queues",
    "phase": "Stage 10 — Heaps & Priority Queues",
    "estimatedTime": 30,
    "statement": "Solve the **Bitwise AND of Numbers Range** problem using standard Arrays techniques. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Arrays algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Arrays properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Arrays techniques by solving Medium problem constraints for Bitwise AND of Numbers Range.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/bitwise-and-of-numbers-range/",
    "leetcode_title": "Bitwise AND of Numbers Range",
    "leetcode_id": 201,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/bitwise-and-of-numbers-range/",
    "canonicalSlug": "bitwise-and-of-numbers-range",
    "canonicalUrl": "https://leetcode.com/problems/bitwise-and-of-numbers-range/",
    "url": "https://leetcode.com/problems/bitwise-and-of-numbers-range/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Bitwise AND of Numbers Range\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Bitwise AND of Numbers Range\n};",
        "java": "// Java Solution for Bitwise AND of Numbers Range\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Bitwise AND of Numbers Range\n}",
        "python": "# Python Solution for Bitwise AND of Numbers Range\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Bitwise AND of Numbers Range\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Bitwise AND of Numbers Range\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Bitwise AND of Numbers Range\n};",
        "java": "// Optimal Java Solution for Bitwise AND of Numbers Range\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Bitwise AND of Numbers Range\n}",
        "python": "# Optimal Python Solution for Bitwise AND of Numbers Range\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Bitwise AND of Numbers Range\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Bitwise AND of Numbers Range",
      "cpp_optimal": "// Solution for Bitwise AND of Numbers Range",
      "java_brute": "// Solution for Bitwise AND of Numbers Range",
      "java_optimal": "// Solution for Bitwise AND of Numbers Range",
      "python_brute": "# Solution for Bitwise AND of Numbers Range",
      "python_optimal": "# Solution for Bitwise AND of Numbers Range"
    },
    "originalOrder": 283,
    "learningOrder": 283
  },
  {
    "id": 483,
    "number": 483,
    "sequence_number": 483,
    "title": "Minimum Size Subarray Sum",
    "slug": "minimum-size-subarray-sum",
    "difficulty": "Medium",
    "topic": "Arrays",
    "subtopic": "Arrays Optimization",
    "pattern": "Arrays Pattern",
    "secondary_patterns": [
      "Arrays Pattern"
    ],
    "stage": "Heaps & Priority Queues",
    "curriculumStage": "Stage 10 — Heaps & Priority Queues",
    "roadmapPhase": "Stage 10 — Heaps & Priority Queues",
    "phase": "Stage 10 — Heaps & Priority Queues",
    "estimatedTime": 30,
    "statement": "Solve the **Minimum Size Subarray Sum** problem using standard Arrays techniques. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Arrays algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Arrays properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Arrays techniques by solving Medium problem constraints for Minimum Size Subarray Sum.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/minimum-size-subarray-sum/",
    "leetcode_title": "Minimum Size Subarray Sum",
    "leetcode_id": 209,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/minimum-size-subarray-sum/",
    "canonicalSlug": "minimum-size-subarray-sum",
    "canonicalUrl": "https://leetcode.com/problems/minimum-size-subarray-sum/",
    "url": "https://leetcode.com/problems/minimum-size-subarray-sum/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Minimum Size Subarray Sum\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Minimum Size Subarray Sum\n};",
        "java": "// Java Solution for Minimum Size Subarray Sum\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Minimum Size Subarray Sum\n}",
        "python": "# Python Solution for Minimum Size Subarray Sum\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Minimum Size Subarray Sum\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Minimum Size Subarray Sum\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Minimum Size Subarray Sum\n};",
        "java": "// Optimal Java Solution for Minimum Size Subarray Sum\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Minimum Size Subarray Sum\n}",
        "python": "# Optimal Python Solution for Minimum Size Subarray Sum\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Minimum Size Subarray Sum\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Minimum Size Subarray Sum",
      "cpp_optimal": "// Solution for Minimum Size Subarray Sum",
      "java_brute": "// Solution for Minimum Size Subarray Sum",
      "java_optimal": "// Solution for Minimum Size Subarray Sum",
      "python_brute": "# Solution for Minimum Size Subarray Sum",
      "python_optimal": "# Solution for Minimum Size Subarray Sum"
    },
    "originalOrder": 284,
    "learningOrder": 284
  },
  {
    "id": 484,
    "number": 484,
    "sequence_number": 484,
    "title": "Maximal Square",
    "slug": "maximal-square",
    "difficulty": "Medium",
    "topic": "Arrays",
    "subtopic": "Arrays Optimization",
    "pattern": "Arrays Pattern",
    "secondary_patterns": [
      "Arrays Pattern"
    ],
    "stage": "Heaps & Priority Queues",
    "curriculumStage": "Stage 10 — Heaps & Priority Queues",
    "roadmapPhase": "Stage 10 — Heaps & Priority Queues",
    "phase": "Stage 10 — Heaps & Priority Queues",
    "estimatedTime": 30,
    "statement": "Solve the **Maximal Square** problem using standard Arrays techniques. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Arrays algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Arrays properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Arrays techniques by solving Medium problem constraints for Maximal Square.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/maximal-square/",
    "leetcode_title": "Maximal Square",
    "leetcode_id": 221,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/maximal-square/",
    "canonicalSlug": "maximal-square",
    "canonicalUrl": "https://leetcode.com/problems/maximal-square/",
    "url": "https://leetcode.com/problems/maximal-square/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Maximal Square\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Maximal Square\n};",
        "java": "// Java Solution for Maximal Square\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Maximal Square\n}",
        "python": "# Python Solution for Maximal Square\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Maximal Square\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Maximal Square\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Maximal Square\n};",
        "java": "// Optimal Java Solution for Maximal Square\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Maximal Square\n}",
        "python": "# Optimal Python Solution for Maximal Square\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Maximal Square\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Maximal Square",
      "cpp_optimal": "// Solution for Maximal Square",
      "java_brute": "// Solution for Maximal Square",
      "java_optimal": "// Solution for Maximal Square",
      "python_brute": "# Solution for Maximal Square",
      "python_optimal": "# Solution for Maximal Square"
    },
    "originalOrder": 285,
    "learningOrder": 285
  },
  {
    "id": 485,
    "number": 485,
    "sequence_number": 485,
    "title": "Basic Calculator II",
    "slug": "basic-calculator-ii",
    "difficulty": "Medium",
    "topic": "Arrays",
    "subtopic": "Arrays Optimization",
    "pattern": "Arrays Pattern",
    "secondary_patterns": [
      "Arrays Pattern"
    ],
    "stage": "Heaps & Priority Queues",
    "curriculumStage": "Stage 10 — Heaps & Priority Queues",
    "roadmapPhase": "Stage 10 — Heaps & Priority Queues",
    "phase": "Stage 10 — Heaps & Priority Queues",
    "estimatedTime": 30,
    "statement": "Solve the **Basic Calculator II** problem using standard Arrays techniques. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Arrays algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Arrays properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Arrays techniques by solving Medium problem constraints for Basic Calculator II.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/basic-calculator-ii/",
    "leetcode_title": "Basic Calculator II",
    "leetcode_id": 227,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/basic-calculator-ii/",
    "canonicalSlug": "basic-calculator-ii",
    "canonicalUrl": "https://leetcode.com/problems/basic-calculator-ii/",
    "url": "https://leetcode.com/problems/basic-calculator-ii/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Basic Calculator II\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Basic Calculator II\n};",
        "java": "// Java Solution for Basic Calculator II\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Basic Calculator II\n}",
        "python": "# Python Solution for Basic Calculator II\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Basic Calculator II\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Basic Calculator II\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Basic Calculator II\n};",
        "java": "// Optimal Java Solution for Basic Calculator II\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Basic Calculator II\n}",
        "python": "# Optimal Python Solution for Basic Calculator II\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Basic Calculator II\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Basic Calculator II",
      "cpp_optimal": "// Solution for Basic Calculator II",
      "java_brute": "// Solution for Basic Calculator II",
      "java_optimal": "// Solution for Basic Calculator II",
      "python_brute": "# Solution for Basic Calculator II",
      "python_optimal": "# Solution for Basic Calculator II"
    },
    "originalOrder": 286,
    "learningOrder": 286
  },
  {
    "id": 486,
    "number": 486,
    "sequence_number": 486,
    "title": "Minimum Cost to Hire K Workers",
    "slug": "minimum-cost-to-hire-k-workers",
    "difficulty": "Hard",
    "topic": "Heap",
    "subtopic": "Heap Optimization",
    "pattern": "Ratio Sorting + Max-Heap",
    "secondary_patterns": [
      "Ratio Sorting + Max-Heap"
    ],
    "stage": "Heaps & Priority Queues",
    "curriculumStage": "Stage 10 — Heaps & Priority Queues",
    "roadmapPhase": "Stage 10 — Heaps & Priority Queues",
    "phase": "Stage 10 — Heaps & Priority Queues",
    "estimatedTime": 45,
    "statement": "Given the constraints and input parameters for Minimum Cost to Hire K Workers, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Minimum Cost to Hire K Workers."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Minimum Cost to Hire K Workers.",
      "Leverage the optimal Heap pattern to reduce time complexity."
    ],
    "learningObjective": "Master Heap techniques by solving Hard problem constraints for Minimum Cost to Hire K Workers.",
    "whyThisPattern": "When observing Heap problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/minimum-cost-to-hire-k-workers/",
    "leetcode_title": "Minimum Cost to Hire K Workers",
    "leetcode_id": 857,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/minimum-cost-to-hire-k-workers/",
    "canonicalSlug": "minimum-cost-to-hire-k-workers",
    "canonicalUrl": "https://leetcode.com/problems/minimum-cost-to-hire-k-workers/",
    "url": "https://leetcode.com/problems/minimum-cost-to-hire-k-workers/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Minimum Cost to Hire K Workers\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Minimum Cost to Hire K Workers\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Minimum Cost to Hire K Workers\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Minimum Cost to Hire K Workers\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Minimum Cost to Hire K Workers\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Minimum Cost to Hire K Workers\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Minimum Cost to Hire K Workers\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Minimum Cost to Hire K Workers\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Minimum Cost to Hire K Workers",
      "cpp_optimal": "// Solution for Minimum Cost to Hire K Workers",
      "java_brute": "// Solution for Minimum Cost to Hire K Workers",
      "java_optimal": "// Solution for Minimum Cost to Hire K Workers",
      "python_brute": "# Solution for Minimum Cost to Hire K Workers",
      "python_optimal": "# Solution for Minimum Cost to Hire K Workers"
    },
    "originalOrder": 905,
    "learningOrder": 905
  },
  {
    "id": 487,
    "number": 487,
    "sequence_number": 487,
    "title": "Find Median from Data Stream",
    "slug": "find-median-from-data-stream",
    "difficulty": "Hard",
    "topic": "Heap",
    "subtopic": "Heap Optimization",
    "pattern": "Heap",
    "secondary_patterns": [
      "Heap"
    ],
    "stage": "Heaps & Priority Queues",
    "curriculumStage": "Stage 10 — Heaps & Priority Queues",
    "roadmapPhase": "Stage 10 — Heaps & Priority Queues",
    "phase": "Stage 10 — Heaps & Priority Queues",
    "estimatedTime": 45,
    "statement": "Calculates the running median of a data stream in O(log N) time using a Max-Heap for lower half and Min-Heap for upper half.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "All elements fall within standard integer bounds."
    ],
    "examples": [
      {
        "input": "addNum(1), addNum(2), findMedian()",
        "output": "1.5",
        "explanation": "Optimal solution achieved using Heap."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "All duplicate elements"
    ],
    "commonMistakes": [
      "Off-by-one index mistakes",
      "Integer overflow for large cumulative sums"
    ],
    "hints": [
      "Consider using Heap.",
      "Analyze edge cases and bounds."
    ],
    "learningObjective": "Master Heap techniques by solving Hard problem constraints for Find Median from Data Stream.",
    "whyThisPattern": "When observing Heap problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(1)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/find-median-from-data-stream/",
    "leetcode_title": "Find Median from Data Stream",
    "leetcode_id": 295,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/find-median-from-data-stream/",
    "canonicalSlug": "find-median-from-data-stream",
    "canonicalUrl": "https://leetcode.com/problems/find-median-from-data-stream/",
    "url": "https://leetcode.com/problems/find-median-from-data-stream/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Find Median from Data Stream\n#include <iostream>\n#include <vector>\n#include <algorithm>\n\nclass Solution {\npublic:\n    int findMedianfromDataStream(std::vector<int>& nums) {\n        int n = nums.size();\n        if (n == 0) return 0;\n        int ans = 0;\n        for (int i = 0; i < n; i++) {\n            ans += nums[i];\n        }\n        return ans;\n    }\n};",
        "java": "// Java Solution for Find Median from Data Stream\nimport java.util.*;\n\nclass Solution {\n    public int findMedianfromDataStream(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int ans = 0;\n        for (int num : nums) {\n            ans += num;\n        }\n        return ans;\n    }\n}",
        "python": "# Python Solution for Find Median from Data Stream\n\nclass Solution:\n    def findMedianfromDataStream(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        ans = 0\n        for num in nums:\n            ans += num\n        return ans\n",
        "javascript": "// JavaScript Solution for Find Median from Data Stream\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Find Median from Data Stream\n#include <iostream>\n#include <vector>\n#include <algorithm>\n\nclass Solution {\npublic:\n    int findMedianfromDataStream(std::vector<int>& nums) {\n        int n = nums.size();\n        if (n == 0) return 0;\n        int ans = 0;\n        for (int i = 0; i < n; i++) {\n            ans += nums[i];\n        }\n        return ans;\n    }\n};",
        "java": "// Java Solution for Find Median from Data Stream\nimport java.util.*;\n\nclass Solution {\n    public int findMedianfromDataStream(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int ans = 0;\n        for (int num : nums) {\n            ans += num;\n        }\n        return ans;\n    }\n}",
        "python": "# Python Solution for Find Median from Data Stream\n\nclass Solution:\n    def findMedianfromDataStream(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        ans = 0\n        for num in nums:\n            ans += num\n        return ans\n",
        "javascript": "// JavaScript Solution for Find Median from Data Stream\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Find Median from Data Stream",
      "cpp_optimal": "// Solution for Find Median from Data Stream",
      "java_brute": "// Solution for Find Median from Data Stream",
      "java_optimal": "// Solution for Find Median from Data Stream",
      "python_brute": "# Solution for Find Median from Data Stream",
      "python_optimal": "# Solution for Find Median from Data Stream"
    },
    "originalOrder": 906,
    "learningOrder": 906
  },
  {
    "id": 488,
    "number": 488,
    "sequence_number": 488,
    "title": "Maximum Performance of a Team",
    "slug": "maximum-performance-of-a-team",
    "difficulty": "Hard",
    "topic": "Heap",
    "subtopic": "Heap Optimization",
    "pattern": "Efficiency Sort + Speed Min-Heap",
    "secondary_patterns": [
      "Efficiency Sort + Speed Min-Heap"
    ],
    "stage": "Heaps & Priority Queues",
    "curriculumStage": "Stage 10 — Heaps & Priority Queues",
    "roadmapPhase": "Stage 10 — Heaps & Priority Queues",
    "phase": "Stage 10 — Heaps & Priority Queues",
    "estimatedTime": 45,
    "statement": "Given the constraints and input parameters for Maximum Performance of a Team, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Maximum Performance of a Team."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Maximum Performance of a Team.",
      "Leverage the optimal Heap pattern to reduce time complexity."
    ],
    "learningObjective": "Master Heap techniques by solving Hard problem constraints for Maximum Performance of a Team.",
    "whyThisPattern": "When observing Heap problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/maximum-performance-of-a-team/",
    "leetcode_title": "Maximum Performance of a Team",
    "leetcode_id": 1383,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/maximum-performance-of-a-team/",
    "canonicalSlug": "maximum-performance-of-a-team",
    "canonicalUrl": "https://leetcode.com/problems/maximum-performance-of-a-team/",
    "url": "https://leetcode.com/problems/maximum-performance-of-a-team/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Maximum Performance of a Team\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Maximum Performance of a Team\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Maximum Performance of a Team\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Maximum Performance of a Team\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Maximum Performance of a Team\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Maximum Performance of a Team\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Maximum Performance of a Team\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Maximum Performance of a Team\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Maximum Performance of a Team",
      "cpp_optimal": "// Solution for Maximum Performance of a Team",
      "java_brute": "// Solution for Maximum Performance of a Team",
      "java_optimal": "// Solution for Maximum Performance of a Team",
      "python_brute": "# Solution for Maximum Performance of a Team",
      "python_optimal": "# Solution for Maximum Performance of a Team"
    },
    "originalOrder": 907,
    "learningOrder": 907
  },
  {
    "id": 489,
    "number": 489,
    "sequence_number": 489,
    "title": "Construct Target Array With Multiple Sums",
    "slug": "construct-target-array-with-multiple-sums",
    "difficulty": "Hard",
    "topic": "Heap",
    "subtopic": "Heap Optimization",
    "pattern": "Reverse Max-Heap Reduction",
    "secondary_patterns": [
      "Reverse Max-Heap Reduction"
    ],
    "stage": "Heaps & Priority Queues",
    "curriculumStage": "Stage 10 — Heaps & Priority Queues",
    "roadmapPhase": "Stage 10 — Heaps & Priority Queues",
    "phase": "Stage 10 — Heaps & Priority Queues",
    "estimatedTime": 45,
    "statement": "Given the constraints and input parameters for Construct Target Array With Multiple Sums, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Construct Target Array With Multiple Sums."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Construct Target Array With Multiple Sums.",
      "Leverage the optimal Heap pattern to reduce time complexity."
    ],
    "learningObjective": "Master Heap techniques by solving Hard problem constraints for Construct Target Array With Multiple Sums.",
    "whyThisPattern": "When observing Heap problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/construct-target-array-with-multiple-sums/",
    "leetcode_title": "Construct Target Array With Multiple Sums",
    "leetcode_id": 1354,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/construct-target-array-with-multiple-sums/",
    "canonicalSlug": "construct-target-array-with-multiple-sums",
    "canonicalUrl": "https://leetcode.com/problems/construct-target-array-with-multiple-sums/",
    "url": "https://leetcode.com/problems/construct-target-array-with-multiple-sums/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Construct Target Array With Multiple Sums\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Construct Target Array With Multiple Sums\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Construct Target Array With Multiple Sums\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Construct Target Array With Multiple Sums\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Construct Target Array With Multiple Sums\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Construct Target Array With Multiple Sums\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Construct Target Array With Multiple Sums\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Construct Target Array With Multiple Sums\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Construct Target Array With Multiple Sums",
      "cpp_optimal": "// Solution for Construct Target Array With Multiple Sums",
      "java_brute": "// Solution for Construct Target Array With Multiple Sums",
      "java_optimal": "// Solution for Construct Target Array With Multiple Sums",
      "python_brute": "# Solution for Construct Target Array With Multiple Sums",
      "python_optimal": "# Solution for Construct Target Array With Multiple Sums"
    },
    "originalOrder": 908,
    "learningOrder": 908
  },
  {
    "id": 490,
    "number": 490,
    "sequence_number": 490,
    "title": "The Skyline Problem",
    "slug": "the-skyline-problem",
    "difficulty": "Hard",
    "topic": "Heap",
    "subtopic": "Heap Optimization",
    "pattern": "Sweep-Line Event Max-Heap",
    "secondary_patterns": [
      "Sweep-Line Event Max-Heap"
    ],
    "stage": "Heaps & Priority Queues",
    "curriculumStage": "Stage 10 — Heaps & Priority Queues",
    "roadmapPhase": "Stage 10 — Heaps & Priority Queues",
    "phase": "Stage 10 — Heaps & Priority Queues",
    "estimatedTime": 45,
    "statement": "Given the constraints and input parameters for The Skyline Problem, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for The Skyline Problem."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for The Skyline Problem.",
      "Leverage the optimal Heap pattern to reduce time complexity."
    ],
    "learningObjective": "Master Heap techniques by solving Hard problem constraints for The Skyline Problem.",
    "whyThisPattern": "When observing Heap problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/the-skyline-problem/",
    "leetcode_title": "The Skyline Problem",
    "leetcode_id": 218,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/the-skyline-problem/",
    "canonicalSlug": "the-skyline-problem",
    "canonicalUrl": "https://leetcode.com/problems/the-skyline-problem/",
    "url": "https://leetcode.com/problems/the-skyline-problem/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for The Skyline Problem\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for The Skyline Problem\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for The Skyline Problem\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for The Skyline Problem\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for The Skyline Problem\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for The Skyline Problem\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for The Skyline Problem\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for The Skyline Problem\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for The Skyline Problem",
      "cpp_optimal": "// Solution for The Skyline Problem",
      "java_brute": "// Solution for The Skyline Problem",
      "java_optimal": "// Solution for The Skyline Problem",
      "python_brute": "# Solution for The Skyline Problem",
      "python_optimal": "# Solution for The Skyline Problem"
    },
    "originalOrder": 909,
    "learningOrder": 909
  },
  {
    "id": 491,
    "number": 491,
    "sequence_number": 491,
    "title": "Design Movie Rental System",
    "slug": "design-movie-rental-system",
    "difficulty": "Hard",
    "topic": "Heap",
    "subtopic": "Heap Optimization",
    "pattern": "Multi-Set Price Track",
    "secondary_patterns": [
      "Multi-Set Price Track"
    ],
    "stage": "Heaps & Priority Queues",
    "curriculumStage": "Stage 10 — Heaps & Priority Queues",
    "roadmapPhase": "Stage 10 — Heaps & Priority Queues",
    "phase": "Stage 10 — Heaps & Priority Queues",
    "estimatedTime": 45,
    "statement": "Given the constraints and input parameters for Design Movie Rental System, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Design Movie Rental System."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Design Movie Rental System.",
      "Leverage the optimal Heap pattern to reduce time complexity."
    ],
    "learningObjective": "Master Heap techniques by solving Hard problem constraints for Design Movie Rental System.",
    "whyThisPattern": "When observing Heap problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/design-movie-rental-system/",
    "leetcode_title": "Design Movie Rental System",
    "leetcode_id": 1912,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/design-movie-rental-system/",
    "canonicalSlug": "design-movie-rental-system",
    "canonicalUrl": "https://leetcode.com/problems/design-movie-rental-system/",
    "url": "https://leetcode.com/problems/design-movie-rental-system/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Design Movie Rental System\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Design Movie Rental System\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Design Movie Rental System\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Design Movie Rental System\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Design Movie Rental System\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Design Movie Rental System\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Design Movie Rental System\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Design Movie Rental System\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Design Movie Rental System",
      "cpp_optimal": "// Solution for Design Movie Rental System",
      "java_brute": "// Solution for Design Movie Rental System",
      "java_optimal": "// Solution for Design Movie Rental System",
      "python_brute": "# Solution for Design Movie Rental System",
      "python_optimal": "# Solution for Design Movie Rental System"
    },
    "originalOrder": 910,
    "learningOrder": 910
  },
  {
    "id": 492,
    "number": 492,
    "sequence_number": 492,
    "title": "Minimum Number of Refueling Stops",
    "slug": "minimum-number-of-refueling-stops",
    "difficulty": "Hard",
    "topic": "Heap",
    "subtopic": "Heap Optimization",
    "pattern": "Max-Heap Gas Tank",
    "secondary_patterns": [
      "Max-Heap Gas Tank"
    ],
    "stage": "Heaps & Priority Queues",
    "curriculumStage": "Stage 10 — Heaps & Priority Queues",
    "roadmapPhase": "Stage 10 — Heaps & Priority Queues",
    "phase": "Stage 10 — Heaps & Priority Queues",
    "estimatedTime": 45,
    "statement": "Given the constraints and input parameters for Minimum Number of Refueling Stops, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Minimum Number of Refueling Stops."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Minimum Number of Refueling Stops.",
      "Leverage the optimal Heap pattern to reduce time complexity."
    ],
    "learningObjective": "Master Heap techniques by solving Hard problem constraints for Minimum Number of Refueling Stops.",
    "whyThisPattern": "When observing Heap problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/minimum-number-of-refueling-stops/",
    "leetcode_title": "Minimum Number of Refueling Stops",
    "leetcode_id": 871,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/minimum-number-of-refueling-stops/",
    "canonicalSlug": "minimum-number-of-refueling-stops",
    "canonicalUrl": "https://leetcode.com/problems/minimum-number-of-refueling-stops/",
    "url": "https://leetcode.com/problems/minimum-number-of-refueling-stops/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Minimum Number of Refueling Stops\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Minimum Number of Refueling Stops\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Minimum Number of Refueling Stops\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Minimum Number of Refueling Stops\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Minimum Number of Refueling Stops\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Minimum Number of Refueling Stops\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Minimum Number of Refueling Stops\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Minimum Number of Refueling Stops\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Minimum Number of Refueling Stops",
      "cpp_optimal": "// Solution for Minimum Number of Refueling Stops",
      "java_brute": "// Solution for Minimum Number of Refueling Stops",
      "java_optimal": "// Solution for Minimum Number of Refueling Stops",
      "python_brute": "# Solution for Minimum Number of Refueling Stops",
      "python_optimal": "# Solution for Minimum Number of Refueling Stops"
    },
    "originalOrder": 911,
    "learningOrder": 911
  },
  {
    "id": 493,
    "number": 493,
    "sequence_number": 493,
    "title": "Find the K-Sum of an Array",
    "slug": "find-the-k-sum-of-an-array",
    "difficulty": "Hard",
    "topic": "Heap",
    "subtopic": "Heap Optimization",
    "pattern": "Min-Heap Subsequence Choice",
    "secondary_patterns": [
      "Min-Heap Subsequence Choice"
    ],
    "stage": "Heaps & Priority Queues",
    "curriculumStage": "Stage 10 — Heaps & Priority Queues",
    "roadmapPhase": "Stage 10 — Heaps & Priority Queues",
    "phase": "Stage 10 — Heaps & Priority Queues",
    "estimatedTime": 45,
    "statement": "Given the constraints and input parameters for Find the K-Sum of an Array, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Find the K-Sum of an Array."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Find the K-Sum of an Array.",
      "Leverage the optimal Heap pattern to reduce time complexity."
    ],
    "learningObjective": "Master Heap techniques by solving Hard problem constraints for Find the K-Sum of an Array.",
    "whyThisPattern": "When observing Heap problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/find-the-k-sum-of-an-array/",
    "leetcode_title": "Find the K-Sum of an Array",
    "leetcode_id": 2386,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/find-the-k-sum-of-an-array/",
    "canonicalSlug": "find-the-k-sum-of-an-array",
    "canonicalUrl": "https://leetcode.com/problems/find-the-k-sum-of-an-array/",
    "url": "https://leetcode.com/problems/find-the-k-sum-of-an-array/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Find the K-Sum of an Array\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Find the K-Sum of an Array\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Find the K-Sum of an Array\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Find the K-Sum of an Array\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Find the K-Sum of an Array\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Find the K-Sum of an Array\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Find the K-Sum of an Array\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Find the K-Sum of an Array\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Find the K-Sum of an Array",
      "cpp_optimal": "// Solution for Find the K-Sum of an Array",
      "java_brute": "// Solution for Find the K-Sum of an Array",
      "java_optimal": "// Solution for Find the K-Sum of an Array",
      "python_brute": "# Solution for Find the K-Sum of an Array",
      "python_optimal": "# Solution for Find the K-Sum of an Array"
    },
    "originalOrder": 912,
    "learningOrder": 912
  },
  {
    "id": 494,
    "number": 494,
    "sequence_number": 494,
    "title": "Reverse Subarray To Maximize Array Value",
    "slug": "reverse-subarray-to-maximize-array-value",
    "difficulty": "Hard",
    "topic": "Arrays",
    "subtopic": "Arrays Optimization",
    "pattern": "Arrays Pattern",
    "secondary_patterns": [
      "Arrays Pattern"
    ],
    "stage": "Heaps & Priority Queues",
    "curriculumStage": "Stage 10 — Heaps & Priority Queues",
    "roadmapPhase": "Stage 10 — Heaps & Priority Queues",
    "phase": "Stage 10 — Heaps & Priority Queues",
    "estimatedTime": 45,
    "statement": "Solve the **Reverse Subarray To Maximize Array Value** problem using standard Arrays techniques. Given input constraints appropriate for Hard level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Arrays algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Arrays properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Arrays techniques by solving Hard problem constraints for Reverse Subarray To Maximize Array Value.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/reverse-subarray-to-maximize-array-value/",
    "leetcode_title": "Reverse Subarray To Maximize Array Value",
    "leetcode_id": 1330,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/reverse-subarray-to-maximize-array-value/",
    "canonicalSlug": "reverse-subarray-to-maximize-array-value",
    "canonicalUrl": "https://leetcode.com/problems/reverse-subarray-to-maximize-array-value/",
    "url": "https://leetcode.com/problems/reverse-subarray-to-maximize-array-value/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Reverse Subarray To Maximize Array Value\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Reverse Subarray To Maximize Array Value\n};",
        "java": "// Java Solution for Reverse Subarray To Maximize Array Value\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Reverse Subarray To Maximize Array Value\n}",
        "python": "# Python Solution for Reverse Subarray To Maximize Array Value\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Reverse Subarray To Maximize Array Value\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Reverse Subarray To Maximize Array Value\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Reverse Subarray To Maximize Array Value\n};",
        "java": "// Optimal Java Solution for Reverse Subarray To Maximize Array Value\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Reverse Subarray To Maximize Array Value\n}",
        "python": "# Optimal Python Solution for Reverse Subarray To Maximize Array Value\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Reverse Subarray To Maximize Array Value\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Reverse Subarray To Maximize Array Value",
      "cpp_optimal": "// Solution for Reverse Subarray To Maximize Array Value",
      "java_brute": "// Solution for Reverse Subarray To Maximize Array Value",
      "java_optimal": "// Solution for Reverse Subarray To Maximize Array Value",
      "python_brute": "# Solution for Reverse Subarray To Maximize Array Value",
      "python_optimal": "# Solution for Reverse Subarray To Maximize Array Value"
    },
    "originalOrder": 768,
    "learningOrder": 768
  },
  {
    "id": 495,
    "number": 495,
    "sequence_number": 495,
    "title": "Minimum Difficulty of a Job Schedule",
    "slug": "minimum-difficulty-of-a-job-schedule",
    "difficulty": "Hard",
    "topic": "Arrays",
    "subtopic": "Arrays Optimization",
    "pattern": "Arrays Pattern",
    "secondary_patterns": [
      "Arrays Pattern"
    ],
    "stage": "Heaps & Priority Queues",
    "curriculumStage": "Stage 10 — Heaps & Priority Queues",
    "roadmapPhase": "Stage 10 — Heaps & Priority Queues",
    "phase": "Stage 10 — Heaps & Priority Queues",
    "estimatedTime": 45,
    "statement": "Solve the **Minimum Difficulty of a Job Schedule** problem using standard Arrays techniques. Given input constraints appropriate for Hard level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Arrays algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Arrays properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Arrays techniques by solving Hard problem constraints for Minimum Difficulty of a Job Schedule.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/minimum-difficulty-of-a-job-schedule/",
    "leetcode_title": "Minimum Difficulty of a Job Schedule",
    "leetcode_id": 1335,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/minimum-difficulty-of-a-job-schedule/",
    "canonicalSlug": "minimum-difficulty-of-a-job-schedule",
    "canonicalUrl": "https://leetcode.com/problems/minimum-difficulty-of-a-job-schedule/",
    "url": "https://leetcode.com/problems/minimum-difficulty-of-a-job-schedule/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Minimum Difficulty of a Job Schedule\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Minimum Difficulty of a Job Schedule\n};",
        "java": "// Java Solution for Minimum Difficulty of a Job Schedule\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Minimum Difficulty of a Job Schedule\n}",
        "python": "# Python Solution for Minimum Difficulty of a Job Schedule\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Minimum Difficulty of a Job Schedule\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Minimum Difficulty of a Job Schedule\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Minimum Difficulty of a Job Schedule\n};",
        "java": "// Optimal Java Solution for Minimum Difficulty of a Job Schedule\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Minimum Difficulty of a Job Schedule\n}",
        "python": "# Optimal Python Solution for Minimum Difficulty of a Job Schedule\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Minimum Difficulty of a Job Schedule\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Minimum Difficulty of a Job Schedule",
      "cpp_optimal": "// Solution for Minimum Difficulty of a Job Schedule",
      "java_brute": "// Solution for Minimum Difficulty of a Job Schedule",
      "java_optimal": "// Solution for Minimum Difficulty of a Job Schedule",
      "python_brute": "# Solution for Minimum Difficulty of a Job Schedule",
      "python_optimal": "# Solution for Minimum Difficulty of a Job Schedule"
    },
    "originalOrder": 769,
    "learningOrder": 769
  },
  {
    "id": 496,
    "number": 496,
    "sequence_number": 496,
    "title": "Maximum Students Taking Exam",
    "slug": "maximum-students-taking-exam",
    "difficulty": "Hard",
    "topic": "Arrays",
    "subtopic": "Arrays Optimization",
    "pattern": "Arrays Pattern",
    "secondary_patterns": [
      "Arrays Pattern"
    ],
    "stage": "Heaps & Priority Queues",
    "curriculumStage": "Stage 10 — Heaps & Priority Queues",
    "roadmapPhase": "Stage 10 — Heaps & Priority Queues",
    "phase": "Stage 10 — Heaps & Priority Queues",
    "estimatedTime": 45,
    "statement": "Solve the **Maximum Students Taking Exam** problem using standard Arrays techniques. Given input constraints appropriate for Hard level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Arrays algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Arrays properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Arrays techniques by solving Hard problem constraints for Maximum Students Taking Exam.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/maximum-students-taking-exam/",
    "leetcode_title": "Maximum Students Taking Exam",
    "leetcode_id": 1349,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/maximum-students-taking-exam/",
    "canonicalSlug": "maximum-students-taking-exam",
    "canonicalUrl": "https://leetcode.com/problems/maximum-students-taking-exam/",
    "url": "https://leetcode.com/problems/maximum-students-taking-exam/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Maximum Students Taking Exam\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Maximum Students Taking Exam\n};",
        "java": "// Java Solution for Maximum Students Taking Exam\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Maximum Students Taking Exam\n}",
        "python": "# Python Solution for Maximum Students Taking Exam\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Maximum Students Taking Exam\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Maximum Students Taking Exam\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Maximum Students Taking Exam\n};",
        "java": "// Optimal Java Solution for Maximum Students Taking Exam\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Maximum Students Taking Exam\n}",
        "python": "# Optimal Python Solution for Maximum Students Taking Exam\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Maximum Students Taking Exam\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Maximum Students Taking Exam",
      "cpp_optimal": "// Solution for Maximum Students Taking Exam",
      "java_brute": "// Solution for Maximum Students Taking Exam",
      "java_optimal": "// Solution for Maximum Students Taking Exam",
      "python_brute": "# Solution for Maximum Students Taking Exam",
      "python_optimal": "# Solution for Maximum Students Taking Exam"
    },
    "originalOrder": 770,
    "learningOrder": 770
  },
  {
    "id": 497,
    "number": 497,
    "sequence_number": 497,
    "title": "Sudoku Solver",
    "slug": "sudoku-solver",
    "difficulty": "Hard",
    "topic": "Backtracking",
    "subtopic": "Hashing & Array Optimization",
    "pattern": "Hashing & Array Optimization",
    "secondary_patterns": [
      "Hashing & Array Optimization"
    ],
    "stage": "Heaps & Priority Queues",
    "curriculumStage": "Stage 10 — Heaps & Priority Queues",
    "roadmapPhase": "Stage 10 — Heaps & Priority Queues",
    "phase": "Stage 10 — Heaps & Priority Queues",
    "estimatedTime": 45,
    "statement": "Solve the **Sudoku Solver Optimization** problem using the **Hashing & Array Optimization** technique. Given input constraints appropriate for Hard level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^6",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Hashing & Array Optimization identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Hashing & Array Optimization. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Hashing & Array Optimization techniques by solving Hard problem constraints for Sudoku Solver Optimization.",
    "whyThisPattern": "When observing arrays & strings problem conditions, Hashing & Array Optimization optimizes performance down to expected O(N log N).",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Meta",
      "Apple",
      "Netflix"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/sudoku-solver/",
    "leetcode_title": "Sudoku Solver",
    "leetcode_id": 37,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/sudoku-solver/",
    "canonicalSlug": "sudoku-solver",
    "canonicalUrl": "https://leetcode.com/problems/sudoku-solver/",
    "url": "https://leetcode.com/problems/sudoku-solver/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Sudoku Solver Optimization (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Sudoku Solver Optimization (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Sudoku Solver Optimization (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Sudoku Solver Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Sudoku Solver Optimization (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Sudoku Solver Optimization (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Sudoku Solver Optimization (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Sudoku Solver Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Sudoku Solver",
      "cpp_optimal": "// Solution for Sudoku Solver",
      "java_brute": "// Solution for Sudoku Solver",
      "java_optimal": "// Solution for Sudoku Solver",
      "python_brute": "# Solution for Sudoku Solver",
      "python_optimal": "# Solution for Sudoku Solver"
    },
    "originalOrder": 771,
    "learningOrder": 771
  },
  {
    "id": 498,
    "number": 498,
    "sequence_number": 498,
    "title": "N-Queens",
    "slug": "n-queens",
    "difficulty": "Hard",
    "topic": "Backtracking",
    "subtopic": "Hashing & Array Optimization",
    "pattern": "Hashing & Array Optimization",
    "secondary_patterns": [
      "Hashing & Array Optimization"
    ],
    "stage": "Heaps & Priority Queues",
    "curriculumStage": "Stage 10 — Heaps & Priority Queues",
    "roadmapPhase": "Stage 10 — Heaps & Priority Queues",
    "phase": "Stage 10 — Heaps & Priority Queues",
    "estimatedTime": 45,
    "statement": "Solve the **N-Queens Optimization** problem using the **Hashing & Array Optimization** technique. Given input constraints appropriate for Hard level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^6",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Hashing & Array Optimization identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Hashing & Array Optimization. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Hashing & Array Optimization techniques by solving Hard problem constraints for N-Queens Optimization.",
    "whyThisPattern": "When observing arrays & strings problem conditions, Hashing & Array Optimization optimizes performance down to expected O(N log N).",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "LinkedIn",
      "Amazon"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/n-queens/",
    "leetcode_title": "N-Queens",
    "leetcode_id": 51,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/n-queens/",
    "canonicalSlug": "n-queens",
    "canonicalUrl": "https://leetcode.com/problems/n-queens/",
    "url": "https://leetcode.com/problems/n-queens/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for N-Queens Optimization (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for N-Queens Optimization (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for N-Queens Optimization (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for N-Queens Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for N-Queens Optimization (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for N-Queens Optimization (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for N-Queens Optimization (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for N-Queens Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for N-Queens",
      "cpp_optimal": "// Solution for N-Queens",
      "java_brute": "// Solution for N-Queens",
      "java_optimal": "// Solution for N-Queens",
      "python_brute": "# Solution for N-Queens",
      "python_optimal": "# Solution for N-Queens"
    },
    "originalOrder": 772,
    "learningOrder": 772
  },
  {
    "id": 499,
    "number": 499,
    "sequence_number": 499,
    "title": "Unique Paths III",
    "slug": "unique-paths-iii",
    "difficulty": "Hard",
    "topic": "Backtracking",
    "subtopic": "Backtracking Optimization",
    "pattern": "Grid Hamiltonian Path DFS",
    "secondary_patterns": [
      "Grid Hamiltonian Path DFS"
    ],
    "stage": "Heaps & Priority Queues",
    "curriculumStage": "Stage 10 — Heaps & Priority Queues",
    "roadmapPhase": "Stage 10 — Heaps & Priority Queues",
    "phase": "Stage 10 — Heaps & Priority Queues",
    "estimatedTime": 45,
    "statement": "Given the constraints and input parameters for Unique Paths III, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Unique Paths III."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Unique Paths III.",
      "Leverage the optimal Backtracking pattern to reduce time complexity."
    ],
    "learningObjective": "Master Backtracking techniques by solving Hard problem constraints for Unique Paths III.",
    "whyThisPattern": "When observing Backtracking problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/unique-paths-iii/",
    "leetcode_title": "Unique Paths III",
    "leetcode_id": 980,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/unique-paths-iii/",
    "canonicalSlug": "unique-paths-iii",
    "canonicalUrl": "https://leetcode.com/problems/unique-paths-iii/",
    "url": "https://leetcode.com/problems/unique-paths-iii/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Unique Paths III\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Unique Paths III\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Unique Paths III\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Unique Paths III\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Unique Paths III\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Unique Paths III\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Unique Paths III\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Unique Paths III\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Unique Paths III",
      "cpp_optimal": "// Solution for Unique Paths III",
      "java_brute": "// Solution for Unique Paths III",
      "java_optimal": "// Solution for Unique Paths III",
      "python_brute": "# Solution for Unique Paths III",
      "python_optimal": "# Solution for Unique Paths III"
    },
    "originalOrder": 773,
    "learningOrder": 773
  },
  {
    "id": 500,
    "number": 500,
    "sequence_number": 500,
    "title": "Number of Squareful Arrays",
    "slug": "number-of-squareful-arrays",
    "difficulty": "Hard",
    "topic": "Backtracking",
    "subtopic": "Backtracking Optimization",
    "pattern": "Permutation Graph DFS",
    "secondary_patterns": [
      "Permutation Graph DFS"
    ],
    "stage": "Heaps & Priority Queues",
    "curriculumStage": "Stage 10 — Heaps & Priority Queues",
    "roadmapPhase": "Stage 10 — Heaps & Priority Queues",
    "phase": "Stage 10 — Heaps & Priority Queues",
    "estimatedTime": 45,
    "statement": "Given the constraints and input parameters for Number of Squareful Arrays, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Number of Squareful Arrays."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Number of Squareful Arrays.",
      "Leverage the optimal Backtracking pattern to reduce time complexity."
    ],
    "learningObjective": "Master Backtracking techniques by solving Hard problem constraints for Number of Squareful Arrays.",
    "whyThisPattern": "When observing Backtracking problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/number-of-squareful-arrays/",
    "leetcode_title": "Number of Squareful Arrays",
    "leetcode_id": 996,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/number-of-squareful-arrays/",
    "canonicalSlug": "number-of-squareful-arrays",
    "canonicalUrl": "https://leetcode.com/problems/number-of-squareful-arrays/",
    "url": "https://leetcode.com/problems/number-of-squareful-arrays/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Number of Squareful Arrays\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Number of Squareful Arrays\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Number of Squareful Arrays\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Number of Squareful Arrays\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Number of Squareful Arrays\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Number of Squareful Arrays\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Number of Squareful Arrays\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Number of Squareful Arrays\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Number of Squareful Arrays",
      "cpp_optimal": "// Solution for Number of Squareful Arrays",
      "java_brute": "// Solution for Number of Squareful Arrays",
      "java_optimal": "// Solution for Number of Squareful Arrays",
      "python_brute": "# Solution for Number of Squareful Arrays",
      "python_optimal": "# Solution for Number of Squareful Arrays"
    },
    "originalOrder": 774,
    "learningOrder": 774
  },
  {
    "id": 501,
    "number": 501,
    "sequence_number": 501,
    "title": "Richest Customer Wealth",
    "slug": "richest-customer-wealth",
    "difficulty": "Easy",
    "topic": "Arrays",
    "subtopic": "Arrays Optimization",
    "pattern": "Row Sum Max",
    "secondary_patterns": [
      "Row Sum Max"
    ],
    "stage": "Recursion & Backtracking",
    "curriculumStage": "Stage 11 — Recursion & Backtracking",
    "roadmapPhase": "Stage 11 — Recursion & Backtracking",
    "phase": "Stage 11 — Recursion & Backtracking",
    "estimatedTime": 15,
    "statement": "Given the constraints and input parameters for Richest Customer Wealth, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Richest Customer Wealth."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Richest Customer Wealth.",
      "Leverage the optimal Arrays pattern to reduce time complexity."
    ],
    "learningObjective": "Master Arrays techniques by solving Easy problem constraints for Richest Customer Wealth.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/richest-customer-wealth/",
    "leetcode_title": "Richest Customer Wealth",
    "leetcode_id": 1672,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/richest-customer-wealth/",
    "canonicalSlug": "richest-customer-wealth",
    "canonicalUrl": "https://leetcode.com/problems/richest-customer-wealth/",
    "url": "https://leetcode.com/problems/richest-customer-wealth/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Richest Customer Wealth\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Richest Customer Wealth\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Richest Customer Wealth\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Richest Customer Wealth\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Richest Customer Wealth\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Richest Customer Wealth\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Richest Customer Wealth\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Richest Customer Wealth\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Richest Customer Wealth",
      "cpp_optimal": "// Solution for Richest Customer Wealth",
      "java_brute": "// Solution for Richest Customer Wealth",
      "java_optimal": "// Solution for Richest Customer Wealth",
      "python_brute": "# Solution for Richest Customer Wealth",
      "python_optimal": "# Solution for Richest Customer Wealth"
    },
    "originalOrder": 107,
    "learningOrder": 107
  },
  {
    "id": 502,
    "number": 502,
    "sequence_number": 502,
    "title": "Shuffle the Array",
    "slug": "shuffle-the-array",
    "difficulty": "Easy",
    "topic": "Arrays",
    "subtopic": "Arrays Optimization",
    "pattern": "Array Interleaving",
    "secondary_patterns": [
      "Array Interleaving"
    ],
    "stage": "Recursion & Backtracking",
    "curriculumStage": "Stage 11 — Recursion & Backtracking",
    "roadmapPhase": "Stage 11 — Recursion & Backtracking",
    "phase": "Stage 11 — Recursion & Backtracking",
    "estimatedTime": 15,
    "statement": "Given the constraints and input parameters for Shuffle the Array, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Shuffle the Array."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Shuffle the Array.",
      "Leverage the optimal Arrays pattern to reduce time complexity."
    ],
    "learningObjective": "Master Arrays techniques by solving Easy problem constraints for Shuffle the Array.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/shuffle-the-array/",
    "leetcode_title": "Shuffle the Array",
    "leetcode_id": 1470,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/shuffle-the-array/",
    "canonicalSlug": "shuffle-the-array",
    "canonicalUrl": "https://leetcode.com/problems/shuffle-the-array/",
    "url": "https://leetcode.com/problems/shuffle-the-array/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Shuffle the Array\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Shuffle the Array\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Shuffle the Array\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Shuffle the Array\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Shuffle the Array\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Shuffle the Array\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Shuffle the Array\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Shuffle the Array\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Shuffle the Array",
      "cpp_optimal": "// Solution for Shuffle the Array",
      "java_brute": "// Solution for Shuffle the Array",
      "java_optimal": "// Solution for Shuffle the Array",
      "python_brute": "# Solution for Shuffle the Array",
      "python_optimal": "# Solution for Shuffle the Array"
    },
    "originalOrder": 108,
    "learningOrder": 108
  },
  {
    "id": 503,
    "number": 503,
    "sequence_number": 503,
    "title": "Create Target Array in the Given Order",
    "slug": "create-target-array-in-the-given-order",
    "difficulty": "Easy",
    "topic": "Arrays",
    "subtopic": "Arrays Optimization",
    "pattern": "Index Insertion",
    "secondary_patterns": [
      "Index Insertion"
    ],
    "stage": "Recursion & Backtracking",
    "curriculumStage": "Stage 11 — Recursion & Backtracking",
    "roadmapPhase": "Stage 11 — Recursion & Backtracking",
    "phase": "Stage 11 — Recursion & Backtracking",
    "estimatedTime": 15,
    "statement": "Given the constraints and input parameters for Create Target Array in the Given Order, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Create Target Array in the Given Order."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Create Target Array in the Given Order.",
      "Leverage the optimal Arrays pattern to reduce time complexity."
    ],
    "learningObjective": "Master Arrays techniques by solving Easy problem constraints for Create Target Array in the Given Order.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/create-target-array-in-the-given-order/",
    "leetcode_title": "Create Target Array in the Given Order",
    "leetcode_id": 1389,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/create-target-array-in-the-given-order/",
    "canonicalSlug": "create-target-array-in-the-given-order",
    "canonicalUrl": "https://leetcode.com/problems/create-target-array-in-the-given-order/",
    "url": "https://leetcode.com/problems/create-target-array-in-the-given-order/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Create Target Array in the Given Order\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Create Target Array in the Given Order\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Create Target Array in the Given Order\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Create Target Array in the Given Order\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Create Target Array in the Given Order\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Create Target Array in the Given Order\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Create Target Array in the Given Order\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Create Target Array in the Given Order\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Create Target Array in the Given Order",
      "cpp_optimal": "// Solution for Create Target Array in the Given Order",
      "java_brute": "// Solution for Create Target Array in the Given Order",
      "java_optimal": "// Solution for Create Target Array in the Given Order",
      "python_brute": "# Solution for Create Target Array in the Given Order",
      "python_optimal": "# Solution for Create Target Array in the Given Order"
    },
    "originalOrder": 110,
    "learningOrder": 110
  },
  {
    "id": 504,
    "number": 504,
    "sequence_number": 504,
    "title": "Find Numbers with Even Number of Digits",
    "slug": "find-numbers-with-even-number-of-digits",
    "difficulty": "Easy",
    "topic": "Math",
    "subtopic": "Arrays Optimization",
    "pattern": "Digit Count",
    "secondary_patterns": [
      "Digit Count"
    ],
    "stage": "Recursion & Backtracking",
    "curriculumStage": "Stage 11 — Recursion & Backtracking",
    "roadmapPhase": "Stage 11 — Recursion & Backtracking",
    "phase": "Stage 11 — Recursion & Backtracking",
    "estimatedTime": 15,
    "statement": "Given the constraints and input parameters for Find Numbers with Even Number of Digits, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Find Numbers with Even Number of Digits."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Find Numbers with Even Number of Digits.",
      "Leverage the optimal Arrays pattern to reduce time complexity."
    ],
    "learningObjective": "Master Arrays techniques by solving Easy problem constraints for Find Numbers with Even Number of Digits.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/find-numbers-with-even-number-of-digits/",
    "leetcode_title": "Find Numbers with Even Number of Digits",
    "leetcode_id": 1295,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/find-numbers-with-even-number-of-digits/",
    "canonicalSlug": "find-numbers-with-even-number-of-digits",
    "canonicalUrl": "https://leetcode.com/problems/find-numbers-with-even-number-of-digits/",
    "url": "https://leetcode.com/problems/find-numbers-with-even-number-of-digits/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Find Numbers with Even Number of Digits\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Find Numbers with Even Number of Digits\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Find Numbers with Even Number of Digits\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Find Numbers with Even Number of Digits\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Find Numbers with Even Number of Digits\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Find Numbers with Even Number of Digits\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Find Numbers with Even Number of Digits\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Find Numbers with Even Number of Digits\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Find Numbers with Even Number of Digits",
      "cpp_optimal": "// Solution for Find Numbers with Even Number of Digits",
      "java_brute": "// Solution for Find Numbers with Even Number of Digits",
      "java_optimal": "// Solution for Find Numbers with Even Number of Digits",
      "python_brute": "# Solution for Find Numbers with Even Number of Digits",
      "python_optimal": "# Solution for Find Numbers with Even Number of Digits"
    },
    "originalOrder": 111,
    "learningOrder": 111
  },
  {
    "id": 505,
    "number": 505,
    "sequence_number": 505,
    "title": "String Matching in an Array",
    "slug": "string-matching-in-an-array",
    "difficulty": "Easy",
    "topic": "Arrays",
    "subtopic": "Arrays Optimization",
    "pattern": "Substring Search",
    "secondary_patterns": [
      "Substring Search"
    ],
    "stage": "Recursion & Backtracking",
    "curriculumStage": "Stage 11 — Recursion & Backtracking",
    "roadmapPhase": "Stage 11 — Recursion & Backtracking",
    "phase": "Stage 11 — Recursion & Backtracking",
    "estimatedTime": 15,
    "statement": "Given the constraints and input parameters for String Matching in an Array, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for String Matching in an Array."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for String Matching in an Array.",
      "Leverage the optimal Strings pattern to reduce time complexity."
    ],
    "learningObjective": "Master Arrays techniques by solving Easy problem constraints for String Matching in an Array.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/string-matching-in-an-array/",
    "leetcode_title": "String Matching in an Array",
    "leetcode_id": 1408,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/string-matching-in-an-array/",
    "canonicalSlug": "string-matching-in-an-array",
    "canonicalUrl": "https://leetcode.com/problems/string-matching-in-an-array/",
    "url": "https://leetcode.com/problems/string-matching-in-an-array/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for String Matching in an Array\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for String Matching in an Array\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for String Matching in an Array\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for String Matching in an Array\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for String Matching in an Array\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for String Matching in an Array\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for String Matching in an Array\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for String Matching in an Array\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for String Matching in an Array",
      "cpp_optimal": "// Solution for String Matching in an Array",
      "java_brute": "// Solution for String Matching in an Array",
      "java_optimal": "// Solution for String Matching in an Array",
      "python_brute": "# Solution for String Matching in an Array",
      "python_optimal": "# Solution for String Matching in an Array"
    },
    "originalOrder": 112,
    "learningOrder": 112
  },
  {
    "id": 506,
    "number": 506,
    "sequence_number": 506,
    "title": "Check If All 1's Are at Least Length K Places Away",
    "slug": "check-if-all-1s-are-at-least-length-k-places-away",
    "difficulty": "Easy",
    "topic": "Arrays",
    "subtopic": "Arrays Optimization",
    "pattern": "Index Gap Check",
    "secondary_patterns": [
      "Index Gap Check"
    ],
    "stage": "Recursion & Backtracking",
    "curriculumStage": "Stage 11 — Recursion & Backtracking",
    "roadmapPhase": "Stage 11 — Recursion & Backtracking",
    "phase": "Stage 11 — Recursion & Backtracking",
    "estimatedTime": 15,
    "statement": "Given the constraints and input parameters for Check If All 1's Are at Least Length K Places Away, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Check If All 1's Are at Least Length K Places Away."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Check If All 1's Are at Least Length K Places Away.",
      "Leverage the optimal Arrays pattern to reduce time complexity."
    ],
    "learningObjective": "Master Arrays techniques by solving Easy problem constraints for Check If All 1's Are at Least Length K Places Away.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/check-if-all-1s-are-at-least-length-k-places-away/",
    "leetcode_title": "Check If All 1's Are at Least Length K Places Away",
    "leetcode_id": 1437,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/check-if-all-1s-are-at-least-length-k-places-away/",
    "canonicalSlug": "check-if-all-1s-are-at-least-length-k-places-away",
    "canonicalUrl": "https://leetcode.com/problems/check-if-all-1s-are-at-least-length-k-places-away/",
    "url": "https://leetcode.com/problems/check-if-all-1s-are-at-least-length-k-places-away/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Check If All 1's Are at Least Length K Places Away\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Check If All 1's Are at Least Length K Places Away\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Check If All 1's Are at Least Length K Places Away\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Check If All 1's Are at Least Length K Places Away\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Check If All 1's Are at Least Length K Places Away\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Check If All 1's Are at Least Length K Places Away\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Check If All 1's Are at Least Length K Places Away\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Check If All 1's Are at Least Length K Places Away\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Check If All 1's Are at Least Length K Places Away",
      "cpp_optimal": "// Solution for Check If All 1's Are at Least Length K Places Away",
      "java_brute": "// Solution for Check If All 1's Are at Least Length K Places Away",
      "java_optimal": "// Solution for Check If All 1's Are at Least Length K Places Away",
      "python_brute": "# Solution for Check If All 1's Are at Least Length K Places Away",
      "python_optimal": "# Solution for Check If All 1's Are at Least Length K Places Away"
    },
    "originalOrder": 113,
    "learningOrder": 113
  },
  {
    "id": 507,
    "number": 507,
    "sequence_number": 507,
    "title": "Make Two Arrays Equal by Reversing Subarrays",
    "slug": "make-two-arrays-equal-by-reversing-subarrays",
    "difficulty": "Easy",
    "topic": "Arrays",
    "subtopic": "Arrays Optimization",
    "pattern": "Frequency Equal Test",
    "secondary_patterns": [
      "Frequency Equal Test"
    ],
    "stage": "Recursion & Backtracking",
    "curriculumStage": "Stage 11 — Recursion & Backtracking",
    "roadmapPhase": "Stage 11 — Recursion & Backtracking",
    "phase": "Stage 11 — Recursion & Backtracking",
    "estimatedTime": 15,
    "statement": "Given the constraints and input parameters for Make Two Arrays Equal by Reversing Sub-arrays, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Make Two Arrays Equal by Reversing Sub-arrays."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Make Two Arrays Equal by Reversing Sub-arrays.",
      "Leverage the optimal Hashing pattern to reduce time complexity."
    ],
    "learningObjective": "Master Arrays techniques by solving Easy problem constraints for Make Two Arrays Equal by Reversing Subarrays.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/make-two-arrays-equal-by-reversing-subarrays/",
    "leetcode_title": "Make Two Arrays Equal by Reversing Subarrays",
    "leetcode_id": 1460,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/make-two-arrays-equal-by-reversing-subarrays/",
    "canonicalSlug": "make-two-arrays-equal-by-reversing-subarrays",
    "canonicalUrl": "https://leetcode.com/problems/make-two-arrays-equal-by-reversing-subarrays/",
    "url": "https://leetcode.com/problems/make-two-arrays-equal-by-reversing-subarrays/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Make Two Arrays Equal by Reversing Sub-arrays\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Make Two Arrays Equal by Reversing Sub-arrays\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Make Two Arrays Equal by Reversing Sub-arrays\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Make Two Arrays Equal by Reversing Sub-arrays\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Make Two Arrays Equal by Reversing Sub-arrays\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Make Two Arrays Equal by Reversing Sub-arrays\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Make Two Arrays Equal by Reversing Sub-arrays\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Make Two Arrays Equal by Reversing Sub-arrays\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Make Two Arrays Equal by Reversing Subarrays",
      "cpp_optimal": "// Solution for Make Two Arrays Equal by Reversing Subarrays",
      "java_brute": "// Solution for Make Two Arrays Equal by Reversing Subarrays",
      "java_optimal": "// Solution for Make Two Arrays Equal by Reversing Subarrays",
      "python_brute": "# Solution for Make Two Arrays Equal by Reversing Subarrays",
      "python_optimal": "# Solution for Make Two Arrays Equal by Reversing Subarrays"
    },
    "originalOrder": 114,
    "learningOrder": 114
  },
  {
    "id": 508,
    "number": 508,
    "sequence_number": 508,
    "title": "Maximum Product of Two Elements in an Array",
    "slug": "maximum-product-of-two-elements-in-an-array",
    "difficulty": "Easy",
    "topic": "Arrays",
    "subtopic": "Arrays Optimization",
    "pattern": "Top 2 Max Values",
    "secondary_patterns": [
      "Top 2 Max Values"
    ],
    "stage": "Recursion & Backtracking",
    "curriculumStage": "Stage 11 — Recursion & Backtracking",
    "roadmapPhase": "Stage 11 — Recursion & Backtracking",
    "phase": "Stage 11 — Recursion & Backtracking",
    "estimatedTime": 15,
    "statement": "Given the constraints and input parameters for Maximum Product of Two Elements in an Array, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Maximum Product of Two Elements in an Array."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Maximum Product of Two Elements in an Array.",
      "Leverage the optimal Arrays pattern to reduce time complexity."
    ],
    "learningObjective": "Master Arrays techniques by solving Easy problem constraints for Maximum Product of Two Elements in an Array.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/maximum-product-of-two-elements-in-an-array/",
    "leetcode_title": "Maximum Product of Two Elements in an Array",
    "leetcode_id": 1464,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/maximum-product-of-two-elements-in-an-array/",
    "canonicalSlug": "maximum-product-of-two-elements-in-an-array",
    "canonicalUrl": "https://leetcode.com/problems/maximum-product-of-two-elements-in-an-array/",
    "url": "https://leetcode.com/problems/maximum-product-of-two-elements-in-an-array/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Maximum Product of Two Elements in an Array\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Maximum Product of Two Elements in an Array\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Maximum Product of Two Elements in an Array\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Maximum Product of Two Elements in an Array\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Maximum Product of Two Elements in an Array\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Maximum Product of Two Elements in an Array\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Maximum Product of Two Elements in an Array\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Maximum Product of Two Elements in an Array\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Maximum Product of Two Elements in an Array",
      "cpp_optimal": "// Solution for Maximum Product of Two Elements in an Array",
      "java_brute": "// Solution for Maximum Product of Two Elements in an Array",
      "java_optimal": "// Solution for Maximum Product of Two Elements in an Array",
      "python_brute": "# Solution for Maximum Product of Two Elements in an Array",
      "python_optimal": "# Solution for Maximum Product of Two Elements in an Array"
    },
    "originalOrder": 115,
    "learningOrder": 115
  },
  {
    "id": 509,
    "number": 509,
    "sequence_number": 509,
    "title": "Count Good Triplets",
    "slug": "count-good-triplets",
    "difficulty": "Easy",
    "topic": "Arrays",
    "subtopic": "Arrays Optimization",
    "pattern": "3-Loop Delta Filter",
    "secondary_patterns": [
      "3-Loop Delta Filter"
    ],
    "stage": "Recursion & Backtracking",
    "curriculumStage": "Stage 11 — Recursion & Backtracking",
    "roadmapPhase": "Stage 11 — Recursion & Backtracking",
    "phase": "Stage 11 — Recursion & Backtracking",
    "estimatedTime": 15,
    "statement": "Given the constraints and input parameters for Count Good Triplets, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Count Good Triplets."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Count Good Triplets.",
      "Leverage the optimal Arrays pattern to reduce time complexity."
    ],
    "learningObjective": "Master Arrays techniques by solving Easy problem constraints for Count Good Triplets.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/count-good-triplets/",
    "leetcode_title": "Count Good Triplets",
    "leetcode_id": 1534,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/count-good-triplets/",
    "canonicalSlug": "count-good-triplets",
    "canonicalUrl": "https://leetcode.com/problems/count-good-triplets/",
    "url": "https://leetcode.com/problems/count-good-triplets/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Count Good Triplets\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Count Good Triplets\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Count Good Triplets\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Count Good Triplets\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Count Good Triplets\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Count Good Triplets\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Count Good Triplets\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Count Good Triplets\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Count Good Triplets",
      "cpp_optimal": "// Solution for Count Good Triplets",
      "java_brute": "// Solution for Count Good Triplets",
      "java_optimal": "// Solution for Count Good Triplets",
      "python_brute": "# Solution for Count Good Triplets",
      "python_optimal": "# Solution for Count Good Triplets"
    },
    "originalOrder": 116,
    "learningOrder": 116
  },
  {
    "id": 510,
    "number": 510,
    "sequence_number": 510,
    "title": "Matrix Diagonal Sum",
    "slug": "matrix-diagonal-sum",
    "difficulty": "Easy",
    "topic": "Arrays",
    "subtopic": "Arrays Optimization",
    "pattern": "Main & Anti Diagonal Sum",
    "secondary_patterns": [
      "Main & Anti Diagonal Sum"
    ],
    "stage": "Recursion & Backtracking",
    "curriculumStage": "Stage 11 — Recursion & Backtracking",
    "roadmapPhase": "Stage 11 — Recursion & Backtracking",
    "phase": "Stage 11 — Recursion & Backtracking",
    "estimatedTime": 15,
    "statement": "Given the constraints and input parameters for Matrix Diagonal Sum, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Matrix Diagonal Sum."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Matrix Diagonal Sum.",
      "Leverage the optimal Arrays pattern to reduce time complexity."
    ],
    "learningObjective": "Master Arrays techniques by solving Easy problem constraints for Matrix Diagonal Sum.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/matrix-diagonal-sum/",
    "leetcode_title": "Matrix Diagonal Sum",
    "leetcode_id": 1572,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/matrix-diagonal-sum/",
    "canonicalSlug": "matrix-diagonal-sum",
    "canonicalUrl": "https://leetcode.com/problems/matrix-diagonal-sum/",
    "url": "https://leetcode.com/problems/matrix-diagonal-sum/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Matrix Diagonal Sum\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Matrix Diagonal Sum\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Matrix Diagonal Sum\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Matrix Diagonal Sum\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Matrix Diagonal Sum\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Matrix Diagonal Sum\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Matrix Diagonal Sum\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Matrix Diagonal Sum\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Matrix Diagonal Sum",
      "cpp_optimal": "// Solution for Matrix Diagonal Sum",
      "java_brute": "// Solution for Matrix Diagonal Sum",
      "java_optimal": "// Solution for Matrix Diagonal Sum",
      "python_brute": "# Solution for Matrix Diagonal Sum",
      "python_optimal": "# Solution for Matrix Diagonal Sum"
    },
    "originalOrder": 117,
    "learningOrder": 117
  },
  {
    "id": 511,
    "number": 511,
    "sequence_number": 511,
    "title": "Valid Sudoku",
    "slug": "valid-sudoku",
    "difficulty": "Medium",
    "topic": "Backtracking",
    "subtopic": "Hashing & Array Optimization",
    "pattern": "Hashing & Array Optimization",
    "secondary_patterns": [
      "Hashing & Array Optimization"
    ],
    "stage": "Recursion & Backtracking",
    "curriculumStage": "Stage 11 — Recursion & Backtracking",
    "roadmapPhase": "Stage 11 — Recursion & Backtracking",
    "phase": "Stage 11 — Recursion & Backtracking",
    "estimatedTime": 30,
    "statement": "Solve the **Valid Sudoku Challenge** problem using the **Hashing & Array Optimization** technique. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Hashing & Array Optimization identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Hashing & Array Optimization. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Hashing & Array Optimization techniques by solving Medium problem constraints for Valid Sudoku Challenge.",
    "whyThisPattern": "When observing arrays & strings problem conditions, Hashing & Array Optimization optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Microsoft",
      "Bloomberg",
      "Adobe"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/valid-sudoku/",
    "leetcode_title": "Valid Sudoku",
    "leetcode_id": 36,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/valid-sudoku/",
    "canonicalSlug": "valid-sudoku",
    "canonicalUrl": "https://leetcode.com/problems/valid-sudoku/",
    "url": "https://leetcode.com/problems/valid-sudoku/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Valid Sudoku Challenge (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Valid Sudoku Challenge (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Valid Sudoku Challenge (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Valid Sudoku Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Valid Sudoku Challenge (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Valid Sudoku Challenge (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Valid Sudoku Challenge (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Valid Sudoku Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Valid Sudoku",
      "cpp_optimal": "// Solution for Valid Sudoku",
      "java_brute": "// Solution for Valid Sudoku",
      "java_optimal": "// Solution for Valid Sudoku",
      "python_brute": "# Solution for Valid Sudoku",
      "python_optimal": "# Solution for Valid Sudoku"
    },
    "originalOrder": 379,
    "learningOrder": 379
  },
  {
    "id": 512,
    "number": 512,
    "sequence_number": 512,
    "title": "Combination Sum",
    "slug": "combination-sum",
    "difficulty": "Medium",
    "topic": "Backtracking",
    "subtopic": "Hashing & Array Optimization",
    "pattern": "Hashing & Array Optimization",
    "secondary_patterns": [
      "Hashing & Array Optimization"
    ],
    "stage": "Recursion & Backtracking",
    "curriculumStage": "Stage 11 — Recursion & Backtracking",
    "roadmapPhase": "Stage 11 — Recursion & Backtracking",
    "phase": "Stage 11 — Recursion & Backtracking",
    "estimatedTime": 30,
    "statement": "Solve the **Combination Sum Optimization** problem using the **Hashing & Array Optimization** technique. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Hashing & Array Optimization identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Hashing & Array Optimization. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Hashing & Array Optimization techniques by solving Medium problem constraints for Combination Sum Optimization.",
    "whyThisPattern": "When observing arrays & strings problem conditions, Hashing & Array Optimization optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Apple",
      "Adobe",
      "Atlassian"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/combination-sum/",
    "leetcode_title": "Combination Sum",
    "leetcode_id": 39,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/combination-sum/",
    "canonicalSlug": "combination-sum",
    "canonicalUrl": "https://leetcode.com/problems/combination-sum/",
    "url": "https://leetcode.com/problems/combination-sum/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Combination Sum Optimization (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Combination Sum Optimization (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Combination Sum Optimization (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Combination Sum Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Combination Sum Optimization (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Combination Sum Optimization (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Combination Sum Optimization (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Combination Sum Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Combination Sum",
      "cpp_optimal": "// Solution for Combination Sum",
      "java_brute": "// Solution for Combination Sum",
      "java_optimal": "// Solution for Combination Sum",
      "python_brute": "# Solution for Combination Sum",
      "python_optimal": "# Solution for Combination Sum"
    },
    "originalOrder": 380,
    "learningOrder": 380
  },
  {
    "id": 513,
    "number": 513,
    "sequence_number": 513,
    "title": "Combination Sum II",
    "slug": "combination-sum-ii",
    "difficulty": "Medium",
    "topic": "Backtracking",
    "subtopic": "Hashing & Array Optimization",
    "pattern": "Hashing & Array Optimization",
    "secondary_patterns": [
      "Hashing & Array Optimization"
    ],
    "stage": "Recursion & Backtracking",
    "curriculumStage": "Stage 11 — Recursion & Backtracking",
    "roadmapPhase": "Stage 11 — Recursion & Backtracking",
    "phase": "Stage 11 — Recursion & Backtracking",
    "estimatedTime": 30,
    "statement": "Solve the **Combination Sum II Challenge** problem using the **Hashing & Array Optimization** technique. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Hashing & Array Optimization identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Hashing & Array Optimization. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Hashing & Array Optimization techniques by solving Medium problem constraints for Combination Sum II Challenge.",
    "whyThisPattern": "When observing arrays & strings problem conditions, Hashing & Array Optimization optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Meta",
      "Uber",
      "Databricks"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/combination-sum-ii/",
    "leetcode_title": "Combination Sum II",
    "leetcode_id": 40,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/combination-sum-ii/",
    "canonicalSlug": "combination-sum-ii",
    "canonicalUrl": "https://leetcode.com/problems/combination-sum-ii/",
    "url": "https://leetcode.com/problems/combination-sum-ii/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Combination Sum II Challenge (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Combination Sum II Challenge (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Combination Sum II Challenge (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Combination Sum II Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Combination Sum II Challenge (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Combination Sum II Challenge (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Combination Sum II Challenge (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Combination Sum II Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Combination Sum II",
      "cpp_optimal": "// Solution for Combination Sum II",
      "java_brute": "// Solution for Combination Sum II",
      "java_optimal": "// Solution for Combination Sum II",
      "python_brute": "# Solution for Combination Sum II",
      "python_optimal": "# Solution for Combination Sum II"
    },
    "originalOrder": 381,
    "learningOrder": 381
  },
  {
    "id": 514,
    "number": 514,
    "sequence_number": 514,
    "title": "Permutations",
    "slug": "permutations",
    "difficulty": "Medium",
    "topic": "Backtracking",
    "subtopic": "Hashing & Array Optimization",
    "pattern": "Hashing & Array Optimization",
    "secondary_patterns": [
      "Hashing & Array Optimization"
    ],
    "stage": "Recursion & Backtracking",
    "curriculumStage": "Stage 11 — Recursion & Backtracking",
    "roadmapPhase": "Stage 11 — Recursion & Backtracking",
    "phase": "Stage 11 — Recursion & Backtracking",
    "estimatedTime": 30,
    "statement": "Solve the **Permutations Challenge** problem using the **Hashing & Array Optimization** technique. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Hashing & Array Optimization identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Hashing & Array Optimization. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Hashing & Array Optimization techniques by solving Medium problem constraints for Permutations Challenge.",
    "whyThisPattern": "When observing arrays & strings problem conditions, Hashing & Array Optimization optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Microsoft",
      "Bloomberg",
      "Adobe"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/permutations/",
    "leetcode_title": "Permutations",
    "leetcode_id": 46,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/permutations/",
    "canonicalSlug": "permutations",
    "canonicalUrl": "https://leetcode.com/problems/permutations/",
    "url": "https://leetcode.com/problems/permutations/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Permutations Challenge (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Permutations Challenge (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Permutations Challenge (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Permutations Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Permutations Challenge (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Permutations Challenge (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Permutations Challenge (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Permutations Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Permutations",
      "cpp_optimal": "// Solution for Permutations",
      "java_brute": "// Solution for Permutations",
      "java_optimal": "// Solution for Permutations",
      "python_brute": "# Solution for Permutations",
      "python_optimal": "# Solution for Permutations"
    },
    "originalOrder": 382,
    "learningOrder": 382
  },
  {
    "id": 515,
    "number": 515,
    "sequence_number": 515,
    "title": "Permutations II",
    "slug": "permutations-ii",
    "difficulty": "Medium",
    "topic": "Backtracking",
    "subtopic": "Hashing & Array Optimization",
    "pattern": "Hashing & Array Optimization",
    "secondary_patterns": [
      "Hashing & Array Optimization"
    ],
    "stage": "Recursion & Backtracking",
    "curriculumStage": "Stage 11 — Recursion & Backtracking",
    "roadmapPhase": "Stage 11 — Recursion & Backtracking",
    "phase": "Stage 11 — Recursion & Backtracking",
    "estimatedTime": 30,
    "statement": "Solve the **Permutations II Challenge** problem using the **Hashing & Array Optimization** technique. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Hashing & Array Optimization identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Hashing & Array Optimization. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Hashing & Array Optimization techniques by solving Medium problem constraints for Permutations II Challenge.",
    "whyThisPattern": "When observing arrays & strings problem conditions, Hashing & Array Optimization optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Amazon",
      "Microsoft",
      "Uber"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/permutations-ii/",
    "leetcode_title": "Permutations II",
    "leetcode_id": 47,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/permutations-ii/",
    "canonicalSlug": "permutations-ii",
    "canonicalUrl": "https://leetcode.com/problems/permutations-ii/",
    "url": "https://leetcode.com/problems/permutations-ii/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Permutations II Challenge (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Permutations II Challenge (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Permutations II Challenge (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Permutations II Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Permutations II Challenge (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Permutations II Challenge (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Permutations II Challenge (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Permutations II Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Permutations II",
      "cpp_optimal": "// Solution for Permutations II",
      "java_brute": "// Solution for Permutations II",
      "java_optimal": "// Solution for Permutations II",
      "python_brute": "# Solution for Permutations II",
      "python_optimal": "# Solution for Permutations II"
    },
    "originalOrder": 383,
    "learningOrder": 383
  },
  {
    "id": 516,
    "number": 516,
    "sequence_number": 516,
    "title": "Subsets",
    "slug": "subsets",
    "difficulty": "Medium",
    "topic": "Backtracking",
    "subtopic": "Hashing & Array Optimization",
    "pattern": "Hashing & Array Optimization",
    "secondary_patterns": [
      "Hashing & Array Optimization"
    ],
    "stage": "Recursion & Backtracking",
    "curriculumStage": "Stage 11 — Recursion & Backtracking",
    "roadmapPhase": "Stage 11 — Recursion & Backtracking",
    "phase": "Stage 11 — Recursion & Backtracking",
    "estimatedTime": 30,
    "statement": "Solve the **Subsets Challenge** problem using the **Hashing & Array Optimization** technique. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Hashing & Array Optimization identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Hashing & Array Optimization. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Hashing & Array Optimization techniques by solving Medium problem constraints for Subsets Challenge.",
    "whyThisPattern": "When observing arrays & strings problem conditions, Hashing & Array Optimization optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Meta",
      "Uber",
      "Databricks"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/subsets/",
    "leetcode_title": "Subsets",
    "leetcode_id": 78,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/subsets/",
    "canonicalSlug": "subsets",
    "canonicalUrl": "https://leetcode.com/problems/subsets/",
    "url": "https://leetcode.com/problems/subsets/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Subsets Challenge (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Subsets Challenge (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Subsets Challenge (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Subsets Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Subsets Challenge (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Subsets Challenge (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Subsets Challenge (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Subsets Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Subsets",
      "cpp_optimal": "// Solution for Subsets",
      "java_brute": "// Solution for Subsets",
      "java_optimal": "// Solution for Subsets",
      "python_brute": "# Solution for Subsets",
      "python_optimal": "# Solution for Subsets"
    },
    "originalOrder": 384,
    "learningOrder": 384
  },
  {
    "id": 517,
    "number": 517,
    "sequence_number": 517,
    "title": "Word Search",
    "slug": "word-search",
    "difficulty": "Medium",
    "topic": "Backtracking",
    "subtopic": "Hashing & Array Optimization",
    "pattern": "Hashing & Array Optimization",
    "secondary_patterns": [
      "Hashing & Array Optimization"
    ],
    "stage": "Recursion & Backtracking",
    "curriculumStage": "Stage 11 — Recursion & Backtracking",
    "roadmapPhase": "Stage 11 — Recursion & Backtracking",
    "phase": "Stage 11 — Recursion & Backtracking",
    "estimatedTime": 30,
    "statement": "Solve the **Word Search Challenge** problem using the **Hashing & Array Optimization** technique. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Hashing & Array Optimization identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Hashing & Array Optimization. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Hashing & Array Optimization techniques by solving Medium problem constraints for Word Search Challenge.",
    "whyThisPattern": "When observing arrays & strings problem conditions, Hashing & Array Optimization optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Amazon",
      "Microsoft",
      "Uber"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/word-search/",
    "leetcode_title": "Word Search",
    "leetcode_id": 79,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/word-search/",
    "canonicalSlug": "word-search",
    "canonicalUrl": "https://leetcode.com/problems/word-search/",
    "url": "https://leetcode.com/problems/word-search/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Word Search Challenge (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Word Search Challenge (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Word Search Challenge (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Word Search Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Word Search Challenge (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Word Search Challenge (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Word Search Challenge (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Word Search Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Word Search",
      "cpp_optimal": "// Solution for Word Search",
      "java_brute": "// Solution for Word Search",
      "java_optimal": "// Solution for Word Search",
      "python_brute": "# Solution for Word Search",
      "python_optimal": "# Solution for Word Search"
    },
    "originalOrder": 385,
    "learningOrder": 385
  },
  {
    "id": 518,
    "number": 518,
    "sequence_number": 518,
    "title": "Subsets II",
    "slug": "subsets-ii",
    "difficulty": "Medium",
    "topic": "Backtracking",
    "subtopic": "Hashing & Array Optimization",
    "pattern": "Hashing & Array Optimization",
    "secondary_patterns": [
      "Hashing & Array Optimization"
    ],
    "stage": "Recursion & Backtracking",
    "curriculumStage": "Stage 11 — Recursion & Backtracking",
    "roadmapPhase": "Stage 11 — Recursion & Backtracking",
    "phase": "Stage 11 — Recursion & Backtracking",
    "estimatedTime": 30,
    "statement": "Solve the **Subsets II Challenge** problem using the **Hashing & Array Optimization** technique. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Hashing & Array Optimization identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Hashing & Array Optimization. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Hashing & Array Optimization techniques by solving Medium problem constraints for Subsets II Challenge.",
    "whyThisPattern": "When observing arrays & strings problem conditions, Hashing & Array Optimization optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Microsoft",
      "Bloomberg"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/subsets-ii/",
    "leetcode_title": "Subsets II",
    "leetcode_id": 90,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/subsets-ii/",
    "canonicalSlug": "subsets-ii",
    "canonicalUrl": "https://leetcode.com/problems/subsets-ii/",
    "url": "https://leetcode.com/problems/subsets-ii/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Subsets II Challenge (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Subsets II Challenge (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Subsets II Challenge (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Subsets II Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Subsets II Challenge (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Subsets II Challenge (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Subsets II Challenge (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Subsets II Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Subsets II",
      "cpp_optimal": "// Solution for Subsets II",
      "java_brute": "// Solution for Subsets II",
      "java_optimal": "// Solution for Subsets II",
      "python_brute": "# Solution for Subsets II",
      "python_optimal": "# Solution for Subsets II"
    },
    "originalOrder": 386,
    "learningOrder": 386
  },
  {
    "id": 519,
    "number": 519,
    "sequence_number": 519,
    "title": "Combination Sum III",
    "slug": "combination-sum-iii",
    "difficulty": "Medium",
    "topic": "Backtracking",
    "subtopic": "Hashing & Array Optimization",
    "pattern": "Hashing & Array Optimization",
    "secondary_patterns": [
      "Hashing & Array Optimization"
    ],
    "stage": "Recursion & Backtracking",
    "curriculumStage": "Stage 11 — Recursion & Backtracking",
    "roadmapPhase": "Stage 11 — Recursion & Backtracking",
    "phase": "Stage 11 — Recursion & Backtracking",
    "estimatedTime": 30,
    "statement": "Solve the **Combination Sum III Challenge** problem using the **Hashing & Array Optimization** technique. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Hashing & Array Optimization identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Hashing & Array Optimization. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Hashing & Array Optimization techniques by solving Medium problem constraints for Combination Sum III Challenge.",
    "whyThisPattern": "When observing arrays & strings problem conditions, Hashing & Array Optimization optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Amazon",
      "Microsoft",
      "Uber"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/combination-sum-iii/",
    "leetcode_title": "Combination Sum III",
    "leetcode_id": 216,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/combination-sum-iii/",
    "canonicalSlug": "combination-sum-iii",
    "canonicalUrl": "https://leetcode.com/problems/combination-sum-iii/",
    "url": "https://leetcode.com/problems/combination-sum-iii/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Combination Sum III Challenge (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Combination Sum III Challenge (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Combination Sum III Challenge (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Combination Sum III Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Combination Sum III Challenge (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Combination Sum III Challenge (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Combination Sum III Challenge (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Combination Sum III Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Combination Sum III",
      "cpp_optimal": "// Solution for Combination Sum III",
      "java_brute": "// Solution for Combination Sum III",
      "java_optimal": "// Solution for Combination Sum III",
      "python_brute": "# Solution for Combination Sum III",
      "python_optimal": "# Solution for Combination Sum III"
    },
    "originalOrder": 387,
    "learningOrder": 387
  },
  {
    "id": 520,
    "number": 520,
    "sequence_number": 520,
    "title": "Combination Sum IV",
    "slug": "combination-sum-iv",
    "difficulty": "Medium",
    "topic": "Backtracking",
    "subtopic": "Hashing & Array Optimization",
    "pattern": "Hashing & Array Optimization",
    "secondary_patterns": [
      "Hashing & Array Optimization"
    ],
    "stage": "Recursion & Backtracking",
    "curriculumStage": "Stage 11 — Recursion & Backtracking",
    "roadmapPhase": "Stage 11 — Recursion & Backtracking",
    "phase": "Stage 11 — Recursion & Backtracking",
    "estimatedTime": 30,
    "statement": "Solve the **Combination Sum IV Challenge** problem using the **Hashing & Array Optimization** technique. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Hashing & Array Optimization identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Hashing & Array Optimization. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Hashing & Array Optimization techniques by solving Medium problem constraints for Combination Sum IV Challenge.",
    "whyThisPattern": "When observing arrays & strings problem conditions, Hashing & Array Optimization optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Meta",
      "Uber",
      "Databricks"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/combination-sum-iv/",
    "leetcode_title": "Combination Sum IV",
    "leetcode_id": 377,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/combination-sum-iv/",
    "canonicalSlug": "combination-sum-iv",
    "canonicalUrl": "https://leetcode.com/problems/combination-sum-iv/",
    "url": "https://leetcode.com/problems/combination-sum-iv/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Combination Sum IV Challenge (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Combination Sum IV Challenge (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Combination Sum IV Challenge (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Combination Sum IV Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Combination Sum IV Challenge (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Combination Sum IV Challenge (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Combination Sum IV Challenge (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Combination Sum IV Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Combination Sum IV",
      "cpp_optimal": "// Solution for Combination Sum IV",
      "java_brute": "// Solution for Combination Sum IV",
      "java_optimal": "// Solution for Combination Sum IV",
      "python_brute": "# Solution for Combination Sum IV",
      "python_optimal": "# Solution for Combination Sum IV"
    },
    "originalOrder": 388,
    "learningOrder": 388
  },
  {
    "id": 521,
    "number": 521,
    "sequence_number": 521,
    "title": "Partition to K Equal Sum Subsets",
    "slug": "partition-to-k-equal-sum-subsets",
    "difficulty": "Medium",
    "topic": "Backtracking",
    "subtopic": "Hashing & Array Optimization",
    "pattern": "Hashing & Array Optimization",
    "secondary_patterns": [
      "Hashing & Array Optimization"
    ],
    "stage": "Recursion & Backtracking",
    "curriculumStage": "Stage 11 — Recursion & Backtracking",
    "roadmapPhase": "Stage 11 — Recursion & Backtracking",
    "phase": "Stage 11 — Recursion & Backtracking",
    "estimatedTime": 30,
    "statement": "Solve the **Partition to K Equal Sum Subsets Optimization** problem using the **Hashing & Array Optimization** technique. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Hashing & Array Optimization identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Hashing & Array Optimization. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Hashing & Array Optimization techniques by solving Medium problem constraints for Partition to K Equal Sum Subsets Optimization.",
    "whyThisPattern": "When observing arrays & strings problem conditions, Hashing & Array Optimization optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/partition-to-k-equal-sum-subsets/",
    "leetcode_title": "Partition to K Equal Sum Subsets",
    "leetcode_id": 698,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/partition-to-k-equal-sum-subsets/",
    "canonicalSlug": "partition-to-k-equal-sum-subsets",
    "canonicalUrl": "https://leetcode.com/problems/partition-to-k-equal-sum-subsets/",
    "url": "https://leetcode.com/problems/partition-to-k-equal-sum-subsets/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Partition to K Equal Sum Subsets Optimization (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Partition to K Equal Sum Subsets Optimization (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Partition to K Equal Sum Subsets Optimization (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Partition to K Equal Sum Subsets Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Partition to K Equal Sum Subsets Optimization (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Partition to K Equal Sum Subsets Optimization (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Partition to K Equal Sum Subsets Optimization (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Partition to K Equal Sum Subsets Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Partition to K Equal Sum Subsets",
      "cpp_optimal": "// Solution for Partition to K Equal Sum Subsets",
      "java_brute": "// Solution for Partition to K Equal Sum Subsets",
      "java_optimal": "// Solution for Partition to K Equal Sum Subsets",
      "python_brute": "# Solution for Partition to K Equal Sum Subsets",
      "python_optimal": "# Solution for Partition to K Equal Sum Subsets"
    },
    "originalOrder": 389,
    "learningOrder": 389
  },
  {
    "id": 522,
    "number": 522,
    "sequence_number": 522,
    "title": "Word Subsets",
    "slug": "word-subsets",
    "difficulty": "Medium",
    "topic": "Backtracking",
    "subtopic": "Hashing & Array Optimization",
    "pattern": "Hashing & Array Optimization",
    "secondary_patterns": [
      "Hashing & Array Optimization"
    ],
    "stage": "Recursion & Backtracking",
    "curriculumStage": "Stage 11 — Recursion & Backtracking",
    "roadmapPhase": "Stage 11 — Recursion & Backtracking",
    "phase": "Stage 11 — Recursion & Backtracking",
    "estimatedTime": 30,
    "statement": "Solve the **Word Subsets Optimization** problem using the **Hashing & Array Optimization** technique. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Hashing & Array Optimization identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Hashing & Array Optimization. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Hashing & Array Optimization techniques by solving Medium problem constraints for Word Subsets Optimization.",
    "whyThisPattern": "When observing arrays & strings problem conditions, Hashing & Array Optimization optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Meta",
      "Apple",
      "Netflix"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/word-subsets/",
    "leetcode_title": "Word Subsets",
    "leetcode_id": 916,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/word-subsets/",
    "canonicalSlug": "word-subsets",
    "canonicalUrl": "https://leetcode.com/problems/word-subsets/",
    "url": "https://leetcode.com/problems/word-subsets/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Word Subsets Optimization (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Word Subsets Optimization (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Word Subsets Optimization (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Word Subsets Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Word Subsets Optimization (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Word Subsets Optimization (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Word Subsets Optimization (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Word Subsets Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Word Subsets",
      "cpp_optimal": "// Solution for Word Subsets",
      "java_brute": "// Solution for Word Subsets",
      "java_optimal": "// Solution for Word Subsets",
      "python_brute": "# Solution for Word Subsets",
      "python_optimal": "# Solution for Word Subsets"
    },
    "originalOrder": 390,
    "learningOrder": 390
  },
  {
    "id": 523,
    "number": 523,
    "sequence_number": 523,
    "title": "Split Array into Fibonacci Sequence",
    "slug": "split-array-into-fibonacci-sequence",
    "difficulty": "Medium",
    "topic": "Backtracking",
    "subtopic": "Backtracking Optimization",
    "pattern": "Fibonacci Backtracking",
    "secondary_patterns": [
      "Fibonacci Backtracking"
    ],
    "stage": "Recursion & Backtracking",
    "curriculumStage": "Stage 11 — Recursion & Backtracking",
    "roadmapPhase": "Stage 11 — Recursion & Backtracking",
    "phase": "Stage 11 — Recursion & Backtracking",
    "estimatedTime": 30,
    "statement": "Given the constraints and input parameters for Split Array into Fibonacci Sequence, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Split Array into Fibonacci Sequence."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Split Array into Fibonacci Sequence.",
      "Leverage the optimal Backtracking pattern to reduce time complexity."
    ],
    "learningObjective": "Master Backtracking techniques by solving Medium problem constraints for Split Array into Fibonacci Sequence.",
    "whyThisPattern": "When observing Backtracking problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/split-array-into-fibonacci-sequence/",
    "leetcode_title": "Split Array into Fibonacci Sequence",
    "leetcode_id": 842,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/split-array-into-fibonacci-sequence/",
    "canonicalSlug": "split-array-into-fibonacci-sequence",
    "canonicalUrl": "https://leetcode.com/problems/split-array-into-fibonacci-sequence/",
    "url": "https://leetcode.com/problems/split-array-into-fibonacci-sequence/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Split Array into Fibonacci Sequence\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Split Array into Fibonacci Sequence\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Split Array into Fibonacci Sequence\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Split Array into Fibonacci Sequence\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Split Array into Fibonacci Sequence\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Split Array into Fibonacci Sequence\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Split Array into Fibonacci Sequence\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Split Array into Fibonacci Sequence\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Split Array into Fibonacci Sequence",
      "cpp_optimal": "// Solution for Split Array into Fibonacci Sequence",
      "java_brute": "// Solution for Split Array into Fibonacci Sequence",
      "java_optimal": "// Solution for Split Array into Fibonacci Sequence",
      "python_brute": "# Solution for Split Array into Fibonacci Sequence",
      "python_optimal": "# Solution for Split Array into Fibonacci Sequence"
    },
    "originalOrder": 391,
    "learningOrder": 391
  },
  {
    "id": 524,
    "number": 524,
    "sequence_number": 524,
    "title": "Construct the Lexicographically Largest Valid Sequence",
    "slug": "construct-the-lexicographically-largest-valid-sequence",
    "difficulty": "Medium",
    "topic": "Backtracking",
    "subtopic": "Backtracking Optimization",
    "pattern": "Pruned Distance Backtracking",
    "secondary_patterns": [
      "Pruned Distance Backtracking"
    ],
    "stage": "Recursion & Backtracking",
    "curriculumStage": "Stage 11 — Recursion & Backtracking",
    "roadmapPhase": "Stage 11 — Recursion & Backtracking",
    "phase": "Stage 11 — Recursion & Backtracking",
    "estimatedTime": 30,
    "statement": "Given the constraints and input parameters for Construct the Lexicographically Largest Valid Sequence, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Construct the Lexicographically Largest Valid Sequence."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Construct the Lexicographically Largest Valid Sequence.",
      "Leverage the optimal Backtracking pattern to reduce time complexity."
    ],
    "learningObjective": "Master Backtracking techniques by solving Medium problem constraints for Construct the Lexicographically Largest Valid Sequence.",
    "whyThisPattern": "When observing Backtracking problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/construct-the-lexicographically-largest-valid-sequence/",
    "leetcode_title": "Construct the Lexicographically Largest Valid Sequence",
    "leetcode_id": 1718,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/construct-the-lexicographically-largest-valid-sequence/",
    "canonicalSlug": "construct-the-lexicographically-largest-valid-sequence",
    "canonicalUrl": "https://leetcode.com/problems/construct-the-lexicographically-largest-valid-sequence/",
    "url": "https://leetcode.com/problems/construct-the-lexicographically-largest-valid-sequence/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Construct the Lexicographically Largest Valid Sequence\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Construct the Lexicographically Largest Valid Sequence\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Construct the Lexicographically Largest Valid Sequence\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Construct the Lexicographically Largest Valid Sequence\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Construct the Lexicographically Largest Valid Sequence\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Construct the Lexicographically Largest Valid Sequence\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Construct the Lexicographically Largest Valid Sequence\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Construct the Lexicographically Largest Valid Sequence\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Construct the Lexicographically Largest Valid Sequence",
      "cpp_optimal": "// Solution for Construct the Lexicographically Largest Valid Sequence",
      "java_brute": "// Solution for Construct the Lexicographically Largest Valid Sequence",
      "java_optimal": "// Solution for Construct the Lexicographically Largest Valid Sequence",
      "python_brute": "# Solution for Construct the Lexicographically Largest Valid Sequence",
      "python_optimal": "# Solution for Construct the Lexicographically Largest Valid Sequence"
    },
    "originalOrder": 392,
    "learningOrder": 392
  },
  {
    "id": 525,
    "number": 525,
    "sequence_number": 525,
    "title": "Split a String Into the Max Number of Unique Substrings",
    "slug": "split-a-string-into-the-max-number-of-unique-substrings",
    "difficulty": "Medium",
    "topic": "Backtracking",
    "subtopic": "Backtracking Optimization",
    "pattern": "HashSet String Branching",
    "secondary_patterns": [
      "HashSet String Branching"
    ],
    "stage": "Recursion & Backtracking",
    "curriculumStage": "Stage 11 — Recursion & Backtracking",
    "roadmapPhase": "Stage 11 — Recursion & Backtracking",
    "phase": "Stage 11 — Recursion & Backtracking",
    "estimatedTime": 30,
    "statement": "Given the constraints and input parameters for Split a String Into the Max Number of Unique Substrings, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Split a String Into the Max Number of Unique Substrings."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Split a String Into the Max Number of Unique Substrings.",
      "Leverage the optimal Backtracking pattern to reduce time complexity."
    ],
    "learningObjective": "Master Backtracking techniques by solving Medium problem constraints for Split a String Into the Max Number of Unique Substrings.",
    "whyThisPattern": "When observing Backtracking problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/split-a-string-into-the-max-number-of-unique-substrings/",
    "leetcode_title": "Split a String Into the Max Number of Unique Substrings",
    "leetcode_id": 1593,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/split-a-string-into-the-max-number-of-unique-substrings/",
    "canonicalSlug": "split-a-string-into-the-max-number-of-unique-substrings",
    "canonicalUrl": "https://leetcode.com/problems/split-a-string-into-the-max-number-of-unique-substrings/",
    "url": "https://leetcode.com/problems/split-a-string-into-the-max-number-of-unique-substrings/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Split a String Into the Max Number of Unique Substrings\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Split a String Into the Max Number of Unique Substrings\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Split a String Into the Max Number of Unique Substrings\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Split a String Into the Max Number of Unique Substrings\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Split a String Into the Max Number of Unique Substrings\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Split a String Into the Max Number of Unique Substrings\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Split a String Into the Max Number of Unique Substrings\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Split a String Into the Max Number of Unique Substrings\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Split a String Into the Max Number of Unique Substrings",
      "cpp_optimal": "// Solution for Split a String Into the Max Number of Unique Substrings",
      "java_brute": "// Solution for Split a String Into the Max Number of Unique Substrings",
      "java_optimal": "// Solution for Split a String Into the Max Number of Unique Substrings",
      "python_brute": "# Solution for Split a String Into the Max Number of Unique Substrings",
      "python_optimal": "# Solution for Split a String Into the Max Number of Unique Substrings"
    },
    "originalOrder": 393,
    "learningOrder": 393
  },
  {
    "id": 526,
    "number": 526,
    "sequence_number": 526,
    "title": "The k-th Lexicographical String of All Happy Strings of Length n",
    "slug": "the-k-th-lexicographical-string-of-all-happy-strings-of-length-n",
    "difficulty": "Medium",
    "topic": "Backtracking",
    "subtopic": "Backtracking Optimization",
    "pattern": "Pruned String Generation",
    "secondary_patterns": [
      "Pruned String Generation"
    ],
    "stage": "Recursion & Backtracking",
    "curriculumStage": "Stage 11 — Recursion & Backtracking",
    "roadmapPhase": "Stage 11 — Recursion & Backtracking",
    "phase": "Stage 11 — Recursion & Backtracking",
    "estimatedTime": 30,
    "statement": "Given the constraints and input parameters for The k-th Lexicographical String of All Happy Strings of Length n, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for The k-th Lexicographical String of All Happy Strings of Length n."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for The k-th Lexicographical String of All Happy Strings of Length n.",
      "Leverage the optimal Backtracking pattern to reduce time complexity."
    ],
    "learningObjective": "Master Backtracking techniques by solving Medium problem constraints for The k-th Lexicographical String of All Happy Strings of Length n.",
    "whyThisPattern": "When observing Backtracking problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/the-k-th-lexicographical-string-of-all-happy-strings-of-length-n/",
    "leetcode_title": "The k-th Lexicographical String of All Happy Strings of Length n",
    "leetcode_id": 1415,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/the-k-th-lexicographical-string-of-all-happy-strings-of-length-n/",
    "canonicalSlug": "the-k-th-lexicographical-string-of-all-happy-strings-of-length-n",
    "canonicalUrl": "https://leetcode.com/problems/the-k-th-lexicographical-string-of-all-happy-strings-of-length-n/",
    "url": "https://leetcode.com/problems/the-k-th-lexicographical-string-of-all-happy-strings-of-length-n/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for The k-th Lexicographical String of All Happy Strings of Length n\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for The k-th Lexicographical String of All Happy Strings of Length n\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for The k-th Lexicographical String of All Happy Strings of Length n\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for The k-th Lexicographical String of All Happy Strings of Length n\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for The k-th Lexicographical String of All Happy Strings of Length n\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for The k-th Lexicographical String of All Happy Strings of Length n\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for The k-th Lexicographical String of All Happy Strings of Length n\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for The k-th Lexicographical String of All Happy Strings of Length n\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for The k-th Lexicographical String of All Happy Strings of Length n",
      "cpp_optimal": "// Solution for The k-th Lexicographical String of All Happy Strings of Length n",
      "java_brute": "// Solution for The k-th Lexicographical String of All Happy Strings of Length n",
      "java_optimal": "// Solution for The k-th Lexicographical String of All Happy Strings of Length n",
      "python_brute": "# Solution for The k-th Lexicographical String of All Happy Strings of Length n",
      "python_optimal": "# Solution for The k-th Lexicographical String of All Happy Strings of Length n"
    },
    "originalOrder": 394,
    "learningOrder": 394
  },
  {
    "id": 527,
    "number": 527,
    "sequence_number": 527,
    "title": "Letter Combinations of a Phone Number",
    "slug": "letter-combinations-of-a-phone-number",
    "difficulty": "Medium",
    "topic": "Backtracking",
    "subtopic": "Backtracking Optimization",
    "pattern": "Digit Map Backtracking",
    "secondary_patterns": [
      "Digit Map Backtracking"
    ],
    "stage": "Recursion & Backtracking",
    "curriculumStage": "Stage 11 — Recursion & Backtracking",
    "roadmapPhase": "Stage 11 — Recursion & Backtracking",
    "phase": "Stage 11 — Recursion & Backtracking",
    "estimatedTime": 30,
    "statement": "Given the constraints and input parameters for Letter Combinations of a Phone Number, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Letter Combinations of a Phone Number."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Letter Combinations of a Phone Number.",
      "Leverage the optimal Backtracking pattern to reduce time complexity."
    ],
    "learningObjective": "Master Backtracking techniques by solving Medium problem constraints for Letter Combinations of a Phone Number.",
    "whyThisPattern": "When observing Backtracking problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/letter-combinations-of-a-phone-number/",
    "leetcode_title": "Letter Combinations of a Phone Number",
    "leetcode_id": 17,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/letter-combinations-of-a-phone-number/",
    "canonicalSlug": "letter-combinations-of-a-phone-number",
    "canonicalUrl": "https://leetcode.com/problems/letter-combinations-of-a-phone-number/",
    "url": "https://leetcode.com/problems/letter-combinations-of-a-phone-number/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Letter Combinations of a Phone Number\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Letter Combinations of a Phone Number\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Letter Combinations of a Phone Number\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Letter Combinations of a Phone Number\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Letter Combinations of a Phone Number\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Letter Combinations of a Phone Number\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Letter Combinations of a Phone Number\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Letter Combinations of a Phone Number\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Letter Combinations of a Phone Number",
      "cpp_optimal": "// Solution for Letter Combinations of a Phone Number",
      "java_brute": "// Solution for Letter Combinations of a Phone Number",
      "java_optimal": "// Solution for Letter Combinations of a Phone Number",
      "python_brute": "# Solution for Letter Combinations of a Phone Number",
      "python_optimal": "# Solution for Letter Combinations of a Phone Number"
    },
    "originalOrder": 395,
    "learningOrder": 395
  },
  {
    "id": 528,
    "number": 528,
    "sequence_number": 528,
    "title": "Matchsticks to Square",
    "slug": "matchsticks-to-square",
    "difficulty": "Medium",
    "topic": "Backtracking",
    "subtopic": "Backtracking Optimization",
    "pattern": "4-Subset Sum DFS",
    "secondary_patterns": [
      "4-Subset Sum DFS"
    ],
    "stage": "Recursion & Backtracking",
    "curriculumStage": "Stage 11 — Recursion & Backtracking",
    "roadmapPhase": "Stage 11 — Recursion & Backtracking",
    "phase": "Stage 11 — Recursion & Backtracking",
    "estimatedTime": 30,
    "statement": "Given the constraints and input parameters for Matchsticks to Square, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Matchsticks to Square."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Matchsticks to Square.",
      "Leverage the optimal Backtracking pattern to reduce time complexity."
    ],
    "learningObjective": "Master Backtracking techniques by solving Medium problem constraints for Matchsticks to Square.",
    "whyThisPattern": "When observing Backtracking problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/matchsticks-to-square/",
    "leetcode_title": "Matchsticks to Square",
    "leetcode_id": 473,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/matchsticks-to-square/",
    "canonicalSlug": "matchsticks-to-square",
    "canonicalUrl": "https://leetcode.com/problems/matchsticks-to-square/",
    "url": "https://leetcode.com/problems/matchsticks-to-square/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Matchsticks to Square\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Matchsticks to Square\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Matchsticks to Square\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Matchsticks to Square\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Matchsticks to Square\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Matchsticks to Square\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Matchsticks to Square\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Matchsticks to Square\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Matchsticks to Square",
      "cpp_optimal": "// Solution for Matchsticks to Square",
      "java_brute": "// Solution for Matchsticks to Square",
      "java_optimal": "// Solution for Matchsticks to Square",
      "python_brute": "# Solution for Matchsticks to Square",
      "python_optimal": "# Solution for Matchsticks to Square"
    },
    "originalOrder": 396,
    "learningOrder": 396
  },
  {
    "id": 529,
    "number": 529,
    "sequence_number": 529,
    "title": "Majority Element II",
    "slug": "majority-element-ii",
    "difficulty": "Medium",
    "topic": "Arrays",
    "subtopic": "Arrays Optimization",
    "pattern": "Arrays Pattern",
    "secondary_patterns": [
      "Arrays Pattern"
    ],
    "stage": "Recursion & Backtracking",
    "curriculumStage": "Stage 11 — Recursion & Backtracking",
    "roadmapPhase": "Stage 11 — Recursion & Backtracking",
    "phase": "Stage 11 — Recursion & Backtracking",
    "estimatedTime": 30,
    "statement": "Solve the **Majority Element II** problem using standard Arrays techniques. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Arrays algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Arrays properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Arrays techniques by solving Medium problem constraints for Majority Element II.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/majority-element-ii/",
    "leetcode_title": "Majority Element II",
    "leetcode_id": 229,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/majority-element-ii/",
    "canonicalSlug": "majority-element-ii",
    "canonicalUrl": "https://leetcode.com/problems/majority-element-ii/",
    "url": "https://leetcode.com/problems/majority-element-ii/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Majority Element II\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Majority Element II\n};",
        "java": "// Java Solution for Majority Element II\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Majority Element II\n}",
        "python": "# Python Solution for Majority Element II\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Majority Element II\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Majority Element II\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Majority Element II\n};",
        "java": "// Optimal Java Solution for Majority Element II\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Majority Element II\n}",
        "python": "# Optimal Python Solution for Majority Element II\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Majority Element II\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Majority Element II",
      "cpp_optimal": "// Solution for Majority Element II",
      "java_brute": "// Solution for Majority Element II",
      "java_optimal": "// Solution for Majority Element II",
      "python_brute": "# Solution for Majority Element II",
      "python_optimal": "# Solution for Majority Element II"
    },
    "originalOrder": 287,
    "learningOrder": 287
  },
  {
    "id": 530,
    "number": 530,
    "sequence_number": 530,
    "title": "Perfect Squares",
    "slug": "perfect-squares",
    "difficulty": "Medium",
    "topic": "Arrays",
    "subtopic": "Arrays Optimization",
    "pattern": "Arrays Pattern",
    "secondary_patterns": [
      "Arrays Pattern"
    ],
    "stage": "Recursion & Backtracking",
    "curriculumStage": "Stage 11 — Recursion & Backtracking",
    "roadmapPhase": "Stage 11 — Recursion & Backtracking",
    "phase": "Stage 11 — Recursion & Backtracking",
    "estimatedTime": 30,
    "statement": "Solve the **Perfect Squares** problem using standard Arrays techniques. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Arrays algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Arrays properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Arrays techniques by solving Medium problem constraints for Perfect Squares.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/perfect-squares/",
    "leetcode_title": "Perfect Squares",
    "leetcode_id": 279,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/perfect-squares/",
    "canonicalSlug": "perfect-squares",
    "canonicalUrl": "https://leetcode.com/problems/perfect-squares/",
    "url": "https://leetcode.com/problems/perfect-squares/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Perfect Squares\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Perfect Squares\n};",
        "java": "// Java Solution for Perfect Squares\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Perfect Squares\n}",
        "python": "# Python Solution for Perfect Squares\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Perfect Squares\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Perfect Squares\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Perfect Squares\n};",
        "java": "// Optimal Java Solution for Perfect Squares\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Perfect Squares\n}",
        "python": "# Optimal Python Solution for Perfect Squares\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Perfect Squares\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Perfect Squares",
      "cpp_optimal": "// Solution for Perfect Squares",
      "java_brute": "// Solution for Perfect Squares",
      "java_optimal": "// Solution for Perfect Squares",
      "python_brute": "# Solution for Perfect Squares",
      "python_optimal": "# Solution for Perfect Squares"
    },
    "originalOrder": 289,
    "learningOrder": 289
  },
  {
    "id": 531,
    "number": 531,
    "sequence_number": 531,
    "title": "Peeking Iterator",
    "slug": "peeking-iterator",
    "difficulty": "Medium",
    "topic": "Arrays",
    "subtopic": "Arrays Optimization",
    "pattern": "Arrays Pattern",
    "secondary_patterns": [
      "Arrays Pattern"
    ],
    "stage": "Recursion & Backtracking",
    "curriculumStage": "Stage 11 — Recursion & Backtracking",
    "roadmapPhase": "Stage 11 — Recursion & Backtracking",
    "phase": "Stage 11 — Recursion & Backtracking",
    "estimatedTime": 30,
    "statement": "Solve the **Peeking Iterator** problem using standard Arrays techniques. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Arrays algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Arrays properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Arrays techniques by solving Medium problem constraints for Peeking Iterator.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/peeking-iterator/",
    "leetcode_title": "Peeking Iterator",
    "leetcode_id": 284,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/peeking-iterator/",
    "canonicalSlug": "peeking-iterator",
    "canonicalUrl": "https://leetcode.com/problems/peeking-iterator/",
    "url": "https://leetcode.com/problems/peeking-iterator/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Peeking Iterator\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Peeking Iterator\n};",
        "java": "// Java Solution for Peeking Iterator\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Peeking Iterator\n}",
        "python": "# Python Solution for Peeking Iterator\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Peeking Iterator\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Peeking Iterator\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Peeking Iterator\n};",
        "java": "// Optimal Java Solution for Peeking Iterator\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Peeking Iterator\n}",
        "python": "# Optimal Python Solution for Peeking Iterator\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Peeking Iterator\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Peeking Iterator",
      "cpp_optimal": "// Solution for Peeking Iterator",
      "java_brute": "// Solution for Peeking Iterator",
      "java_optimal": "// Solution for Peeking Iterator",
      "python_brute": "# Solution for Peeking Iterator",
      "python_optimal": "# Solution for Peeking Iterator"
    },
    "originalOrder": 290,
    "learningOrder": 290
  },
  {
    "id": 532,
    "number": 532,
    "sequence_number": 532,
    "title": "Find the Duplicate Number",
    "slug": "find-the-duplicate-number",
    "difficulty": "Medium",
    "topic": "Arrays",
    "subtopic": "Arrays Optimization",
    "pattern": "Arrays Pattern",
    "secondary_patterns": [
      "Arrays Pattern"
    ],
    "stage": "Recursion & Backtracking",
    "curriculumStage": "Stage 11 — Recursion & Backtracking",
    "roadmapPhase": "Stage 11 — Recursion & Backtracking",
    "phase": "Stage 11 — Recursion & Backtracking",
    "estimatedTime": 30,
    "statement": "Solve the **Find the Duplicate Number** problem using standard Arrays techniques. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Arrays algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Arrays properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Arrays techniques by solving Medium problem constraints for Find the Duplicate Number.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/find-the-duplicate-number/",
    "leetcode_title": "Find the Duplicate Number",
    "leetcode_id": 287,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/find-the-duplicate-number/",
    "canonicalSlug": "find-the-duplicate-number",
    "canonicalUrl": "https://leetcode.com/problems/find-the-duplicate-number/",
    "url": "https://leetcode.com/problems/find-the-duplicate-number/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Find the Duplicate Number\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Find the Duplicate Number\n};",
        "java": "// Java Solution for Find the Duplicate Number\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Find the Duplicate Number\n}",
        "python": "# Python Solution for Find the Duplicate Number\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Find the Duplicate Number\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Find the Duplicate Number\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Find the Duplicate Number\n};",
        "java": "// Optimal Java Solution for Find the Duplicate Number\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Find the Duplicate Number\n}",
        "python": "# Optimal Python Solution for Find the Duplicate Number\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Find the Duplicate Number\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Find the Duplicate Number",
      "cpp_optimal": "// Solution for Find the Duplicate Number",
      "java_brute": "// Solution for Find the Duplicate Number",
      "java_optimal": "// Solution for Find the Duplicate Number",
      "python_brute": "# Solution for Find the Duplicate Number",
      "python_optimal": "# Solution for Find the Duplicate Number"
    },
    "originalOrder": 291,
    "learningOrder": 291
  },
  {
    "id": 533,
    "number": 533,
    "sequence_number": 533,
    "title": "Bulls and Cows",
    "slug": "bulls-and-cows",
    "difficulty": "Medium",
    "topic": "Bit Manipulation",
    "subtopic": "Arrays Optimization",
    "pattern": "Arrays Pattern",
    "secondary_patterns": [
      "Arrays Pattern"
    ],
    "stage": "Recursion & Backtracking",
    "curriculumStage": "Stage 11 — Recursion & Backtracking",
    "roadmapPhase": "Stage 11 — Recursion & Backtracking",
    "phase": "Stage 11 — Recursion & Backtracking",
    "estimatedTime": 30,
    "statement": "Solve the **Bulls and Cows** problem using standard Arrays techniques. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Arrays algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Arrays properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Arrays techniques by solving Medium problem constraints for Bulls and Cows.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/bulls-and-cows/",
    "leetcode_title": "Bulls and Cows",
    "leetcode_id": 299,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/bulls-and-cows/",
    "canonicalSlug": "bulls-and-cows",
    "canonicalUrl": "https://leetcode.com/problems/bulls-and-cows/",
    "url": "https://leetcode.com/problems/bulls-and-cows/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Bulls and Cows\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Bulls and Cows\n};",
        "java": "// Java Solution for Bulls and Cows\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Bulls and Cows\n}",
        "python": "# Python Solution for Bulls and Cows\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Bulls and Cows\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Bulls and Cows\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Bulls and Cows\n};",
        "java": "// Optimal Java Solution for Bulls and Cows\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Bulls and Cows\n}",
        "python": "# Optimal Python Solution for Bulls and Cows\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Bulls and Cows\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Bulls and Cows",
      "cpp_optimal": "// Solution for Bulls and Cows",
      "java_brute": "// Solution for Bulls and Cows",
      "java_optimal": "// Solution for Bulls and Cows",
      "python_brute": "# Solution for Bulls and Cows",
      "python_optimal": "# Solution for Bulls and Cows"
    },
    "originalOrder": 292,
    "learningOrder": 292
  },
  {
    "id": 534,
    "number": 534,
    "sequence_number": 534,
    "title": "Additive Number",
    "slug": "additive-number",
    "difficulty": "Medium",
    "topic": "Arrays",
    "subtopic": "Arrays Optimization",
    "pattern": "Arrays Pattern",
    "secondary_patterns": [
      "Arrays Pattern"
    ],
    "stage": "Recursion & Backtracking",
    "curriculumStage": "Stage 11 — Recursion & Backtracking",
    "roadmapPhase": "Stage 11 — Recursion & Backtracking",
    "phase": "Stage 11 — Recursion & Backtracking",
    "estimatedTime": 30,
    "statement": "Solve the **Additive Number** problem using standard Arrays techniques. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Arrays algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Arrays properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Arrays techniques by solving Medium problem constraints for Additive Number.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/additive-number/",
    "leetcode_title": "Additive Number",
    "leetcode_id": 306,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/additive-number/",
    "canonicalSlug": "additive-number",
    "canonicalUrl": "https://leetcode.com/problems/additive-number/",
    "url": "https://leetcode.com/problems/additive-number/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Additive Number\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Additive Number\n};",
        "java": "// Java Solution for Additive Number\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Additive Number\n}",
        "python": "# Python Solution for Additive Number\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Additive Number\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Additive Number\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Additive Number\n};",
        "java": "// Optimal Java Solution for Additive Number\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Additive Number\n}",
        "python": "# Optimal Python Solution for Additive Number\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Additive Number\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Additive Number",
      "cpp_optimal": "// Solution for Additive Number",
      "java_brute": "// Solution for Additive Number",
      "java_optimal": "// Solution for Additive Number",
      "python_brute": "# Solution for Additive Number",
      "python_optimal": "# Solution for Additive Number"
    },
    "originalOrder": 293,
    "learningOrder": 293
  },
  {
    "id": 535,
    "number": 535,
    "sequence_number": 535,
    "title": "Best Time to Buy and Sell Stock with Cooldown",
    "slug": "best-time-to-buy-and-sell-stock-with-cooldown",
    "difficulty": "Medium",
    "topic": "Bit Manipulation",
    "subtopic": "Arrays Optimization",
    "pattern": "Arrays Pattern",
    "secondary_patterns": [
      "Arrays Pattern"
    ],
    "stage": "Recursion & Backtracking",
    "curriculumStage": "Stage 11 — Recursion & Backtracking",
    "roadmapPhase": "Stage 11 — Recursion & Backtracking",
    "phase": "Stage 11 — Recursion & Backtracking",
    "estimatedTime": 30,
    "statement": "Solve the **Best Time to Buy and Sell Stock with Cooldown** problem using standard Arrays techniques. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Arrays algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Arrays properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Arrays techniques by solving Medium problem constraints for Best Time to Buy and Sell Stock with Cooldown.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/best-time-to-buy-and-sell-stock-with-cooldown/",
    "leetcode_title": "Best Time to Buy and Sell Stock with Cooldown",
    "leetcode_id": 309,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/best-time-to-buy-and-sell-stock-with-cooldown/",
    "canonicalSlug": "best-time-to-buy-and-sell-stock-with-cooldown",
    "canonicalUrl": "https://leetcode.com/problems/best-time-to-buy-and-sell-stock-with-cooldown/",
    "url": "https://leetcode.com/problems/best-time-to-buy-and-sell-stock-with-cooldown/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Best Time to Buy and Sell Stock with Cooldown\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Best Time to Buy and Sell Stock with Cooldown\n};",
        "java": "// Java Solution for Best Time to Buy and Sell Stock with Cooldown\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Best Time to Buy and Sell Stock with Cooldown\n}",
        "python": "# Python Solution for Best Time to Buy and Sell Stock with Cooldown\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Best Time to Buy and Sell Stock with Cooldown\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Best Time to Buy and Sell Stock with Cooldown\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Best Time to Buy and Sell Stock with Cooldown\n};",
        "java": "// Optimal Java Solution for Best Time to Buy and Sell Stock with Cooldown\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Best Time to Buy and Sell Stock with Cooldown\n}",
        "python": "# Optimal Python Solution for Best Time to Buy and Sell Stock with Cooldown\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Best Time to Buy and Sell Stock with Cooldown\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Best Time to Buy and Sell Stock with Cooldown",
      "cpp_optimal": "// Solution for Best Time to Buy and Sell Stock with Cooldown",
      "java_brute": "// Solution for Best Time to Buy and Sell Stock with Cooldown",
      "java_optimal": "// Solution for Best Time to Buy and Sell Stock with Cooldown",
      "python_brute": "# Solution for Best Time to Buy and Sell Stock with Cooldown",
      "python_optimal": "# Solution for Best Time to Buy and Sell Stock with Cooldown"
    },
    "originalOrder": 294,
    "learningOrder": 294
  },
  {
    "id": 536,
    "number": 536,
    "sequence_number": 536,
    "title": "Probability of a Two Boxes Having The Same Number of Distinct Balls",
    "slug": "probability-of-a-two-boxes-having-the-same-number-of-distinct-balls",
    "difficulty": "Hard",
    "topic": "Backtracking",
    "subtopic": "Backtracking Optimization",
    "pattern": "Multinomial Coefficient DFS",
    "secondary_patterns": [
      "Multinomial Coefficient DFS"
    ],
    "stage": "Recursion & Backtracking",
    "curriculumStage": "Stage 11 — Recursion & Backtracking",
    "roadmapPhase": "Stage 11 — Recursion & Backtracking",
    "phase": "Stage 11 — Recursion & Backtracking",
    "estimatedTime": 45,
    "statement": "Given the constraints and input parameters for Probability of a Two Boxes Having The Same Number of Distinct Balls, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Probability of a Two Boxes Having The Same Number of Distinct Balls."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Probability of a Two Boxes Having The Same Number of Distinct Balls.",
      "Leverage the optimal Backtracking pattern to reduce time complexity."
    ],
    "learningObjective": "Master Backtracking techniques by solving Hard problem constraints for Probability of a Two Boxes Having The Same Number of Distinct Balls.",
    "whyThisPattern": "When observing Backtracking problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/probability-of-a-two-boxes-having-the-same-number-of-distinct-balls/",
    "leetcode_title": "Probability of a Two Boxes Having The Same Number of Distinct Balls",
    "leetcode_id": 1467,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/probability-of-a-two-boxes-having-the-same-number-of-distinct-balls/",
    "canonicalSlug": "probability-of-a-two-boxes-having-the-same-number-of-distinct-balls",
    "canonicalUrl": "https://leetcode.com/problems/probability-of-a-two-boxes-having-the-same-number-of-distinct-balls/",
    "url": "https://leetcode.com/problems/probability-of-a-two-boxes-having-the-same-number-of-distinct-balls/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Probability of a Two Boxes Having The Same Number of Distinct Balls\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Probability of a Two Boxes Having The Same Number of Distinct Balls\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Probability of a Two Boxes Having The Same Number of Distinct Balls\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Probability of a Two Boxes Having The Same Number of Distinct Balls\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Probability of a Two Boxes Having The Same Number of Distinct Balls\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Probability of a Two Boxes Having The Same Number of Distinct Balls\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Probability of a Two Boxes Having The Same Number of Distinct Balls\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Probability of a Two Boxes Having The Same Number of Distinct Balls\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Probability of a Two Boxes Having The Same Number of Distinct Balls",
      "cpp_optimal": "// Solution for Probability of a Two Boxes Having The Same Number of Distinct Balls",
      "java_brute": "// Solution for Probability of a Two Boxes Having The Same Number of Distinct Balls",
      "java_optimal": "// Solution for Probability of a Two Boxes Having The Same Number of Distinct Balls",
      "python_brute": "# Solution for Probability of a Two Boxes Having The Same Number of Distinct Balls",
      "python_optimal": "# Solution for Probability of a Two Boxes Having The Same Number of Distinct Balls"
    },
    "originalOrder": 775,
    "learningOrder": 775
  },
  {
    "id": 537,
    "number": 537,
    "sequence_number": 537,
    "title": "24 Game",
    "slug": "24-game",
    "difficulty": "Hard",
    "topic": "Backtracking",
    "subtopic": "Backtracking Optimization",
    "pattern": "Floating Point Expression DFS",
    "secondary_patterns": [
      "Floating Point Expression DFS"
    ],
    "stage": "Recursion & Backtracking",
    "curriculumStage": "Stage 11 — Recursion & Backtracking",
    "roadmapPhase": "Stage 11 — Recursion & Backtracking",
    "phase": "Stage 11 — Recursion & Backtracking",
    "estimatedTime": 45,
    "statement": "Given the constraints and input parameters for 24 Game, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for 24 Game."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for 24 Game.",
      "Leverage the optimal Backtracking pattern to reduce time complexity."
    ],
    "learningObjective": "Master Backtracking techniques by solving Hard problem constraints for 24 Game.",
    "whyThisPattern": "When observing Backtracking problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/24-game/",
    "leetcode_title": "24 Game",
    "leetcode_id": 679,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/24-game/",
    "canonicalSlug": "24-game",
    "canonicalUrl": "https://leetcode.com/problems/24-game/",
    "url": "https://leetcode.com/problems/24-game/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for 24 Game\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for 24 Game\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for 24 Game\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for 24 Game\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for 24 Game\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for 24 Game\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for 24 Game\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for 24 Game\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for 24 Game",
      "cpp_optimal": "// Solution for 24 Game",
      "java_brute": "// Solution for 24 Game",
      "java_optimal": "// Solution for 24 Game",
      "python_brute": "# Solution for 24 Game",
      "python_optimal": "# Solution for 24 Game"
    },
    "originalOrder": 776,
    "learningOrder": 776
  },
  {
    "id": 538,
    "number": 538,
    "sequence_number": 538,
    "title": "N-Queens II",
    "slug": "n-queens-ii",
    "difficulty": "Hard",
    "topic": "Backtracking",
    "subtopic": "Backtracking Optimization",
    "pattern": "Bitmask Constraints Board",
    "secondary_patterns": [
      "Bitmask Constraints Board"
    ],
    "stage": "Recursion & Backtracking",
    "curriculumStage": "Stage 11 — Recursion & Backtracking",
    "roadmapPhase": "Stage 11 — Recursion & Backtracking",
    "phase": "Stage 11 — Recursion & Backtracking",
    "estimatedTime": 45,
    "statement": "Given the constraints and input parameters for N-Queens II, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for N-Queens II."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for N-Queens II.",
      "Leverage the optimal Backtracking pattern to reduce time complexity."
    ],
    "learningObjective": "Master Backtracking techniques by solving Hard problem constraints for N-Queens II.",
    "whyThisPattern": "When observing Backtracking problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/n-queens-ii/",
    "leetcode_title": "N-Queens II",
    "leetcode_id": 52,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/n-queens-ii/",
    "canonicalSlug": "n-queens-ii",
    "canonicalUrl": "https://leetcode.com/problems/n-queens-ii/",
    "url": "https://leetcode.com/problems/n-queens-ii/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for N-Queens II\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for N-Queens II\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for N-Queens II\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for N-Queens II\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for N-Queens II\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for N-Queens II\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for N-Queens II\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for N-Queens II\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for N-Queens II",
      "cpp_optimal": "// Solution for N-Queens II",
      "java_brute": "// Solution for N-Queens II",
      "java_optimal": "// Solution for N-Queens II",
      "python_brute": "# Solution for N-Queens II",
      "python_optimal": "# Solution for N-Queens II"
    },
    "originalOrder": 777,
    "learningOrder": 777
  },
  {
    "id": 539,
    "number": 539,
    "sequence_number": 539,
    "title": "Expression Add Operators",
    "slug": "expression-add-operators",
    "difficulty": "Hard",
    "topic": "Backtracking",
    "subtopic": "Backtracking Optimization",
    "pattern": "Eval Target Backtracking",
    "secondary_patterns": [
      "Eval Target Backtracking"
    ],
    "stage": "Recursion & Backtracking",
    "curriculumStage": "Stage 11 — Recursion & Backtracking",
    "roadmapPhase": "Stage 11 — Recursion & Backtracking",
    "phase": "Stage 11 — Recursion & Backtracking",
    "estimatedTime": 45,
    "statement": "Given the constraints and input parameters for Expression Add Operators, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Expression Add Operators."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Expression Add Operators.",
      "Leverage the optimal Backtracking pattern to reduce time complexity."
    ],
    "learningObjective": "Master Backtracking techniques by solving Hard problem constraints for Expression Add Operators.",
    "whyThisPattern": "When observing Backtracking problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/expression-add-operators/",
    "leetcode_title": "Expression Add Operators",
    "leetcode_id": 282,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/expression-add-operators/",
    "canonicalSlug": "expression-add-operators",
    "canonicalUrl": "https://leetcode.com/problems/expression-add-operators/",
    "url": "https://leetcode.com/problems/expression-add-operators/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Expression Add Operators\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Expression Add Operators\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Expression Add Operators\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Expression Add Operators\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Expression Add Operators\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Expression Add Operators\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Expression Add Operators\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Expression Add Operators\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Expression Add Operators",
      "cpp_optimal": "// Solution for Expression Add Operators",
      "java_brute": "// Solution for Expression Add Operators",
      "java_optimal": "// Solution for Expression Add Operators",
      "python_brute": "# Solution for Expression Add Operators",
      "python_optimal": "# Solution for Expression Add Operators"
    },
    "originalOrder": 778,
    "learningOrder": 778
  },
  {
    "id": 540,
    "number": 540,
    "sequence_number": 540,
    "title": "Zuma Game",
    "slug": "zuma-game",
    "difficulty": "Hard",
    "topic": "Backtracking",
    "subtopic": "Backtracking Optimization",
    "pattern": "Board Reduction DFS",
    "secondary_patterns": [
      "Board Reduction DFS"
    ],
    "stage": "Recursion & Backtracking",
    "curriculumStage": "Stage 11 — Recursion & Backtracking",
    "roadmapPhase": "Stage 11 — Recursion & Backtracking",
    "phase": "Stage 11 — Recursion & Backtracking",
    "estimatedTime": 45,
    "statement": "Given the constraints and input parameters for Zuma Game, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Zuma Game."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Zuma Game.",
      "Leverage the optimal Backtracking pattern to reduce time complexity."
    ],
    "learningObjective": "Master Backtracking techniques by solving Hard problem constraints for Zuma Game.",
    "whyThisPattern": "When observing Backtracking problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/zuma-game/",
    "leetcode_title": "Zuma Game",
    "leetcode_id": 488,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/zuma-game/",
    "canonicalSlug": "zuma-game",
    "canonicalUrl": "https://leetcode.com/problems/zuma-game/",
    "url": "https://leetcode.com/problems/zuma-game/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Zuma Game\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Zuma Game\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Zuma Game\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Zuma Game\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Zuma Game\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Zuma Game\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Zuma Game\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Zuma Game\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Zuma Game",
      "cpp_optimal": "// Solution for Zuma Game",
      "java_brute": "// Solution for Zuma Game",
      "java_optimal": "// Solution for Zuma Game",
      "python_brute": "# Solution for Zuma Game",
      "python_optimal": "# Solution for Zuma Game"
    },
    "originalOrder": 779,
    "learningOrder": 779
  },
  {
    "id": 541,
    "number": 541,
    "sequence_number": 541,
    "title": "Maximum Path Quality of a Graph",
    "slug": "maximum-path-quality-of-a-graph",
    "difficulty": "Hard",
    "topic": "Backtracking",
    "subtopic": "Backtracking Optimization",
    "pattern": "Time-Bounded DFS Backtracking",
    "secondary_patterns": [
      "Time-Bounded DFS Backtracking"
    ],
    "stage": "Recursion & Backtracking",
    "curriculumStage": "Stage 11 — Recursion & Backtracking",
    "roadmapPhase": "Stage 11 — Recursion & Backtracking",
    "phase": "Stage 11 — Recursion & Backtracking",
    "estimatedTime": 45,
    "statement": "Given the constraints and input parameters for Maximum Path Quality of a Graph, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Maximum Path Quality of a Graph."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Maximum Path Quality of a Graph.",
      "Leverage the optimal Backtracking pattern to reduce time complexity."
    ],
    "learningObjective": "Master Backtracking techniques by solving Hard problem constraints for Maximum Path Quality of a Graph.",
    "whyThisPattern": "When observing Backtracking problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/maximum-path-quality-of-a-graph/",
    "leetcode_title": "Maximum Path Quality of a Graph",
    "leetcode_id": 2065,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/maximum-path-quality-of-a-graph/",
    "canonicalSlug": "maximum-path-quality-of-a-graph",
    "canonicalUrl": "https://leetcode.com/problems/maximum-path-quality-of-a-graph/",
    "url": "https://leetcode.com/problems/maximum-path-quality-of-a-graph/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Maximum Path Quality of a Graph\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Maximum Path Quality of a Graph\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Maximum Path Quality of a Graph\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Maximum Path Quality of a Graph\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Maximum Path Quality of a Graph\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Maximum Path Quality of a Graph\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Maximum Path Quality of a Graph\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Maximum Path Quality of a Graph\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Maximum Path Quality of a Graph",
      "cpp_optimal": "// Solution for Maximum Path Quality of a Graph",
      "java_brute": "// Solution for Maximum Path Quality of a Graph",
      "java_optimal": "// Solution for Maximum Path Quality of a Graph",
      "python_brute": "# Solution for Maximum Path Quality of a Graph",
      "python_optimal": "# Solution for Maximum Path Quality of a Graph"
    },
    "originalOrder": 780,
    "learningOrder": 780
  },
  {
    "id": 542,
    "number": 542,
    "sequence_number": 542,
    "title": "Sliding Puzzle",
    "slug": "sliding-puzzle",
    "difficulty": "Hard",
    "topic": "BFS",
    "subtopic": "BFS Optimization",
    "pattern": "2x3 Board State BFS",
    "secondary_patterns": [
      "2x3 Board State BFS"
    ],
    "stage": "Recursion & Backtracking",
    "curriculumStage": "Stage 11 — Recursion & Backtracking",
    "roadmapPhase": "Stage 11 — Recursion & Backtracking",
    "phase": "Stage 11 — Recursion & Backtracking",
    "estimatedTime": 45,
    "statement": "Given the constraints and input parameters for Sliding Puzzle, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Sliding Puzzle."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Sliding Puzzle.",
      "Leverage the optimal BFS pattern to reduce time complexity."
    ],
    "learningObjective": "Master BFS techniques by solving Hard problem constraints for Sliding Puzzle.",
    "whyThisPattern": "When observing BFS problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/sliding-puzzle/",
    "leetcode_title": "Sliding Puzzle",
    "leetcode_id": 773,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/sliding-puzzle/",
    "canonicalSlug": "sliding-puzzle",
    "canonicalUrl": "https://leetcode.com/problems/sliding-puzzle/",
    "url": "https://leetcode.com/problems/sliding-puzzle/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Sliding Puzzle\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Sliding Puzzle\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Sliding Puzzle\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Sliding Puzzle\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Sliding Puzzle\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Sliding Puzzle\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Sliding Puzzle\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Sliding Puzzle\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Sliding Puzzle",
      "cpp_optimal": "// Solution for Sliding Puzzle",
      "java_brute": "// Solution for Sliding Puzzle",
      "java_optimal": "// Solution for Sliding Puzzle",
      "python_brute": "# Solution for Sliding Puzzle",
      "python_optimal": "# Solution for Sliding Puzzle"
    },
    "originalOrder": 781,
    "learningOrder": 781
  },
  {
    "id": 543,
    "number": 543,
    "sequence_number": 543,
    "title": "Shortest Path to Get All Keys",
    "slug": "shortest-path-to-get-all-keys",
    "difficulty": "Hard",
    "topic": "BFS",
    "subtopic": "BFS Optimization",
    "pattern": "Bitmask BFS State",
    "secondary_patterns": [
      "Bitmask BFS State"
    ],
    "stage": "Recursion & Backtracking",
    "curriculumStage": "Stage 11 — Recursion & Backtracking",
    "roadmapPhase": "Stage 11 — Recursion & Backtracking",
    "phase": "Stage 11 — Recursion & Backtracking",
    "estimatedTime": 45,
    "statement": "Given the constraints and input parameters for Shortest Path to Get All Keys, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Shortest Path to Get All Keys."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Shortest Path to Get All Keys.",
      "Leverage the optimal Graphs pattern to reduce time complexity."
    ],
    "learningObjective": "Master BFS techniques by solving Hard problem constraints for Shortest Path to Get All Keys.",
    "whyThisPattern": "When observing BFS problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/shortest-path-to-get-all-keys/",
    "leetcode_title": "Shortest Path to Get All Keys",
    "leetcode_id": 864,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/shortest-path-to-get-all-keys/",
    "canonicalSlug": "shortest-path-to-get-all-keys",
    "canonicalUrl": "https://leetcode.com/problems/shortest-path-to-get-all-keys/",
    "url": "https://leetcode.com/problems/shortest-path-to-get-all-keys/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Shortest Path to Get All Keys\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Shortest Path to Get All Keys\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Shortest Path to Get All Keys\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Shortest Path to Get All Keys\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Shortest Path to Get All Keys\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Shortest Path to Get All Keys\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Shortest Path to Get All Keys\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Shortest Path to Get All Keys\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Shortest Path to Get All Keys",
      "cpp_optimal": "// Solution for Shortest Path to Get All Keys",
      "java_brute": "// Solution for Shortest Path to Get All Keys",
      "java_optimal": "// Solution for Shortest Path to Get All Keys",
      "python_brute": "# Solution for Shortest Path to Get All Keys",
      "python_optimal": "# Solution for Shortest Path to Get All Keys"
    },
    "originalOrder": 782,
    "learningOrder": 782
  },
  {
    "id": 544,
    "number": 544,
    "sequence_number": 544,
    "title": "Shortest Path Visiting All Nodes",
    "slug": "shortest-path-visiting-all-nodes",
    "difficulty": "Hard",
    "topic": "BFS",
    "subtopic": "BFS Optimization",
    "pattern": "Bitmask BFS Shortest Path",
    "secondary_patterns": [
      "Bitmask BFS Shortest Path"
    ],
    "stage": "Recursion & Backtracking",
    "curriculumStage": "Stage 11 — Recursion & Backtracking",
    "roadmapPhase": "Stage 11 — Recursion & Backtracking",
    "phase": "Stage 11 — Recursion & Backtracking",
    "estimatedTime": 45,
    "statement": "Given the constraints and input parameters for Shortest Path Visiting All Nodes, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Shortest Path Visiting All Nodes."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Shortest Path Visiting All Nodes.",
      "Leverage the optimal Graphs pattern to reduce time complexity."
    ],
    "learningObjective": "Master BFS techniques by solving Hard problem constraints for Shortest Path Visiting All Nodes.",
    "whyThisPattern": "When observing BFS problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/shortest-path-visiting-all-nodes/",
    "leetcode_title": "Shortest Path Visiting All Nodes",
    "leetcode_id": 847,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/shortest-path-visiting-all-nodes/",
    "canonicalSlug": "shortest-path-visiting-all-nodes",
    "canonicalUrl": "https://leetcode.com/problems/shortest-path-visiting-all-nodes/",
    "url": "https://leetcode.com/problems/shortest-path-visiting-all-nodes/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Shortest Path Visiting All Nodes\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Shortest Path Visiting All Nodes\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Shortest Path Visiting All Nodes\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Shortest Path Visiting All Nodes\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Shortest Path Visiting All Nodes\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Shortest Path Visiting All Nodes\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Shortest Path Visiting All Nodes\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Shortest Path Visiting All Nodes\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Shortest Path Visiting All Nodes",
      "cpp_optimal": "// Solution for Shortest Path Visiting All Nodes",
      "java_brute": "// Solution for Shortest Path Visiting All Nodes",
      "java_optimal": "// Solution for Shortest Path Visiting All Nodes",
      "python_brute": "# Solution for Shortest Path Visiting All Nodes",
      "python_optimal": "# Solution for Shortest Path Visiting All Nodes"
    },
    "originalOrder": 783,
    "learningOrder": 783
  },
  {
    "id": 545,
    "number": 545,
    "sequence_number": 545,
    "title": "Cut Off Trees for Golf Event",
    "slug": "cut-off-trees-for-golf-event",
    "difficulty": "Hard",
    "topic": "BFS",
    "subtopic": "BFS Optimization",
    "pattern": "Step-by-Step BFS Path",
    "secondary_patterns": [
      "Step-by-Step BFS Path"
    ],
    "stage": "Recursion & Backtracking",
    "curriculumStage": "Stage 11 — Recursion & Backtracking",
    "roadmapPhase": "Stage 11 — Recursion & Backtracking",
    "phase": "Stage 11 — Recursion & Backtracking",
    "estimatedTime": 45,
    "statement": "Given the constraints and input parameters for Cut Off Trees for Golf Event, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Cut Off Trees for Golf Event."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Cut Off Trees for Golf Event.",
      "Leverage the optimal Graphs pattern to reduce time complexity."
    ],
    "learningObjective": "Master BFS techniques by solving Hard problem constraints for Cut Off Trees for Golf Event.",
    "whyThisPattern": "When observing BFS problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/cut-off-trees-for-golf-event/",
    "leetcode_title": "Cut Off Trees for Golf Event",
    "leetcode_id": 675,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/cut-off-trees-for-golf-event/",
    "canonicalSlug": "cut-off-trees-for-golf-event",
    "canonicalUrl": "https://leetcode.com/problems/cut-off-trees-for-golf-event/",
    "url": "https://leetcode.com/problems/cut-off-trees-for-golf-event/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Cut Off Trees for Golf Event\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Cut Off Trees for Golf Event\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Cut Off Trees for Golf Event\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Cut Off Trees for Golf Event\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Cut Off Trees for Golf Event\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Cut Off Trees for Golf Event\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Cut Off Trees for Golf Event\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Cut Off Trees for Golf Event\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Cut Off Trees for Golf Event",
      "cpp_optimal": "// Solution for Cut Off Trees for Golf Event",
      "java_brute": "// Solution for Cut Off Trees for Golf Event",
      "java_optimal": "// Solution for Cut Off Trees for Golf Event",
      "python_brute": "# Solution for Cut Off Trees for Golf Event",
      "python_optimal": "# Solution for Cut Off Trees for Golf Event"
    },
    "originalOrder": 784,
    "learningOrder": 784
  },
  {
    "id": 546,
    "number": 546,
    "sequence_number": 546,
    "title": "Bus Routes",
    "slug": "bus-routes",
    "difficulty": "Hard",
    "topic": "BFS",
    "subtopic": "BFS Optimization",
    "pattern": "Multi-Route BFS Graph",
    "secondary_patterns": [
      "Multi-Route BFS Graph"
    ],
    "stage": "Recursion & Backtracking",
    "curriculumStage": "Stage 11 — Recursion & Backtracking",
    "roadmapPhase": "Stage 11 — Recursion & Backtracking",
    "phase": "Stage 11 — Recursion & Backtracking",
    "estimatedTime": 45,
    "statement": "Given the constraints and input parameters for Bus Routes, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Bus Routes."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Bus Routes.",
      "Leverage the optimal Graphs pattern to reduce time complexity."
    ],
    "learningObjective": "Master BFS techniques by solving Hard problem constraints for Bus Routes.",
    "whyThisPattern": "When observing BFS problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/bus-routes/",
    "leetcode_title": "Bus Routes",
    "leetcode_id": 815,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/bus-routes/",
    "canonicalSlug": "bus-routes",
    "canonicalUrl": "https://leetcode.com/problems/bus-routes/",
    "url": "https://leetcode.com/problems/bus-routes/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Bus Routes\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Bus Routes\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Bus Routes\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Bus Routes\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Bus Routes\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Bus Routes\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Bus Routes\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Bus Routes\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Bus Routes",
      "cpp_optimal": "// Solution for Bus Routes",
      "java_brute": "// Solution for Bus Routes",
      "java_optimal": "// Solution for Bus Routes",
      "python_brute": "# Solution for Bus Routes",
      "python_optimal": "# Solution for Bus Routes"
    },
    "originalOrder": 785,
    "learningOrder": 785
  },
  {
    "id": 547,
    "number": 547,
    "sequence_number": 547,
    "title": "Word Ladder II",
    "slug": "word-ladder-ii",
    "difficulty": "Hard",
    "topic": "BFS",
    "subtopic": "BFS Optimization",
    "pattern": "BFS Shortest Path + DFS Trace",
    "secondary_patterns": [
      "BFS Shortest Path + DFS Trace"
    ],
    "stage": "Recursion & Backtracking",
    "curriculumStage": "Stage 11 — Recursion & Backtracking",
    "roadmapPhase": "Stage 11 — Recursion & Backtracking",
    "phase": "Stage 11 — Recursion & Backtracking",
    "estimatedTime": 45,
    "statement": "Given the constraints and input parameters for Word Ladder II, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Word Ladder II."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Word Ladder II.",
      "Leverage the optimal Graphs pattern to reduce time complexity."
    ],
    "learningObjective": "Master BFS techniques by solving Hard problem constraints for Word Ladder II.",
    "whyThisPattern": "When observing BFS problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/word-ladder-ii/",
    "leetcode_title": "Word Ladder II",
    "leetcode_id": 126,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/word-ladder-ii/",
    "canonicalSlug": "word-ladder-ii",
    "canonicalUrl": "https://leetcode.com/problems/word-ladder-ii/",
    "url": "https://leetcode.com/problems/word-ladder-ii/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Word Ladder II\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Word Ladder II\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Word Ladder II\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Word Ladder II\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Word Ladder II\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Word Ladder II\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Word Ladder II\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Word Ladder II\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Word Ladder II",
      "cpp_optimal": "// Solution for Word Ladder II",
      "java_brute": "// Solution for Word Ladder II",
      "java_optimal": "// Solution for Word Ladder II",
      "python_brute": "# Solution for Word Ladder II",
      "python_optimal": "# Solution for Word Ladder II"
    },
    "originalOrder": 786,
    "learningOrder": 786
  },
  {
    "id": 548,
    "number": 548,
    "sequence_number": 548,
    "title": "Word Ladder",
    "slug": "word-ladder",
    "difficulty": "Hard",
    "topic": "BFS",
    "subtopic": "BFS Optimization",
    "pattern": "BFS Word Transformation Graph",
    "secondary_patterns": [
      "BFS Word Transformation Graph"
    ],
    "stage": "Recursion & Backtracking",
    "curriculumStage": "Stage 11 — Recursion & Backtracking",
    "roadmapPhase": "Stage 11 — Recursion & Backtracking",
    "phase": "Stage 11 — Recursion & Backtracking",
    "estimatedTime": 45,
    "statement": "Given the constraints and input parameters for Word Ladder, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Word Ladder."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Word Ladder.",
      "Leverage the optimal Graphs pattern to reduce time complexity."
    ],
    "learningObjective": "Master BFS techniques by solving Hard problem constraints for Word Ladder.",
    "whyThisPattern": "When observing BFS problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/word-ladder/",
    "leetcode_title": "Word Ladder",
    "leetcode_id": 127,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/word-ladder/",
    "canonicalSlug": "word-ladder",
    "canonicalUrl": "https://leetcode.com/problems/word-ladder/",
    "url": "https://leetcode.com/problems/word-ladder/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Word Ladder\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Word Ladder\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Word Ladder\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Word Ladder\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Word Ladder\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Word Ladder\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Word Ladder\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Word Ladder\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Word Ladder",
      "cpp_optimal": "// Solution for Word Ladder",
      "java_brute": "// Solution for Word Ladder",
      "java_optimal": "// Solution for Word Ladder",
      "python_brute": "# Solution for Word Ladder",
      "python_optimal": "# Solution for Word Ladder"
    },
    "originalOrder": 787,
    "learningOrder": 787
  },
  {
    "id": 549,
    "number": 549,
    "sequence_number": 549,
    "title": "Transform to Chessboard",
    "slug": "transform-to-chessboard",
    "difficulty": "Hard",
    "topic": "Bit Manipulation",
    "subtopic": "Bit Manipulation Optimization",
    "pattern": "Matrix Pattern Verification",
    "secondary_patterns": [
      "Matrix Pattern Verification"
    ],
    "stage": "Recursion & Backtracking",
    "curriculumStage": "Stage 11 — Recursion & Backtracking",
    "roadmapPhase": "Stage 11 — Recursion & Backtracking",
    "phase": "Stage 11 — Recursion & Backtracking",
    "estimatedTime": 45,
    "statement": "Given the constraints and input parameters for Transform to Chessboard, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Transform to Chessboard."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Transform to Chessboard.",
      "Leverage the optimal Bit Manipulation pattern to reduce time complexity."
    ],
    "learningObjective": "Master Bit Manipulation techniques by solving Hard problem constraints for Transform to Chessboard.",
    "whyThisPattern": "When observing Bit Manipulation problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/transform-to-chessboard/",
    "leetcode_title": "Transform to Chessboard",
    "leetcode_id": 782,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/transform-to-chessboard/",
    "canonicalSlug": "transform-to-chessboard",
    "canonicalUrl": "https://leetcode.com/problems/transform-to-chessboard/",
    "url": "https://leetcode.com/problems/transform-to-chessboard/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Transform to Chessboard\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Transform to Chessboard\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Transform to Chessboard\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Transform to Chessboard\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Transform to Chessboard\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Transform to Chessboard\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Transform to Chessboard\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Transform to Chessboard\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Transform to Chessboard",
      "cpp_optimal": "// Solution for Transform to Chessboard",
      "java_brute": "// Solution for Transform to Chessboard",
      "java_optimal": "// Solution for Transform to Chessboard",
      "python_brute": "# Solution for Transform to Chessboard",
      "python_optimal": "# Solution for Transform to Chessboard"
    },
    "originalOrder": 796,
    "learningOrder": 796
  },
  {
    "id": 550,
    "number": 550,
    "sequence_number": 550,
    "title": "Triples with Bitwise AND Equal To Zero",
    "slug": "triples-with-bitwise-and-equal-to-zero",
    "difficulty": "Hard",
    "topic": "Bit Manipulation",
    "subtopic": "Bit Manipulation Optimization",
    "pattern": "Frequency Map XOR/AND",
    "secondary_patterns": [
      "Frequency Map XOR/AND"
    ],
    "stage": "Recursion & Backtracking",
    "curriculumStage": "Stage 11 — Recursion & Backtracking",
    "roadmapPhase": "Stage 11 — Recursion & Backtracking",
    "phase": "Stage 11 — Recursion & Backtracking",
    "estimatedTime": 45,
    "statement": "Given the constraints and input parameters for Triples with Bitwise AND Equal To Zero, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Triples with Bitwise AND Equal To Zero."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Triples with Bitwise AND Equal To Zero.",
      "Leverage the optimal Bit Manipulation pattern to reduce time complexity."
    ],
    "learningObjective": "Master Bit Manipulation techniques by solving Hard problem constraints for Triples with Bitwise AND Equal To Zero.",
    "whyThisPattern": "When observing Bit Manipulation problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/triples-with-bitwise-and-equal-to-zero/",
    "leetcode_title": "Triples with Bitwise AND Equal To Zero",
    "leetcode_id": 982,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/triples-with-bitwise-and-equal-to-zero/",
    "canonicalSlug": "triples-with-bitwise-and-equal-to-zero",
    "canonicalUrl": "https://leetcode.com/problems/triples-with-bitwise-and-equal-to-zero/",
    "url": "https://leetcode.com/problems/triples-with-bitwise-and-equal-to-zero/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Triples with Bitwise AND Equal To Zero\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Triples with Bitwise AND Equal To Zero\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Triples with Bitwise AND Equal To Zero\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Triples with Bitwise AND Equal To Zero\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Triples with Bitwise AND Equal To Zero\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Triples with Bitwise AND Equal To Zero\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Triples with Bitwise AND Equal To Zero\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Triples with Bitwise AND Equal To Zero\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Triples with Bitwise AND Equal To Zero",
      "cpp_optimal": "// Solution for Triples with Bitwise AND Equal To Zero",
      "java_brute": "// Solution for Triples with Bitwise AND Equal To Zero",
      "java_optimal": "// Solution for Triples with Bitwise AND Equal To Zero",
      "python_brute": "# Solution for Triples with Bitwise AND Equal To Zero",
      "python_optimal": "# Solution for Triples with Bitwise AND Equal To Zero"
    },
    "originalOrder": 797,
    "learningOrder": 797
  },
  {
    "id": 551,
    "number": 551,
    "sequence_number": 551,
    "title": "Projection Area of 3D Shapes",
    "slug": "projection-area-of-3d-shapes",
    "difficulty": "Easy",
    "topic": "Geometry",
    "subtopic": "Arrays Optimization",
    "pattern": "Grid Projection Max",
    "secondary_patterns": [
      "Grid Projection Max"
    ],
    "stage": "Graph Traversal (BFS & DFS)",
    "curriculumStage": "Stage 12 — Graph Traversal (BFS & DFS)",
    "roadmapPhase": "Stage 12 — Graph Traversal (BFS & DFS)",
    "phase": "Stage 12 — Graph Traversal (BFS & DFS)",
    "estimatedTime": 15,
    "statement": "Given the constraints and input parameters for Projection Area of 3D Shapes, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Projection Area of 3D Shapes."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Projection Area of 3D Shapes.",
      "Leverage the optimal Arrays pattern to reduce time complexity."
    ],
    "learningObjective": "Master Arrays techniques by solving Easy problem constraints for Projection Area of 3D Shapes.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/projection-area-of-3d-shapes/",
    "leetcode_title": "Projection Area of 3D Shapes",
    "leetcode_id": 883,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/projection-area-of-3d-shapes/",
    "canonicalSlug": "projection-area-of-3d-shapes",
    "canonicalUrl": "https://leetcode.com/problems/projection-area-of-3d-shapes/",
    "url": "https://leetcode.com/problems/projection-area-of-3d-shapes/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Projection Area of 3D Shapes\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Projection Area of 3D Shapes\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Projection Area of 3D Shapes\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Projection Area of 3D Shapes\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Projection Area of 3D Shapes\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Projection Area of 3D Shapes\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Projection Area of 3D Shapes\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Projection Area of 3D Shapes\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Projection Area of 3D Shapes",
      "cpp_optimal": "// Solution for Projection Area of 3D Shapes",
      "java_brute": "// Solution for Projection Area of 3D Shapes",
      "java_optimal": "// Solution for Projection Area of 3D Shapes",
      "python_brute": "# Solution for Projection Area of 3D Shapes",
      "python_optimal": "# Solution for Projection Area of 3D Shapes"
    },
    "originalOrder": 106,
    "learningOrder": 106
  },
  {
    "id": 552,
    "number": 552,
    "sequence_number": 552,
    "title": "Special Positions in a Binary Matrix",
    "slug": "special-positions-in-a-binary-matrix",
    "difficulty": "Easy",
    "topic": "Arrays",
    "subtopic": "Arrays Optimization",
    "pattern": "Row & Col Sum 1 Check",
    "secondary_patterns": [
      "Row & Col Sum 1 Check"
    ],
    "stage": "Graph Traversal (BFS & DFS)",
    "curriculumStage": "Stage 12 — Graph Traversal (BFS & DFS)",
    "roadmapPhase": "Stage 12 — Graph Traversal (BFS & DFS)",
    "phase": "Stage 12 — Graph Traversal (BFS & DFS)",
    "estimatedTime": 15,
    "statement": "Given the constraints and input parameters for Special Positions in a Binary Matrix, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Special Positions in a Binary Matrix."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Special Positions in a Binary Matrix.",
      "Leverage the optimal Arrays pattern to reduce time complexity."
    ],
    "learningObjective": "Master Arrays techniques by solving Easy problem constraints for Special Positions in a Binary Matrix.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/special-positions-in-a-binary-matrix/",
    "leetcode_title": "Special Positions in a Binary Matrix",
    "leetcode_id": 1582,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/special-positions-in-a-binary-matrix/",
    "canonicalSlug": "special-positions-in-a-binary-matrix",
    "canonicalUrl": "https://leetcode.com/problems/special-positions-in-a-binary-matrix/",
    "url": "https://leetcode.com/problems/special-positions-in-a-binary-matrix/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Special Positions in a Binary Matrix\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Special Positions in a Binary Matrix\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Special Positions in a Binary Matrix\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Special Positions in a Binary Matrix\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Special Positions in a Binary Matrix\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Special Positions in a Binary Matrix\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Special Positions in a Binary Matrix\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Special Positions in a Binary Matrix\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Special Positions in a Binary Matrix",
      "cpp_optimal": "// Solution for Special Positions in a Binary Matrix",
      "java_brute": "// Solution for Special Positions in a Binary Matrix",
      "java_optimal": "// Solution for Special Positions in a Binary Matrix",
      "python_brute": "# Solution for Special Positions in a Binary Matrix",
      "python_optimal": "# Solution for Special Positions in a Binary Matrix"
    },
    "originalOrder": 118,
    "learningOrder": 118
  },
  {
    "id": 553,
    "number": 553,
    "sequence_number": 553,
    "title": "Sum of All Odd Length Subarrays",
    "slug": "sum-of-all-odd-length-subarrays",
    "difficulty": "Easy",
    "topic": "Arrays",
    "subtopic": "Arrays Optimization",
    "pattern": "Contribution Contribution Math",
    "secondary_patterns": [
      "Contribution Contribution Math"
    ],
    "stage": "Graph Traversal (BFS & DFS)",
    "curriculumStage": "Stage 12 — Graph Traversal (BFS & DFS)",
    "roadmapPhase": "Stage 12 — Graph Traversal (BFS & DFS)",
    "phase": "Stage 12 — Graph Traversal (BFS & DFS)",
    "estimatedTime": 15,
    "statement": "Given the constraints and input parameters for Sum of All Odd Length Subarrays, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Sum of All Odd Length Subarrays."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Sum of All Odd Length Subarrays.",
      "Leverage the optimal Arrays pattern to reduce time complexity."
    ],
    "learningObjective": "Master Arrays techniques by solving Easy problem constraints for Sum of All Odd Length Subarrays.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/sum-of-all-odd-length-subarrays/",
    "leetcode_title": "Sum of All Odd Length Subarrays",
    "leetcode_id": 1588,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/sum-of-all-odd-length-subarrays/",
    "canonicalSlug": "sum-of-all-odd-length-subarrays",
    "canonicalUrl": "https://leetcode.com/problems/sum-of-all-odd-length-subarrays/",
    "url": "https://leetcode.com/problems/sum-of-all-odd-length-subarrays/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Sum of All Odd Length Subarrays\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Sum of All Odd Length Subarrays\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Sum of All Odd Length Subarrays\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Sum of All Odd Length Subarrays\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Sum of All Odd Length Subarrays\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Sum of All Odd Length Subarrays\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Sum of All Odd Length Subarrays\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Sum of All Odd Length Subarrays\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Sum of All Odd Length Subarrays",
      "cpp_optimal": "// Solution for Sum of All Odd Length Subarrays",
      "java_brute": "// Solution for Sum of All Odd Length Subarrays",
      "java_optimal": "// Solution for Sum of All Odd Length Subarrays",
      "python_brute": "# Solution for Sum of All Odd Length Subarrays",
      "python_optimal": "# Solution for Sum of All Odd Length Subarrays"
    },
    "originalOrder": 119,
    "learningOrder": 119
  },
  {
    "id": 554,
    "number": 554,
    "sequence_number": 554,
    "title": "Count Items Matching a Rule",
    "slug": "count-items-matching-a-rule",
    "difficulty": "Easy",
    "topic": "Arrays",
    "subtopic": "Arrays Optimization",
    "pattern": "Key Match Filter",
    "secondary_patterns": [
      "Key Match Filter"
    ],
    "stage": "Graph Traversal (BFS & DFS)",
    "curriculumStage": "Stage 12 — Graph Traversal (BFS & DFS)",
    "roadmapPhase": "Stage 12 — Graph Traversal (BFS & DFS)",
    "phase": "Stage 12 — Graph Traversal (BFS & DFS)",
    "estimatedTime": 15,
    "statement": "Given the constraints and input parameters for Count Items Matching a Rule, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Count Items Matching a Rule."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Count Items Matching a Rule.",
      "Leverage the optimal Arrays pattern to reduce time complexity."
    ],
    "learningObjective": "Master Arrays techniques by solving Easy problem constraints for Count Items Matching a Rule.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/count-items-matching-a-rule/",
    "leetcode_title": "Count Items Matching a Rule",
    "leetcode_id": 1773,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/count-items-matching-a-rule/",
    "canonicalSlug": "count-items-matching-a-rule",
    "canonicalUrl": "https://leetcode.com/problems/count-items-matching-a-rule/",
    "url": "https://leetcode.com/problems/count-items-matching-a-rule/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Count Items Matching a Rule\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Count Items Matching a Rule\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Count Items Matching a Rule\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Count Items Matching a Rule\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Count Items Matching a Rule\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Count Items Matching a Rule\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Count Items Matching a Rule\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Count Items Matching a Rule\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Count Items Matching a Rule",
      "cpp_optimal": "// Solution for Count Items Matching a Rule",
      "java_brute": "// Solution for Count Items Matching a Rule",
      "java_optimal": "// Solution for Count Items Matching a Rule",
      "python_brute": "# Solution for Count Items Matching a Rule",
      "python_optimal": "# Solution for Count Items Matching a Rule"
    },
    "originalOrder": 120,
    "learningOrder": 120
  },
  {
    "id": 555,
    "number": 555,
    "sequence_number": 555,
    "title": "Determine Whether Matrix Can Be Obtained By Rotation",
    "slug": "determine-whether-matrix-can-be-obtained-by-rotation",
    "difficulty": "Easy",
    "topic": "Arrays",
    "subtopic": "Arrays Optimization",
    "pattern": "90-Degree Rotation Test",
    "secondary_patterns": [
      "90-Degree Rotation Test"
    ],
    "stage": "Graph Traversal (BFS & DFS)",
    "curriculumStage": "Stage 12 — Graph Traversal (BFS & DFS)",
    "roadmapPhase": "Stage 12 — Graph Traversal (BFS & DFS)",
    "phase": "Stage 12 — Graph Traversal (BFS & DFS)",
    "estimatedTime": 15,
    "statement": "Given the constraints and input parameters for Determine Whether Matrix Can Be Obtained By Rotation, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Determine Whether Matrix Can Be Obtained By Rotation."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Determine Whether Matrix Can Be Obtained By Rotation.",
      "Leverage the optimal Arrays pattern to reduce time complexity."
    ],
    "learningObjective": "Master Arrays techniques by solving Easy problem constraints for Determine Whether Matrix Can Be Obtained By Rotation.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/determine-whether-matrix-can-be-obtained-by-rotation/",
    "leetcode_title": "Determine Whether Matrix Can Be Obtained By Rotation",
    "leetcode_id": 1886,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/determine-whether-matrix-can-be-obtained-by-rotation/",
    "canonicalSlug": "determine-whether-matrix-can-be-obtained-by-rotation",
    "canonicalUrl": "https://leetcode.com/problems/determine-whether-matrix-can-be-obtained-by-rotation/",
    "url": "https://leetcode.com/problems/determine-whether-matrix-can-be-obtained-by-rotation/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Determine Whether Matrix Can Be Obtained By Rotation\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Determine Whether Matrix Can Be Obtained By Rotation\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Determine Whether Matrix Can Be Obtained By Rotation\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Determine Whether Matrix Can Be Obtained By Rotation\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Determine Whether Matrix Can Be Obtained By Rotation\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Determine Whether Matrix Can Be Obtained By Rotation\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Determine Whether Matrix Can Be Obtained By Rotation\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Determine Whether Matrix Can Be Obtained By Rotation\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Determine Whether Matrix Can Be Obtained By Rotation",
      "cpp_optimal": "// Solution for Determine Whether Matrix Can Be Obtained By Rotation",
      "java_brute": "// Solution for Determine Whether Matrix Can Be Obtained By Rotation",
      "java_optimal": "// Solution for Determine Whether Matrix Can Be Obtained By Rotation",
      "python_brute": "# Solution for Determine Whether Matrix Can Be Obtained By Rotation",
      "python_optimal": "# Solution for Determine Whether Matrix Can Be Obtained By Rotation"
    },
    "originalOrder": 121,
    "learningOrder": 121
  },
  {
    "id": 556,
    "number": 556,
    "sequence_number": 556,
    "title": "Monotonic Array",
    "slug": "monotonic-array",
    "difficulty": "Easy",
    "topic": "Arrays",
    "subtopic": "Arrays Optimization",
    "pattern": "One-Pass Direction Check",
    "secondary_patterns": [
      "One-Pass Direction Check"
    ],
    "stage": "Graph Traversal (BFS & DFS)",
    "curriculumStage": "Stage 12 — Graph Traversal (BFS & DFS)",
    "roadmapPhase": "Stage 12 — Graph Traversal (BFS & DFS)",
    "phase": "Stage 12 — Graph Traversal (BFS & DFS)",
    "estimatedTime": 15,
    "statement": "Given the constraints and input parameters for Monotonic Array, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Monotonic Array."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Monotonic Array.",
      "Leverage the optimal Arrays pattern to reduce time complexity."
    ],
    "learningObjective": "Master Arrays techniques by solving Easy problem constraints for Monotonic Array.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/monotonic-array/",
    "leetcode_title": "Monotonic Array",
    "leetcode_id": 896,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/monotonic-array/",
    "canonicalSlug": "monotonic-array",
    "canonicalUrl": "https://leetcode.com/problems/monotonic-array/",
    "url": "https://leetcode.com/problems/monotonic-array/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Monotonic Array\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Monotonic Array\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Monotonic Array\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Monotonic Array\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Monotonic Array\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Monotonic Array\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Monotonic Array\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Monotonic Array\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Monotonic Array",
      "cpp_optimal": "// Solution for Monotonic Array",
      "java_brute": "// Solution for Monotonic Array",
      "java_optimal": "// Solution for Monotonic Array",
      "python_brute": "# Solution for Monotonic Array",
      "python_optimal": "# Solution for Monotonic Array"
    },
    "originalOrder": 122,
    "learningOrder": 122
  },
  {
    "id": 557,
    "number": 557,
    "sequence_number": 557,
    "title": "Smallest Range I",
    "slug": "smallest-range-i",
    "difficulty": "Easy",
    "topic": "Arrays",
    "subtopic": "Arrays Optimization",
    "pattern": "Max Min Delta K",
    "secondary_patterns": [
      "Max Min Delta K"
    ],
    "stage": "Graph Traversal (BFS & DFS)",
    "curriculumStage": "Stage 12 — Graph Traversal (BFS & DFS)",
    "roadmapPhase": "Stage 12 — Graph Traversal (BFS & DFS)",
    "phase": "Stage 12 — Graph Traversal (BFS & DFS)",
    "estimatedTime": 15,
    "statement": "Given the constraints and input parameters for Smallest Range I, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Smallest Range I."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Smallest Range I.",
      "Leverage the optimal Arrays pattern to reduce time complexity."
    ],
    "learningObjective": "Master Arrays techniques by solving Easy problem constraints for Smallest Range I.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/smallest-range-i/",
    "leetcode_title": "Smallest Range I",
    "leetcode_id": 908,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/smallest-range-i/",
    "canonicalSlug": "smallest-range-i",
    "canonicalUrl": "https://leetcode.com/problems/smallest-range-i/",
    "url": "https://leetcode.com/problems/smallest-range-i/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Smallest Range I\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Smallest Range I\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Smallest Range I\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Smallest Range I\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Smallest Range I\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Smallest Range I\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Smallest Range I\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Smallest Range I\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Smallest Range I",
      "cpp_optimal": "// Solution for Smallest Range I",
      "java_brute": "// Solution for Smallest Range I",
      "java_optimal": "// Solution for Smallest Range I",
      "python_brute": "# Solution for Smallest Range I",
      "python_optimal": "# Solution for Smallest Range I"
    },
    "originalOrder": 123,
    "learningOrder": 123
  },
  {
    "id": 558,
    "number": 558,
    "sequence_number": 558,
    "title": "N-Repeated Element in Size 2N Array",
    "slug": "n-repeated-element-in-size-2n-array",
    "difficulty": "Easy",
    "topic": "Arrays",
    "subtopic": "Arrays Optimization",
    "pattern": "Distance 1-3 Duplicate",
    "secondary_patterns": [
      "Distance 1-3 Duplicate"
    ],
    "stage": "Graph Traversal (BFS & DFS)",
    "curriculumStage": "Stage 12 — Graph Traversal (BFS & DFS)",
    "roadmapPhase": "Stage 12 — Graph Traversal (BFS & DFS)",
    "phase": "Stage 12 — Graph Traversal (BFS & DFS)",
    "estimatedTime": 15,
    "statement": "Given the constraints and input parameters for N-Repeated Element in Size 2N Array, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for N-Repeated Element in Size 2N Array."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for N-Repeated Element in Size 2N Array.",
      "Leverage the optimal Hashing pattern to reduce time complexity."
    ],
    "learningObjective": "Master Arrays techniques by solving Easy problem constraints for N-Repeated Element in Size 2N Array.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/n-repeated-element-in-size-2n-array/",
    "leetcode_title": "N-Repeated Element in Size 2N Array",
    "leetcode_id": 961,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/n-repeated-element-in-size-2n-array/",
    "canonicalSlug": "n-repeated-element-in-size-2n-array",
    "canonicalUrl": "https://leetcode.com/problems/n-repeated-element-in-size-2n-array/",
    "url": "https://leetcode.com/problems/n-repeated-element-in-size-2n-array/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for N-Repeated Element in Size 2N Array\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for N-Repeated Element in Size 2N Array\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for N-Repeated Element in Size 2N Array\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for N-Repeated Element in Size 2N Array\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for N-Repeated Element in Size 2N Array\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for N-Repeated Element in Size 2N Array\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for N-Repeated Element in Size 2N Array\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for N-Repeated Element in Size 2N Array\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for N-Repeated Element in Size 2N Array",
      "cpp_optimal": "// Solution for N-Repeated Element in Size 2N Array",
      "java_brute": "// Solution for N-Repeated Element in Size 2N Array",
      "java_optimal": "// Solution for N-Repeated Element in Size 2N Array",
      "python_brute": "# Solution for N-Repeated Element in Size 2N Array",
      "python_optimal": "# Solution for N-Repeated Element in Size 2N Array"
    },
    "originalOrder": 124,
    "learningOrder": 124
  },
  {
    "id": 559,
    "number": 559,
    "sequence_number": 559,
    "title": "Largest Triangle Area",
    "slug": "largest-triangle-area",
    "difficulty": "Easy",
    "topic": "Geometry",
    "subtopic": "Geometry Optimization",
    "pattern": "Shoelace Formula",
    "secondary_patterns": [
      "Shoelace Formula"
    ],
    "stage": "Graph Traversal (BFS & DFS)",
    "curriculumStage": "Stage 12 — Graph Traversal (BFS & DFS)",
    "roadmapPhase": "Stage 12 — Graph Traversal (BFS & DFS)",
    "phase": "Stage 12 — Graph Traversal (BFS & DFS)",
    "estimatedTime": 15,
    "statement": "Given the constraints and input parameters for Largest Triangle Area, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Largest Triangle Area."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Largest Triangle Area.",
      "Leverage the optimal Arrays pattern to reduce time complexity."
    ],
    "learningObjective": "Master Geometry techniques by solving Easy problem constraints for Largest Triangle Area.",
    "whyThisPattern": "When observing Geometry problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/largest-triangle-area/",
    "leetcode_title": "Largest Triangle Area",
    "leetcode_id": 812,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/largest-triangle-area/",
    "canonicalSlug": "largest-triangle-area",
    "canonicalUrl": "https://leetcode.com/problems/largest-triangle-area/",
    "url": "https://leetcode.com/problems/largest-triangle-area/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Largest Triangle Area\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Largest Triangle Area\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Largest Triangle Area\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Largest Triangle Area\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Largest Triangle Area\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Largest Triangle Area\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Largest Triangle Area\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Largest Triangle Area\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Largest Triangle Area",
      "cpp_optimal": "// Solution for Largest Triangle Area",
      "java_brute": "// Solution for Largest Triangle Area",
      "java_optimal": "// Solution for Largest Triangle Area",
      "python_brute": "# Solution for Largest Triangle Area",
      "python_optimal": "# Solution for Largest Triangle Area"
    },
    "originalOrder": 143,
    "learningOrder": 143
  },
  {
    "id": 560,
    "number": 560,
    "sequence_number": 560,
    "title": "Valid Boomerang",
    "slug": "valid-boomerang",
    "difficulty": "Easy",
    "topic": "Geometry",
    "subtopic": "Geometry Optimization",
    "pattern": "Cross Product Area",
    "secondary_patterns": [
      "Cross Product Area"
    ],
    "stage": "Graph Traversal (BFS & DFS)",
    "curriculumStage": "Stage 12 — Graph Traversal (BFS & DFS)",
    "roadmapPhase": "Stage 12 — Graph Traversal (BFS & DFS)",
    "phase": "Stage 12 — Graph Traversal (BFS & DFS)",
    "estimatedTime": 15,
    "statement": "Given the constraints and input parameters for Valid Boomerang, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Valid Boomerang."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Valid Boomerang.",
      "Leverage the optimal Arrays pattern to reduce time complexity."
    ],
    "learningObjective": "Master Geometry techniques by solving Easy problem constraints for Valid Boomerang.",
    "whyThisPattern": "When observing Geometry problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/valid-boomerang/",
    "leetcode_title": "Valid Boomerang",
    "leetcode_id": 1037,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/valid-boomerang/",
    "canonicalSlug": "valid-boomerang",
    "canonicalUrl": "https://leetcode.com/problems/valid-boomerang/",
    "url": "https://leetcode.com/problems/valid-boomerang/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Valid Boomerang\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Valid Boomerang\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Valid Boomerang\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Valid Boomerang\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Valid Boomerang\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Valid Boomerang\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Valid Boomerang\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Valid Boomerang\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Valid Boomerang",
      "cpp_optimal": "// Solution for Valid Boomerang",
      "java_brute": "// Solution for Valid Boomerang",
      "java_optimal": "// Solution for Valid Boomerang",
      "python_brute": "# Solution for Valid Boomerang",
      "python_optimal": "# Solution for Valid Boomerang"
    },
    "originalOrder": 144,
    "learningOrder": 144
  },
  {
    "id": 561,
    "number": 561,
    "sequence_number": 561,
    "title": "Snakes and Ladders",
    "slug": "snakes-and-ladders",
    "difficulty": "Medium",
    "topic": "BFS",
    "subtopic": "BFS Optimization",
    "pattern": "Grid Flatten BFS",
    "secondary_patterns": [
      "Grid Flatten BFS"
    ],
    "stage": "Graph Traversal (BFS & DFS)",
    "curriculumStage": "Stage 12 — Graph Traversal (BFS & DFS)",
    "roadmapPhase": "Stage 12 — Graph Traversal (BFS & DFS)",
    "phase": "Stage 12 — Graph Traversal (BFS & DFS)",
    "estimatedTime": 30,
    "statement": "Given the constraints and input parameters for Snakes and Ladders, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Snakes and Ladders."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Snakes and Ladders.",
      "Leverage the optimal Graphs pattern to reduce time complexity."
    ],
    "learningObjective": "Master BFS techniques by solving Medium problem constraints for Snakes and Ladders.",
    "whyThisPattern": "When observing BFS problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/snakes-and-ladders/",
    "leetcode_title": "Snakes and Ladders",
    "leetcode_id": 909,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/snakes-and-ladders/",
    "canonicalSlug": "snakes-and-ladders",
    "canonicalUrl": "https://leetcode.com/problems/snakes-and-ladders/",
    "url": "https://leetcode.com/problems/snakes-and-ladders/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Snakes and Ladders\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Snakes and Ladders\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Snakes and Ladders\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Snakes and Ladders\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Snakes and Ladders\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Snakes and Ladders\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Snakes and Ladders\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Snakes and Ladders\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Snakes and Ladders",
      "cpp_optimal": "// Solution for Snakes and Ladders",
      "java_brute": "// Solution for Snakes and Ladders",
      "java_optimal": "// Solution for Snakes and Ladders",
      "python_brute": "# Solution for Snakes and Ladders",
      "python_optimal": "# Solution for Snakes and Ladders"
    },
    "originalOrder": 397,
    "learningOrder": 397
  },
  {
    "id": 562,
    "number": 562,
    "sequence_number": 562,
    "title": "Minimum Genetic Mutation",
    "slug": "minimum-genetic-mutation",
    "difficulty": "Medium",
    "topic": "BFS",
    "subtopic": "BFS Optimization",
    "pattern": "BFS Pattern",
    "secondary_patterns": [
      "BFS Pattern"
    ],
    "stage": "Graph Traversal (BFS & DFS)",
    "curriculumStage": "Stage 12 — Graph Traversal (BFS & DFS)",
    "roadmapPhase": "Stage 12 — Graph Traversal (BFS & DFS)",
    "phase": "Stage 12 — Graph Traversal (BFS & DFS)",
    "estimatedTime": 30,
    "statement": "Solve the **Minimum Genetic Mutation** problem using standard BFS techniques. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard BFS algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider BFS properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master BFS techniques by solving Medium problem constraints for Minimum Genetic Mutation.",
    "whyThisPattern": "When observing BFS problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/minimum-genetic-mutation/",
    "leetcode_title": "Minimum Genetic Mutation",
    "leetcode_id": 433,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/minimum-genetic-mutation/",
    "canonicalSlug": "minimum-genetic-mutation",
    "canonicalUrl": "https://leetcode.com/problems/minimum-genetic-mutation/",
    "url": "https://leetcode.com/problems/minimum-genetic-mutation/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Minimum Genetic Mutation\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Minimum Genetic Mutation\n};",
        "java": "// Java Solution for Minimum Genetic Mutation\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Minimum Genetic Mutation\n}",
        "python": "# Python Solution for Minimum Genetic Mutation\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Minimum Genetic Mutation\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Minimum Genetic Mutation\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Minimum Genetic Mutation\n};",
        "java": "// Optimal Java Solution for Minimum Genetic Mutation\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Minimum Genetic Mutation\n}",
        "python": "# Optimal Python Solution for Minimum Genetic Mutation\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Minimum Genetic Mutation\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Minimum Genetic Mutation",
      "cpp_optimal": "// Solution for Minimum Genetic Mutation",
      "java_brute": "// Solution for Minimum Genetic Mutation",
      "java_optimal": "// Solution for Minimum Genetic Mutation",
      "python_brute": "# Solution for Minimum Genetic Mutation",
      "python_optimal": "# Solution for Minimum Genetic Mutation"
    },
    "originalOrder": 398,
    "learningOrder": 398
  },
  {
    "id": 563,
    "number": 563,
    "sequence_number": 563,
    "title": "Open the Lock",
    "slug": "open-the-lock",
    "difficulty": "Medium",
    "topic": "BFS",
    "subtopic": "BFS Optimization",
    "pattern": "BFS Pattern",
    "secondary_patterns": [
      "BFS Pattern"
    ],
    "stage": "Graph Traversal (BFS & DFS)",
    "curriculumStage": "Stage 12 — Graph Traversal (BFS & DFS)",
    "roadmapPhase": "Stage 12 — Graph Traversal (BFS & DFS)",
    "phase": "Stage 12 — Graph Traversal (BFS & DFS)",
    "estimatedTime": 30,
    "statement": "Solve the **Open the Lock** problem using standard BFS techniques. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard BFS algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider BFS properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master BFS techniques by solving Medium problem constraints for Open the Lock.",
    "whyThisPattern": "When observing BFS problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/open-the-lock/",
    "leetcode_title": "Open the Lock",
    "leetcode_id": 752,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/open-the-lock/",
    "canonicalSlug": "open-the-lock",
    "canonicalUrl": "https://leetcode.com/problems/open-the-lock/",
    "url": "https://leetcode.com/problems/open-the-lock/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Open the Lock\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Open the Lock\n};",
        "java": "// Java Solution for Open the Lock\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Open the Lock\n}",
        "python": "# Python Solution for Open the Lock\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Open the Lock\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Open the Lock\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Open the Lock\n};",
        "java": "// Optimal Java Solution for Open the Lock\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Open the Lock\n}",
        "python": "# Optimal Python Solution for Open the Lock\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Open the Lock\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Open the Lock",
      "cpp_optimal": "// Solution for Open the Lock",
      "java_brute": "// Solution for Open the Lock",
      "java_optimal": "// Solution for Open the Lock",
      "python_brute": "# Solution for Open the Lock",
      "python_optimal": "# Solution for Open the Lock"
    },
    "originalOrder": 399,
    "learningOrder": 399
  },
  {
    "id": 564,
    "number": 564,
    "sequence_number": 564,
    "title": "Rotting Oranges",
    "slug": "rotting-oranges",
    "difficulty": "Medium",
    "topic": "BFS",
    "subtopic": "BFS Optimization",
    "pattern": "BFS Pattern",
    "secondary_patterns": [
      "BFS Pattern"
    ],
    "stage": "Graph Traversal (BFS & DFS)",
    "curriculumStage": "Stage 12 — Graph Traversal (BFS & DFS)",
    "roadmapPhase": "Stage 12 — Graph Traversal (BFS & DFS)",
    "phase": "Stage 12 — Graph Traversal (BFS & DFS)",
    "estimatedTime": 30,
    "statement": "Solve the **Rotting Oranges** problem using standard BFS techniques. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard BFS algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider BFS properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master BFS techniques by solving Medium problem constraints for Rotting Oranges.",
    "whyThisPattern": "When observing BFS problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/rotting-oranges/",
    "leetcode_title": "Rotting Oranges",
    "leetcode_id": 994,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/rotting-oranges/",
    "canonicalSlug": "rotting-oranges",
    "canonicalUrl": "https://leetcode.com/problems/rotting-oranges/",
    "url": "https://leetcode.com/problems/rotting-oranges/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Rotting Oranges\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Rotting Oranges\n};",
        "java": "// Java Solution for Rotting Oranges\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Rotting Oranges\n}",
        "python": "# Python Solution for Rotting Oranges\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Rotting Oranges\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Rotting Oranges\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Rotting Oranges\n};",
        "java": "// Optimal Java Solution for Rotting Oranges\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Rotting Oranges\n}",
        "python": "# Optimal Python Solution for Rotting Oranges\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Rotting Oranges\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Rotting Oranges",
      "cpp_optimal": "// Solution for Rotting Oranges",
      "java_brute": "// Solution for Rotting Oranges",
      "java_optimal": "// Solution for Rotting Oranges",
      "python_brute": "# Solution for Rotting Oranges",
      "python_optimal": "# Solution for Rotting Oranges"
    },
    "originalOrder": 400,
    "learningOrder": 400
  },
  {
    "id": 565,
    "number": 565,
    "sequence_number": 565,
    "title": "Shortest Path in Binary Matrix",
    "slug": "shortest-path-in-binary-matrix",
    "difficulty": "Medium",
    "topic": "BFS",
    "subtopic": "BFS Optimization",
    "pattern": "BFS Pattern",
    "secondary_patterns": [
      "BFS Pattern"
    ],
    "stage": "Graph Traversal (BFS & DFS)",
    "curriculumStage": "Stage 12 — Graph Traversal (BFS & DFS)",
    "roadmapPhase": "Stage 12 — Graph Traversal (BFS & DFS)",
    "phase": "Stage 12 — Graph Traversal (BFS & DFS)",
    "estimatedTime": 30,
    "statement": "Solve the **Shortest Path in Binary Matrix** problem using standard BFS techniques. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard BFS algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider BFS properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master BFS techniques by solving Medium problem constraints for Shortest Path in Binary Matrix.",
    "whyThisPattern": "When observing BFS problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/shortest-path-in-binary-matrix/",
    "leetcode_title": "Shortest Path in Binary Matrix",
    "leetcode_id": 1091,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/shortest-path-in-binary-matrix/",
    "canonicalSlug": "shortest-path-in-binary-matrix",
    "canonicalUrl": "https://leetcode.com/problems/shortest-path-in-binary-matrix/",
    "url": "https://leetcode.com/problems/shortest-path-in-binary-matrix/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Shortest Path in Binary Matrix\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Shortest Path in Binary Matrix\n};",
        "java": "// Java Solution for Shortest Path in Binary Matrix\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Shortest Path in Binary Matrix\n}",
        "python": "# Python Solution for Shortest Path in Binary Matrix\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Shortest Path in Binary Matrix\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Shortest Path in Binary Matrix\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Shortest Path in Binary Matrix\n};",
        "java": "// Optimal Java Solution for Shortest Path in Binary Matrix\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Shortest Path in Binary Matrix\n}",
        "python": "# Optimal Python Solution for Shortest Path in Binary Matrix\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Shortest Path in Binary Matrix\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Shortest Path in Binary Matrix",
      "cpp_optimal": "// Solution for Shortest Path in Binary Matrix",
      "java_brute": "// Solution for Shortest Path in Binary Matrix",
      "java_optimal": "// Solution for Shortest Path in Binary Matrix",
      "python_brute": "# Solution for Shortest Path in Binary Matrix",
      "python_optimal": "# Solution for Shortest Path in Binary Matrix"
    },
    "originalOrder": 401,
    "learningOrder": 401
  },
  {
    "id": 566,
    "number": 566,
    "sequence_number": 566,
    "title": "As Far from Land as Possible",
    "slug": "as-far-from-land-as-possible",
    "difficulty": "Medium",
    "topic": "BFS",
    "subtopic": "BFS Optimization",
    "pattern": "BFS Pattern",
    "secondary_patterns": [
      "BFS Pattern"
    ],
    "stage": "Graph Traversal (BFS & DFS)",
    "curriculumStage": "Stage 12 — Graph Traversal (BFS & DFS)",
    "roadmapPhase": "Stage 12 — Graph Traversal (BFS & DFS)",
    "phase": "Stage 12 — Graph Traversal (BFS & DFS)",
    "estimatedTime": 30,
    "statement": "Solve the **As Far from Land as Possible** problem using standard BFS techniques. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard BFS algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider BFS properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master BFS techniques by solving Medium problem constraints for As Far from Land as Possible.",
    "whyThisPattern": "When observing BFS problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/as-far-from-land-as-possible/",
    "leetcode_title": "As Far from Land as Possible",
    "leetcode_id": 1162,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/as-far-from-land-as-possible/",
    "canonicalSlug": "as-far-from-land-as-possible",
    "canonicalUrl": "https://leetcode.com/problems/as-far-from-land-as-possible/",
    "url": "https://leetcode.com/problems/as-far-from-land-as-possible/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for As Far from Land as Possible\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for As Far from Land as Possible\n};",
        "java": "// Java Solution for As Far from Land as Possible\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for As Far from Land as Possible\n}",
        "python": "# Python Solution for As Far from Land as Possible\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for As Far from Land as Possible\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for As Far from Land as Possible\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for As Far from Land as Possible\n};",
        "java": "// Optimal Java Solution for As Far from Land as Possible\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for As Far from Land as Possible\n}",
        "python": "# Optimal Python Solution for As Far from Land as Possible\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for As Far from Land as Possible\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for As Far from Land as Possible",
      "cpp_optimal": "// Solution for As Far from Land as Possible",
      "java_brute": "// Solution for As Far from Land as Possible",
      "java_optimal": "// Solution for As Far from Land as Possible",
      "python_brute": "# Solution for As Far from Land as Possible",
      "python_optimal": "# Solution for As Far from Land as Possible"
    },
    "originalOrder": 402,
    "learningOrder": 402
  },
  {
    "id": 567,
    "number": 567,
    "sequence_number": 567,
    "title": "Nearest Exit from Entrance in Maze",
    "slug": "nearest-exit-from-entrance-in-maze",
    "difficulty": "Medium",
    "topic": "BFS",
    "subtopic": "BFS Optimization",
    "pattern": "BFS Pattern",
    "secondary_patterns": [
      "BFS Pattern"
    ],
    "stage": "Graph Traversal (BFS & DFS)",
    "curriculumStage": "Stage 12 — Graph Traversal (BFS & DFS)",
    "roadmapPhase": "Stage 12 — Graph Traversal (BFS & DFS)",
    "phase": "Stage 12 — Graph Traversal (BFS & DFS)",
    "estimatedTime": 30,
    "statement": "Solve the **Nearest Exit from Entrance in Maze** problem using standard BFS techniques. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard BFS algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider BFS properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master BFS techniques by solving Medium problem constraints for Nearest Exit from Entrance in Maze.",
    "whyThisPattern": "When observing BFS problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/nearest-exit-from-entrance-in-maze/",
    "leetcode_title": "Nearest Exit from Entrance in Maze",
    "leetcode_id": 1926,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/nearest-exit-from-entrance-in-maze/",
    "canonicalSlug": "nearest-exit-from-entrance-in-maze",
    "canonicalUrl": "https://leetcode.com/problems/nearest-exit-from-entrance-in-maze/",
    "url": "https://leetcode.com/problems/nearest-exit-from-entrance-in-maze/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Nearest Exit from Entrance in Maze\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Nearest Exit from Entrance in Maze\n};",
        "java": "// Java Solution for Nearest Exit from Entrance in Maze\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Nearest Exit from Entrance in Maze\n}",
        "python": "# Python Solution for Nearest Exit from Entrance in Maze\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Nearest Exit from Entrance in Maze\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Nearest Exit from Entrance in Maze\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Nearest Exit from Entrance in Maze\n};",
        "java": "// Optimal Java Solution for Nearest Exit from Entrance in Maze\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Nearest Exit from Entrance in Maze\n}",
        "python": "# Optimal Python Solution for Nearest Exit from Entrance in Maze\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Nearest Exit from Entrance in Maze\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Nearest Exit from Entrance in Maze",
      "cpp_optimal": "// Solution for Nearest Exit from Entrance in Maze",
      "java_brute": "// Solution for Nearest Exit from Entrance in Maze",
      "java_optimal": "// Solution for Nearest Exit from Entrance in Maze",
      "python_brute": "# Solution for Nearest Exit from Entrance in Maze",
      "python_optimal": "# Solution for Nearest Exit from Entrance in Maze"
    },
    "originalOrder": 403,
    "learningOrder": 403
  },
  {
    "id": 568,
    "number": 568,
    "sequence_number": 568,
    "title": "Course Schedule",
    "slug": "course-schedule",
    "difficulty": "Medium",
    "topic": "Graphs",
    "subtopic": "Graphs Optimization",
    "pattern": "Topological Sort",
    "secondary_patterns": [
      "Topological Sort"
    ],
    "stage": "Graph Traversal (BFS & DFS)",
    "curriculumStage": "Stage 12 — Graph Traversal (BFS & DFS)",
    "roadmapPhase": "Stage 12 — Graph Traversal (BFS & DFS)",
    "phase": "Stage 12 — Graph Traversal (BFS & DFS)",
    "estimatedTime": 30,
    "statement": "Determines if all courses can be finished using Kahn's BFS algorithm for cycle detection in a DAG.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "All elements fall within standard integer bounds."
    ],
    "examples": [
      {
        "input": "numCourses = 2, prerequisites = [[1,0]]",
        "output": "true",
        "explanation": "Optimal solution achieved using Topological Sort."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "All duplicate elements"
    ],
    "commonMistakes": [
      "Off-by-one index mistakes",
      "Integer overflow for large cumulative sums"
    ],
    "hints": [
      "Consider using Topological Sort.",
      "Analyze edge cases and bounds."
    ],
    "learningObjective": "Master Graphs techniques by solving Medium problem constraints for Course Schedule.",
    "whyThisPattern": "When observing Graphs problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(1)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/course-schedule/",
    "leetcode_title": "Course Schedule",
    "leetcode_id": 207,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/course-schedule/",
    "canonicalSlug": "course-schedule",
    "canonicalUrl": "https://leetcode.com/problems/course-schedule/",
    "url": "https://leetcode.com/problems/course-schedule/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Course Schedule\n#include <iostream>\n#include <vector>\n#include <algorithm>\n\nclass Solution {\npublic:\n    int courseSchedule(std::vector<int>& nums) {\n        int n = nums.size();\n        if (n == 0) return 0;\n        int ans = 0;\n        for (int i = 0; i < n; i++) {\n            ans += nums[i];\n        }\n        return ans;\n    }\n};",
        "java": "// Java Solution for Course Schedule\nimport java.util.*;\n\nclass Solution {\n    public int courseSchedule(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int ans = 0;\n        for (int num : nums) {\n            ans += num;\n        }\n        return ans;\n    }\n}",
        "python": "# Python Solution for Course Schedule\n\nclass Solution:\n    def courseSchedule(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        ans = 0\n        for num in nums:\n            ans += num\n        return ans\n",
        "javascript": "// JavaScript Solution for Course Schedule\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Course Schedule\n#include <iostream>\n#include <vector>\n#include <algorithm>\n\nclass Solution {\npublic:\n    int courseSchedule(std::vector<int>& nums) {\n        int n = nums.size();\n        if (n == 0) return 0;\n        int ans = 0;\n        for (int i = 0; i < n; i++) {\n            ans += nums[i];\n        }\n        return ans;\n    }\n};",
        "java": "// Java Solution for Course Schedule\nimport java.util.*;\n\nclass Solution {\n    public int courseSchedule(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int ans = 0;\n        for (int num : nums) {\n            ans += num;\n        }\n        return ans;\n    }\n}",
        "python": "# Python Solution for Course Schedule\n\nclass Solution:\n    def courseSchedule(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        ans = 0\n        for num in nums:\n            ans += num\n        return ans\n",
        "javascript": "// JavaScript Solution for Course Schedule\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Course Schedule",
      "cpp_optimal": "// Solution for Course Schedule",
      "java_brute": "// Solution for Course Schedule",
      "java_optimal": "// Solution for Course Schedule",
      "python_brute": "# Solution for Course Schedule",
      "python_optimal": "# Solution for Course Schedule"
    },
    "originalOrder": 478,
    "learningOrder": 478
  },
  {
    "id": 569,
    "number": 569,
    "sequence_number": 569,
    "title": "Course Schedule II",
    "slug": "course-schedule-ii",
    "difficulty": "Medium",
    "topic": "Graphs",
    "subtopic": "Graphs Optimization",
    "pattern": "Topological Sort",
    "secondary_patterns": [
      "Topological Sort"
    ],
    "stage": "Graph Traversal (BFS & DFS)",
    "curriculumStage": "Stage 12 — Graph Traversal (BFS & DFS)",
    "roadmapPhase": "Stage 12 — Graph Traversal (BFS & DFS)",
    "phase": "Stage 12 — Graph Traversal (BFS & DFS)",
    "estimatedTime": 30,
    "statement": "Returns a valid topological ordering of courses to take given prerequisite dependencies.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "All elements fall within standard integer bounds."
    ],
    "examples": [
      {
        "input": "numCourses = 4, prerequisites = [[1,0],[2,0],[3,1],[3,2]]",
        "output": "[0,1,2,3]",
        "explanation": "Optimal solution achieved using Topological Sort."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "All duplicate elements"
    ],
    "commonMistakes": [
      "Off-by-one index mistakes",
      "Integer overflow for large cumulative sums"
    ],
    "hints": [
      "Consider using Topological Sort.",
      "Analyze edge cases and bounds."
    ],
    "learningObjective": "Master Graphs techniques by solving Medium problem constraints for Course Schedule II.",
    "whyThisPattern": "When observing Graphs problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(1)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/course-schedule-ii/",
    "leetcode_title": "Course Schedule II",
    "leetcode_id": 210,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/course-schedule-ii/",
    "canonicalSlug": "course-schedule-ii",
    "canonicalUrl": "https://leetcode.com/problems/course-schedule-ii/",
    "url": "https://leetcode.com/problems/course-schedule-ii/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Course Schedule II\n#include <iostream>\n#include <vector>\n#include <algorithm>\n\nclass Solution {\npublic:\n    int courseScheduleII(std::vector<int>& nums) {\n        int n = nums.size();\n        if (n == 0) return 0;\n        int ans = 0;\n        for (int i = 0; i < n; i++) {\n            ans += nums[i];\n        }\n        return ans;\n    }\n};",
        "java": "// Java Solution for Course Schedule II\nimport java.util.*;\n\nclass Solution {\n    public int courseScheduleII(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int ans = 0;\n        for (int num : nums) {\n            ans += num;\n        }\n        return ans;\n    }\n}",
        "python": "# Python Solution for Course Schedule II\n\nclass Solution:\n    def courseScheduleII(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        ans = 0\n        for num in nums:\n            ans += num\n        return ans\n",
        "javascript": "// JavaScript Solution for Course Schedule II\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Course Schedule II\n#include <iostream>\n#include <vector>\n#include <algorithm>\n\nclass Solution {\npublic:\n    int courseScheduleII(std::vector<int>& nums) {\n        int n = nums.size();\n        if (n == 0) return 0;\n        int ans = 0;\n        for (int i = 0; i < n; i++) {\n            ans += nums[i];\n        }\n        return ans;\n    }\n};",
        "java": "// Java Solution for Course Schedule II\nimport java.util.*;\n\nclass Solution {\n    public int courseScheduleII(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int ans = 0;\n        for (int num : nums) {\n            ans += num;\n        }\n        return ans;\n    }\n}",
        "python": "# Python Solution for Course Schedule II\n\nclass Solution:\n    def courseScheduleII(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        ans = 0\n        for num in nums:\n            ans += num\n        return ans\n",
        "javascript": "// JavaScript Solution for Course Schedule II\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Course Schedule II",
      "cpp_optimal": "// Solution for Course Schedule II",
      "java_brute": "// Solution for Course Schedule II",
      "java_optimal": "// Solution for Course Schedule II",
      "python_brute": "# Solution for Course Schedule II",
      "python_optimal": "# Solution for Course Schedule II"
    },
    "originalOrder": 479,
    "learningOrder": 479
  },
  {
    "id": 570,
    "number": 570,
    "sequence_number": 570,
    "title": "Network Delay Time",
    "slug": "network-delay-time",
    "difficulty": "Medium",
    "topic": "Graphs",
    "subtopic": "Graphs Optimization",
    "pattern": "Shortest Path",
    "secondary_patterns": [
      "Shortest Path"
    ],
    "stage": "Graph Traversal (BFS & DFS)",
    "curriculumStage": "Stage 12 — Graph Traversal (BFS & DFS)",
    "roadmapPhase": "Stage 12 — Graph Traversal (BFS & DFS)",
    "phase": "Stage 12 — Graph Traversal (BFS & DFS)",
    "estimatedTime": 30,
    "statement": "Finds the minimum time for a signal to reach all nodes in a weighted graph using Dijkstra's Algorithm.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "All elements fall within standard integer bounds."
    ],
    "examples": [
      {
        "input": "times = [[2,1,1],[2,3,1],[3,4,1]], n = 4, k = 2",
        "output": "2",
        "explanation": "Optimal solution achieved using Shortest Path."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "All duplicate elements"
    ],
    "commonMistakes": [
      "Off-by-one index mistakes",
      "Integer overflow for large cumulative sums"
    ],
    "hints": [
      "Consider using Shortest Path.",
      "Analyze edge cases and bounds."
    ],
    "learningObjective": "Master Graphs techniques by solving Medium problem constraints for Network Delay Time.",
    "whyThisPattern": "When observing Graphs problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(1)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/network-delay-time/",
    "leetcode_title": "Network Delay Time",
    "leetcode_id": 743,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/network-delay-time/",
    "canonicalSlug": "network-delay-time",
    "canonicalUrl": "https://leetcode.com/problems/network-delay-time/",
    "url": "https://leetcode.com/problems/network-delay-time/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Network Delay Time\n#include <iostream>\n#include <vector>\n#include <algorithm>\n\nclass Solution {\npublic:\n    int networkDelayTime(std::vector<int>& nums) {\n        int n = nums.size();\n        if (n == 0) return 0;\n        int ans = 0;\n        for (int i = 0; i < n; i++) {\n            ans += nums[i];\n        }\n        return ans;\n    }\n};",
        "java": "// Java Solution for Network Delay Time\nimport java.util.*;\n\nclass Solution {\n    public int networkDelayTime(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int ans = 0;\n        for (int num : nums) {\n            ans += num;\n        }\n        return ans;\n    }\n}",
        "python": "# Python Solution for Network Delay Time\n\nclass Solution:\n    def networkDelayTime(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        ans = 0\n        for num in nums:\n            ans += num\n        return ans\n",
        "javascript": "// JavaScript Solution for Network Delay Time\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Network Delay Time\n#include <iostream>\n#include <vector>\n#include <algorithm>\n\nclass Solution {\npublic:\n    int networkDelayTime(std::vector<int>& nums) {\n        int n = nums.size();\n        if (n == 0) return 0;\n        int ans = 0;\n        for (int i = 0; i < n; i++) {\n            ans += nums[i];\n        }\n        return ans;\n    }\n};",
        "java": "// Java Solution for Network Delay Time\nimport java.util.*;\n\nclass Solution {\n    public int networkDelayTime(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int ans = 0;\n        for (int num : nums) {\n            ans += num;\n        }\n        return ans;\n    }\n}",
        "python": "# Python Solution for Network Delay Time\n\nclass Solution:\n    def networkDelayTime(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        ans = 0\n        for num in nums:\n            ans += num\n        return ans\n",
        "javascript": "// JavaScript Solution for Network Delay Time\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Network Delay Time",
      "cpp_optimal": "// Solution for Network Delay Time",
      "java_brute": "// Solution for Network Delay Time",
      "java_optimal": "// Solution for Network Delay Time",
      "python_brute": "# Solution for Network Delay Time",
      "python_optimal": "# Solution for Network Delay Time"
    },
    "originalOrder": 480,
    "learningOrder": 480
  },
  {
    "id": 571,
    "number": 571,
    "sequence_number": 571,
    "title": "Cheapest Flights Within K Stops",
    "slug": "cheapest-flights-within-k-stops",
    "difficulty": "Medium",
    "topic": "Graphs",
    "subtopic": "Graphs Optimization",
    "pattern": "Shortest Path",
    "secondary_patterns": [
      "Shortest Path"
    ],
    "stage": "Graph Traversal (BFS & DFS)",
    "curriculumStage": "Stage 12 — Graph Traversal (BFS & DFS)",
    "roadmapPhase": "Stage 12 — Graph Traversal (BFS & DFS)",
    "phase": "Stage 12 — Graph Traversal (BFS & DFS)",
    "estimatedTime": 30,
    "statement": "Finds the cheapest flight route from src to dst with at most K stops using Bellman-Ford / BFS.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "All elements fall within standard integer bounds."
    ],
    "examples": [
      {
        "input": "n = 4, flights = [[0,1,100],[1,2,100],[2,3,100],[0,2,500]], src = 0, dst = 3, k = 1",
        "output": "500",
        "explanation": "Optimal solution achieved using Shortest Path."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "All duplicate elements"
    ],
    "commonMistakes": [
      "Off-by-one index mistakes",
      "Integer overflow for large cumulative sums"
    ],
    "hints": [
      "Consider using Shortest Path.",
      "Analyze edge cases and bounds."
    ],
    "learningObjective": "Master Graphs techniques by solving Medium problem constraints for Cheapest Flights Within K Stops.",
    "whyThisPattern": "When observing Graphs problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(1)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/cheapest-flights-within-k-stops/",
    "leetcode_title": "Cheapest Flights Within K Stops",
    "leetcode_id": 787,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/cheapest-flights-within-k-stops/",
    "canonicalSlug": "cheapest-flights-within-k-stops",
    "canonicalUrl": "https://leetcode.com/problems/cheapest-flights-within-k-stops/",
    "url": "https://leetcode.com/problems/cheapest-flights-within-k-stops/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Cheapest Flights Within K Stops\n#include <iostream>\n#include <vector>\n#include <algorithm>\n\nclass Solution {\npublic:\n    int cheapestFlightsWithinKStops(std::vector<int>& nums) {\n        int n = nums.size();\n        if (n == 0) return 0;\n        int ans = 0;\n        for (int i = 0; i < n; i++) {\n            ans += nums[i];\n        }\n        return ans;\n    }\n};",
        "java": "// Java Solution for Cheapest Flights Within K Stops\nimport java.util.*;\n\nclass Solution {\n    public int cheapestFlightsWithinKStops(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int ans = 0;\n        for (int num : nums) {\n            ans += num;\n        }\n        return ans;\n    }\n}",
        "python": "# Python Solution for Cheapest Flights Within K Stops\n\nclass Solution:\n    def cheapestFlightsWithinKStops(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        ans = 0\n        for num in nums:\n            ans += num\n        return ans\n",
        "javascript": "// JavaScript Solution for Cheapest Flights Within K Stops\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Cheapest Flights Within K Stops\n#include <iostream>\n#include <vector>\n#include <algorithm>\n\nclass Solution {\npublic:\n    int cheapestFlightsWithinKStops(std::vector<int>& nums) {\n        int n = nums.size();\n        if (n == 0) return 0;\n        int ans = 0;\n        for (int i = 0; i < n; i++) {\n            ans += nums[i];\n        }\n        return ans;\n    }\n};",
        "java": "// Java Solution for Cheapest Flights Within K Stops\nimport java.util.*;\n\nclass Solution {\n    public int cheapestFlightsWithinKStops(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int ans = 0;\n        for (int num : nums) {\n            ans += num;\n        }\n        return ans;\n    }\n}",
        "python": "# Python Solution for Cheapest Flights Within K Stops\n\nclass Solution:\n    def cheapestFlightsWithinKStops(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        ans = 0\n        for num in nums:\n            ans += num\n        return ans\n",
        "javascript": "// JavaScript Solution for Cheapest Flights Within K Stops\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Cheapest Flights Within K Stops",
      "cpp_optimal": "// Solution for Cheapest Flights Within K Stops",
      "java_brute": "// Solution for Cheapest Flights Within K Stops",
      "java_optimal": "// Solution for Cheapest Flights Within K Stops",
      "python_brute": "# Solution for Cheapest Flights Within K Stops",
      "python_optimal": "# Solution for Cheapest Flights Within K Stops"
    },
    "originalOrder": 481,
    "learningOrder": 481
  },
  {
    "id": 572,
    "number": 572,
    "sequence_number": 572,
    "title": "Path With Minimum Effort",
    "slug": "path-with-minimum-effort",
    "difficulty": "Medium",
    "topic": "Graphs",
    "subtopic": "Graphs Optimization",
    "pattern": "Shortest Path",
    "secondary_patterns": [
      "Shortest Path"
    ],
    "stage": "Graph Traversal (BFS & DFS)",
    "curriculumStage": "Stage 12 — Graph Traversal (BFS & DFS)",
    "roadmapPhase": "Stage 12 — Graph Traversal (BFS & DFS)",
    "phase": "Stage 12 — Graph Traversal (BFS & DFS)",
    "estimatedTime": 30,
    "statement": "Finds a path from top-left to bottom-right of a grid minimizing maximum height difference using Dijkstra.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "All elements fall within standard integer bounds."
    ],
    "examples": [
      {
        "input": "heights = [[1,2,2],[3,8,2],[5,3,5]]",
        "output": "2",
        "explanation": "Optimal solution achieved using Shortest Path."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "All duplicate elements"
    ],
    "commonMistakes": [
      "Off-by-one index mistakes",
      "Integer overflow for large cumulative sums"
    ],
    "hints": [
      "Consider using Shortest Path.",
      "Analyze edge cases and bounds."
    ],
    "learningObjective": "Master Graphs techniques by solving Medium problem constraints for Path With Minimum Effort.",
    "whyThisPattern": "When observing Graphs problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(1)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/path-with-minimum-effort/",
    "leetcode_title": "Path With Minimum Effort",
    "leetcode_id": 1631,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/path-with-minimum-effort/",
    "canonicalSlug": "path-with-minimum-effort",
    "canonicalUrl": "https://leetcode.com/problems/path-with-minimum-effort/",
    "url": "https://leetcode.com/problems/path-with-minimum-effort/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Path with Minimum Effort\n#include <iostream>\n#include <vector>\n#include <algorithm>\n\nclass Solution {\npublic:\n    int pathwithMinimumEffort(std::vector<int>& nums) {\n        int n = nums.size();\n        if (n == 0) return 0;\n        int ans = 0;\n        for (int i = 0; i < n; i++) {\n            ans += nums[i];\n        }\n        return ans;\n    }\n};",
        "java": "// Java Solution for Path with Minimum Effort\nimport java.util.*;\n\nclass Solution {\n    public int pathwithMinimumEffort(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int ans = 0;\n        for (int num : nums) {\n            ans += num;\n        }\n        return ans;\n    }\n}",
        "python": "# Python Solution for Path with Minimum Effort\n\nclass Solution:\n    def pathwithMinimumEffort(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        ans = 0\n        for num in nums:\n            ans += num\n        return ans\n",
        "javascript": "// JavaScript Solution for Path with Minimum Effort\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Path with Minimum Effort\n#include <iostream>\n#include <vector>\n#include <algorithm>\n\nclass Solution {\npublic:\n    int pathwithMinimumEffort(std::vector<int>& nums) {\n        int n = nums.size();\n        if (n == 0) return 0;\n        int ans = 0;\n        for (int i = 0; i < n; i++) {\n            ans += nums[i];\n        }\n        return ans;\n    }\n};",
        "java": "// Java Solution for Path with Minimum Effort\nimport java.util.*;\n\nclass Solution {\n    public int pathwithMinimumEffort(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int ans = 0;\n        for (int num : nums) {\n            ans += num;\n        }\n        return ans;\n    }\n}",
        "python": "# Python Solution for Path with Minimum Effort\n\nclass Solution:\n    def pathwithMinimumEffort(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        ans = 0\n        for num in nums:\n            ans += num\n        return ans\n",
        "javascript": "// JavaScript Solution for Path with Minimum Effort\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Path With Minimum Effort",
      "cpp_optimal": "// Solution for Path With Minimum Effort",
      "java_brute": "// Solution for Path With Minimum Effort",
      "java_optimal": "// Solution for Path With Minimum Effort",
      "python_brute": "# Solution for Path With Minimum Effort",
      "python_optimal": "# Solution for Path With Minimum Effort"
    },
    "originalOrder": 482,
    "learningOrder": 482
  },
  {
    "id": 573,
    "number": 573,
    "sequence_number": 573,
    "title": "Shortest Bridge",
    "slug": "shortest-bridge",
    "difficulty": "Medium",
    "topic": "Graphs",
    "subtopic": "Graphs Optimization",
    "pattern": "Multi-Source BFS",
    "secondary_patterns": [
      "Multi-Source BFS"
    ],
    "stage": "Graph Traversal (BFS & DFS)",
    "curriculumStage": "Stage 12 — Graph Traversal (BFS & DFS)",
    "roadmapPhase": "Stage 12 — Graph Traversal (BFS & DFS)",
    "phase": "Stage 12 — Graph Traversal (BFS & DFS)",
    "estimatedTime": 30,
    "statement": "Given the constraints and input parameters for Shortest Bridge, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Shortest Bridge."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Shortest Bridge.",
      "Leverage the optimal Graphs pattern to reduce time complexity."
    ],
    "learningObjective": "Master Graphs techniques by solving Medium problem constraints for Shortest Bridge.",
    "whyThisPattern": "When observing Graphs problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/shortest-bridge/",
    "leetcode_title": "Shortest Bridge",
    "leetcode_id": 934,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/shortest-bridge/",
    "canonicalSlug": "shortest-bridge",
    "canonicalUrl": "https://leetcode.com/problems/shortest-bridge/",
    "url": "https://leetcode.com/problems/shortest-bridge/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Shortest Bridge\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Shortest Bridge\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Shortest Bridge\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Shortest Bridge\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Shortest Bridge\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Shortest Bridge\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Shortest Bridge\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Shortest Bridge\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Shortest Bridge",
      "cpp_optimal": "// Solution for Shortest Bridge",
      "java_brute": "// Solution for Shortest Bridge",
      "java_optimal": "// Solution for Shortest Bridge",
      "python_brute": "# Solution for Shortest Bridge",
      "python_optimal": "# Solution for Shortest Bridge"
    },
    "originalOrder": 483,
    "learningOrder": 483
  },
  {
    "id": 574,
    "number": 574,
    "sequence_number": 574,
    "title": "All Paths From Source to Target",
    "slug": "all-paths-from-source-to-target",
    "difficulty": "Medium",
    "topic": "Graphs",
    "subtopic": "Graphs Optimization",
    "pattern": "DAG DFS Backtracking",
    "secondary_patterns": [
      "DAG DFS Backtracking"
    ],
    "stage": "Graph Traversal (BFS & DFS)",
    "curriculumStage": "Stage 12 — Graph Traversal (BFS & DFS)",
    "roadmapPhase": "Stage 12 — Graph Traversal (BFS & DFS)",
    "phase": "Stage 12 — Graph Traversal (BFS & DFS)",
    "estimatedTime": 30,
    "statement": "Given the constraints and input parameters for All Paths From Source to Target, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for All Paths From Source to Target."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for All Paths From Source to Target.",
      "Leverage the optimal Graphs pattern to reduce time complexity."
    ],
    "learningObjective": "Master Graphs techniques by solving Medium problem constraints for All Paths From Source to Target.",
    "whyThisPattern": "When observing Graphs problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/all-paths-from-source-to-target/",
    "leetcode_title": "All Paths From Source to Target",
    "leetcode_id": 797,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/all-paths-from-source-to-target/",
    "canonicalSlug": "all-paths-from-source-to-target",
    "canonicalUrl": "https://leetcode.com/problems/all-paths-from-source-to-target/",
    "url": "https://leetcode.com/problems/all-paths-from-source-to-target/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for All Paths From Source to Target\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for All Paths From Source to Target\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for All Paths From Source to Target\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for All Paths From Source to Target\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for All Paths From Source to Target\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for All Paths From Source to Target\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for All Paths From Source to Target\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for All Paths From Source to Target\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for All Paths From Source to Target",
      "cpp_optimal": "// Solution for All Paths From Source to Target",
      "java_brute": "// Solution for All Paths From Source to Target",
      "java_optimal": "// Solution for All Paths From Source to Target",
      "python_brute": "# Solution for All Paths From Source to Target",
      "python_optimal": "# Solution for All Paths From Source to Target"
    },
    "originalOrder": 484,
    "learningOrder": 484
  },
  {
    "id": 575,
    "number": 575,
    "sequence_number": 575,
    "title": "Find Eventual Safe States",
    "slug": "find-eventual-safe-states",
    "difficulty": "Medium",
    "topic": "Graphs",
    "subtopic": "Graphs Optimization",
    "pattern": "DFS Tri-Color Cycle Check",
    "secondary_patterns": [
      "DFS Tri-Color Cycle Check"
    ],
    "stage": "Graph Traversal (BFS & DFS)",
    "curriculumStage": "Stage 12 — Graph Traversal (BFS & DFS)",
    "roadmapPhase": "Stage 12 — Graph Traversal (BFS & DFS)",
    "phase": "Stage 12 — Graph Traversal (BFS & DFS)",
    "estimatedTime": 30,
    "statement": "Given the constraints and input parameters for Find Eventual Safe States, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Find Eventual Safe States."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Find Eventual Safe States.",
      "Leverage the optimal Graphs pattern to reduce time complexity."
    ],
    "learningObjective": "Master Graphs techniques by solving Medium problem constraints for Find Eventual Safe States.",
    "whyThisPattern": "When observing Graphs problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/find-eventual-safe-states/",
    "leetcode_title": "Find Eventual Safe States",
    "leetcode_id": 802,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/find-eventual-safe-states/",
    "canonicalSlug": "find-eventual-safe-states",
    "canonicalUrl": "https://leetcode.com/problems/find-eventual-safe-states/",
    "url": "https://leetcode.com/problems/find-eventual-safe-states/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Find Eventual Safe States\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Find Eventual Safe States\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Find Eventual Safe States\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Find Eventual Safe States\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Find Eventual Safe States\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Find Eventual Safe States\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Find Eventual Safe States\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Find Eventual Safe States\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Find Eventual Safe States",
      "cpp_optimal": "// Solution for Find Eventual Safe States",
      "java_brute": "// Solution for Find Eventual Safe States",
      "java_optimal": "// Solution for Find Eventual Safe States",
      "python_brute": "# Solution for Find Eventual Safe States",
      "python_optimal": "# Solution for Find Eventual Safe States"
    },
    "originalOrder": 485,
    "learningOrder": 485
  },
  {
    "id": 576,
    "number": 576,
    "sequence_number": 576,
    "title": "Loud and Rich",
    "slug": "loud-and-rich",
    "difficulty": "Medium",
    "topic": "Graphs",
    "subtopic": "Graphs Optimization",
    "pattern": "Topological Sort / DFS Memo",
    "secondary_patterns": [
      "Topological Sort / DFS Memo"
    ],
    "stage": "Graph Traversal (BFS & DFS)",
    "curriculumStage": "Stage 12 — Graph Traversal (BFS & DFS)",
    "roadmapPhase": "Stage 12 — Graph Traversal (BFS & DFS)",
    "phase": "Stage 12 — Graph Traversal (BFS & DFS)",
    "estimatedTime": 30,
    "statement": "Given the constraints and input parameters for Loud and Rich, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Loud and Rich."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Loud and Rich.",
      "Leverage the optimal Graphs pattern to reduce time complexity."
    ],
    "learningObjective": "Master Graphs techniques by solving Medium problem constraints for Loud and Rich.",
    "whyThisPattern": "When observing Graphs problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/loud-and-rich/",
    "leetcode_title": "Loud and Rich",
    "leetcode_id": 851,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/loud-and-rich/",
    "canonicalSlug": "loud-and-rich",
    "canonicalUrl": "https://leetcode.com/problems/loud-and-rich/",
    "url": "https://leetcode.com/problems/loud-and-rich/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Loud and Rich\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Loud and Rich\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Loud and Rich\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Loud and Rich\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Loud and Rich\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Loud and Rich\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Loud and Rich\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Loud and Rich\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Loud and Rich",
      "cpp_optimal": "// Solution for Loud and Rich",
      "java_brute": "// Solution for Loud and Rich",
      "java_optimal": "// Solution for Loud and Rich",
      "python_brute": "# Solution for Loud and Rich",
      "python_optimal": "# Solution for Loud and Rich"
    },
    "originalOrder": 486,
    "learningOrder": 486
  },
  {
    "id": 577,
    "number": 577,
    "sequence_number": 577,
    "title": "Keys and Rooms",
    "slug": "keys-and-rooms",
    "difficulty": "Medium",
    "topic": "Graphs",
    "subtopic": "Graphs Optimization",
    "pattern": "BFS Room Graph",
    "secondary_patterns": [
      "BFS Room Graph"
    ],
    "stage": "Graph Traversal (BFS & DFS)",
    "curriculumStage": "Stage 12 — Graph Traversal (BFS & DFS)",
    "roadmapPhase": "Stage 12 — Graph Traversal (BFS & DFS)",
    "phase": "Stage 12 — Graph Traversal (BFS & DFS)",
    "estimatedTime": 30,
    "statement": "Given the constraints and input parameters for Keys and Rooms, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Keys and Rooms."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Keys and Rooms.",
      "Leverage the optimal Graphs pattern to reduce time complexity."
    ],
    "learningObjective": "Master Graphs techniques by solving Medium problem constraints for Keys and Rooms.",
    "whyThisPattern": "When observing Graphs problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/keys-and-rooms/",
    "leetcode_title": "Keys and Rooms",
    "leetcode_id": 841,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/keys-and-rooms/",
    "canonicalSlug": "keys-and-rooms",
    "canonicalUrl": "https://leetcode.com/problems/keys-and-rooms/",
    "url": "https://leetcode.com/problems/keys-and-rooms/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Keys and Rooms\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Keys and Rooms\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Keys and Rooms\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Keys and Rooms\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Keys and Rooms\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Keys and Rooms\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Keys and Rooms\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Keys and Rooms\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Keys and Rooms",
      "cpp_optimal": "// Solution for Keys and Rooms",
      "java_brute": "// Solution for Keys and Rooms",
      "java_optimal": "// Solution for Keys and Rooms",
      "python_brute": "# Solution for Keys and Rooms",
      "python_optimal": "# Solution for Keys and Rooms"
    },
    "originalOrder": 487,
    "learningOrder": 487
  },
  {
    "id": 578,
    "number": 578,
    "sequence_number": 578,
    "title": "Find the City With the Smallest Number of Neighbors at a Threshold Distance",
    "slug": "find-the-city-with-the-smallest-number-of-neighbors-at-a-threshold-distance",
    "difficulty": "Medium",
    "topic": "Graphs",
    "subtopic": "Graphs Optimization",
    "pattern": "Floyd-Warshall Shortest Path",
    "secondary_patterns": [
      "Floyd-Warshall Shortest Path"
    ],
    "stage": "Graph Traversal (BFS & DFS)",
    "curriculumStage": "Stage 12 — Graph Traversal (BFS & DFS)",
    "roadmapPhase": "Stage 12 — Graph Traversal (BFS & DFS)",
    "phase": "Stage 12 — Graph Traversal (BFS & DFS)",
    "estimatedTime": 30,
    "statement": "Given the constraints and input parameters for Find the City With the Smallest Number of Neighbors at a Threshold Distance, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Find the City With the Smallest Number of Neighbors at a Threshold Distance."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Find the City With the Smallest Number of Neighbors at a Threshold Distance.",
      "Leverage the optimal Graphs pattern to reduce time complexity."
    ],
    "learningObjective": "Master Graphs techniques by solving Medium problem constraints for Find the City With the Smallest Number of Neighbors at a Threshold Distance.",
    "whyThisPattern": "When observing Graphs problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/find-the-city-with-the-smallest-number-of-neighbors-at-a-threshold-distance/",
    "leetcode_title": "Find the City With the Smallest Number of Neighbors at a Threshold Distance",
    "leetcode_id": 1334,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/find-the-city-with-the-smallest-number-of-neighbors-at-a-threshold-distance/",
    "canonicalSlug": "find-the-city-with-the-smallest-number-of-neighbors-at-a-threshold-distance",
    "canonicalUrl": "https://leetcode.com/problems/find-the-city-with-the-smallest-number-of-neighbors-at-a-threshold-distance/",
    "url": "https://leetcode.com/problems/find-the-city-with-the-smallest-number-of-neighbors-at-a-threshold-distance/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Find the City With the Smallest Number of Neighbors at a Threshold Distance\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Find the City With the Smallest Number of Neighbors at a Threshold Distance\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Find the City With the Smallest Number of Neighbors at a Threshold Distance\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Find the City With the Smallest Number of Neighbors at a Threshold Distance\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Find the City With the Smallest Number of Neighbors at a Threshold Distance\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Find the City With the Smallest Number of Neighbors at a Threshold Distance\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Find the City With the Smallest Number of Neighbors at a Threshold Distance\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Find the City With the Smallest Number of Neighbors at a Threshold Distance\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Find the City With the Smallest Number of Neighbors at a Threshold Distance",
      "cpp_optimal": "// Solution for Find the City With the Smallest Number of Neighbors at a Threshold Distance",
      "java_brute": "// Solution for Find the City With the Smallest Number of Neighbors at a Threshold Distance",
      "java_optimal": "// Solution for Find the City With the Smallest Number of Neighbors at a Threshold Distance",
      "python_brute": "# Solution for Find the City With the Smallest Number of Neighbors at a Threshold Distance",
      "python_optimal": "# Solution for Find the City With the Smallest Number of Neighbors at a Threshold Distance"
    },
    "originalOrder": 488,
    "learningOrder": 488
  },
  {
    "id": 579,
    "number": 579,
    "sequence_number": 579,
    "title": "Reorder Routes to Make All Paths Lead to the City Zero",
    "slug": "reorder-routes-to-make-all-paths-lead-to-the-city-zero",
    "difficulty": "Medium",
    "topic": "Graphs",
    "subtopic": "Graphs Optimization",
    "pattern": "Directed Tree Reversal BFS",
    "secondary_patterns": [
      "Directed Tree Reversal BFS"
    ],
    "stage": "Graph Traversal (BFS & DFS)",
    "curriculumStage": "Stage 12 — Graph Traversal (BFS & DFS)",
    "roadmapPhase": "Stage 12 — Graph Traversal (BFS & DFS)",
    "phase": "Stage 12 — Graph Traversal (BFS & DFS)",
    "estimatedTime": 30,
    "statement": "Given the constraints and input parameters for Reorder Routes to Make All Paths Lead to the City Zero, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Reorder Routes to Make All Paths Lead to the City Zero."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Reorder Routes to Make All Paths Lead to the City Zero.",
      "Leverage the optimal Graphs pattern to reduce time complexity."
    ],
    "learningObjective": "Master Graphs techniques by solving Medium problem constraints for Reorder Routes to Make All Paths Lead to the City Zero.",
    "whyThisPattern": "When observing Graphs problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/reorder-routes-to-make-all-paths-lead-to-the-city-zero/",
    "leetcode_title": "Reorder Routes to Make All Paths Lead to the City Zero",
    "leetcode_id": 1466,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/reorder-routes-to-make-all-paths-lead-to-the-city-zero/",
    "canonicalSlug": "reorder-routes-to-make-all-paths-lead-to-the-city-zero",
    "canonicalUrl": "https://leetcode.com/problems/reorder-routes-to-make-all-paths-lead-to-the-city-zero/",
    "url": "https://leetcode.com/problems/reorder-routes-to-make-all-paths-lead-to-the-city-zero/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Reorder Routes to Make All Paths Lead to the City Zero\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Reorder Routes to Make All Paths Lead to the City Zero\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Reorder Routes to Make All Paths Lead to the City Zero\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Reorder Routes to Make All Paths Lead to the City Zero\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Reorder Routes to Make All Paths Lead to the City Zero\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Reorder Routes to Make All Paths Lead to the City Zero\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Reorder Routes to Make All Paths Lead to the City Zero\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Reorder Routes to Make All Paths Lead to the City Zero\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Reorder Routes to Make All Paths Lead to the City Zero",
      "cpp_optimal": "// Solution for Reorder Routes to Make All Paths Lead to the City Zero",
      "java_brute": "// Solution for Reorder Routes to Make All Paths Lead to the City Zero",
      "java_optimal": "// Solution for Reorder Routes to Make All Paths Lead to the City Zero",
      "python_brute": "# Solution for Reorder Routes to Make All Paths Lead to the City Zero",
      "python_optimal": "# Solution for Reorder Routes to Make All Paths Lead to the City Zero"
    },
    "originalOrder": 489,
    "learningOrder": 489
  },
  {
    "id": 580,
    "number": 580,
    "sequence_number": 580,
    "title": "Minimum Number of Vertices to Reach All Nodes",
    "slug": "minimum-number-of-vertices-to-reach-all-nodes",
    "difficulty": "Medium",
    "topic": "Graphs",
    "subtopic": "Graphs Optimization",
    "pattern": "In-Degree Zero Vertices",
    "secondary_patterns": [
      "In-Degree Zero Vertices"
    ],
    "stage": "Graph Traversal (BFS & DFS)",
    "curriculumStage": "Stage 12 — Graph Traversal (BFS & DFS)",
    "roadmapPhase": "Stage 12 — Graph Traversal (BFS & DFS)",
    "phase": "Stage 12 — Graph Traversal (BFS & DFS)",
    "estimatedTime": 30,
    "statement": "Given the constraints and input parameters for Minimum Number of Vertices to Reach All Nodes, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Minimum Number of Vertices to Reach All Nodes."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Minimum Number of Vertices to Reach All Nodes.",
      "Leverage the optimal Graphs pattern to reduce time complexity."
    ],
    "learningObjective": "Master Graphs techniques by solving Medium problem constraints for Minimum Number of Vertices to Reach All Nodes.",
    "whyThisPattern": "When observing Graphs problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/minimum-number-of-vertices-to-reach-all-nodes/",
    "leetcode_title": "Minimum Number of Vertices to Reach All Nodes",
    "leetcode_id": 1557,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/minimum-number-of-vertices-to-reach-all-nodes/",
    "canonicalSlug": "minimum-number-of-vertices-to-reach-all-nodes",
    "canonicalUrl": "https://leetcode.com/problems/minimum-number-of-vertices-to-reach-all-nodes/",
    "url": "https://leetcode.com/problems/minimum-number-of-vertices-to-reach-all-nodes/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Minimum Number of Vertices to Reach All Nodes\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Minimum Number of Vertices to Reach All Nodes\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Minimum Number of Vertices to Reach All Nodes\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Minimum Number of Vertices to Reach All Nodes\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Minimum Number of Vertices to Reach All Nodes\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Minimum Number of Vertices to Reach All Nodes\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Minimum Number of Vertices to Reach All Nodes\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Minimum Number of Vertices to Reach All Nodes\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Minimum Number of Vertices to Reach All Nodes",
      "cpp_optimal": "// Solution for Minimum Number of Vertices to Reach All Nodes",
      "java_brute": "// Solution for Minimum Number of Vertices to Reach All Nodes",
      "java_optimal": "// Solution for Minimum Number of Vertices to Reach All Nodes",
      "python_brute": "# Solution for Minimum Number of Vertices to Reach All Nodes",
      "python_optimal": "# Solution for Minimum Number of Vertices to Reach All Nodes"
    },
    "originalOrder": 490,
    "learningOrder": 490
  },
  {
    "id": 581,
    "number": 581,
    "sequence_number": 581,
    "title": "Map of Highest Peak",
    "slug": "map-of-highest-peak",
    "difficulty": "Medium",
    "topic": "Graphs",
    "subtopic": "Graphs Optimization",
    "pattern": "Multi-Source Water BFS",
    "secondary_patterns": [
      "Multi-Source Water BFS"
    ],
    "stage": "Graph Traversal (BFS & DFS)",
    "curriculumStage": "Stage 12 — Graph Traversal (BFS & DFS)",
    "roadmapPhase": "Stage 12 — Graph Traversal (BFS & DFS)",
    "phase": "Stage 12 — Graph Traversal (BFS & DFS)",
    "estimatedTime": 30,
    "statement": "Given the constraints and input parameters for Map of Highest Peak, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Map of Highest Peak."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Map of Highest Peak.",
      "Leverage the optimal Graphs pattern to reduce time complexity."
    ],
    "learningObjective": "Master Graphs techniques by solving Medium problem constraints for Map of Highest Peak.",
    "whyThisPattern": "When observing Graphs problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/map-of-highest-peak/",
    "leetcode_title": "Map of Highest Peak",
    "leetcode_id": 1765,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/map-of-highest-peak/",
    "canonicalSlug": "map-of-highest-peak",
    "canonicalUrl": "https://leetcode.com/problems/map-of-highest-peak/",
    "url": "https://leetcode.com/problems/map-of-highest-peak/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Map of Highest Peak\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Map of Highest Peak\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Map of Highest Peak\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Map of Highest Peak\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Map of Highest Peak\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Map of Highest Peak\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Map of Highest Peak\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Map of Highest Peak\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Map of Highest Peak",
      "cpp_optimal": "// Solution for Map of Highest Peak",
      "java_brute": "// Solution for Map of Highest Peak",
      "java_optimal": "// Solution for Map of Highest Peak",
      "python_brute": "# Solution for Map of Highest Peak",
      "python_optimal": "# Solution for Map of Highest Peak"
    },
    "originalOrder": 491,
    "learningOrder": 491
  },
  {
    "id": 582,
    "number": 582,
    "sequence_number": 582,
    "title": "Surrounded Regions",
    "slug": "surrounded-regions",
    "difficulty": "Medium",
    "topic": "Graphs",
    "subtopic": "Graphs Optimization",
    "pattern": "Boundary Connected DFS",
    "secondary_patterns": [
      "Boundary Connected DFS"
    ],
    "stage": "Graph Traversal (BFS & DFS)",
    "curriculumStage": "Stage 12 — Graph Traversal (BFS & DFS)",
    "roadmapPhase": "Stage 12 — Graph Traversal (BFS & DFS)",
    "phase": "Stage 12 — Graph Traversal (BFS & DFS)",
    "estimatedTime": 30,
    "statement": "Given the constraints and input parameters for Surrounded Regions, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Surrounded Regions."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Surrounded Regions.",
      "Leverage the optimal Graphs pattern to reduce time complexity."
    ],
    "learningObjective": "Master Graphs techniques by solving Medium problem constraints for Surrounded Regions.",
    "whyThisPattern": "When observing Graphs problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/surrounded-regions/",
    "leetcode_title": "Surrounded Regions",
    "leetcode_id": 130,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/surrounded-regions/",
    "canonicalSlug": "surrounded-regions",
    "canonicalUrl": "https://leetcode.com/problems/surrounded-regions/",
    "url": "https://leetcode.com/problems/surrounded-regions/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Surrounded Regions\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Surrounded Regions\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Surrounded Regions\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Surrounded Regions\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Surrounded Regions\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Surrounded Regions\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Surrounded Regions\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Surrounded Regions\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Surrounded Regions",
      "cpp_optimal": "// Solution for Surrounded Regions",
      "java_brute": "// Solution for Surrounded Regions",
      "java_optimal": "// Solution for Surrounded Regions",
      "python_brute": "# Solution for Surrounded Regions",
      "python_optimal": "# Solution for Surrounded Regions"
    },
    "originalOrder": 492,
    "learningOrder": 492
  },
  {
    "id": 583,
    "number": 583,
    "sequence_number": 583,
    "title": "Number of Islands",
    "slug": "number-of-islands",
    "difficulty": "Medium",
    "topic": "Graphs",
    "subtopic": "Graphs Optimization",
    "pattern": "Grid DFS Connected Components",
    "secondary_patterns": [
      "Grid DFS Connected Components"
    ],
    "stage": "Graph Traversal (BFS & DFS)",
    "curriculumStage": "Stage 12 — Graph Traversal (BFS & DFS)",
    "roadmapPhase": "Stage 12 — Graph Traversal (BFS & DFS)",
    "phase": "Stage 12 — Graph Traversal (BFS & DFS)",
    "estimatedTime": 30,
    "statement": "Given the constraints and input parameters for Number of Islands, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Number of Islands."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Number of Islands.",
      "Leverage the optimal Graphs pattern to reduce time complexity."
    ],
    "learningObjective": "Master Graphs techniques by solving Medium problem constraints for Number of Islands.",
    "whyThisPattern": "When observing Graphs problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/number-of-islands/",
    "leetcode_title": "Number of Islands",
    "leetcode_id": 200,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/number-of-islands/",
    "canonicalSlug": "number-of-islands",
    "canonicalUrl": "https://leetcode.com/problems/number-of-islands/",
    "url": "https://leetcode.com/problems/number-of-islands/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Number of Islands\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Number of Islands\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Number of Islands\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Number of Islands\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Number of Islands\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Number of Islands\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Number of Islands\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Number of Islands\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Number of Islands",
      "cpp_optimal": "// Solution for Number of Islands",
      "java_brute": "// Solution for Number of Islands",
      "java_optimal": "// Solution for Number of Islands",
      "python_brute": "# Solution for Number of Islands",
      "python_optimal": "# Solution for Number of Islands"
    },
    "originalOrder": 493,
    "learningOrder": 493
  },
  {
    "id": 584,
    "number": 584,
    "sequence_number": 584,
    "title": "Pacific Atlantic Water Flow",
    "slug": "pacific-atlantic-water-flow",
    "difficulty": "Medium",
    "topic": "Graphs",
    "subtopic": "Graphs Optimization",
    "pattern": "Multi-Source Reverse DFS",
    "secondary_patterns": [
      "Multi-Source Reverse DFS"
    ],
    "stage": "Graph Traversal (BFS & DFS)",
    "curriculumStage": "Stage 12 — Graph Traversal (BFS & DFS)",
    "roadmapPhase": "Stage 12 — Graph Traversal (BFS & DFS)",
    "phase": "Stage 12 — Graph Traversal (BFS & DFS)",
    "estimatedTime": 30,
    "statement": "Given the constraints and input parameters for Pacific Atlantic Water Flow, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Pacific Atlantic Water Flow."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Pacific Atlantic Water Flow.",
      "Leverage the optimal Graphs pattern to reduce time complexity."
    ],
    "learningObjective": "Master Graphs techniques by solving Medium problem constraints for Pacific Atlantic Water Flow.",
    "whyThisPattern": "When observing Graphs problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/pacific-atlantic-water-flow/",
    "leetcode_title": "Pacific Atlantic Water Flow",
    "leetcode_id": 417,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/pacific-atlantic-water-flow/",
    "canonicalSlug": "pacific-atlantic-water-flow",
    "canonicalUrl": "https://leetcode.com/problems/pacific-atlantic-water-flow/",
    "url": "https://leetcode.com/problems/pacific-atlantic-water-flow/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Pacific Atlantic Water Flow\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Pacific Atlantic Water Flow\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Pacific Atlantic Water Flow\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Pacific Atlantic Water Flow\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Pacific Atlantic Water Flow\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Pacific Atlantic Water Flow\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Pacific Atlantic Water Flow\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Pacific Atlantic Water Flow\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Pacific Atlantic Water Flow",
      "cpp_optimal": "// Solution for Pacific Atlantic Water Flow",
      "java_brute": "// Solution for Pacific Atlantic Water Flow",
      "java_optimal": "// Solution for Pacific Atlantic Water Flow",
      "python_brute": "# Solution for Pacific Atlantic Water Flow",
      "python_optimal": "# Solution for Pacific Atlantic Water Flow"
    },
    "originalOrder": 494,
    "learningOrder": 494
  },
  {
    "id": 585,
    "number": 585,
    "sequence_number": 585,
    "title": "Clone Graph",
    "slug": "clone-graph",
    "difficulty": "Medium",
    "topic": "Graphs",
    "subtopic": "Graphs Optimization",
    "pattern": "Graphs Pattern",
    "secondary_patterns": [
      "Graphs Pattern"
    ],
    "stage": "Graph Traversal (BFS & DFS)",
    "curriculumStage": "Stage 12 — Graph Traversal (BFS & DFS)",
    "roadmapPhase": "Stage 12 — Graph Traversal (BFS & DFS)",
    "phase": "Stage 12 — Graph Traversal (BFS & DFS)",
    "estimatedTime": 30,
    "statement": "Solve the **Clone Graph** problem using standard Graphs techniques. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Graphs algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Graphs properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Graphs techniques by solving Medium problem constraints for Clone Graph.",
    "whyThisPattern": "When observing Graphs problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/clone-graph/",
    "leetcode_title": "Clone Graph",
    "leetcode_id": 133,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/clone-graph/",
    "canonicalSlug": "clone-graph",
    "canonicalUrl": "https://leetcode.com/problems/clone-graph/",
    "url": "https://leetcode.com/problems/clone-graph/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Clone Graph\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Clone Graph\n};",
        "java": "// Java Solution for Clone Graph\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Clone Graph\n}",
        "python": "# Python Solution for Clone Graph\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Clone Graph\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Clone Graph\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Clone Graph\n};",
        "java": "// Optimal Java Solution for Clone Graph\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Clone Graph\n}",
        "python": "# Optimal Python Solution for Clone Graph\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Clone Graph\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Clone Graph",
      "cpp_optimal": "// Solution for Clone Graph",
      "java_brute": "// Solution for Clone Graph",
      "java_optimal": "// Solution for Clone Graph",
      "python_brute": "# Solution for Clone Graph",
      "python_optimal": "# Solution for Clone Graph"
    },
    "originalOrder": 495,
    "learningOrder": 495
  },
  {
    "id": 586,
    "number": 586,
    "sequence_number": 586,
    "title": "K-Similar Strings",
    "slug": "k-similar-strings",
    "difficulty": "Hard",
    "topic": "Graphs",
    "subtopic": "Graphs Optimization",
    "pattern": "BFS String Swap State",
    "secondary_patterns": [
      "BFS String Swap State"
    ],
    "stage": "Graph Traversal (BFS & DFS)",
    "curriculumStage": "Stage 12 — Graph Traversal (BFS & DFS)",
    "roadmapPhase": "Stage 12 — Graph Traversal (BFS & DFS)",
    "phase": "Stage 12 — Graph Traversal (BFS & DFS)",
    "estimatedTime": 45,
    "statement": "Given the constraints and input parameters for K-Similar Strings, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for K-Similar Strings."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for K-Similar Strings.",
      "Leverage the optimal Graphs pattern to reduce time complexity."
    ],
    "learningObjective": "Master Graphs techniques by solving Hard problem constraints for K-Similar Strings.",
    "whyThisPattern": "When observing Graphs problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/k-similar-strings/",
    "leetcode_title": "K-Similar Strings",
    "leetcode_id": 854,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/k-similar-strings/",
    "canonicalSlug": "k-similar-strings",
    "canonicalUrl": "https://leetcode.com/problems/k-similar-strings/",
    "url": "https://leetcode.com/problems/k-similar-strings/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for K-Similar Strings\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for K-Similar Strings\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for K-Similar Strings\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for K-Similar Strings\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for K-Similar Strings\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for K-Similar Strings\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for K-Similar Strings\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for K-Similar Strings\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for K-Similar Strings",
      "cpp_optimal": "// Solution for K-Similar Strings",
      "java_brute": "// Solution for K-Similar Strings",
      "java_optimal": "// Solution for K-Similar Strings",
      "python_brute": "# Solution for K-Similar Strings",
      "python_optimal": "# Solution for K-Similar Strings"
    },
    "originalOrder": 871,
    "learningOrder": 871
  },
  {
    "id": 587,
    "number": 587,
    "sequence_number": 587,
    "title": "Cracking the Safe",
    "slug": "cracking-the-safe",
    "difficulty": "Hard",
    "topic": "Graphs",
    "subtopic": "Graphs Optimization",
    "pattern": "De Bruijn Cycle Eulerian Path",
    "secondary_patterns": [
      "De Bruijn Cycle Eulerian Path"
    ],
    "stage": "Graph Traversal (BFS & DFS)",
    "curriculumStage": "Stage 12 — Graph Traversal (BFS & DFS)",
    "roadmapPhase": "Stage 12 — Graph Traversal (BFS & DFS)",
    "phase": "Stage 12 — Graph Traversal (BFS & DFS)",
    "estimatedTime": 45,
    "statement": "Given the constraints and input parameters for Cracking the Safe, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Cracking the Safe."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Cracking the Safe.",
      "Leverage the optimal Graphs pattern to reduce time complexity."
    ],
    "learningObjective": "Master Graphs techniques by solving Hard problem constraints for Cracking the Safe.",
    "whyThisPattern": "When observing Graphs problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/cracking-the-safe/",
    "leetcode_title": "Cracking the Safe",
    "leetcode_id": 753,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/cracking-the-safe/",
    "canonicalSlug": "cracking-the-safe",
    "canonicalUrl": "https://leetcode.com/problems/cracking-the-safe/",
    "url": "https://leetcode.com/problems/cracking-the-safe/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Cracking the Safe\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Cracking the Safe\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Cracking the Safe\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Cracking the Safe\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Cracking the Safe\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Cracking the Safe\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Cracking the Safe\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Cracking the Safe\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Cracking the Safe",
      "cpp_optimal": "// Solution for Cracking the Safe",
      "java_brute": "// Solution for Cracking the Safe",
      "java_optimal": "// Solution for Cracking the Safe",
      "python_brute": "# Solution for Cracking the Safe",
      "python_optimal": "# Solution for Cracking the Safe"
    },
    "originalOrder": 872,
    "learningOrder": 872
  },
  {
    "id": 588,
    "number": 588,
    "sequence_number": 588,
    "title": "Swim in Rising Water",
    "slug": "swim-in-rising-water",
    "difficulty": "Hard",
    "topic": "Graphs",
    "subtopic": "Graphs Optimization",
    "pattern": "Dijkstra Grid Binary Search",
    "secondary_patterns": [
      "Dijkstra Grid Binary Search"
    ],
    "stage": "Graph Traversal (BFS & DFS)",
    "curriculumStage": "Stage 12 — Graph Traversal (BFS & DFS)",
    "roadmapPhase": "Stage 12 — Graph Traversal (BFS & DFS)",
    "phase": "Stage 12 — Graph Traversal (BFS & DFS)",
    "estimatedTime": 45,
    "statement": "Given the constraints and input parameters for Swim in Rising Water, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Swim in Rising Water."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Swim in Rising Water.",
      "Leverage the optimal Graphs pattern to reduce time complexity."
    ],
    "learningObjective": "Master Graphs techniques by solving Hard problem constraints for Swim in Rising Water.",
    "whyThisPattern": "When observing Graphs problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/swim-in-rising-water/",
    "leetcode_title": "Swim in Rising Water",
    "leetcode_id": 778,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/swim-in-rising-water/",
    "canonicalSlug": "swim-in-rising-water",
    "canonicalUrl": "https://leetcode.com/problems/swim-in-rising-water/",
    "url": "https://leetcode.com/problems/swim-in-rising-water/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Swim in Rising Water\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Swim in Rising Water\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Swim in Rising Water\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Swim in Rising Water\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Swim in Rising Water\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Swim in Rising Water\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Swim in Rising Water\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Swim in Rising Water\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Swim in Rising Water",
      "cpp_optimal": "// Solution for Swim in Rising Water",
      "java_brute": "// Solution for Swim in Rising Water",
      "java_optimal": "// Solution for Swim in Rising Water",
      "python_brute": "# Solution for Swim in Rising Water",
      "python_optimal": "# Solution for Swim in Rising Water"
    },
    "originalOrder": 873,
    "learningOrder": 873
  },
  {
    "id": 589,
    "number": 589,
    "sequence_number": 589,
    "title": "Strange Printer II",
    "slug": "strange-printer-ii",
    "difficulty": "Hard",
    "topic": "Graphs",
    "subtopic": "Graphs Optimization",
    "pattern": "Topological Sort Color Overlap",
    "secondary_patterns": [
      "Topological Sort Color Overlap"
    ],
    "stage": "Graph Traversal (BFS & DFS)",
    "curriculumStage": "Stage 12 — Graph Traversal (BFS & DFS)",
    "roadmapPhase": "Stage 12 — Graph Traversal (BFS & DFS)",
    "phase": "Stage 12 — Graph Traversal (BFS & DFS)",
    "estimatedTime": 45,
    "statement": "Given the constraints and input parameters for Strange Printer II, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Strange Printer II."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Strange Printer II.",
      "Leverage the optimal Graphs pattern to reduce time complexity."
    ],
    "learningObjective": "Master Graphs techniques by solving Hard problem constraints for Strange Printer II.",
    "whyThisPattern": "When observing Graphs problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/strange-printer-ii/",
    "leetcode_title": "Strange Printer II",
    "leetcode_id": 1591,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/strange-printer-ii/",
    "canonicalSlug": "strange-printer-ii",
    "canonicalUrl": "https://leetcode.com/problems/strange-printer-ii/",
    "url": "https://leetcode.com/problems/strange-printer-ii/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Strange Printer II\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Strange Printer II\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Strange Printer II\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Strange Printer II\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Strange Printer II\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Strange Printer II\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Strange Printer II\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Strange Printer II\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Strange Printer II",
      "cpp_optimal": "// Solution for Strange Printer II",
      "java_brute": "// Solution for Strange Printer II",
      "java_optimal": "// Solution for Strange Printer II",
      "python_brute": "# Solution for Strange Printer II",
      "python_optimal": "# Solution for Strange Printer II"
    },
    "originalOrder": 874,
    "learningOrder": 874
  },
  {
    "id": 590,
    "number": 590,
    "sequence_number": 590,
    "title": "Minimum Cost to Make at Least One Valid Path in a Grid",
    "slug": "minimum-cost-to-make-at-least-one-valid-path-in-a-grid",
    "difficulty": "Hard",
    "topic": "Graphs",
    "subtopic": "Graphs Optimization",
    "pattern": "0-1 BFS Grid Shortest Path",
    "secondary_patterns": [
      "0-1 BFS Grid Shortest Path"
    ],
    "stage": "Graph Traversal (BFS & DFS)",
    "curriculumStage": "Stage 12 — Graph Traversal (BFS & DFS)",
    "roadmapPhase": "Stage 12 — Graph Traversal (BFS & DFS)",
    "phase": "Stage 12 — Graph Traversal (BFS & DFS)",
    "estimatedTime": 45,
    "statement": "Given the constraints and input parameters for Minimum Cost to Make at Least One Valid Path in a Grid, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Minimum Cost to Make at Least One Valid Path in a Grid."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Minimum Cost to Make at Least One Valid Path in a Grid.",
      "Leverage the optimal Graphs pattern to reduce time complexity."
    ],
    "learningObjective": "Master Graphs techniques by solving Hard problem constraints for Minimum Cost to Make at Least One Valid Path in a Grid.",
    "whyThisPattern": "When observing Graphs problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/minimum-cost-to-make-at-least-one-valid-path-in-a-grid/",
    "leetcode_title": "Minimum Cost to Make at Least One Valid Path in a Grid",
    "leetcode_id": 1368,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/minimum-cost-to-make-at-least-one-valid-path-in-a-grid/",
    "canonicalSlug": "minimum-cost-to-make-at-least-one-valid-path-in-a-grid",
    "canonicalUrl": "https://leetcode.com/problems/minimum-cost-to-make-at-least-one-valid-path-in-a-grid/",
    "url": "https://leetcode.com/problems/minimum-cost-to-make-at-least-one-valid-path-in-a-grid/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Minimum Cost to Make at Least One Valid Path in a Grid\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Minimum Cost to Make at Least One Valid Path in a Grid\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Minimum Cost to Make at Least One Valid Path in a Grid\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Minimum Cost to Make at Least One Valid Path in a Grid\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Minimum Cost to Make at Least One Valid Path in a Grid\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Minimum Cost to Make at Least One Valid Path in a Grid\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Minimum Cost to Make at Least One Valid Path in a Grid\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Minimum Cost to Make at Least One Valid Path in a Grid\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Minimum Cost to Make at Least One Valid Path in a Grid",
      "cpp_optimal": "// Solution for Minimum Cost to Make at Least One Valid Path in a Grid",
      "java_brute": "// Solution for Minimum Cost to Make at Least One Valid Path in a Grid",
      "java_optimal": "// Solution for Minimum Cost to Make at Least One Valid Path in a Grid",
      "python_brute": "# Solution for Minimum Cost to Make at Least One Valid Path in a Grid",
      "python_optimal": "# Solution for Minimum Cost to Make at Least One Valid Path in a Grid"
    },
    "originalOrder": 875,
    "learningOrder": 875
  },
  {
    "id": 591,
    "number": 591,
    "sequence_number": 591,
    "title": "Contain Virus",
    "slug": "contain-virus",
    "difficulty": "Hard",
    "topic": "Graphs",
    "subtopic": "Graphs Optimization",
    "pattern": "Grid BFS Wall Simulation",
    "secondary_patterns": [
      "Grid BFS Wall Simulation"
    ],
    "stage": "Graph Traversal (BFS & DFS)",
    "curriculumStage": "Stage 12 — Graph Traversal (BFS & DFS)",
    "roadmapPhase": "Stage 12 — Graph Traversal (BFS & DFS)",
    "phase": "Stage 12 — Graph Traversal (BFS & DFS)",
    "estimatedTime": 45,
    "statement": "Given the constraints and input parameters for Contain Virus, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Contain Virus."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Contain Virus.",
      "Leverage the optimal Graphs pattern to reduce time complexity."
    ],
    "learningObjective": "Master Graphs techniques by solving Hard problem constraints for Contain Virus.",
    "whyThisPattern": "When observing Graphs problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/contain-virus/",
    "leetcode_title": "Contain Virus",
    "leetcode_id": 749,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/contain-virus/",
    "canonicalSlug": "contain-virus",
    "canonicalUrl": "https://leetcode.com/problems/contain-virus/",
    "url": "https://leetcode.com/problems/contain-virus/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Contain Virus\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Contain Virus\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Contain Virus\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Contain Virus\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Contain Virus\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Contain Virus\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Contain Virus\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Contain Virus\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Contain Virus",
      "cpp_optimal": "// Solution for Contain Virus",
      "java_brute": "// Solution for Contain Virus",
      "java_optimal": "// Solution for Contain Virus",
      "python_brute": "# Solution for Contain Virus",
      "python_optimal": "# Solution for Contain Virus"
    },
    "originalOrder": 876,
    "learningOrder": 876
  },
  {
    "id": 592,
    "number": 592,
    "sequence_number": 592,
    "title": "Reconstruct Itinerary",
    "slug": "reconstruct-itinerary",
    "difficulty": "Hard",
    "topic": "Graphs",
    "subtopic": "Graphs Optimization",
    "pattern": "Eulerian Path Hierholzer DFS",
    "secondary_patterns": [
      "Eulerian Path Hierholzer DFS"
    ],
    "stage": "Graph Traversal (BFS & DFS)",
    "curriculumStage": "Stage 12 — Graph Traversal (BFS & DFS)",
    "roadmapPhase": "Stage 12 — Graph Traversal (BFS & DFS)",
    "phase": "Stage 12 — Graph Traversal (BFS & DFS)",
    "estimatedTime": 45,
    "statement": "Given the constraints and input parameters for Reconstruct Itinerary, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Reconstruct Itinerary."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Reconstruct Itinerary.",
      "Leverage the optimal Graphs pattern to reduce time complexity."
    ],
    "learningObjective": "Master Graphs techniques by solving Hard problem constraints for Reconstruct Itinerary.",
    "whyThisPattern": "When observing Graphs problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/reconstruct-itinerary/",
    "leetcode_title": "Reconstruct Itinerary",
    "leetcode_id": 332,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/reconstruct-itinerary/",
    "canonicalSlug": "reconstruct-itinerary",
    "canonicalUrl": "https://leetcode.com/problems/reconstruct-itinerary/",
    "url": "https://leetcode.com/problems/reconstruct-itinerary/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Reconstruct Itinerary\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Reconstruct Itinerary\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Reconstruct Itinerary\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Reconstruct Itinerary\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Reconstruct Itinerary\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Reconstruct Itinerary\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Reconstruct Itinerary\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Reconstruct Itinerary\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Reconstruct Itinerary",
      "cpp_optimal": "// Solution for Reconstruct Itinerary",
      "java_brute": "// Solution for Reconstruct Itinerary",
      "java_optimal": "// Solution for Reconstruct Itinerary",
      "python_brute": "# Solution for Reconstruct Itinerary",
      "python_optimal": "# Solution for Reconstruct Itinerary"
    },
    "originalOrder": 877,
    "learningOrder": 877
  },
  {
    "id": 593,
    "number": 593,
    "sequence_number": 593,
    "title": "Shortest Path in a Grid with Obstacles Elimination",
    "slug": "shortest-path-in-a-grid-with-obstacles-elimination",
    "difficulty": "Hard",
    "topic": "Graphs",
    "subtopic": "Graphs Optimization",
    "pattern": "BFS Grid State K",
    "secondary_patterns": [
      "BFS Grid State K"
    ],
    "stage": "Graph Traversal (BFS & DFS)",
    "curriculumStage": "Stage 12 — Graph Traversal (BFS & DFS)",
    "roadmapPhase": "Stage 12 — Graph Traversal (BFS & DFS)",
    "phase": "Stage 12 — Graph Traversal (BFS & DFS)",
    "estimatedTime": 45,
    "statement": "Given the constraints and input parameters for Shortest Path in a Grid with Obstacles Elimination, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Shortest Path in a Grid with Obstacles Elimination."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Shortest Path in a Grid with Obstacles Elimination.",
      "Leverage the optimal Graphs pattern to reduce time complexity."
    ],
    "learningObjective": "Master Graphs techniques by solving Hard problem constraints for Shortest Path in a Grid with Obstacles Elimination.",
    "whyThisPattern": "When observing Graphs problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/shortest-path-in-a-grid-with-obstacles-elimination/",
    "leetcode_title": "Shortest Path in a Grid with Obstacles Elimination",
    "leetcode_id": 1293,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/shortest-path-in-a-grid-with-obstacles-elimination/",
    "canonicalSlug": "shortest-path-in-a-grid-with-obstacles-elimination",
    "canonicalUrl": "https://leetcode.com/problems/shortest-path-in-a-grid-with-obstacles-elimination/",
    "url": "https://leetcode.com/problems/shortest-path-in-a-grid-with-obstacles-elimination/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Shortest Path in a Grid with Obstacles Elimination\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Shortest Path in a Grid with Obstacles Elimination\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Shortest Path in a Grid with Obstacles Elimination\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Shortest Path in a Grid with Obstacles Elimination\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Shortest Path in a Grid with Obstacles Elimination\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Shortest Path in a Grid with Obstacles Elimination\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Shortest Path in a Grid with Obstacles Elimination\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Shortest Path in a Grid with Obstacles Elimination\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Shortest Path in a Grid with Obstacles Elimination",
      "cpp_optimal": "// Solution for Shortest Path in a Grid with Obstacles Elimination",
      "java_brute": "// Solution for Shortest Path in a Grid with Obstacles Elimination",
      "java_optimal": "// Solution for Shortest Path in a Grid with Obstacles Elimination",
      "python_brute": "# Solution for Shortest Path in a Grid with Obstacles Elimination",
      "python_optimal": "# Solution for Shortest Path in a Grid with Obstacles Elimination"
    },
    "originalOrder": 878,
    "learningOrder": 878
  },
  {
    "id": 594,
    "number": 594,
    "sequence_number": 594,
    "title": "Parallel Courses III",
    "slug": "parallel-courses-iii",
    "difficulty": "Hard",
    "topic": "Graphs",
    "subtopic": "Graphs Optimization",
    "pattern": "Topological Sort Max Time DP",
    "secondary_patterns": [
      "Topological Sort Max Time DP"
    ],
    "stage": "Graph Traversal (BFS & DFS)",
    "curriculumStage": "Stage 12 — Graph Traversal (BFS & DFS)",
    "roadmapPhase": "Stage 12 — Graph Traversal (BFS & DFS)",
    "phase": "Stage 12 — Graph Traversal (BFS & DFS)",
    "estimatedTime": 45,
    "statement": "Given the constraints and input parameters for Parallel Courses III, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Parallel Courses III."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Parallel Courses III.",
      "Leverage the optimal Graphs pattern to reduce time complexity."
    ],
    "learningObjective": "Master Graphs techniques by solving Hard problem constraints for Parallel Courses III.",
    "whyThisPattern": "When observing Graphs problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/parallel-courses-iii/",
    "leetcode_title": "Parallel Courses III",
    "leetcode_id": 2050,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/parallel-courses-iii/",
    "canonicalSlug": "parallel-courses-iii",
    "canonicalUrl": "https://leetcode.com/problems/parallel-courses-iii/",
    "url": "https://leetcode.com/problems/parallel-courses-iii/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Parallel Courses III\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Parallel Courses III\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Parallel Courses III\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Parallel Courses III\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Parallel Courses III\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Parallel Courses III\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Parallel Courses III\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Parallel Courses III\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Parallel Courses III",
      "cpp_optimal": "// Solution for Parallel Courses III",
      "java_brute": "// Solution for Parallel Courses III",
      "java_optimal": "// Solution for Parallel Courses III",
      "python_brute": "# Solution for Parallel Courses III",
      "python_optimal": "# Solution for Parallel Courses III"
    },
    "originalOrder": 879,
    "learningOrder": 879
  },
  {
    "id": 595,
    "number": 595,
    "sequence_number": 595,
    "title": "Build a Matrix With Conditions",
    "slug": "build-a-matrix-with-conditions",
    "difficulty": "Hard",
    "topic": "Graphs",
    "subtopic": "Graphs Optimization",
    "pattern": "Row Col Topological Sort",
    "secondary_patterns": [
      "Row Col Topological Sort"
    ],
    "stage": "Graph Traversal (BFS & DFS)",
    "curriculumStage": "Stage 12 — Graph Traversal (BFS & DFS)",
    "roadmapPhase": "Stage 12 — Graph Traversal (BFS & DFS)",
    "phase": "Stage 12 — Graph Traversal (BFS & DFS)",
    "estimatedTime": 45,
    "statement": "Given the constraints and input parameters for Build a Matrix With Conditions, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Build a Matrix With Conditions."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Build a Matrix With Conditions.",
      "Leverage the optimal Graphs pattern to reduce time complexity."
    ],
    "learningObjective": "Master Graphs techniques by solving Hard problem constraints for Build a Matrix With Conditions.",
    "whyThisPattern": "When observing Graphs problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/build-a-matrix-with-conditions/",
    "leetcode_title": "Build a Matrix With Conditions",
    "leetcode_id": 2392,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/build-a-matrix-with-conditions/",
    "canonicalSlug": "build-a-matrix-with-conditions",
    "canonicalUrl": "https://leetcode.com/problems/build-a-matrix-with-conditions/",
    "url": "https://leetcode.com/problems/build-a-matrix-with-conditions/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Build a Matrix With Conditions\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Build a Matrix With Conditions\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Build a Matrix With Conditions\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Build a Matrix With Conditions\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Build a Matrix With Conditions\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Build a Matrix With Conditions\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Build a Matrix With Conditions\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Build a Matrix With Conditions\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Build a Matrix With Conditions",
      "cpp_optimal": "// Solution for Build a Matrix With Conditions",
      "java_brute": "// Solution for Build a Matrix With Conditions",
      "java_optimal": "// Solution for Build a Matrix With Conditions",
      "python_brute": "# Solution for Build a Matrix With Conditions",
      "python_optimal": "# Solution for Build a Matrix With Conditions"
    },
    "originalOrder": 880,
    "learningOrder": 880
  },
  {
    "id": 596,
    "number": 596,
    "sequence_number": 596,
    "title": "Minimum Time to Visit a Cell In a Grid",
    "slug": "minimum-time-to-visit-a-cell-in-a-grid",
    "difficulty": "Hard",
    "topic": "Graphs",
    "subtopic": "Graphs Optimization",
    "pattern": "Grid Dijkstra Ping-Pong",
    "secondary_patterns": [
      "Grid Dijkstra Ping-Pong"
    ],
    "stage": "Graph Traversal (BFS & DFS)",
    "curriculumStage": "Stage 12 — Graph Traversal (BFS & DFS)",
    "roadmapPhase": "Stage 12 — Graph Traversal (BFS & DFS)",
    "phase": "Stage 12 — Graph Traversal (BFS & DFS)",
    "estimatedTime": 45,
    "statement": "Given the constraints and input parameters for Minimum Time to Visit a Cell In a Grid, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Minimum Time to Visit a Cell In a Grid."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Minimum Time to Visit a Cell In a Grid.",
      "Leverage the optimal Graphs pattern to reduce time complexity."
    ],
    "learningObjective": "Master Graphs techniques by solving Hard problem constraints for Minimum Time to Visit a Cell In a Grid.",
    "whyThisPattern": "When observing Graphs problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/minimum-time-to-visit-a-cell-in-a-grid/",
    "leetcode_title": "Minimum Time to Visit a Cell In a Grid",
    "leetcode_id": 2577,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/minimum-time-to-visit-a-cell-in-a-grid/",
    "canonicalSlug": "minimum-time-to-visit-a-cell-in-a-grid",
    "canonicalUrl": "https://leetcode.com/problems/minimum-time-to-visit-a-cell-in-a-grid/",
    "url": "https://leetcode.com/problems/minimum-time-to-visit-a-cell-in-a-grid/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Minimum Time to Visit a Cell In a Grid\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Minimum Time to Visit a Cell In a Grid\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Minimum Time to Visit a Cell In a Grid\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Minimum Time to Visit a Cell In a Grid\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Minimum Time to Visit a Cell In a Grid\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Minimum Time to Visit a Cell In a Grid\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Minimum Time to Visit a Cell In a Grid\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Minimum Time to Visit a Cell In a Grid\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Minimum Time to Visit a Cell In a Grid",
      "cpp_optimal": "// Solution for Minimum Time to Visit a Cell In a Grid",
      "java_brute": "// Solution for Minimum Time to Visit a Cell In a Grid",
      "java_optimal": "// Solution for Minimum Time to Visit a Cell In a Grid",
      "python_brute": "# Solution for Minimum Time to Visit a Cell In a Grid",
      "python_optimal": "# Solution for Minimum Time to Visit a Cell In a Grid"
    },
    "originalOrder": 881,
    "learningOrder": 881
  },
  {
    "id": 597,
    "number": 597,
    "sequence_number": 597,
    "title": "Design Graph With Shortest Path Calculator",
    "slug": "design-graph-with-shortest-path-calculator",
    "difficulty": "Hard",
    "topic": "Graphs",
    "subtopic": "Graphs Optimization",
    "pattern": "Dijkstra Priority Queue Graph",
    "secondary_patterns": [
      "Dijkstra Priority Queue Graph"
    ],
    "stage": "Graph Traversal (BFS & DFS)",
    "curriculumStage": "Stage 12 — Graph Traversal (BFS & DFS)",
    "roadmapPhase": "Stage 12 — Graph Traversal (BFS & DFS)",
    "phase": "Stage 12 — Graph Traversal (BFS & DFS)",
    "estimatedTime": 45,
    "statement": "Given the constraints and input parameters for Design Graph With Shortest Path Calculator, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Design Graph With Shortest Path Calculator."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Design Graph With Shortest Path Calculator.",
      "Leverage the optimal Graphs pattern to reduce time complexity."
    ],
    "learningObjective": "Master Graphs techniques by solving Hard problem constraints for Design Graph With Shortest Path Calculator.",
    "whyThisPattern": "When observing Graphs problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/design-graph-with-shortest-path-calculator/",
    "leetcode_title": "Design Graph With Shortest Path Calculator",
    "leetcode_id": 2642,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/design-graph-with-shortest-path-calculator/",
    "canonicalSlug": "design-graph-with-shortest-path-calculator",
    "canonicalUrl": "https://leetcode.com/problems/design-graph-with-shortest-path-calculator/",
    "url": "https://leetcode.com/problems/design-graph-with-shortest-path-calculator/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Design Graph With Shortest Path Calculator\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Design Graph With Shortest Path Calculator\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Design Graph With Shortest Path Calculator\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Design Graph With Shortest Path Calculator\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Design Graph With Shortest Path Calculator\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Design Graph With Shortest Path Calculator\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Design Graph With Shortest Path Calculator\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Design Graph With Shortest Path Calculator\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Design Graph With Shortest Path Calculator",
      "cpp_optimal": "// Solution for Design Graph With Shortest Path Calculator",
      "java_brute": "// Solution for Design Graph With Shortest Path Calculator",
      "java_optimal": "// Solution for Design Graph With Shortest Path Calculator",
      "python_brute": "# Solution for Design Graph With Shortest Path Calculator",
      "python_optimal": "# Solution for Design Graph With Shortest Path Calculator"
    },
    "originalOrder": 882,
    "learningOrder": 882
  },
  {
    "id": 598,
    "number": 598,
    "sequence_number": 598,
    "title": "Modify Graph Edge Weights",
    "slug": "modify-graph-edge-weights",
    "difficulty": "Hard",
    "topic": "Graphs",
    "subtopic": "Graphs Optimization",
    "pattern": "Dijkstra Two-Pass Edge Modification",
    "secondary_patterns": [
      "Dijkstra Two-Pass Edge Modification"
    ],
    "stage": "Graph Traversal (BFS & DFS)",
    "curriculumStage": "Stage 12 — Graph Traversal (BFS & DFS)",
    "roadmapPhase": "Stage 12 — Graph Traversal (BFS & DFS)",
    "phase": "Stage 12 — Graph Traversal (BFS & DFS)",
    "estimatedTime": 45,
    "statement": "Given the constraints and input parameters for Modify Graph Edge Weights, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Modify Graph Edge Weights."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Modify Graph Edge Weights.",
      "Leverage the optimal Graphs pattern to reduce time complexity."
    ],
    "learningObjective": "Master Graphs techniques by solving Hard problem constraints for Modify Graph Edge Weights.",
    "whyThisPattern": "When observing Graphs problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/modify-graph-edge-weights/",
    "leetcode_title": "Modify Graph Edge Weights",
    "leetcode_id": 2699,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/modify-graph-edge-weights/",
    "canonicalSlug": "modify-graph-edge-weights",
    "canonicalUrl": "https://leetcode.com/problems/modify-graph-edge-weights/",
    "url": "https://leetcode.com/problems/modify-graph-edge-weights/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Modify Graph Edge Weights\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Modify Graph Edge Weights\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Modify Graph Edge Weights\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Modify Graph Edge Weights\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Modify Graph Edge Weights\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Modify Graph Edge Weights\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Modify Graph Edge Weights\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Modify Graph Edge Weights\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Modify Graph Edge Weights",
      "cpp_optimal": "// Solution for Modify Graph Edge Weights",
      "java_brute": "// Solution for Modify Graph Edge Weights",
      "java_optimal": "// Solution for Modify Graph Edge Weights",
      "python_brute": "# Solution for Modify Graph Edge Weights",
      "python_optimal": "# Solution for Modify Graph Edge Weights"
    },
    "originalOrder": 883,
    "learningOrder": 883
  },
  {
    "id": 599,
    "number": 599,
    "sequence_number": 599,
    "title": "Minimum Obstacle Removal to Reach Corner",
    "slug": "minimum-obstacle-removal-to-reach-corner",
    "difficulty": "Hard",
    "topic": "Graphs",
    "subtopic": "Graphs Optimization",
    "pattern": "0-1 Deque BFS Obstacles",
    "secondary_patterns": [
      "0-1 Deque BFS Obstacles"
    ],
    "stage": "Graph Traversal (BFS & DFS)",
    "curriculumStage": "Stage 12 — Graph Traversal (BFS & DFS)",
    "roadmapPhase": "Stage 12 — Graph Traversal (BFS & DFS)",
    "phase": "Stage 12 — Graph Traversal (BFS & DFS)",
    "estimatedTime": 45,
    "statement": "Given the constraints and input parameters for Minimum Obstacle Removal to Reach Corner, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Minimum Obstacle Removal to Reach Corner."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Minimum Obstacle Removal to Reach Corner.",
      "Leverage the optimal Graphs pattern to reduce time complexity."
    ],
    "learningObjective": "Master Graphs techniques by solving Hard problem constraints for Minimum Obstacle Removal to Reach Corner.",
    "whyThisPattern": "When observing Graphs problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/minimum-obstacle-removal-to-reach-corner/",
    "leetcode_title": "Minimum Obstacle Removal to Reach Corner",
    "leetcode_id": 2290,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/minimum-obstacle-removal-to-reach-corner/",
    "canonicalSlug": "minimum-obstacle-removal-to-reach-corner",
    "canonicalUrl": "https://leetcode.com/problems/minimum-obstacle-removal-to-reach-corner/",
    "url": "https://leetcode.com/problems/minimum-obstacle-removal-to-reach-corner/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Minimum Obstacle Removal to Reach Corner\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Minimum Obstacle Removal to Reach Corner\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Minimum Obstacle Removal to Reach Corner\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Minimum Obstacle Removal to Reach Corner\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Minimum Obstacle Removal to Reach Corner\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Minimum Obstacle Removal to Reach Corner\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Minimum Obstacle Removal to Reach Corner\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Minimum Obstacle Removal to Reach Corner\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Minimum Obstacle Removal to Reach Corner",
      "cpp_optimal": "// Solution for Minimum Obstacle Removal to Reach Corner",
      "java_brute": "// Solution for Minimum Obstacle Removal to Reach Corner",
      "java_optimal": "// Solution for Minimum Obstacle Removal to Reach Corner",
      "python_brute": "# Solution for Minimum Obstacle Removal to Reach Corner",
      "python_optimal": "# Solution for Minimum Obstacle Removal to Reach Corner"
    },
    "originalOrder": 884,
    "learningOrder": 884
  },
  {
    "id": 600,
    "number": 600,
    "sequence_number": 600,
    "title": "K-th Smallest in Lexicographical Order",
    "slug": "k-th-smallest-in-lexicographical-order",
    "difficulty": "Hard",
    "topic": "Graphs",
    "subtopic": "Graphs Optimization",
    "pattern": "Graphs Pattern",
    "secondary_patterns": [
      "Graphs Pattern"
    ],
    "stage": "Graph Traversal (BFS & DFS)",
    "curriculumStage": "Stage 12 — Graph Traversal (BFS & DFS)",
    "roadmapPhase": "Stage 12 — Graph Traversal (BFS & DFS)",
    "phase": "Stage 12 — Graph Traversal (BFS & DFS)",
    "estimatedTime": 45,
    "statement": "Solve the **K-th Smallest in Lexicographical Order** problem using standard Graphs techniques. Given input constraints appropriate for Hard level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Graphs algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Graphs properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Graphs techniques by solving Hard problem constraints for K-th Smallest in Lexicographical Order.",
    "whyThisPattern": "When observing Graphs problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/k-th-smallest-in-lexicographical-order/",
    "leetcode_title": "K-th Smallest in Lexicographical Order",
    "leetcode_id": 440,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/k-th-smallest-in-lexicographical-order/",
    "canonicalSlug": "k-th-smallest-in-lexicographical-order",
    "canonicalUrl": "https://leetcode.com/problems/k-th-smallest-in-lexicographical-order/",
    "url": "https://leetcode.com/problems/k-th-smallest-in-lexicographical-order/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for K-th Smallest in Lexicographical Order\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for K-th Smallest in Lexicographical Order\n};",
        "java": "// Java Solution for K-th Smallest in Lexicographical Order\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for K-th Smallest in Lexicographical Order\n}",
        "python": "# Python Solution for K-th Smallest in Lexicographical Order\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for K-th Smallest in Lexicographical Order\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for K-th Smallest in Lexicographical Order\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for K-th Smallest in Lexicographical Order\n};",
        "java": "// Optimal Java Solution for K-th Smallest in Lexicographical Order\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for K-th Smallest in Lexicographical Order\n}",
        "python": "# Optimal Python Solution for K-th Smallest in Lexicographical Order\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for K-th Smallest in Lexicographical Order\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for K-th Smallest in Lexicographical Order",
      "cpp_optimal": "// Solution for K-th Smallest in Lexicographical Order",
      "java_brute": "// Solution for K-th Smallest in Lexicographical Order",
      "java_optimal": "// Solution for K-th Smallest in Lexicographical Order",
      "python_brute": "# Solution for K-th Smallest in Lexicographical Order",
      "python_optimal": "# Solution for K-th Smallest in Lexicographical Order"
    },
    "originalOrder": 885,
    "learningOrder": 885
  },
  {
    "id": 601,
    "number": 601,
    "sequence_number": 601,
    "title": "Construct the Rectangle",
    "slug": "construct-the-rectangle",
    "difficulty": "Easy",
    "topic": "Geometry",
    "subtopic": "Hashing & Array Optimization",
    "pattern": "Hashing & Array Optimization",
    "secondary_patterns": [
      "Hashing & Array Optimization"
    ],
    "stage": "Advanced Graphs & Topological Sort",
    "curriculumStage": "Stage 13 — Advanced Graphs & Topological Sort",
    "roadmapPhase": "Stage 13 — Advanced Graphs & Topological Sort",
    "phase": "Stage 13 — Advanced Graphs & Topological Sort",
    "estimatedTime": 15,
    "statement": "Solve the **Construct the Rectangle Optimization** problem using the **Hashing & Array Optimization** technique. Given input constraints appropriate for Easy level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^4",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Hashing & Array Optimization identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Hashing & Array Optimization. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Hashing & Array Optimization techniques by solving Easy problem constraints for Construct the Rectangle Optimization.",
    "whyThisPattern": "When observing arrays & strings problem conditions, Hashing & Array Optimization optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Apple",
      "Adobe",
      "Atlassian"
    ],
    "companyRelevanceTier": "Medium",
    "leetcode_url": "https://leetcode.com/problems/construct-the-rectangle/",
    "leetcode_title": "Construct the Rectangle",
    "leetcode_id": 492,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/construct-the-rectangle/",
    "canonicalSlug": "construct-the-rectangle",
    "canonicalUrl": "https://leetcode.com/problems/construct-the-rectangle/",
    "url": "https://leetcode.com/problems/construct-the-rectangle/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Construct the Rectangle Optimization (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Construct the Rectangle Optimization (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Construct the Rectangle Optimization (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Construct the Rectangle Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Construct the Rectangle Optimization (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Construct the Rectangle Optimization (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Construct the Rectangle Optimization (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Construct the Rectangle Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Construct the Rectangle",
      "cpp_optimal": "// Solution for Construct the Rectangle",
      "java_brute": "// Solution for Construct the Rectangle",
      "java_optimal": "// Solution for Construct the Rectangle",
      "python_brute": "# Solution for Construct the Rectangle",
      "python_optimal": "# Solution for Construct the Rectangle"
    },
    "originalOrder": 145,
    "learningOrder": 145
  },
  {
    "id": 602,
    "number": 602,
    "sequence_number": 602,
    "title": "Number of Lines To Write String",
    "slug": "number-of-lines-to-write-string",
    "difficulty": "Easy",
    "topic": "Geometry",
    "subtopic": "Geometry Optimization",
    "pattern": "Width Counter",
    "secondary_patterns": [
      "Width Counter"
    ],
    "stage": "Advanced Graphs & Topological Sort",
    "curriculumStage": "Stage 13 — Advanced Graphs & Topological Sort",
    "roadmapPhase": "Stage 13 — Advanced Graphs & Topological Sort",
    "phase": "Stage 13 — Advanced Graphs & Topological Sort",
    "estimatedTime": 15,
    "statement": "Given the constraints and input parameters for Number of Lines To Write String, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Number of Lines To Write String."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Number of Lines To Write String.",
      "Leverage the optimal Strings pattern to reduce time complexity."
    ],
    "learningObjective": "Master Geometry techniques by solving Easy problem constraints for Number of Lines To Write String.",
    "whyThisPattern": "When observing Geometry problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/number-of-lines-to-write-string/",
    "leetcode_title": "Number of Lines To Write String",
    "leetcode_id": 806,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/number-of-lines-to-write-string/",
    "canonicalSlug": "number-of-lines-to-write-string",
    "canonicalUrl": "https://leetcode.com/problems/number-of-lines-to-write-string/",
    "url": "https://leetcode.com/problems/number-of-lines-to-write-string/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Number of Lines To Write String\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Number of Lines To Write String\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Number of Lines To Write String\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Number of Lines To Write String\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Number of Lines To Write String\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Number of Lines To Write String\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Number of Lines To Write String\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Number of Lines To Write String\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Number of Lines To Write String",
      "cpp_optimal": "// Solution for Number of Lines To Write String",
      "java_brute": "// Solution for Number of Lines To Write String",
      "java_optimal": "// Solution for Number of Lines To Write String",
      "python_brute": "# Solution for Number of Lines To Write String",
      "python_optimal": "# Solution for Number of Lines To Write String"
    },
    "originalOrder": 146,
    "learningOrder": 146
  },
  {
    "id": 603,
    "number": 603,
    "sequence_number": 603,
    "title": "Leaf-Similar Trees",
    "slug": "leaf-similar-trees",
    "difficulty": "Easy",
    "topic": "Trees",
    "subtopic": "Tree Traversal & Recursion",
    "pattern": "Tree Traversal & Recursion",
    "secondary_patterns": [
      "Tree Traversal & Recursion"
    ],
    "stage": "Advanced Graphs & Topological Sort",
    "curriculumStage": "Stage 13 — Advanced Graphs & Topological Sort",
    "roadmapPhase": "Stage 13 — Advanced Graphs & Topological Sort",
    "phase": "Stage 13 — Advanced Graphs & Topological Sort",
    "estimatedTime": 15,
    "statement": "Solve the **Leaf-Similar Trees Challenge** problem using the **Tree Traversal & Recursion** technique. Given input constraints appropriate for Easy level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^4",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Tree Traversal & Recursion identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Tree Traversal & Recursion. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Tree Traversal & Recursion techniques by solving Easy problem constraints for Leaf-Similar Trees Challenge.",
    "whyThisPattern": "When observing binary trees problem conditions, Tree Traversal & Recursion optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Amazon",
      "Microsoft",
      "Uber"
    ],
    "companyRelevanceTier": "Medium",
    "leetcode_url": "https://leetcode.com/problems/leaf-similar-trees/",
    "leetcode_title": "Leaf-Similar Trees",
    "leetcode_id": 872,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/leaf-similar-trees/",
    "canonicalSlug": "leaf-similar-trees",
    "canonicalUrl": "https://leetcode.com/problems/leaf-similar-trees/",
    "url": "https://leetcode.com/problems/leaf-similar-trees/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Leaf-Similar Trees Challenge (Tree Traversal & Recursion)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Leaf-Similar Trees Challenge (Tree Traversal & Recursion)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Leaf-Similar Trees Challenge (Tree Traversal & Recursion)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Leaf-Similar Trees Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Leaf-Similar Trees Challenge (Tree Traversal & Recursion)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Leaf-Similar Trees Challenge (Tree Traversal & Recursion)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Leaf-Similar Trees Challenge (Tree Traversal & Recursion)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Leaf-Similar Trees Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Leaf-Similar Trees",
      "cpp_optimal": "// Solution for Leaf-Similar Trees",
      "java_brute": "// Solution for Leaf-Similar Trees",
      "java_optimal": "// Solution for Leaf-Similar Trees",
      "python_brute": "# Solution for Leaf-Similar Trees",
      "python_optimal": "# Solution for Leaf-Similar Trees"
    },
    "originalOrder": 227,
    "learningOrder": 227
  },
  {
    "id": 604,
    "number": 604,
    "sequence_number": 604,
    "title": "Increasing Order Search Tree",
    "slug": "increasing-order-search-tree",
    "difficulty": "Easy",
    "topic": "Trees",
    "subtopic": "Tree Traversal & Recursion",
    "pattern": "Tree Traversal & Recursion",
    "secondary_patterns": [
      "Tree Traversal & Recursion"
    ],
    "stage": "Advanced Graphs & Topological Sort",
    "curriculumStage": "Stage 13 — Advanced Graphs & Topological Sort",
    "roadmapPhase": "Stage 13 — Advanced Graphs & Topological Sort",
    "phase": "Stage 13 — Advanced Graphs & Topological Sort",
    "estimatedTime": 15,
    "statement": "Solve the **Increasing Order Search Tree Optimization** problem using the **Tree Traversal & Recursion** technique. Given input constraints appropriate for Easy level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^4",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Tree Traversal & Recursion identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Tree Traversal & Recursion. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Tree Traversal & Recursion techniques by solving Easy problem constraints for Increasing Order Search Tree Optimization.",
    "whyThisPattern": "When observing binary trees problem conditions, Tree Traversal & Recursion optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Apple",
      "Adobe",
      "Atlassian"
    ],
    "companyRelevanceTier": "Medium",
    "leetcode_url": "https://leetcode.com/problems/increasing-order-search-tree/",
    "leetcode_title": "Increasing Order Search Tree",
    "leetcode_id": 897,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/increasing-order-search-tree/",
    "canonicalSlug": "increasing-order-search-tree",
    "canonicalUrl": "https://leetcode.com/problems/increasing-order-search-tree/",
    "url": "https://leetcode.com/problems/increasing-order-search-tree/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Increasing Order Search Tree Optimization (Tree Traversal & Recursion)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Increasing Order Search Tree Optimization (Tree Traversal & Recursion)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Increasing Order Search Tree Optimization (Tree Traversal & Recursion)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Increasing Order Search Tree Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Increasing Order Search Tree Optimization (Tree Traversal & Recursion)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Increasing Order Search Tree Optimization (Tree Traversal & Recursion)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Increasing Order Search Tree Optimization (Tree Traversal & Recursion)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Increasing Order Search Tree Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Increasing Order Search Tree",
      "cpp_optimal": "// Solution for Increasing Order Search Tree",
      "java_brute": "// Solution for Increasing Order Search Tree",
      "java_optimal": "// Solution for Increasing Order Search Tree",
      "python_brute": "# Solution for Increasing Order Search Tree",
      "python_optimal": "# Solution for Increasing Order Search Tree"
    },
    "originalOrder": 228,
    "learningOrder": 228
  },
  {
    "id": 605,
    "number": 605,
    "sequence_number": 605,
    "title": "Univalued Binary Tree",
    "slug": "univalued-binary-tree",
    "difficulty": "Easy",
    "topic": "Trees",
    "subtopic": "Tree Traversal & Recursion",
    "pattern": "Tree Traversal & Recursion",
    "secondary_patterns": [
      "Tree Traversal & Recursion"
    ],
    "stage": "Advanced Graphs & Topological Sort",
    "curriculumStage": "Stage 13 — Advanced Graphs & Topological Sort",
    "roadmapPhase": "Stage 13 — Advanced Graphs & Topological Sort",
    "phase": "Stage 13 — Advanced Graphs & Topological Sort",
    "estimatedTime": 15,
    "statement": "Solve the **Univalued Binary Tree Optimization** problem using the **Tree Traversal & Recursion** technique. Given input constraints appropriate for Easy level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^4",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Tree Traversal & Recursion identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Tree Traversal & Recursion. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Tree Traversal & Recursion techniques by solving Easy problem constraints for Univalued Binary Tree Optimization.",
    "whyThisPattern": "When observing binary trees problem conditions, Tree Traversal & Recursion optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Meta",
      "Apple",
      "Netflix"
    ],
    "companyRelevanceTier": "Medium",
    "leetcode_url": "https://leetcode.com/problems/univalued-binary-tree/",
    "leetcode_title": "Univalued Binary Tree",
    "leetcode_id": 965,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/univalued-binary-tree/",
    "canonicalSlug": "univalued-binary-tree",
    "canonicalUrl": "https://leetcode.com/problems/univalued-binary-tree/",
    "url": "https://leetcode.com/problems/univalued-binary-tree/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Univalued Binary Tree Optimization (Tree Traversal & Recursion)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Univalued Binary Tree Optimization (Tree Traversal & Recursion)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Univalued Binary Tree Optimization (Tree Traversal & Recursion)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Univalued Binary Tree Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Univalued Binary Tree Optimization (Tree Traversal & Recursion)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Univalued Binary Tree Optimization (Tree Traversal & Recursion)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Univalued Binary Tree Optimization (Tree Traversal & Recursion)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Univalued Binary Tree Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Univalued Binary Tree",
      "cpp_optimal": "// Solution for Univalued Binary Tree",
      "java_brute": "// Solution for Univalued Binary Tree",
      "java_optimal": "// Solution for Univalued Binary Tree",
      "python_brute": "# Solution for Univalued Binary Tree",
      "python_optimal": "# Solution for Univalued Binary Tree"
    },
    "originalOrder": 229,
    "learningOrder": 229
  },
  {
    "id": 606,
    "number": 606,
    "sequence_number": 606,
    "title": "Cousins in Binary Tree",
    "slug": "cousins-in-binary-tree",
    "difficulty": "Easy",
    "topic": "Trees",
    "subtopic": "Tree Traversal & Recursion",
    "pattern": "Tree Traversal & Recursion",
    "secondary_patterns": [
      "Tree Traversal & Recursion"
    ],
    "stage": "Advanced Graphs & Topological Sort",
    "curriculumStage": "Stage 13 — Advanced Graphs & Topological Sort",
    "roadmapPhase": "Stage 13 — Advanced Graphs & Topological Sort",
    "phase": "Stage 13 — Advanced Graphs & Topological Sort",
    "estimatedTime": 15,
    "statement": "Solve the **Cousins in Binary Tree Challenge** problem using the **Tree Traversal & Recursion** technique. Given input constraints appropriate for Easy level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^4",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Tree Traversal & Recursion identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Tree Traversal & Recursion. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Tree Traversal & Recursion techniques by solving Easy problem constraints for Cousins in Binary Tree Challenge.",
    "whyThisPattern": "When observing binary trees problem conditions, Tree Traversal & Recursion optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Microsoft",
      "Bloomberg",
      "Adobe"
    ],
    "companyRelevanceTier": "Medium",
    "leetcode_url": "https://leetcode.com/problems/cousins-in-binary-tree/",
    "leetcode_title": "Cousins in Binary Tree",
    "leetcode_id": 993,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/cousins-in-binary-tree/",
    "canonicalSlug": "cousins-in-binary-tree",
    "canonicalUrl": "https://leetcode.com/problems/cousins-in-binary-tree/",
    "url": "https://leetcode.com/problems/cousins-in-binary-tree/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Cousins in Binary Tree Challenge (Tree Traversal & Recursion)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Cousins in Binary Tree Challenge (Tree Traversal & Recursion)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Cousins in Binary Tree Challenge (Tree Traversal & Recursion)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Cousins in Binary Tree Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Cousins in Binary Tree Challenge (Tree Traversal & Recursion)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Cousins in Binary Tree Challenge (Tree Traversal & Recursion)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Cousins in Binary Tree Challenge (Tree Traversal & Recursion)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Cousins in Binary Tree Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Cousins in Binary Tree",
      "cpp_optimal": "// Solution for Cousins in Binary Tree",
      "java_brute": "// Solution for Cousins in Binary Tree",
      "java_optimal": "// Solution for Cousins in Binary Tree",
      "python_brute": "# Solution for Cousins in Binary Tree",
      "python_optimal": "# Solution for Cousins in Binary Tree"
    },
    "originalOrder": 230,
    "learningOrder": 230
  },
  {
    "id": 607,
    "number": 607,
    "sequence_number": 607,
    "title": "Minimum Depth of Binary Tree",
    "slug": "minimum-depth-of-binary-tree",
    "difficulty": "Easy",
    "topic": "Trees",
    "subtopic": "Tree Traversal & Recursion",
    "pattern": "Tree Traversal & Recursion",
    "secondary_patterns": [
      "Tree Traversal & Recursion"
    ],
    "stage": "Advanced Graphs & Topological Sort",
    "curriculumStage": "Stage 13 — Advanced Graphs & Topological Sort",
    "roadmapPhase": "Stage 13 — Advanced Graphs & Topological Sort",
    "phase": "Stage 13 — Advanced Graphs & Topological Sort",
    "estimatedTime": 15,
    "statement": "Solve the **Minimum Depth of Binary Tree Optimization** problem using the **Tree Traversal & Recursion** technique. Given input constraints appropriate for Easy level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^4",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Tree Traversal & Recursion identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Tree Traversal & Recursion. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Tree Traversal & Recursion techniques by solving Easy problem constraints for Minimum Depth of Binary Tree Optimization.",
    "whyThisPattern": "When observing binary trees problem conditions, Tree Traversal & Recursion optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Meta",
      "Apple",
      "Netflix"
    ],
    "companyRelevanceTier": "Medium",
    "leetcode_url": "https://leetcode.com/problems/minimum-depth-of-binary-tree/",
    "leetcode_title": "Minimum Depth of Binary Tree",
    "leetcode_id": 111,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/minimum-depth-of-binary-tree/",
    "canonicalSlug": "minimum-depth-of-binary-tree",
    "canonicalUrl": "https://leetcode.com/problems/minimum-depth-of-binary-tree/",
    "url": "https://leetcode.com/problems/minimum-depth-of-binary-tree/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Minimum Depth of Binary Tree Optimization (Tree Traversal & Recursion)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Minimum Depth of Binary Tree Optimization (Tree Traversal & Recursion)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Minimum Depth of Binary Tree Optimization (Tree Traversal & Recursion)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Minimum Depth of Binary Tree Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Minimum Depth of Binary Tree Optimization (Tree Traversal & Recursion)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Minimum Depth of Binary Tree Optimization (Tree Traversal & Recursion)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Minimum Depth of Binary Tree Optimization (Tree Traversal & Recursion)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Minimum Depth of Binary Tree Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Minimum Depth of Binary Tree",
      "cpp_optimal": "// Solution for Minimum Depth of Binary Tree",
      "java_brute": "// Solution for Minimum Depth of Binary Tree",
      "java_optimal": "// Solution for Minimum Depth of Binary Tree",
      "python_brute": "# Solution for Minimum Depth of Binary Tree",
      "python_optimal": "# Solution for Minimum Depth of Binary Tree"
    },
    "originalOrder": 231,
    "learningOrder": 231
  },
  {
    "id": 608,
    "number": 608,
    "sequence_number": 608,
    "title": "Binary Tree Preorder Traversal",
    "slug": "binary-tree-preorder-traversal",
    "difficulty": "Easy",
    "topic": "Trees",
    "subtopic": "Tree Traversal & Recursion",
    "pattern": "Tree Traversal & Recursion",
    "secondary_patterns": [
      "Tree Traversal & Recursion"
    ],
    "stage": "Advanced Graphs & Topological Sort",
    "curriculumStage": "Stage 13 — Advanced Graphs & Topological Sort",
    "roadmapPhase": "Stage 13 — Advanced Graphs & Topological Sort",
    "phase": "Stage 13 — Advanced Graphs & Topological Sort",
    "estimatedTime": 15,
    "statement": "Solve the **Binary Tree Preorder Traversal Optimization** problem using the **Tree Traversal & Recursion** technique. Given input constraints appropriate for Easy level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^4",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Tree Traversal & Recursion identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Tree Traversal & Recursion. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Tree Traversal & Recursion techniques by solving Easy problem constraints for Binary Tree Preorder Traversal Optimization.",
    "whyThisPattern": "When observing binary trees problem conditions, Tree Traversal & Recursion optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "LinkedIn",
      "Amazon"
    ],
    "companyRelevanceTier": "Medium",
    "leetcode_url": "https://leetcode.com/problems/binary-tree-preorder-traversal/",
    "leetcode_title": "Binary Tree Preorder Traversal",
    "leetcode_id": 144,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/binary-tree-preorder-traversal/",
    "canonicalSlug": "binary-tree-preorder-traversal",
    "canonicalUrl": "https://leetcode.com/problems/binary-tree-preorder-traversal/",
    "url": "https://leetcode.com/problems/binary-tree-preorder-traversal/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Binary Tree Preorder Traversal Optimization (Tree Traversal & Recursion)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Binary Tree Preorder Traversal Optimization (Tree Traversal & Recursion)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Binary Tree Preorder Traversal Optimization (Tree Traversal & Recursion)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Binary Tree Preorder Traversal Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Binary Tree Preorder Traversal Optimization (Tree Traversal & Recursion)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Binary Tree Preorder Traversal Optimization (Tree Traversal & Recursion)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Binary Tree Preorder Traversal Optimization (Tree Traversal & Recursion)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Binary Tree Preorder Traversal Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Binary Tree Preorder Traversal",
      "cpp_optimal": "// Solution for Binary Tree Preorder Traversal",
      "java_brute": "// Solution for Binary Tree Preorder Traversal",
      "java_optimal": "// Solution for Binary Tree Preorder Traversal",
      "python_brute": "# Solution for Binary Tree Preorder Traversal",
      "python_optimal": "# Solution for Binary Tree Preorder Traversal"
    },
    "originalOrder": 232,
    "learningOrder": 232
  },
  {
    "id": 609,
    "number": 609,
    "sequence_number": 609,
    "title": "Find a Corresponding Node of a Binary Tree in a Clone of That Tree",
    "slug": "find-a-corresponding-node-of-a-binary-tree-in-a-clone-of-that-tree",
    "difficulty": "Easy",
    "topic": "Trees",
    "subtopic": "Pointer Manipulation",
    "pattern": "Pointer Manipulation",
    "secondary_patterns": [
      "Pointer Manipulation"
    ],
    "stage": "Advanced Graphs & Topological Sort",
    "curriculumStage": "Stage 13 — Advanced Graphs & Topological Sort",
    "roadmapPhase": "Stage 13 — Advanced Graphs & Topological Sort",
    "phase": "Stage 13 — Advanced Graphs & Topological Sort",
    "estimatedTime": 15,
    "statement": "Solve the **Find a Corresponding Node of a Binary Tree in a Clone of That Tree Challenge** problem using the **Pointer Manipulation** technique. Given input constraints appropriate for Easy level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^4",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Pointer Manipulation identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Pointer Manipulation. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Pointer Manipulation techniques by solving Easy problem constraints for Find a Corresponding Node of a Binary Tree in a Clone of That Tree Challenge.",
    "whyThisPattern": "When observing binary trees problem conditions, Pointer Manipulation optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Amazon",
      "Microsoft",
      "Uber"
    ],
    "companyRelevanceTier": "Medium",
    "leetcode_url": "https://leetcode.com/problems/find-a-corresponding-node-of-a-binary-tree-in-a-clone-of-that-tree/",
    "leetcode_title": "Find a Corresponding Node of a Binary Tree in a Clone of That Tree",
    "leetcode_id": 1379,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/find-a-corresponding-node-of-a-binary-tree-in-a-clone-of-that-tree/",
    "canonicalSlug": "find-a-corresponding-node-of-a-binary-tree-in-a-clone-of-that-tree",
    "canonicalUrl": "https://leetcode.com/problems/find-a-corresponding-node-of-a-binary-tree-in-a-clone-of-that-tree/",
    "url": "https://leetcode.com/problems/find-a-corresponding-node-of-a-binary-tree-in-a-clone-of-that-tree/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Find a Corresponding Node of a Binary Tree in a Clone of That Tree Challenge (Pointer Manipulation)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Find a Corresponding Node of a Binary Tree in a Clone of That Tree Challenge (Pointer Manipulation)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Find a Corresponding Node of a Binary Tree in a Clone of That Tree Challenge (Pointer Manipulation)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Find a Corresponding Node of a Binary Tree in a Clone of That Tree Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Find a Corresponding Node of a Binary Tree in a Clone of That Tree Challenge (Pointer Manipulation)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Find a Corresponding Node of a Binary Tree in a Clone of That Tree Challenge (Pointer Manipulation)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Find a Corresponding Node of a Binary Tree in a Clone of That Tree Challenge (Pointer Manipulation)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Find a Corresponding Node of a Binary Tree in a Clone of That Tree Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Find a Corresponding Node of a Binary Tree in a Clone of That Tree",
      "cpp_optimal": "// Solution for Find a Corresponding Node of a Binary Tree in a Clone of That Tree",
      "java_brute": "// Solution for Find a Corresponding Node of a Binary Tree in a Clone of That Tree",
      "java_optimal": "// Solution for Find a Corresponding Node of a Binary Tree in a Clone of That Tree",
      "python_brute": "# Solution for Find a Corresponding Node of a Binary Tree in a Clone of That Tree",
      "python_optimal": "# Solution for Find a Corresponding Node of a Binary Tree in a Clone of That Tree"
    },
    "originalOrder": 233,
    "learningOrder": 233
  },
  {
    "id": 610,
    "number": 610,
    "sequence_number": 610,
    "title": "Binary Tree Postorder Traversal",
    "slug": "binary-tree-postorder-traversal",
    "difficulty": "Easy",
    "topic": "Trees",
    "subtopic": "Tree Traversal & Recursion",
    "pattern": "Tree Traversal & Recursion",
    "secondary_patterns": [
      "Tree Traversal & Recursion"
    ],
    "stage": "Advanced Graphs & Topological Sort",
    "curriculumStage": "Stage 13 — Advanced Graphs & Topological Sort",
    "roadmapPhase": "Stage 13 — Advanced Graphs & Topological Sort",
    "phase": "Stage 13 — Advanced Graphs & Topological Sort",
    "estimatedTime": 15,
    "statement": "Solve the **Binary Tree Postorder Traversal Optimization** problem using the **Tree Traversal & Recursion** technique. Given input constraints appropriate for Easy level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^4",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Tree Traversal & Recursion identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Tree Traversal & Recursion. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Tree Traversal & Recursion techniques by solving Easy problem constraints for Binary Tree Postorder Traversal Optimization.",
    "whyThisPattern": "When observing binary trees problem conditions, Tree Traversal & Recursion optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta"
    ],
    "companyRelevanceTier": "Medium",
    "leetcode_url": "https://leetcode.com/problems/binary-tree-postorder-traversal/",
    "leetcode_title": "Binary Tree Postorder Traversal",
    "leetcode_id": 145,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/binary-tree-postorder-traversal/",
    "canonicalSlug": "binary-tree-postorder-traversal",
    "canonicalUrl": "https://leetcode.com/problems/binary-tree-postorder-traversal/",
    "url": "https://leetcode.com/problems/binary-tree-postorder-traversal/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Binary Tree Postorder Traversal Optimization (Tree Traversal & Recursion)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Binary Tree Postorder Traversal Optimization (Tree Traversal & Recursion)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Binary Tree Postorder Traversal Optimization (Tree Traversal & Recursion)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Binary Tree Postorder Traversal Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Binary Tree Postorder Traversal Optimization (Tree Traversal & Recursion)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Binary Tree Postorder Traversal Optimization (Tree Traversal & Recursion)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Binary Tree Postorder Traversal Optimization (Tree Traversal & Recursion)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Binary Tree Postorder Traversal Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Binary Tree Postorder Traversal",
      "cpp_optimal": "// Solution for Binary Tree Postorder Traversal",
      "java_brute": "// Solution for Binary Tree Postorder Traversal",
      "java_optimal": "// Solution for Binary Tree Postorder Traversal",
      "python_brute": "# Solution for Binary Tree Postorder Traversal",
      "python_optimal": "# Solution for Binary Tree Postorder Traversal"
    },
    "originalOrder": 234,
    "learningOrder": 234
  },
  {
    "id": 611,
    "number": 611,
    "sequence_number": 611,
    "title": "Lexicographical Numbers",
    "slug": "lexicographical-numbers",
    "difficulty": "Medium",
    "topic": "Graphs",
    "subtopic": "Graphs Optimization",
    "pattern": "Graphs Pattern",
    "secondary_patterns": [
      "Graphs Pattern"
    ],
    "stage": "Advanced Graphs & Topological Sort",
    "curriculumStage": "Stage 13 — Advanced Graphs & Topological Sort",
    "roadmapPhase": "Stage 13 — Advanced Graphs & Topological Sort",
    "phase": "Stage 13 — Advanced Graphs & Topological Sort",
    "estimatedTime": 30,
    "statement": "Solve the **Lexicographical Numbers** problem using standard Graphs techniques. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Graphs algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Graphs properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Graphs techniques by solving Medium problem constraints for Lexicographical Numbers.",
    "whyThisPattern": "When observing Graphs problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/lexicographical-numbers/",
    "leetcode_title": "Lexicographical Numbers",
    "leetcode_id": 386,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/lexicographical-numbers/",
    "canonicalSlug": "lexicographical-numbers",
    "canonicalUrl": "https://leetcode.com/problems/lexicographical-numbers/",
    "url": "https://leetcode.com/problems/lexicographical-numbers/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Lexicographical Numbers\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Lexicographical Numbers\n};",
        "java": "// Java Solution for Lexicographical Numbers\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Lexicographical Numbers\n}",
        "python": "# Python Solution for Lexicographical Numbers\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Lexicographical Numbers\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Lexicographical Numbers\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Lexicographical Numbers\n};",
        "java": "// Optimal Java Solution for Lexicographical Numbers\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Lexicographical Numbers\n}",
        "python": "# Optimal Python Solution for Lexicographical Numbers\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Lexicographical Numbers\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Lexicographical Numbers",
      "cpp_optimal": "// Solution for Lexicographical Numbers",
      "java_brute": "// Solution for Lexicographical Numbers",
      "java_optimal": "// Solution for Lexicographical Numbers",
      "python_brute": "# Solution for Lexicographical Numbers",
      "python_optimal": "# Solution for Lexicographical Numbers"
    },
    "originalOrder": 496,
    "learningOrder": 496
  },
  {
    "id": 612,
    "number": 612,
    "sequence_number": 612,
    "title": "Is Graph Bipartite?",
    "slug": "is-graph-bipartite",
    "difficulty": "Medium",
    "topic": "Graphs",
    "subtopic": "Graphs Optimization",
    "pattern": "Graphs Pattern",
    "secondary_patterns": [
      "Graphs Pattern"
    ],
    "stage": "Advanced Graphs & Topological Sort",
    "curriculumStage": "Stage 13 — Advanced Graphs & Topological Sort",
    "roadmapPhase": "Stage 13 — Advanced Graphs & Topological Sort",
    "phase": "Stage 13 — Advanced Graphs & Topological Sort",
    "estimatedTime": 30,
    "statement": "Solve the **Is Graph Bipartite?** problem using standard Graphs techniques. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Graphs algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Graphs properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Graphs techniques by solving Medium problem constraints for Is Graph Bipartite?.",
    "whyThisPattern": "When observing Graphs problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/is-graph-bipartite/",
    "leetcode_title": "Is Graph Bipartite?",
    "leetcode_id": 785,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/is-graph-bipartite/",
    "canonicalSlug": "is-graph-bipartite",
    "canonicalUrl": "https://leetcode.com/problems/is-graph-bipartite/",
    "url": "https://leetcode.com/problems/is-graph-bipartite/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Is Graph Bipartite?\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Is Graph Bipartite?\n};",
        "java": "// Java Solution for Is Graph Bipartite?\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Is Graph Bipartite?\n}",
        "python": "# Python Solution for Is Graph Bipartite?\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Is Graph Bipartite?\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Is Graph Bipartite?\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Is Graph Bipartite?\n};",
        "java": "// Optimal Java Solution for Is Graph Bipartite?\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Is Graph Bipartite?\n}",
        "python": "# Optimal Python Solution for Is Graph Bipartite?\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Is Graph Bipartite?\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Is Graph Bipartite?",
      "cpp_optimal": "// Solution for Is Graph Bipartite?",
      "java_brute": "// Solution for Is Graph Bipartite?",
      "java_optimal": "// Solution for Is Graph Bipartite?",
      "python_brute": "# Solution for Is Graph Bipartite?",
      "python_optimal": "# Solution for Is Graph Bipartite?"
    },
    "originalOrder": 497,
    "learningOrder": 497
  },
  {
    "id": 613,
    "number": 613,
    "sequence_number": 613,
    "title": "Lexicographically Smallest Equivalent String",
    "slug": "lexicographically-smallest-equivalent-string",
    "difficulty": "Medium",
    "topic": "Graphs",
    "subtopic": "Graphs Optimization",
    "pattern": "Graphs Pattern",
    "secondary_patterns": [
      "Graphs Pattern"
    ],
    "stage": "Advanced Graphs & Topological Sort",
    "curriculumStage": "Stage 13 — Advanced Graphs & Topological Sort",
    "roadmapPhase": "Stage 13 — Advanced Graphs & Topological Sort",
    "phase": "Stage 13 — Advanced Graphs & Topological Sort",
    "estimatedTime": 30,
    "statement": "Solve the **Lexicographically Smallest Equivalent String** problem using standard Graphs techniques. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Graphs algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Graphs properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Graphs techniques by solving Medium problem constraints for Lexicographically Smallest Equivalent String.",
    "whyThisPattern": "When observing Graphs problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/lexicographically-smallest-equivalent-string/",
    "leetcode_title": "Lexicographically Smallest Equivalent String",
    "leetcode_id": 1061,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/lexicographically-smallest-equivalent-string/",
    "canonicalSlug": "lexicographically-smallest-equivalent-string",
    "canonicalUrl": "https://leetcode.com/problems/lexicographically-smallest-equivalent-string/",
    "url": "https://leetcode.com/problems/lexicographically-smallest-equivalent-string/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Lexicographically Smallest Equivalent String\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Lexicographically Smallest Equivalent String\n};",
        "java": "// Java Solution for Lexicographically Smallest Equivalent String\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Lexicographically Smallest Equivalent String\n}",
        "python": "# Python Solution for Lexicographically Smallest Equivalent String\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Lexicographically Smallest Equivalent String\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Lexicographically Smallest Equivalent String\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Lexicographically Smallest Equivalent String\n};",
        "java": "// Optimal Java Solution for Lexicographically Smallest Equivalent String\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Lexicographically Smallest Equivalent String\n}",
        "python": "# Optimal Python Solution for Lexicographically Smallest Equivalent String\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Lexicographically Smallest Equivalent String\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Lexicographically Smallest Equivalent String",
      "cpp_optimal": "// Solution for Lexicographically Smallest Equivalent String",
      "java_brute": "// Solution for Lexicographically Smallest Equivalent String",
      "java_optimal": "// Solution for Lexicographically Smallest Equivalent String",
      "python_brute": "# Solution for Lexicographically Smallest Equivalent String",
      "python_optimal": "# Solution for Lexicographically Smallest Equivalent String"
    },
    "originalOrder": 498,
    "learningOrder": 498
  },
  {
    "id": 614,
    "number": 614,
    "sequence_number": 614,
    "title": "Course Schedule IV",
    "slug": "course-schedule-iv",
    "difficulty": "Medium",
    "topic": "Graphs",
    "subtopic": "Graphs Optimization",
    "pattern": "Graphs Pattern",
    "secondary_patterns": [
      "Graphs Pattern"
    ],
    "stage": "Advanced Graphs & Topological Sort",
    "curriculumStage": "Stage 13 — Advanced Graphs & Topological Sort",
    "roadmapPhase": "Stage 13 — Advanced Graphs & Topological Sort",
    "phase": "Stage 13 — Advanced Graphs & Topological Sort",
    "estimatedTime": 30,
    "statement": "Solve the **Course Schedule IV** problem using standard Graphs techniques. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Graphs algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Graphs properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Graphs techniques by solving Medium problem constraints for Course Schedule IV.",
    "whyThisPattern": "When observing Graphs problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/course-schedule-iv/",
    "leetcode_title": "Course Schedule IV",
    "leetcode_id": 1462,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/course-schedule-iv/",
    "canonicalSlug": "course-schedule-iv",
    "canonicalUrl": "https://leetcode.com/problems/course-schedule-iv/",
    "url": "https://leetcode.com/problems/course-schedule-iv/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Course Schedule IV\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Course Schedule IV\n};",
        "java": "// Java Solution for Course Schedule IV\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Course Schedule IV\n}",
        "python": "# Python Solution for Course Schedule IV\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Course Schedule IV\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Course Schedule IV\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Course Schedule IV\n};",
        "java": "// Optimal Java Solution for Course Schedule IV\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Course Schedule IV\n}",
        "python": "# Optimal Python Solution for Course Schedule IV\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Course Schedule IV\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Course Schedule IV",
      "cpp_optimal": "// Solution for Course Schedule IV",
      "java_brute": "// Solution for Course Schedule IV",
      "java_optimal": "// Solution for Course Schedule IV",
      "python_brute": "# Solution for Course Schedule IV",
      "python_optimal": "# Solution for Course Schedule IV"
    },
    "originalOrder": 499,
    "learningOrder": 499
  },
  {
    "id": 615,
    "number": 615,
    "sequence_number": 615,
    "title": "Lexicographically Smallest String After Applying Operations",
    "slug": "lexicographically-smallest-string-after-applying-operations",
    "difficulty": "Medium",
    "topic": "Graphs",
    "subtopic": "Graphs Optimization",
    "pattern": "Graphs Pattern",
    "secondary_patterns": [
      "Graphs Pattern"
    ],
    "stage": "Advanced Graphs & Topological Sort",
    "curriculumStage": "Stage 13 — Advanced Graphs & Topological Sort",
    "roadmapPhase": "Stage 13 — Advanced Graphs & Topological Sort",
    "phase": "Stage 13 — Advanced Graphs & Topological Sort",
    "estimatedTime": 30,
    "statement": "Solve the **Lexicographically Smallest String After Applying Operations** problem using standard Graphs techniques. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Graphs algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Graphs properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Graphs techniques by solving Medium problem constraints for Lexicographically Smallest String After Applying Operations.",
    "whyThisPattern": "When observing Graphs problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/lexicographically-smallest-string-after-applying-operations/",
    "leetcode_title": "Lexicographically Smallest String After Applying Operations",
    "leetcode_id": 1625,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/lexicographically-smallest-string-after-applying-operations/",
    "canonicalSlug": "lexicographically-smallest-string-after-applying-operations",
    "canonicalUrl": "https://leetcode.com/problems/lexicographically-smallest-string-after-applying-operations/",
    "url": "https://leetcode.com/problems/lexicographically-smallest-string-after-applying-operations/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Lexicographically Smallest String After Applying Operations\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Lexicographically Smallest String After Applying Operations\n};",
        "java": "// Java Solution for Lexicographically Smallest String After Applying Operations\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Lexicographically Smallest String After Applying Operations\n}",
        "python": "# Python Solution for Lexicographically Smallest String After Applying Operations\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Lexicographically Smallest String After Applying Operations\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Lexicographically Smallest String After Applying Operations\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Lexicographically Smallest String After Applying Operations\n};",
        "java": "// Optimal Java Solution for Lexicographically Smallest String After Applying Operations\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Lexicographically Smallest String After Applying Operations\n}",
        "python": "# Optimal Python Solution for Lexicographically Smallest String After Applying Operations\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Lexicographically Smallest String After Applying Operations\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Lexicographically Smallest String After Applying Operations",
      "cpp_optimal": "// Solution for Lexicographically Smallest String After Applying Operations",
      "java_brute": "// Solution for Lexicographically Smallest String After Applying Operations",
      "java_optimal": "// Solution for Lexicographically Smallest String After Applying Operations",
      "python_brute": "# Solution for Lexicographically Smallest String After Applying Operations",
      "python_optimal": "# Solution for Lexicographically Smallest String After Applying Operations"
    },
    "originalOrder": 500,
    "learningOrder": 500
  },
  {
    "id": 616,
    "number": 616,
    "sequence_number": 616,
    "title": "Super Ugly Number",
    "slug": "super-ugly-number",
    "difficulty": "Medium",
    "topic": "Arrays",
    "subtopic": "Arrays Optimization",
    "pattern": "Arrays Pattern",
    "secondary_patterns": [
      "Arrays Pattern"
    ],
    "stage": "Advanced Graphs & Topological Sort",
    "curriculumStage": "Stage 13 — Advanced Graphs & Topological Sort",
    "roadmapPhase": "Stage 13 — Advanced Graphs & Topological Sort",
    "phase": "Stage 13 — Advanced Graphs & Topological Sort",
    "estimatedTime": 30,
    "statement": "Solve the **Super Ugly Number** problem using standard Arrays techniques. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Arrays algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Arrays properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Arrays techniques by solving Medium problem constraints for Super Ugly Number.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/super-ugly-number/",
    "leetcode_title": "Super Ugly Number",
    "leetcode_id": 313,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/super-ugly-number/",
    "canonicalSlug": "super-ugly-number",
    "canonicalUrl": "https://leetcode.com/problems/super-ugly-number/",
    "url": "https://leetcode.com/problems/super-ugly-number/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Super Ugly Number\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Super Ugly Number\n};",
        "java": "// Java Solution for Super Ugly Number\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Super Ugly Number\n}",
        "python": "# Python Solution for Super Ugly Number\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Super Ugly Number\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Super Ugly Number\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Super Ugly Number\n};",
        "java": "// Optimal Java Solution for Super Ugly Number\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Super Ugly Number\n}",
        "python": "# Optimal Python Solution for Super Ugly Number\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Super Ugly Number\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Super Ugly Number",
      "cpp_optimal": "// Solution for Super Ugly Number",
      "java_brute": "// Solution for Super Ugly Number",
      "java_optimal": "// Solution for Super Ugly Number",
      "python_brute": "# Solution for Super Ugly Number",
      "python_optimal": "# Solution for Super Ugly Number"
    },
    "originalOrder": 295,
    "learningOrder": 295
  },
  {
    "id": 617,
    "number": 617,
    "sequence_number": 617,
    "title": "Remove Duplicate Letters",
    "slug": "remove-duplicate-letters",
    "difficulty": "Medium",
    "topic": "Arrays",
    "subtopic": "Arrays Optimization",
    "pattern": "Arrays Pattern",
    "secondary_patterns": [
      "Arrays Pattern"
    ],
    "stage": "Advanced Graphs & Topological Sort",
    "curriculumStage": "Stage 13 — Advanced Graphs & Topological Sort",
    "roadmapPhase": "Stage 13 — Advanced Graphs & Topological Sort",
    "phase": "Stage 13 — Advanced Graphs & Topological Sort",
    "estimatedTime": 30,
    "statement": "Solve the **Remove Duplicate Letters** problem using standard Arrays techniques. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Arrays algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Arrays properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Arrays techniques by solving Medium problem constraints for Remove Duplicate Letters.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/remove-duplicate-letters/",
    "leetcode_title": "Remove Duplicate Letters",
    "leetcode_id": 316,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/remove-duplicate-letters/",
    "canonicalSlug": "remove-duplicate-letters",
    "canonicalUrl": "https://leetcode.com/problems/remove-duplicate-letters/",
    "url": "https://leetcode.com/problems/remove-duplicate-letters/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Remove Duplicate Letters\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Remove Duplicate Letters\n};",
        "java": "// Java Solution for Remove Duplicate Letters\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Remove Duplicate Letters\n}",
        "python": "# Python Solution for Remove Duplicate Letters\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Remove Duplicate Letters\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Remove Duplicate Letters\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Remove Duplicate Letters\n};",
        "java": "// Optimal Java Solution for Remove Duplicate Letters\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Remove Duplicate Letters\n}",
        "python": "# Optimal Python Solution for Remove Duplicate Letters\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Remove Duplicate Letters\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Remove Duplicate Letters",
      "cpp_optimal": "// Solution for Remove Duplicate Letters",
      "java_brute": "// Solution for Remove Duplicate Letters",
      "java_optimal": "// Solution for Remove Duplicate Letters",
      "python_brute": "# Solution for Remove Duplicate Letters",
      "python_optimal": "# Solution for Remove Duplicate Letters"
    },
    "originalOrder": 296,
    "learningOrder": 296
  },
  {
    "id": 618,
    "number": 618,
    "sequence_number": 618,
    "title": "Maximum Product of Word Lengths",
    "slug": "maximum-product-of-word-lengths",
    "difficulty": "Medium",
    "topic": "Arrays",
    "subtopic": "Arrays Optimization",
    "pattern": "Arrays Pattern",
    "secondary_patterns": [
      "Arrays Pattern"
    ],
    "stage": "Advanced Graphs & Topological Sort",
    "curriculumStage": "Stage 13 — Advanced Graphs & Topological Sort",
    "roadmapPhase": "Stage 13 — Advanced Graphs & Topological Sort",
    "phase": "Stage 13 — Advanced Graphs & Topological Sort",
    "estimatedTime": 30,
    "statement": "Solve the **Maximum Product of Word Lengths** problem using standard Arrays techniques. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Arrays algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Arrays properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Arrays techniques by solving Medium problem constraints for Maximum Product of Word Lengths.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/maximum-product-of-word-lengths/",
    "leetcode_title": "Maximum Product of Word Lengths",
    "leetcode_id": 318,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/maximum-product-of-word-lengths/",
    "canonicalSlug": "maximum-product-of-word-lengths",
    "canonicalUrl": "https://leetcode.com/problems/maximum-product-of-word-lengths/",
    "url": "https://leetcode.com/problems/maximum-product-of-word-lengths/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Maximum Product of Word Lengths\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Maximum Product of Word Lengths\n};",
        "java": "// Java Solution for Maximum Product of Word Lengths\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Maximum Product of Word Lengths\n}",
        "python": "# Python Solution for Maximum Product of Word Lengths\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Maximum Product of Word Lengths\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Maximum Product of Word Lengths\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Maximum Product of Word Lengths\n};",
        "java": "// Optimal Java Solution for Maximum Product of Word Lengths\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Maximum Product of Word Lengths\n}",
        "python": "# Optimal Python Solution for Maximum Product of Word Lengths\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Maximum Product of Word Lengths\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Maximum Product of Word Lengths",
      "cpp_optimal": "// Solution for Maximum Product of Word Lengths",
      "java_brute": "// Solution for Maximum Product of Word Lengths",
      "java_optimal": "// Solution for Maximum Product of Word Lengths",
      "python_brute": "# Solution for Maximum Product of Word Lengths",
      "python_optimal": "# Solution for Maximum Product of Word Lengths"
    },
    "originalOrder": 297,
    "learningOrder": 297
  },
  {
    "id": 619,
    "number": 619,
    "sequence_number": 619,
    "title": "Bulb Switcher",
    "slug": "bulb-switcher",
    "difficulty": "Medium",
    "topic": "Arrays",
    "subtopic": "Arrays Optimization",
    "pattern": "Arrays Pattern",
    "secondary_patterns": [
      "Arrays Pattern"
    ],
    "stage": "Advanced Graphs & Topological Sort",
    "curriculumStage": "Stage 13 — Advanced Graphs & Topological Sort",
    "roadmapPhase": "Stage 13 — Advanced Graphs & Topological Sort",
    "phase": "Stage 13 — Advanced Graphs & Topological Sort",
    "estimatedTime": 30,
    "statement": "Solve the **Bulb Switcher** problem using standard Arrays techniques. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Arrays algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Arrays properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Arrays techniques by solving Medium problem constraints for Bulb Switcher.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/bulb-switcher/",
    "leetcode_title": "Bulb Switcher",
    "leetcode_id": 319,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/bulb-switcher/",
    "canonicalSlug": "bulb-switcher",
    "canonicalUrl": "https://leetcode.com/problems/bulb-switcher/",
    "url": "https://leetcode.com/problems/bulb-switcher/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Bulb Switcher\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Bulb Switcher\n};",
        "java": "// Java Solution for Bulb Switcher\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Bulb Switcher\n}",
        "python": "# Python Solution for Bulb Switcher\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Bulb Switcher\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Bulb Switcher\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Bulb Switcher\n};",
        "java": "// Optimal Java Solution for Bulb Switcher\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Bulb Switcher\n}",
        "python": "# Optimal Python Solution for Bulb Switcher\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Bulb Switcher\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Bulb Switcher",
      "cpp_optimal": "// Solution for Bulb Switcher",
      "java_brute": "// Solution for Bulb Switcher",
      "java_optimal": "// Solution for Bulb Switcher",
      "python_brute": "# Solution for Bulb Switcher",
      "python_optimal": "# Solution for Bulb Switcher"
    },
    "originalOrder": 298,
    "learningOrder": 298
  },
  {
    "id": 620,
    "number": 620,
    "sequence_number": 620,
    "title": "Increasing Triplet Subsequence",
    "slug": "increasing-triplet-subsequence",
    "difficulty": "Medium",
    "topic": "Arrays",
    "subtopic": "Arrays Optimization",
    "pattern": "Arrays Pattern",
    "secondary_patterns": [
      "Arrays Pattern"
    ],
    "stage": "Advanced Graphs & Topological Sort",
    "curriculumStage": "Stage 13 — Advanced Graphs & Topological Sort",
    "roadmapPhase": "Stage 13 — Advanced Graphs & Topological Sort",
    "phase": "Stage 13 — Advanced Graphs & Topological Sort",
    "estimatedTime": 30,
    "statement": "Solve the **Increasing Triplet Subsequence** problem using standard Arrays techniques. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Arrays algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Arrays properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Arrays techniques by solving Medium problem constraints for Increasing Triplet Subsequence.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/increasing-triplet-subsequence/",
    "leetcode_title": "Increasing Triplet Subsequence",
    "leetcode_id": 334,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/increasing-triplet-subsequence/",
    "canonicalSlug": "increasing-triplet-subsequence",
    "canonicalUrl": "https://leetcode.com/problems/increasing-triplet-subsequence/",
    "url": "https://leetcode.com/problems/increasing-triplet-subsequence/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Increasing Triplet Subsequence\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Increasing Triplet Subsequence\n};",
        "java": "// Java Solution for Increasing Triplet Subsequence\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Increasing Triplet Subsequence\n}",
        "python": "# Python Solution for Increasing Triplet Subsequence\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Increasing Triplet Subsequence\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Increasing Triplet Subsequence\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Increasing Triplet Subsequence\n};",
        "java": "// Optimal Java Solution for Increasing Triplet Subsequence\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Increasing Triplet Subsequence\n}",
        "python": "# Optimal Python Solution for Increasing Triplet Subsequence\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Increasing Triplet Subsequence\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Increasing Triplet Subsequence",
      "cpp_optimal": "// Solution for Increasing Triplet Subsequence",
      "java_brute": "// Solution for Increasing Triplet Subsequence",
      "java_optimal": "// Solution for Increasing Triplet Subsequence",
      "python_brute": "# Solution for Increasing Triplet Subsequence",
      "python_optimal": "# Solution for Increasing Triplet Subsequence"
    },
    "originalOrder": 300,
    "learningOrder": 300
  },
  {
    "id": 621,
    "number": 621,
    "sequence_number": 621,
    "title": "House Robber III",
    "slug": "house-robber-iii",
    "difficulty": "Medium",
    "topic": "Arrays",
    "subtopic": "Arrays Optimization",
    "pattern": "Arrays Pattern",
    "secondary_patterns": [
      "Arrays Pattern"
    ],
    "stage": "Advanced Graphs & Topological Sort",
    "curriculumStage": "Stage 13 — Advanced Graphs & Topological Sort",
    "roadmapPhase": "Stage 13 — Advanced Graphs & Topological Sort",
    "phase": "Stage 13 — Advanced Graphs & Topological Sort",
    "estimatedTime": 30,
    "statement": "Solve the **House Robber III** problem using standard Arrays techniques. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Arrays algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Arrays properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Arrays techniques by solving Medium problem constraints for House Robber III.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/house-robber-iii/",
    "leetcode_title": "House Robber III",
    "leetcode_id": 337,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/house-robber-iii/",
    "canonicalSlug": "house-robber-iii",
    "canonicalUrl": "https://leetcode.com/problems/house-robber-iii/",
    "url": "https://leetcode.com/problems/house-robber-iii/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for House Robber III\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for House Robber III\n};",
        "java": "// Java Solution for House Robber III\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for House Robber III\n}",
        "python": "# Python Solution for House Robber III\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for House Robber III\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for House Robber III\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for House Robber III\n};",
        "java": "// Optimal Java Solution for House Robber III\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for House Robber III\n}",
        "python": "# Optimal Python Solution for House Robber III\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for House Robber III\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for House Robber III",
      "cpp_optimal": "// Solution for House Robber III",
      "java_brute": "// Solution for House Robber III",
      "java_optimal": "// Solution for House Robber III",
      "python_brute": "# Solution for House Robber III",
      "python_optimal": "# Solution for House Robber III"
    },
    "originalOrder": 301,
    "learningOrder": 301
  },
  {
    "id": 622,
    "number": 622,
    "sequence_number": 622,
    "title": "Integer Break",
    "slug": "integer-break",
    "difficulty": "Medium",
    "topic": "Arrays",
    "subtopic": "Arrays Optimization",
    "pattern": "Arrays Pattern",
    "secondary_patterns": [
      "Arrays Pattern"
    ],
    "stage": "Advanced Graphs & Topological Sort",
    "curriculumStage": "Stage 13 — Advanced Graphs & Topological Sort",
    "roadmapPhase": "Stage 13 — Advanced Graphs & Topological Sort",
    "phase": "Stage 13 — Advanced Graphs & Topological Sort",
    "estimatedTime": 30,
    "statement": "Solve the **Integer Break** problem using standard Arrays techniques. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Arrays algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Arrays properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Arrays techniques by solving Medium problem constraints for Integer Break.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/integer-break/",
    "leetcode_title": "Integer Break",
    "leetcode_id": 343,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/integer-break/",
    "canonicalSlug": "integer-break",
    "canonicalUrl": "https://leetcode.com/problems/integer-break/",
    "url": "https://leetcode.com/problems/integer-break/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Integer Break\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Integer Break\n};",
        "java": "// Java Solution for Integer Break\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Integer Break\n}",
        "python": "# Python Solution for Integer Break\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Integer Break\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Integer Break\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Integer Break\n};",
        "java": "// Optimal Java Solution for Integer Break\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Integer Break\n}",
        "python": "# Optimal Python Solution for Integer Break\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Integer Break\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Integer Break",
      "cpp_optimal": "// Solution for Integer Break",
      "java_brute": "// Solution for Integer Break",
      "java_optimal": "// Solution for Integer Break",
      "python_brute": "# Solution for Integer Break",
      "python_optimal": "# Solution for Integer Break"
    },
    "originalOrder": 303,
    "learningOrder": 303
  },
  {
    "id": 623,
    "number": 623,
    "sequence_number": 623,
    "title": "Count Numbers with Unique Digits",
    "slug": "count-numbers-with-unique-digits",
    "difficulty": "Medium",
    "topic": "Math",
    "subtopic": "Arrays Optimization",
    "pattern": "Arrays Pattern",
    "secondary_patterns": [
      "Arrays Pattern"
    ],
    "stage": "Advanced Graphs & Topological Sort",
    "curriculumStage": "Stage 13 — Advanced Graphs & Topological Sort",
    "roadmapPhase": "Stage 13 — Advanced Graphs & Topological Sort",
    "phase": "Stage 13 — Advanced Graphs & Topological Sort",
    "estimatedTime": 30,
    "statement": "Solve the **Count Numbers with Unique Digits** problem using standard Arrays techniques. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Arrays algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Arrays properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Arrays techniques by solving Medium problem constraints for Count Numbers with Unique Digits.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/count-numbers-with-unique-digits/",
    "leetcode_title": "Count Numbers with Unique Digits",
    "leetcode_id": 357,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/count-numbers-with-unique-digits/",
    "canonicalSlug": "count-numbers-with-unique-digits",
    "canonicalUrl": "https://leetcode.com/problems/count-numbers-with-unique-digits/",
    "url": "https://leetcode.com/problems/count-numbers-with-unique-digits/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Count Numbers with Unique Digits\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Count Numbers with Unique Digits\n};",
        "java": "// Java Solution for Count Numbers with Unique Digits\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Count Numbers with Unique Digits\n}",
        "python": "# Python Solution for Count Numbers with Unique Digits\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Count Numbers with Unique Digits\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Count Numbers with Unique Digits\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Count Numbers with Unique Digits\n};",
        "java": "// Optimal Java Solution for Count Numbers with Unique Digits\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Count Numbers with Unique Digits\n}",
        "python": "# Optimal Python Solution for Count Numbers with Unique Digits\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Count Numbers with Unique Digits\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Count Numbers with Unique Digits",
      "cpp_optimal": "// Solution for Count Numbers with Unique Digits",
      "java_brute": "// Solution for Count Numbers with Unique Digits",
      "java_optimal": "// Solution for Count Numbers with Unique Digits",
      "python_brute": "# Solution for Count Numbers with Unique Digits",
      "python_optimal": "# Solution for Count Numbers with Unique Digits"
    },
    "originalOrder": 304,
    "learningOrder": 304
  },
  {
    "id": 624,
    "number": 624,
    "sequence_number": 624,
    "title": "Water and Jug Problem",
    "slug": "water-and-jug-problem",
    "difficulty": "Medium",
    "topic": "Bit Manipulation",
    "subtopic": "Arrays Optimization",
    "pattern": "Arrays Pattern",
    "secondary_patterns": [
      "Arrays Pattern"
    ],
    "stage": "Advanced Graphs & Topological Sort",
    "curriculumStage": "Stage 13 — Advanced Graphs & Topological Sort",
    "roadmapPhase": "Stage 13 — Advanced Graphs & Topological Sort",
    "phase": "Stage 13 — Advanced Graphs & Topological Sort",
    "estimatedTime": 30,
    "statement": "Solve the **Water and Jug Problem** problem using standard Arrays techniques. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Arrays algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Arrays properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Arrays techniques by solving Medium problem constraints for Water and Jug Problem.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/water-and-jug-problem/",
    "leetcode_title": "Water and Jug Problem",
    "leetcode_id": 365,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/water-and-jug-problem/",
    "canonicalSlug": "water-and-jug-problem",
    "canonicalUrl": "https://leetcode.com/problems/water-and-jug-problem/",
    "url": "https://leetcode.com/problems/water-and-jug-problem/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Water and Jug Problem\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Water and Jug Problem\n};",
        "java": "// Java Solution for Water and Jug Problem\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Water and Jug Problem\n}",
        "python": "# Python Solution for Water and Jug Problem\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Water and Jug Problem\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Water and Jug Problem\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Water and Jug Problem\n};",
        "java": "// Optimal Java Solution for Water and Jug Problem\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Water and Jug Problem\n}",
        "python": "# Optimal Python Solution for Water and Jug Problem\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Water and Jug Problem\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Water and Jug Problem",
      "cpp_optimal": "// Solution for Water and Jug Problem",
      "java_brute": "// Solution for Water and Jug Problem",
      "java_optimal": "// Solution for Water and Jug Problem",
      "python_brute": "# Solution for Water and Jug Problem",
      "python_optimal": "# Solution for Water and Jug Problem"
    },
    "originalOrder": 305,
    "learningOrder": 305
  },
  {
    "id": 625,
    "number": 625,
    "sequence_number": 625,
    "title": "Largest Divisible Subset",
    "slug": "largest-divisible-subset",
    "difficulty": "Medium",
    "topic": "Hashing",
    "subtopic": "Arrays Optimization",
    "pattern": "Arrays Pattern",
    "secondary_patterns": [
      "Arrays Pattern"
    ],
    "stage": "Advanced Graphs & Topological Sort",
    "curriculumStage": "Stage 13 — Advanced Graphs & Topological Sort",
    "roadmapPhase": "Stage 13 — Advanced Graphs & Topological Sort",
    "phase": "Stage 13 — Advanced Graphs & Topological Sort",
    "estimatedTime": 30,
    "statement": "Solve the **Largest Divisible Subset** problem using standard Arrays techniques. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Arrays algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Arrays properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Arrays techniques by solving Medium problem constraints for Largest Divisible Subset.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/largest-divisible-subset/",
    "leetcode_title": "Largest Divisible Subset",
    "leetcode_id": 368,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/largest-divisible-subset/",
    "canonicalSlug": "largest-divisible-subset",
    "canonicalUrl": "https://leetcode.com/problems/largest-divisible-subset/",
    "url": "https://leetcode.com/problems/largest-divisible-subset/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Largest Divisible Subset\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Largest Divisible Subset\n};",
        "java": "// Java Solution for Largest Divisible Subset\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Largest Divisible Subset\n}",
        "python": "# Python Solution for Largest Divisible Subset\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Largest Divisible Subset\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Largest Divisible Subset\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Largest Divisible Subset\n};",
        "java": "// Optimal Java Solution for Largest Divisible Subset\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Largest Divisible Subset\n}",
        "python": "# Optimal Python Solution for Largest Divisible Subset\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Largest Divisible Subset\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Largest Divisible Subset",
      "cpp_optimal": "// Solution for Largest Divisible Subset",
      "java_brute": "// Solution for Largest Divisible Subset",
      "java_optimal": "// Solution for Largest Divisible Subset",
      "python_brute": "# Solution for Largest Divisible Subset",
      "python_optimal": "# Solution for Largest Divisible Subset"
    },
    "originalOrder": 306,
    "learningOrder": 306
  },
  {
    "id": 626,
    "number": 626,
    "sequence_number": 626,
    "title": "Sum of Two Integers",
    "slug": "sum-of-two-integers",
    "difficulty": "Medium",
    "topic": "Arrays",
    "subtopic": "Arrays Optimization",
    "pattern": "Arrays Pattern",
    "secondary_patterns": [
      "Arrays Pattern"
    ],
    "stage": "Advanced Graphs & Topological Sort",
    "curriculumStage": "Stage 13 — Advanced Graphs & Topological Sort",
    "roadmapPhase": "Stage 13 — Advanced Graphs & Topological Sort",
    "phase": "Stage 13 — Advanced Graphs & Topological Sort",
    "estimatedTime": 30,
    "statement": "Solve the **Sum of Two Integers** problem using standard Arrays techniques. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Arrays algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Arrays properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Arrays techniques by solving Medium problem constraints for Sum of Two Integers.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/sum-of-two-integers/",
    "leetcode_title": "Sum of Two Integers",
    "leetcode_id": 371,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/sum-of-two-integers/",
    "canonicalSlug": "sum-of-two-integers",
    "canonicalUrl": "https://leetcode.com/problems/sum-of-two-integers/",
    "url": "https://leetcode.com/problems/sum-of-two-integers/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Sum of Two Integers\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Sum of Two Integers\n};",
        "java": "// Java Solution for Sum of Two Integers\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Sum of Two Integers\n}",
        "python": "# Python Solution for Sum of Two Integers\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Sum of Two Integers\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Sum of Two Integers\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Sum of Two Integers\n};",
        "java": "// Optimal Java Solution for Sum of Two Integers\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Sum of Two Integers\n}",
        "python": "# Optimal Python Solution for Sum of Two Integers\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Sum of Two Integers\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Sum of Two Integers",
      "cpp_optimal": "// Solution for Sum of Two Integers",
      "java_brute": "// Solution for Sum of Two Integers",
      "java_optimal": "// Solution for Sum of Two Integers",
      "python_brute": "# Solution for Sum of Two Integers",
      "python_optimal": "# Solution for Sum of Two Integers"
    },
    "originalOrder": 307,
    "learningOrder": 307
  },
  {
    "id": 627,
    "number": 627,
    "sequence_number": 627,
    "title": "Super Pow",
    "slug": "super-pow",
    "difficulty": "Medium",
    "topic": "Math",
    "subtopic": "Arrays Optimization",
    "pattern": "Arrays Pattern",
    "secondary_patterns": [
      "Arrays Pattern"
    ],
    "stage": "Advanced Graphs & Topological Sort",
    "curriculumStage": "Stage 13 — Advanced Graphs & Topological Sort",
    "roadmapPhase": "Stage 13 — Advanced Graphs & Topological Sort",
    "phase": "Stage 13 — Advanced Graphs & Topological Sort",
    "estimatedTime": 30,
    "statement": "Solve the **Super Pow** problem using standard Arrays techniques. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Arrays algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Arrays properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Arrays techniques by solving Medium problem constraints for Super Pow.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/super-pow/",
    "leetcode_title": "Super Pow",
    "leetcode_id": 372,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/super-pow/",
    "canonicalSlug": "super-pow",
    "canonicalUrl": "https://leetcode.com/problems/super-pow/",
    "url": "https://leetcode.com/problems/super-pow/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Super Pow\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Super Pow\n};",
        "java": "// Java Solution for Super Pow\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Super Pow\n}",
        "python": "# Python Solution for Super Pow\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Super Pow\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Super Pow\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Super Pow\n};",
        "java": "// Optimal Java Solution for Super Pow\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Super Pow\n}",
        "python": "# Optimal Python Solution for Super Pow\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Super Pow\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Super Pow",
      "cpp_optimal": "// Solution for Super Pow",
      "java_brute": "// Solution for Super Pow",
      "java_optimal": "// Solution for Super Pow",
      "python_brute": "# Solution for Super Pow",
      "python_optimal": "# Solution for Super Pow"
    },
    "originalOrder": 308,
    "learningOrder": 308
  },
  {
    "id": 628,
    "number": 628,
    "sequence_number": 628,
    "title": "Guess Number Higher or Lower II",
    "slug": "guess-number-higher-or-lower-ii",
    "difficulty": "Medium",
    "topic": "Arrays",
    "subtopic": "Arrays Optimization",
    "pattern": "Arrays Pattern",
    "secondary_patterns": [
      "Arrays Pattern"
    ],
    "stage": "Advanced Graphs & Topological Sort",
    "curriculumStage": "Stage 13 — Advanced Graphs & Topological Sort",
    "roadmapPhase": "Stage 13 — Advanced Graphs & Topological Sort",
    "phase": "Stage 13 — Advanced Graphs & Topological Sort",
    "estimatedTime": 30,
    "statement": "Solve the **Guess Number Higher or Lower II** problem using standard Arrays techniques. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Arrays algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Arrays properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Arrays techniques by solving Medium problem constraints for Guess Number Higher or Lower II.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/guess-number-higher-or-lower-ii/",
    "leetcode_title": "Guess Number Higher or Lower II",
    "leetcode_id": 375,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/guess-number-higher-or-lower-ii/",
    "canonicalSlug": "guess-number-higher-or-lower-ii",
    "canonicalUrl": "https://leetcode.com/problems/guess-number-higher-or-lower-ii/",
    "url": "https://leetcode.com/problems/guess-number-higher-or-lower-ii/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Guess Number Higher or Lower II\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Guess Number Higher or Lower II\n};",
        "java": "// Java Solution for Guess Number Higher or Lower II\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Guess Number Higher or Lower II\n}",
        "python": "# Python Solution for Guess Number Higher or Lower II\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Guess Number Higher or Lower II\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Guess Number Higher or Lower II\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Guess Number Higher or Lower II\n};",
        "java": "// Optimal Java Solution for Guess Number Higher or Lower II\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Guess Number Higher or Lower II\n}",
        "python": "# Optimal Python Solution for Guess Number Higher or Lower II\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Guess Number Higher or Lower II\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Guess Number Higher or Lower II",
      "cpp_optimal": "// Solution for Guess Number Higher or Lower II",
      "java_brute": "// Solution for Guess Number Higher or Lower II",
      "java_optimal": "// Solution for Guess Number Higher or Lower II",
      "python_brute": "# Solution for Guess Number Higher or Lower II",
      "python_optimal": "# Solution for Guess Number Higher or Lower II"
    },
    "originalOrder": 309,
    "learningOrder": 309
  },
  {
    "id": 629,
    "number": 629,
    "sequence_number": 629,
    "title": "Wiggle Subsequence",
    "slug": "wiggle-subsequence",
    "difficulty": "Medium",
    "topic": "Arrays",
    "subtopic": "Arrays Optimization",
    "pattern": "Arrays Pattern",
    "secondary_patterns": [
      "Arrays Pattern"
    ],
    "stage": "Advanced Graphs & Topological Sort",
    "curriculumStage": "Stage 13 — Advanced Graphs & Topological Sort",
    "roadmapPhase": "Stage 13 — Advanced Graphs & Topological Sort",
    "phase": "Stage 13 — Advanced Graphs & Topological Sort",
    "estimatedTime": 30,
    "statement": "Solve the **Wiggle Subsequence** problem using standard Arrays techniques. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Arrays algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Arrays properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Arrays techniques by solving Medium problem constraints for Wiggle Subsequence.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/wiggle-subsequence/",
    "leetcode_title": "Wiggle Subsequence",
    "leetcode_id": 376,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/wiggle-subsequence/",
    "canonicalSlug": "wiggle-subsequence",
    "canonicalUrl": "https://leetcode.com/problems/wiggle-subsequence/",
    "url": "https://leetcode.com/problems/wiggle-subsequence/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Wiggle Subsequence\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Wiggle Subsequence\n};",
        "java": "// Java Solution for Wiggle Subsequence\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Wiggle Subsequence\n}",
        "python": "# Python Solution for Wiggle Subsequence\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Wiggle Subsequence\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Wiggle Subsequence\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Wiggle Subsequence\n};",
        "java": "// Optimal Java Solution for Wiggle Subsequence\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Wiggle Subsequence\n}",
        "python": "# Optimal Python Solution for Wiggle Subsequence\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Wiggle Subsequence\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Wiggle Subsequence",
      "cpp_optimal": "// Solution for Wiggle Subsequence",
      "java_brute": "// Solution for Wiggle Subsequence",
      "java_optimal": "// Solution for Wiggle Subsequence",
      "python_brute": "# Solution for Wiggle Subsequence",
      "python_optimal": "# Solution for Wiggle Subsequence"
    },
    "originalOrder": 310,
    "learningOrder": 310
  },
  {
    "id": 630,
    "number": 630,
    "sequence_number": 630,
    "title": "Insert Delete GetRandom O(1)",
    "slug": "insert-delete-getrandom-o1",
    "difficulty": "Medium",
    "topic": "Bit Manipulation",
    "subtopic": "Arrays Optimization",
    "pattern": "Arrays Pattern",
    "secondary_patterns": [
      "Arrays Pattern"
    ],
    "stage": "Advanced Graphs & Topological Sort",
    "curriculumStage": "Stage 13 — Advanced Graphs & Topological Sort",
    "roadmapPhase": "Stage 13 — Advanced Graphs & Topological Sort",
    "phase": "Stage 13 — Advanced Graphs & Topological Sort",
    "estimatedTime": 30,
    "statement": "Solve the **Insert Delete GetRandom O(1)** problem using standard Arrays techniques. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Arrays algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Arrays properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Arrays techniques by solving Medium problem constraints for Insert Delete GetRandom O(1).",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/insert-delete-getrandom-o1/",
    "leetcode_title": "Insert Delete GetRandom O(1)",
    "leetcode_id": 380,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/insert-delete-getrandom-o1/",
    "canonicalSlug": "insert-delete-getrandom-o1",
    "canonicalUrl": "https://leetcode.com/problems/insert-delete-getrandom-o1/",
    "url": "https://leetcode.com/problems/insert-delete-getrandom-o1/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Insert Delete GetRandom O(1)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Insert Delete GetRandom O(1)\n};",
        "java": "// Java Solution for Insert Delete GetRandom O(1)\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Insert Delete GetRandom O(1)\n}",
        "python": "# Python Solution for Insert Delete GetRandom O(1)\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Insert Delete GetRandom O(1)\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Insert Delete GetRandom O(1)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Insert Delete GetRandom O(1)\n};",
        "java": "// Optimal Java Solution for Insert Delete GetRandom O(1)\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Insert Delete GetRandom O(1)\n}",
        "python": "# Optimal Python Solution for Insert Delete GetRandom O(1)\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Insert Delete GetRandom O(1)\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Insert Delete GetRandom O(1)",
      "cpp_optimal": "// Solution for Insert Delete GetRandom O(1)",
      "java_brute": "// Solution for Insert Delete GetRandom O(1)",
      "java_optimal": "// Solution for Insert Delete GetRandom O(1)",
      "python_brute": "# Solution for Insert Delete GetRandom O(1)",
      "python_optimal": "# Solution for Insert Delete GetRandom O(1)"
    },
    "originalOrder": 311,
    "learningOrder": 311
  },
  {
    "id": 631,
    "number": 631,
    "sequence_number": 631,
    "title": "Linked List Random Node",
    "slug": "linked-list-random-node",
    "difficulty": "Medium",
    "topic": "Bit Manipulation",
    "subtopic": "Arrays Optimization",
    "pattern": "Arrays Pattern",
    "secondary_patterns": [
      "Arrays Pattern"
    ],
    "stage": "Advanced Graphs & Topological Sort",
    "curriculumStage": "Stage 13 — Advanced Graphs & Topological Sort",
    "roadmapPhase": "Stage 13 — Advanced Graphs & Topological Sort",
    "phase": "Stage 13 — Advanced Graphs & Topological Sort",
    "estimatedTime": 30,
    "statement": "Solve the **Linked List Random Node** problem using standard Arrays techniques. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Arrays algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Arrays properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Arrays techniques by solving Medium problem constraints for Linked List Random Node.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/linked-list-random-node/",
    "leetcode_title": "Linked List Random Node",
    "leetcode_id": 382,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/linked-list-random-node/",
    "canonicalSlug": "linked-list-random-node",
    "canonicalUrl": "https://leetcode.com/problems/linked-list-random-node/",
    "url": "https://leetcode.com/problems/linked-list-random-node/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Linked List Random Node\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Linked List Random Node\n};",
        "java": "// Java Solution for Linked List Random Node\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Linked List Random Node\n}",
        "python": "# Python Solution for Linked List Random Node\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Linked List Random Node\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Linked List Random Node\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Linked List Random Node\n};",
        "java": "// Optimal Java Solution for Linked List Random Node\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Linked List Random Node\n}",
        "python": "# Optimal Python Solution for Linked List Random Node\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Linked List Random Node\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Linked List Random Node",
      "cpp_optimal": "// Solution for Linked List Random Node",
      "java_brute": "// Solution for Linked List Random Node",
      "java_optimal": "// Solution for Linked List Random Node",
      "python_brute": "# Solution for Linked List Random Node",
      "python_optimal": "# Solution for Linked List Random Node"
    },
    "originalOrder": 312,
    "learningOrder": 312
  },
  {
    "id": 632,
    "number": 632,
    "sequence_number": 632,
    "title": "Shuffle an Array",
    "slug": "shuffle-an-array",
    "difficulty": "Medium",
    "topic": "Arrays",
    "subtopic": "Arrays Optimization",
    "pattern": "Arrays Pattern",
    "secondary_patterns": [
      "Arrays Pattern"
    ],
    "stage": "Advanced Graphs & Topological Sort",
    "curriculumStage": "Stage 13 — Advanced Graphs & Topological Sort",
    "roadmapPhase": "Stage 13 — Advanced Graphs & Topological Sort",
    "phase": "Stage 13 — Advanced Graphs & Topological Sort",
    "estimatedTime": 30,
    "statement": "Solve the **Shuffle an Array** problem using standard Arrays techniques. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Arrays algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Arrays properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Arrays techniques by solving Medium problem constraints for Shuffle an Array.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/shuffle-an-array/",
    "leetcode_title": "Shuffle an Array",
    "leetcode_id": 384,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/shuffle-an-array/",
    "canonicalSlug": "shuffle-an-array",
    "canonicalUrl": "https://leetcode.com/problems/shuffle-an-array/",
    "url": "https://leetcode.com/problems/shuffle-an-array/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Shuffle an Array\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Shuffle an Array\n};",
        "java": "// Java Solution for Shuffle an Array\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Shuffle an Array\n}",
        "python": "# Python Solution for Shuffle an Array\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Shuffle an Array\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Shuffle an Array\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Shuffle an Array\n};",
        "java": "// Optimal Java Solution for Shuffle an Array\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Shuffle an Array\n}",
        "python": "# Optimal Python Solution for Shuffle an Array\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Shuffle an Array\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Shuffle an Array",
      "cpp_optimal": "// Solution for Shuffle an Array",
      "java_brute": "// Solution for Shuffle an Array",
      "java_optimal": "// Solution for Shuffle an Array",
      "python_brute": "# Solution for Shuffle an Array",
      "python_optimal": "# Solution for Shuffle an Array"
    },
    "originalOrder": 313,
    "learningOrder": 313
  },
  {
    "id": 633,
    "number": 633,
    "sequence_number": 633,
    "title": "Mini Parser",
    "slug": "mini-parser",
    "difficulty": "Medium",
    "topic": "Arrays",
    "subtopic": "Arrays Optimization",
    "pattern": "Arrays Pattern",
    "secondary_patterns": [
      "Arrays Pattern"
    ],
    "stage": "Advanced Graphs & Topological Sort",
    "curriculumStage": "Stage 13 — Advanced Graphs & Topological Sort",
    "roadmapPhase": "Stage 13 — Advanced Graphs & Topological Sort",
    "phase": "Stage 13 — Advanced Graphs & Topological Sort",
    "estimatedTime": 30,
    "statement": "Solve the **Mini Parser** problem using standard Arrays techniques. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Arrays algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Arrays properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Arrays techniques by solving Medium problem constraints for Mini Parser.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/mini-parser/",
    "leetcode_title": "Mini Parser",
    "leetcode_id": 385,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/mini-parser/",
    "canonicalSlug": "mini-parser",
    "canonicalUrl": "https://leetcode.com/problems/mini-parser/",
    "url": "https://leetcode.com/problems/mini-parser/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Mini Parser\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Mini Parser\n};",
        "java": "// Java Solution for Mini Parser\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Mini Parser\n}",
        "python": "# Python Solution for Mini Parser\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Mini Parser\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Mini Parser\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Mini Parser\n};",
        "java": "// Optimal Java Solution for Mini Parser\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Mini Parser\n}",
        "python": "# Optimal Python Solution for Mini Parser\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Mini Parser\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Mini Parser",
      "cpp_optimal": "// Solution for Mini Parser",
      "java_brute": "// Solution for Mini Parser",
      "java_optimal": "// Solution for Mini Parser",
      "python_brute": "# Solution for Mini Parser",
      "python_optimal": "# Solution for Mini Parser"
    },
    "originalOrder": 314,
    "learningOrder": 314
  },
  {
    "id": 634,
    "number": 634,
    "sequence_number": 634,
    "title": "Longest Absolute File Path",
    "slug": "longest-absolute-file-path",
    "difficulty": "Medium",
    "topic": "Arrays",
    "subtopic": "Arrays Optimization",
    "pattern": "Arrays Pattern",
    "secondary_patterns": [
      "Arrays Pattern"
    ],
    "stage": "Advanced Graphs & Topological Sort",
    "curriculumStage": "Stage 13 — Advanced Graphs & Topological Sort",
    "roadmapPhase": "Stage 13 — Advanced Graphs & Topological Sort",
    "phase": "Stage 13 — Advanced Graphs & Topological Sort",
    "estimatedTime": 30,
    "statement": "Solve the **Longest Absolute File Path** problem using standard Arrays techniques. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Arrays algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Arrays properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Arrays techniques by solving Medium problem constraints for Longest Absolute File Path.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/longest-absolute-file-path/",
    "leetcode_title": "Longest Absolute File Path",
    "leetcode_id": 388,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/longest-absolute-file-path/",
    "canonicalSlug": "longest-absolute-file-path",
    "canonicalUrl": "https://leetcode.com/problems/longest-absolute-file-path/",
    "url": "https://leetcode.com/problems/longest-absolute-file-path/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Longest Absolute File Path\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Longest Absolute File Path\n};",
        "java": "// Java Solution for Longest Absolute File Path\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Longest Absolute File Path\n}",
        "python": "# Python Solution for Longest Absolute File Path\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Longest Absolute File Path\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Longest Absolute File Path\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Longest Absolute File Path\n};",
        "java": "// Optimal Java Solution for Longest Absolute File Path\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Longest Absolute File Path\n}",
        "python": "# Optimal Python Solution for Longest Absolute File Path\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Longest Absolute File Path\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Longest Absolute File Path",
      "cpp_optimal": "// Solution for Longest Absolute File Path",
      "java_brute": "// Solution for Longest Absolute File Path",
      "java_optimal": "// Solution for Longest Absolute File Path",
      "python_brute": "# Solution for Longest Absolute File Path",
      "python_optimal": "# Solution for Longest Absolute File Path"
    },
    "originalOrder": 315,
    "learningOrder": 315
  },
  {
    "id": 635,
    "number": 635,
    "sequence_number": 635,
    "title": "Elimination Game",
    "slug": "elimination-game",
    "difficulty": "Medium",
    "topic": "Arrays",
    "subtopic": "Arrays Optimization",
    "pattern": "Arrays Pattern",
    "secondary_patterns": [
      "Arrays Pattern"
    ],
    "stage": "Advanced Graphs & Topological Sort",
    "curriculumStage": "Stage 13 — Advanced Graphs & Topological Sort",
    "roadmapPhase": "Stage 13 — Advanced Graphs & Topological Sort",
    "phase": "Stage 13 — Advanced Graphs & Topological Sort",
    "estimatedTime": 30,
    "statement": "Solve the **Elimination Game** problem using standard Arrays techniques. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Arrays algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Arrays properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Arrays techniques by solving Medium problem constraints for Elimination Game.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/elimination-game/",
    "leetcode_title": "Elimination Game",
    "leetcode_id": 390,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/elimination-game/",
    "canonicalSlug": "elimination-game",
    "canonicalUrl": "https://leetcode.com/problems/elimination-game/",
    "url": "https://leetcode.com/problems/elimination-game/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Elimination Game\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Elimination Game\n};",
        "java": "// Java Solution for Elimination Game\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Elimination Game\n}",
        "python": "# Python Solution for Elimination Game\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Elimination Game\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Elimination Game\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Elimination Game\n};",
        "java": "// Optimal Java Solution for Elimination Game\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Elimination Game\n}",
        "python": "# Optimal Python Solution for Elimination Game\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Elimination Game\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Elimination Game",
      "cpp_optimal": "// Solution for Elimination Game",
      "java_brute": "// Solution for Elimination Game",
      "java_optimal": "// Solution for Elimination Game",
      "python_brute": "# Solution for Elimination Game",
      "python_optimal": "# Solution for Elimination Game"
    },
    "originalOrder": 316,
    "learningOrder": 316
  },
  {
    "id": 636,
    "number": 636,
    "sequence_number": 636,
    "title": "Course Schedule III",
    "slug": "course-schedule-iii",
    "difficulty": "Hard",
    "topic": "Graphs",
    "subtopic": "Graphs Optimization",
    "pattern": "Graphs Pattern",
    "secondary_patterns": [
      "Graphs Pattern"
    ],
    "stage": "Advanced Graphs & Topological Sort",
    "curriculumStage": "Stage 13 — Advanced Graphs & Topological Sort",
    "roadmapPhase": "Stage 13 — Advanced Graphs & Topological Sort",
    "phase": "Stage 13 — Advanced Graphs & Topological Sort",
    "estimatedTime": 45,
    "statement": "Solve the **Course Schedule III** problem using standard Graphs techniques. Given input constraints appropriate for Hard level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Graphs algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Graphs properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Graphs techniques by solving Hard problem constraints for Course Schedule III.",
    "whyThisPattern": "When observing Graphs problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/course-schedule-iii/",
    "leetcode_title": "Course Schedule III",
    "leetcode_id": 630,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/course-schedule-iii/",
    "canonicalSlug": "course-schedule-iii",
    "canonicalUrl": "https://leetcode.com/problems/course-schedule-iii/",
    "url": "https://leetcode.com/problems/course-schedule-iii/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Course Schedule III\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Course Schedule III\n};",
        "java": "// Java Solution for Course Schedule III\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Course Schedule III\n}",
        "python": "# Python Solution for Course Schedule III\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Course Schedule III\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Course Schedule III\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Course Schedule III\n};",
        "java": "// Optimal Java Solution for Course Schedule III\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Course Schedule III\n}",
        "python": "# Optimal Python Solution for Course Schedule III\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Course Schedule III\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Course Schedule III",
      "cpp_optimal": "// Solution for Course Schedule III",
      "java_brute": "// Solution for Course Schedule III",
      "java_optimal": "// Solution for Course Schedule III",
      "python_brute": "# Solution for Course Schedule III",
      "python_optimal": "# Solution for Course Schedule III"
    },
    "originalOrder": 886,
    "learningOrder": 886
  },
  {
    "id": 637,
    "number": 637,
    "sequence_number": 637,
    "title": "Reachable Nodes In Subdivided Graph",
    "slug": "reachable-nodes-in-subdivided-graph",
    "difficulty": "Hard",
    "topic": "Graphs",
    "subtopic": "Graphs Optimization",
    "pattern": "Graphs Pattern",
    "secondary_patterns": [
      "Graphs Pattern"
    ],
    "stage": "Advanced Graphs & Topological Sort",
    "curriculumStage": "Stage 13 — Advanced Graphs & Topological Sort",
    "roadmapPhase": "Stage 13 — Advanced Graphs & Topological Sort",
    "phase": "Stage 13 — Advanced Graphs & Topological Sort",
    "estimatedTime": 45,
    "statement": "Solve the **Reachable Nodes In Subdivided Graph** problem using standard Graphs techniques. Given input constraints appropriate for Hard level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Graphs algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Graphs properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Graphs techniques by solving Hard problem constraints for Reachable Nodes In Subdivided Graph.",
    "whyThisPattern": "When observing Graphs problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/reachable-nodes-in-subdivided-graph/",
    "leetcode_title": "Reachable Nodes In Subdivided Graph",
    "leetcode_id": 882,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/reachable-nodes-in-subdivided-graph/",
    "canonicalSlug": "reachable-nodes-in-subdivided-graph",
    "canonicalUrl": "https://leetcode.com/problems/reachable-nodes-in-subdivided-graph/",
    "url": "https://leetcode.com/problems/reachable-nodes-in-subdivided-graph/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Reachable Nodes In Subdivided Graph\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Reachable Nodes In Subdivided Graph\n};",
        "java": "// Java Solution for Reachable Nodes In Subdivided Graph\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Reachable Nodes In Subdivided Graph\n}",
        "python": "# Python Solution for Reachable Nodes In Subdivided Graph\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Reachable Nodes In Subdivided Graph\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Reachable Nodes In Subdivided Graph\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Reachable Nodes In Subdivided Graph\n};",
        "java": "// Optimal Java Solution for Reachable Nodes In Subdivided Graph\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Reachable Nodes In Subdivided Graph\n}",
        "python": "# Optimal Python Solution for Reachable Nodes In Subdivided Graph\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Reachable Nodes In Subdivided Graph\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Reachable Nodes In Subdivided Graph",
      "cpp_optimal": "// Solution for Reachable Nodes In Subdivided Graph",
      "java_brute": "// Solution for Reachable Nodes In Subdivided Graph",
      "java_optimal": "// Solution for Reachable Nodes In Subdivided Graph",
      "python_brute": "# Solution for Reachable Nodes In Subdivided Graph",
      "python_optimal": "# Solution for Reachable Nodes In Subdivided Graph"
    },
    "originalOrder": 887,
    "learningOrder": 887
  },
  {
    "id": 638,
    "number": 638,
    "sequence_number": 638,
    "title": "Last Substring in Lexicographical Order",
    "slug": "last-substring-in-lexicographical-order",
    "difficulty": "Hard",
    "topic": "Graphs",
    "subtopic": "Graphs Optimization",
    "pattern": "Graphs Pattern",
    "secondary_patterns": [
      "Graphs Pattern"
    ],
    "stage": "Advanced Graphs & Topological Sort",
    "curriculumStage": "Stage 13 — Advanced Graphs & Topological Sort",
    "roadmapPhase": "Stage 13 — Advanced Graphs & Topological Sort",
    "phase": "Stage 13 — Advanced Graphs & Topological Sort",
    "estimatedTime": 45,
    "statement": "Solve the **Last Substring in Lexicographical Order** problem using standard Graphs techniques. Given input constraints appropriate for Hard level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Graphs algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Graphs properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Graphs techniques by solving Hard problem constraints for Last Substring in Lexicographical Order.",
    "whyThisPattern": "When observing Graphs problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/last-substring-in-lexicographical-order/",
    "leetcode_title": "Last Substring in Lexicographical Order",
    "leetcode_id": 1163,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/last-substring-in-lexicographical-order/",
    "canonicalSlug": "last-substring-in-lexicographical-order",
    "canonicalUrl": "https://leetcode.com/problems/last-substring-in-lexicographical-order/",
    "url": "https://leetcode.com/problems/last-substring-in-lexicographical-order/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Last Substring in Lexicographical Order\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Last Substring in Lexicographical Order\n};",
        "java": "// Java Solution for Last Substring in Lexicographical Order\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Last Substring in Lexicographical Order\n}",
        "python": "# Python Solution for Last Substring in Lexicographical Order\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Last Substring in Lexicographical Order\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Last Substring in Lexicographical Order\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Last Substring in Lexicographical Order\n};",
        "java": "// Optimal Java Solution for Last Substring in Lexicographical Order\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Last Substring in Lexicographical Order\n}",
        "python": "# Optimal Python Solution for Last Substring in Lexicographical Order\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Last Substring in Lexicographical Order\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Last Substring in Lexicographical Order",
      "cpp_optimal": "// Solution for Last Substring in Lexicographical Order",
      "java_brute": "// Solution for Last Substring in Lexicographical Order",
      "java_optimal": "// Solution for Last Substring in Lexicographical Order",
      "python_brute": "# Solution for Last Substring in Lexicographical Order",
      "python_optimal": "# Solution for Last Substring in Lexicographical Order"
    },
    "originalOrder": 888,
    "learningOrder": 888
  },
  {
    "id": 639,
    "number": 639,
    "sequence_number": 639,
    "title": "Critical Connections in a Network",
    "slug": "critical-connections-in-a-network",
    "difficulty": "Hard",
    "topic": "Graphs",
    "subtopic": "Graphs Optimization",
    "pattern": "Graphs Pattern",
    "secondary_patterns": [
      "Graphs Pattern"
    ],
    "stage": "Advanced Graphs & Topological Sort",
    "curriculumStage": "Stage 13 — Advanced Graphs & Topological Sort",
    "roadmapPhase": "Stage 13 — Advanced Graphs & Topological Sort",
    "phase": "Stage 13 — Advanced Graphs & Topological Sort",
    "estimatedTime": 45,
    "statement": "Solve the **Critical Connections in a Network** problem using standard Graphs techniques. Given input constraints appropriate for Hard level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Graphs algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Graphs properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Graphs techniques by solving Hard problem constraints for Critical Connections in a Network.",
    "whyThisPattern": "When observing Graphs problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/critical-connections-in-a-network/",
    "leetcode_title": "Critical Connections in a Network",
    "leetcode_id": 1192,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/critical-connections-in-a-network/",
    "canonicalSlug": "critical-connections-in-a-network",
    "canonicalUrl": "https://leetcode.com/problems/critical-connections-in-a-network/",
    "url": "https://leetcode.com/problems/critical-connections-in-a-network/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Critical Connections in a Network\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Critical Connections in a Network\n};",
        "java": "// Java Solution for Critical Connections in a Network\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Critical Connections in a Network\n}",
        "python": "# Python Solution for Critical Connections in a Network\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Critical Connections in a Network\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Critical Connections in a Network\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Critical Connections in a Network\n};",
        "java": "// Optimal Java Solution for Critical Connections in a Network\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Critical Connections in a Network\n}",
        "python": "# Optimal Python Solution for Critical Connections in a Network\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Critical Connections in a Network\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Critical Connections in a Network",
      "cpp_optimal": "// Solution for Critical Connections in a Network",
      "java_brute": "// Solution for Critical Connections in a Network",
      "java_optimal": "// Solution for Critical Connections in a Network",
      "python_brute": "# Solution for Critical Connections in a Network",
      "python_optimal": "# Solution for Critical Connections in a Network"
    },
    "originalOrder": 889,
    "learningOrder": 889
  },
  {
    "id": 640,
    "number": 640,
    "sequence_number": 640,
    "title": "Graph Connectivity With Threshold",
    "slug": "graph-connectivity-with-threshold",
    "difficulty": "Hard",
    "topic": "Graphs",
    "subtopic": "Graphs Optimization",
    "pattern": "Graphs Pattern",
    "secondary_patterns": [
      "Graphs Pattern"
    ],
    "stage": "Advanced Graphs & Topological Sort",
    "curriculumStage": "Stage 13 — Advanced Graphs & Topological Sort",
    "roadmapPhase": "Stage 13 — Advanced Graphs & Topological Sort",
    "phase": "Stage 13 — Advanced Graphs & Topological Sort",
    "estimatedTime": 45,
    "statement": "Solve the **Graph Connectivity With Threshold** problem using standard Graphs techniques. Given input constraints appropriate for Hard level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Graphs algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Graphs properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Graphs techniques by solving Hard problem constraints for Graph Connectivity With Threshold.",
    "whyThisPattern": "When observing Graphs problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/graph-connectivity-with-threshold/",
    "leetcode_title": "Graph Connectivity With Threshold",
    "leetcode_id": 1627,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/graph-connectivity-with-threshold/",
    "canonicalSlug": "graph-connectivity-with-threshold",
    "canonicalUrl": "https://leetcode.com/problems/graph-connectivity-with-threshold/",
    "url": "https://leetcode.com/problems/graph-connectivity-with-threshold/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Graph Connectivity With Threshold\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Graph Connectivity With Threshold\n};",
        "java": "// Java Solution for Graph Connectivity With Threshold\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Graph Connectivity With Threshold\n}",
        "python": "# Python Solution for Graph Connectivity With Threshold\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Graph Connectivity With Threshold\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Graph Connectivity With Threshold\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Graph Connectivity With Threshold\n};",
        "java": "// Optimal Java Solution for Graph Connectivity With Threshold\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Graph Connectivity With Threshold\n}",
        "python": "# Optimal Python Solution for Graph Connectivity With Threshold\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Graph Connectivity With Threshold\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Graph Connectivity With Threshold",
      "cpp_optimal": "// Solution for Graph Connectivity With Threshold",
      "java_brute": "// Solution for Graph Connectivity With Threshold",
      "java_optimal": "// Solution for Graph Connectivity With Threshold",
      "python_brute": "# Solution for Graph Connectivity With Threshold",
      "python_optimal": "# Solution for Graph Connectivity With Threshold"
    },
    "originalOrder": 890,
    "learningOrder": 890
  },
  {
    "id": 641,
    "number": 641,
    "sequence_number": 641,
    "title": "Minimum Degree of a Connected Trio in a Graph",
    "slug": "minimum-degree-of-a-connected-trio-in-a-graph",
    "difficulty": "Hard",
    "topic": "Graphs",
    "subtopic": "Graphs Optimization",
    "pattern": "Graphs Pattern",
    "secondary_patterns": [
      "Graphs Pattern"
    ],
    "stage": "Advanced Graphs & Topological Sort",
    "curriculumStage": "Stage 13 — Advanced Graphs & Topological Sort",
    "roadmapPhase": "Stage 13 — Advanced Graphs & Topological Sort",
    "phase": "Stage 13 — Advanced Graphs & Topological Sort",
    "estimatedTime": 45,
    "statement": "Solve the **Minimum Degree of a Connected Trio in a Graph** problem using standard Graphs techniques. Given input constraints appropriate for Hard level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Graphs algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Graphs properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Graphs techniques by solving Hard problem constraints for Minimum Degree of a Connected Trio in a Graph.",
    "whyThisPattern": "When observing Graphs problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/minimum-degree-of-a-connected-trio-in-a-graph/",
    "leetcode_title": "Minimum Degree of a Connected Trio in a Graph",
    "leetcode_id": 1761,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/minimum-degree-of-a-connected-trio-in-a-graph/",
    "canonicalSlug": "minimum-degree-of-a-connected-trio-in-a-graph",
    "canonicalUrl": "https://leetcode.com/problems/minimum-degree-of-a-connected-trio-in-a-graph/",
    "url": "https://leetcode.com/problems/minimum-degree-of-a-connected-trio-in-a-graph/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Minimum Degree of a Connected Trio in a Graph\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Minimum Degree of a Connected Trio in a Graph\n};",
        "java": "// Java Solution for Minimum Degree of a Connected Trio in a Graph\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Minimum Degree of a Connected Trio in a Graph\n}",
        "python": "# Python Solution for Minimum Degree of a Connected Trio in a Graph\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Minimum Degree of a Connected Trio in a Graph\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Minimum Degree of a Connected Trio in a Graph\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Minimum Degree of a Connected Trio in a Graph\n};",
        "java": "// Optimal Java Solution for Minimum Degree of a Connected Trio in a Graph\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Minimum Degree of a Connected Trio in a Graph\n}",
        "python": "# Optimal Python Solution for Minimum Degree of a Connected Trio in a Graph\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Minimum Degree of a Connected Trio in a Graph\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Minimum Degree of a Connected Trio in a Graph",
      "cpp_optimal": "// Solution for Minimum Degree of a Connected Trio in a Graph",
      "java_brute": "// Solution for Minimum Degree of a Connected Trio in a Graph",
      "java_optimal": "// Solution for Minimum Degree of a Connected Trio in a Graph",
      "python_brute": "# Solution for Minimum Degree of a Connected Trio in a Graph",
      "python_optimal": "# Solution for Minimum Degree of a Connected Trio in a Graph"
    },
    "originalOrder": 891,
    "learningOrder": 891
  },
  {
    "id": 642,
    "number": 642,
    "sequence_number": 642,
    "title": "Largest Color Value in a Directed Graph",
    "slug": "largest-color-value-in-a-directed-graph",
    "difficulty": "Hard",
    "topic": "Graphs",
    "subtopic": "Graphs Optimization",
    "pattern": "Graphs Pattern",
    "secondary_patterns": [
      "Graphs Pattern"
    ],
    "stage": "Advanced Graphs & Topological Sort",
    "curriculumStage": "Stage 13 — Advanced Graphs & Topological Sort",
    "roadmapPhase": "Stage 13 — Advanced Graphs & Topological Sort",
    "phase": "Stage 13 — Advanced Graphs & Topological Sort",
    "estimatedTime": 45,
    "statement": "Solve the **Largest Color Value in a Directed Graph** problem using standard Graphs techniques. Given input constraints appropriate for Hard level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Graphs algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Graphs properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Graphs techniques by solving Hard problem constraints for Largest Color Value in a Directed Graph.",
    "whyThisPattern": "When observing Graphs problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/largest-color-value-in-a-directed-graph/",
    "leetcode_title": "Largest Color Value in a Directed Graph",
    "leetcode_id": 1857,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/largest-color-value-in-a-directed-graph/",
    "canonicalSlug": "largest-color-value-in-a-directed-graph",
    "canonicalUrl": "https://leetcode.com/problems/largest-color-value-in-a-directed-graph/",
    "url": "https://leetcode.com/problems/largest-color-value-in-a-directed-graph/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Largest Color Value in a Directed Graph\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Largest Color Value in a Directed Graph\n};",
        "java": "// Java Solution for Largest Color Value in a Directed Graph\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Largest Color Value in a Directed Graph\n}",
        "python": "# Python Solution for Largest Color Value in a Directed Graph\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Largest Color Value in a Directed Graph\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Largest Color Value in a Directed Graph\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Largest Color Value in a Directed Graph\n};",
        "java": "// Optimal Java Solution for Largest Color Value in a Directed Graph\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Largest Color Value in a Directed Graph\n}",
        "python": "# Optimal Python Solution for Largest Color Value in a Directed Graph\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Largest Color Value in a Directed Graph\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Largest Color Value in a Directed Graph",
      "cpp_optimal": "// Solution for Largest Color Value in a Directed Graph",
      "java_brute": "// Solution for Largest Color Value in a Directed Graph",
      "java_optimal": "// Solution for Largest Color Value in a Directed Graph",
      "python_brute": "# Solution for Largest Color Value in a Directed Graph",
      "python_optimal": "# Solution for Largest Color Value in a Directed Graph"
    },
    "originalOrder": 892,
    "learningOrder": 892
  },
  {
    "id": 643,
    "number": 643,
    "sequence_number": 643,
    "title": "Find Longest Awesome Substring",
    "slug": "find-longest-awesome-substring",
    "difficulty": "Hard",
    "topic": "Bit Manipulation",
    "subtopic": "Bit Manipulation Optimization",
    "pattern": "Prefix Bitmask Parity Map",
    "secondary_patterns": [
      "Prefix Bitmask Parity Map"
    ],
    "stage": "Advanced Graphs & Topological Sort",
    "curriculumStage": "Stage 13 — Advanced Graphs & Topological Sort",
    "roadmapPhase": "Stage 13 — Advanced Graphs & Topological Sort",
    "phase": "Stage 13 — Advanced Graphs & Topological Sort",
    "estimatedTime": 45,
    "statement": "Given the constraints and input parameters for Find Longest Awesome Substring, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Find Longest Awesome Substring."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Find Longest Awesome Substring.",
      "Leverage the optimal Bit Manipulation pattern to reduce time complexity."
    ],
    "learningObjective": "Master Bit Manipulation techniques by solving Hard problem constraints for Find Longest Awesome Substring.",
    "whyThisPattern": "When observing Bit Manipulation problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/find-longest-awesome-substring/",
    "leetcode_title": "Find Longest Awesome Substring",
    "leetcode_id": 1542,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/find-longest-awesome-substring/",
    "canonicalSlug": "find-longest-awesome-substring",
    "canonicalUrl": "https://leetcode.com/problems/find-longest-awesome-substring/",
    "url": "https://leetcode.com/problems/find-longest-awesome-substring/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Find Longest Awesome Substring\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Find Longest Awesome Substring\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Find Longest Awesome Substring\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Find Longest Awesome Substring\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Find Longest Awesome Substring\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Find Longest Awesome Substring\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Find Longest Awesome Substring\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Find Longest Awesome Substring\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Find Longest Awesome Substring",
      "cpp_optimal": "// Solution for Find Longest Awesome Substring",
      "java_brute": "// Solution for Find Longest Awesome Substring",
      "java_optimal": "// Solution for Find Longest Awesome Substring",
      "python_brute": "# Solution for Find Longest Awesome Substring",
      "python_optimal": "# Solution for Find Longest Awesome Substring"
    },
    "originalOrder": 798,
    "learningOrder": 798
  },
  {
    "id": 644,
    "number": 644,
    "sequence_number": 644,
    "title": "Number of Valid Words for Each Puzzle",
    "slug": "number-of-valid-words-for-each-puzzle",
    "difficulty": "Hard",
    "topic": "Bit Manipulation",
    "subtopic": "Bit Manipulation Optimization",
    "pattern": "Submask Iteration Bitmask",
    "secondary_patterns": [
      "Submask Iteration Bitmask"
    ],
    "stage": "Advanced Graphs & Topological Sort",
    "curriculumStage": "Stage 13 — Advanced Graphs & Topological Sort",
    "roadmapPhase": "Stage 13 — Advanced Graphs & Topological Sort",
    "phase": "Stage 13 — Advanced Graphs & Topological Sort",
    "estimatedTime": 45,
    "statement": "Given the constraints and input parameters for Number of Valid Words for Each Puzzle, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Number of Valid Words for Each Puzzle."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Number of Valid Words for Each Puzzle.",
      "Leverage the optimal Bit Manipulation pattern to reduce time complexity."
    ],
    "learningObjective": "Master Bit Manipulation techniques by solving Hard problem constraints for Number of Valid Words for Each Puzzle.",
    "whyThisPattern": "When observing Bit Manipulation problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/number-of-valid-words-for-each-puzzle/",
    "leetcode_title": "Number of Valid Words for Each Puzzle",
    "leetcode_id": 1178,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/number-of-valid-words-for-each-puzzle/",
    "canonicalSlug": "number-of-valid-words-for-each-puzzle",
    "canonicalUrl": "https://leetcode.com/problems/number-of-valid-words-for-each-puzzle/",
    "url": "https://leetcode.com/problems/number-of-valid-words-for-each-puzzle/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Number of Valid Words for Each Puzzle\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Number of Valid Words for Each Puzzle\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Number of Valid Words for Each Puzzle\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Number of Valid Words for Each Puzzle\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Number of Valid Words for Each Puzzle\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Number of Valid Words for Each Puzzle\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Number of Valid Words for Each Puzzle\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Number of Valid Words for Each Puzzle\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Number of Valid Words for Each Puzzle",
      "cpp_optimal": "// Solution for Number of Valid Words for Each Puzzle",
      "java_brute": "// Solution for Number of Valid Words for Each Puzzle",
      "java_optimal": "// Solution for Number of Valid Words for Each Puzzle",
      "python_brute": "# Solution for Number of Valid Words for Each Puzzle",
      "python_optimal": "# Solution for Number of Valid Words for Each Puzzle"
    },
    "originalOrder": 799,
    "learningOrder": 799
  },
  {
    "id": 645,
    "number": 645,
    "sequence_number": 645,
    "title": "Count Subtrees With Max Distance Between Cities",
    "slug": "count-subtrees-with-max-distance-between-cities",
    "difficulty": "Hard",
    "topic": "Bit Manipulation",
    "subtopic": "Bit Manipulation Optimization",
    "pattern": "Bitmask Tree Diameter BFS",
    "secondary_patterns": [
      "Bitmask Tree Diameter BFS"
    ],
    "stage": "Advanced Graphs & Topological Sort",
    "curriculumStage": "Stage 13 — Advanced Graphs & Topological Sort",
    "roadmapPhase": "Stage 13 — Advanced Graphs & Topological Sort",
    "phase": "Stage 13 — Advanced Graphs & Topological Sort",
    "estimatedTime": 45,
    "statement": "Given the constraints and input parameters for Count Subtrees With Max Distance Between Cities, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Count Subtrees With Max Distance Between Cities."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Count Subtrees With Max Distance Between Cities.",
      "Leverage the optimal Bit Manipulation pattern to reduce time complexity."
    ],
    "learningObjective": "Master Bit Manipulation techniques by solving Hard problem constraints for Count Subtrees With Max Distance Between Cities.",
    "whyThisPattern": "When observing Bit Manipulation problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/count-subtrees-with-max-distance-between-cities/",
    "leetcode_title": "Count Subtrees With Max Distance Between Cities",
    "leetcode_id": 1617,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/count-subtrees-with-max-distance-between-cities/",
    "canonicalSlug": "count-subtrees-with-max-distance-between-cities",
    "canonicalUrl": "https://leetcode.com/problems/count-subtrees-with-max-distance-between-cities/",
    "url": "https://leetcode.com/problems/count-subtrees-with-max-distance-between-cities/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Count Subtrees With Max Distance Between Cities\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Count Subtrees With Max Distance Between Cities\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Count Subtrees With Max Distance Between Cities\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Count Subtrees With Max Distance Between Cities\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Count Subtrees With Max Distance Between Cities\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Count Subtrees With Max Distance Between Cities\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Count Subtrees With Max Distance Between Cities\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Count Subtrees With Max Distance Between Cities\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Count Subtrees With Max Distance Between Cities",
      "cpp_optimal": "// Solution for Count Subtrees With Max Distance Between Cities",
      "java_brute": "// Solution for Count Subtrees With Max Distance Between Cities",
      "java_optimal": "// Solution for Count Subtrees With Max Distance Between Cities",
      "python_brute": "# Solution for Count Subtrees With Max Distance Between Cities",
      "python_optimal": "# Solution for Count Subtrees With Max Distance Between Cities"
    },
    "originalOrder": 800,
    "learningOrder": 800
  },
  {
    "id": 646,
    "number": 646,
    "sequence_number": 646,
    "title": "Minimum One Bit Operations to Make Integers Zero",
    "slug": "minimum-one-bit-operations-to-make-integers-zero",
    "difficulty": "Hard",
    "topic": "Bit Manipulation",
    "subtopic": "Bit Manipulation Optimization",
    "pattern": "Gray Code Reversal",
    "secondary_patterns": [
      "Gray Code Reversal"
    ],
    "stage": "Advanced Graphs & Topological Sort",
    "curriculumStage": "Stage 13 — Advanced Graphs & Topological Sort",
    "roadmapPhase": "Stage 13 — Advanced Graphs & Topological Sort",
    "phase": "Stage 13 — Advanced Graphs & Topological Sort",
    "estimatedTime": 45,
    "statement": "Given the constraints and input parameters for Minimum One Bit Operations to Make Integers Zero, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Minimum One Bit Operations to Make Integers Zero."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Minimum One Bit Operations to Make Integers Zero.",
      "Leverage the optimal Bit Manipulation pattern to reduce time complexity."
    ],
    "learningObjective": "Master Bit Manipulation techniques by solving Hard problem constraints for Minimum One Bit Operations to Make Integers Zero.",
    "whyThisPattern": "When observing Bit Manipulation problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/minimum-one-bit-operations-to-make-integers-zero/",
    "leetcode_title": "Minimum One Bit Operations to Make Integers Zero",
    "leetcode_id": 1611,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/minimum-one-bit-operations-to-make-integers-zero/",
    "canonicalSlug": "minimum-one-bit-operations-to-make-integers-zero",
    "canonicalUrl": "https://leetcode.com/problems/minimum-one-bit-operations-to-make-integers-zero/",
    "url": "https://leetcode.com/problems/minimum-one-bit-operations-to-make-integers-zero/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Minimum One Bit Operations to Make Integers Zero\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Minimum One Bit Operations to Make Integers Zero\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Minimum One Bit Operations to Make Integers Zero\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Minimum One Bit Operations to Make Integers Zero\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Minimum One Bit Operations to Make Integers Zero\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Minimum One Bit Operations to Make Integers Zero\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Minimum One Bit Operations to Make Integers Zero\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Minimum One Bit Operations to Make Integers Zero\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Minimum One Bit Operations to Make Integers Zero",
      "cpp_optimal": "// Solution for Minimum One Bit Operations to Make Integers Zero",
      "java_brute": "// Solution for Minimum One Bit Operations to Make Integers Zero",
      "java_optimal": "// Solution for Minimum One Bit Operations to Make Integers Zero",
      "python_brute": "# Solution for Minimum One Bit Operations to Make Integers Zero",
      "python_optimal": "# Solution for Minimum One Bit Operations to Make Integers Zero"
    },
    "originalOrder": 801,
    "learningOrder": 801
  },
  {
    "id": 647,
    "number": 647,
    "sequence_number": 647,
    "title": "Chalkboard XOR Game",
    "slug": "chalkboard-xor-game",
    "difficulty": "Hard",
    "topic": "Bit Manipulation",
    "subtopic": "Bit Manipulation Optimization",
    "pattern": "XOR Parity Win Condition",
    "secondary_patterns": [
      "XOR Parity Win Condition"
    ],
    "stage": "Advanced Graphs & Topological Sort",
    "curriculumStage": "Stage 13 — Advanced Graphs & Topological Sort",
    "roadmapPhase": "Stage 13 — Advanced Graphs & Topological Sort",
    "phase": "Stage 13 — Advanced Graphs & Topological Sort",
    "estimatedTime": 45,
    "statement": "Given the constraints and input parameters for Chalkboard XOR Game, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Chalkboard XOR Game."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Chalkboard XOR Game.",
      "Leverage the optimal Bit Manipulation pattern to reduce time complexity."
    ],
    "learningObjective": "Master Bit Manipulation techniques by solving Hard problem constraints for Chalkboard XOR Game.",
    "whyThisPattern": "When observing Bit Manipulation problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/chalkboard-xor-game/",
    "leetcode_title": "Chalkboard XOR Game",
    "leetcode_id": 810,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/chalkboard-xor-game/",
    "canonicalSlug": "chalkboard-xor-game",
    "canonicalUrl": "https://leetcode.com/problems/chalkboard-xor-game/",
    "url": "https://leetcode.com/problems/chalkboard-xor-game/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Chalkboard XOR Game\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Chalkboard XOR Game\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Chalkboard XOR Game\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Chalkboard XOR Game\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Chalkboard XOR Game\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Chalkboard XOR Game\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Chalkboard XOR Game\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Chalkboard XOR Game\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Chalkboard XOR Game",
      "cpp_optimal": "// Solution for Chalkboard XOR Game",
      "java_brute": "// Solution for Chalkboard XOR Game",
      "java_optimal": "// Solution for Chalkboard XOR Game",
      "python_brute": "# Solution for Chalkboard XOR Game",
      "python_optimal": "# Solution for Chalkboard XOR Game"
    },
    "originalOrder": 802,
    "learningOrder": 802
  },
  {
    "id": 648,
    "number": 648,
    "sequence_number": 648,
    "title": "Super Egg Drop",
    "slug": "super-egg-drop",
    "difficulty": "Hard",
    "topic": "Dynamic Programming",
    "subtopic": "Dynamic Programming Optimization",
    "pattern": "Binary Search DP State",
    "secondary_patterns": [
      "Binary Search DP State"
    ],
    "stage": "Advanced Graphs & Topological Sort",
    "curriculumStage": "Stage 13 — Advanced Graphs & Topological Sort",
    "roadmapPhase": "Stage 13 — Advanced Graphs & Topological Sort",
    "phase": "Stage 13 — Advanced Graphs & Topological Sort",
    "estimatedTime": 45,
    "statement": "Given the constraints and input parameters for Super Egg Drop, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Super Egg Drop."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Super Egg Drop.",
      "Leverage the optimal Dynamic Programming pattern to reduce time complexity."
    ],
    "learningObjective": "Master Dynamic Programming techniques by solving Hard problem constraints for Super Egg Drop.",
    "whyThisPattern": "When observing Dynamic Programming problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/super-egg-drop/",
    "leetcode_title": "Super Egg Drop",
    "leetcode_id": 887,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/super-egg-drop/",
    "canonicalSlug": "super-egg-drop",
    "canonicalUrl": "https://leetcode.com/problems/super-egg-drop/",
    "url": "https://leetcode.com/problems/super-egg-drop/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Super Egg Drop\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Super Egg Drop\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Super Egg Drop\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Super Egg Drop\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Super Egg Drop\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Super Egg Drop\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Super Egg Drop\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Super Egg Drop\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Super Egg Drop",
      "cpp_optimal": "// Solution for Super Egg Drop",
      "java_brute": "// Solution for Super Egg Drop",
      "java_optimal": "// Solution for Super Egg Drop",
      "python_brute": "# Solution for Super Egg Drop",
      "python_optimal": "# Solution for Super Egg Drop"
    },
    "originalOrder": 806,
    "learningOrder": 806
  },
  {
    "id": 649,
    "number": 649,
    "sequence_number": 649,
    "title": "Cat and Mouse",
    "slug": "cat-and-mouse",
    "difficulty": "Hard",
    "topic": "Dynamic Programming",
    "subtopic": "Dynamic Programming Optimization",
    "pattern": "Minimax Game Graph State",
    "secondary_patterns": [
      "Minimax Game Graph State"
    ],
    "stage": "Advanced Graphs & Topological Sort",
    "curriculumStage": "Stage 13 — Advanced Graphs & Topological Sort",
    "roadmapPhase": "Stage 13 — Advanced Graphs & Topological Sort",
    "phase": "Stage 13 — Advanced Graphs & Topological Sort",
    "estimatedTime": 45,
    "statement": "Given the constraints and input parameters for Cat and Mouse, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Cat and Mouse."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Cat and Mouse.",
      "Leverage the optimal Dynamic Programming pattern to reduce time complexity."
    ],
    "learningObjective": "Master Dynamic Programming techniques by solving Hard problem constraints for Cat and Mouse.",
    "whyThisPattern": "When observing Dynamic Programming problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/cat-and-mouse/",
    "leetcode_title": "Cat and Mouse",
    "leetcode_id": 913,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/cat-and-mouse/",
    "canonicalSlug": "cat-and-mouse",
    "canonicalUrl": "https://leetcode.com/problems/cat-and-mouse/",
    "url": "https://leetcode.com/problems/cat-and-mouse/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Cat and Mouse\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Cat and Mouse\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Cat and Mouse\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Cat and Mouse\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Cat and Mouse\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Cat and Mouse\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Cat and Mouse\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Cat and Mouse\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Cat and Mouse",
      "cpp_optimal": "// Solution for Cat and Mouse",
      "java_brute": "// Solution for Cat and Mouse",
      "java_optimal": "// Solution for Cat and Mouse",
      "python_brute": "# Solution for Cat and Mouse",
      "python_optimal": "# Solution for Cat and Mouse"
    },
    "originalOrder": 807,
    "learningOrder": 807
  },
  {
    "id": 650,
    "number": 650,
    "sequence_number": 650,
    "title": "Tallest Billboard",
    "slug": "tallest-billboard",
    "difficulty": "Hard",
    "topic": "Dynamic Programming",
    "subtopic": "Dynamic Programming Optimization",
    "pattern": "Diff Map State DP",
    "secondary_patterns": [
      "Diff Map State DP"
    ],
    "stage": "Advanced Graphs & Topological Sort",
    "curriculumStage": "Stage 13 — Advanced Graphs & Topological Sort",
    "roadmapPhase": "Stage 13 — Advanced Graphs & Topological Sort",
    "phase": "Stage 13 — Advanced Graphs & Topological Sort",
    "estimatedTime": 45,
    "statement": "Given the constraints and input parameters for Tallest Billboard, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Tallest Billboard."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Tallest Billboard.",
      "Leverage the optimal Dynamic Programming pattern to reduce time complexity."
    ],
    "learningObjective": "Master Dynamic Programming techniques by solving Hard problem constraints for Tallest Billboard.",
    "whyThisPattern": "When observing Dynamic Programming problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/tallest-billboard/",
    "leetcode_title": "Tallest Billboard",
    "leetcode_id": 956,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/tallest-billboard/",
    "canonicalSlug": "tallest-billboard",
    "canonicalUrl": "https://leetcode.com/problems/tallest-billboard/",
    "url": "https://leetcode.com/problems/tallest-billboard/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Tallest Billboard\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Tallest Billboard\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Tallest Billboard\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Tallest Billboard\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Tallest Billboard\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Tallest Billboard\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Tallest Billboard\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Tallest Billboard\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Tallest Billboard",
      "cpp_optimal": "// Solution for Tallest Billboard",
      "java_brute": "// Solution for Tallest Billboard",
      "java_optimal": "// Solution for Tallest Billboard",
      "python_brute": "# Solution for Tallest Billboard",
      "python_optimal": "# Solution for Tallest Billboard"
    },
    "originalOrder": 808,
    "learningOrder": 808
  },
  {
    "id": 651,
    "number": 651,
    "sequence_number": 651,
    "title": "Invert Binary Tree",
    "slug": "invert-binary-tree",
    "difficulty": "Easy",
    "topic": "Trees",
    "subtopic": "Tree Traversal & Recursion",
    "pattern": "Tree Traversal & Recursion",
    "secondary_patterns": [
      "Tree Traversal & Recursion"
    ],
    "stage": "Disjoint Set Union (DSU)",
    "curriculumStage": "Stage 14 — Disjoint Set Union (DSU)",
    "roadmapPhase": "Stage 14 — Disjoint Set Union (DSU)",
    "phase": "Stage 14 — Disjoint Set Union (DSU)",
    "estimatedTime": 15,
    "statement": "Solve the **Invert Binary Tree Optimization** problem using the **Tree Traversal & Recursion** technique. Given input constraints appropriate for Easy level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^4",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Tree Traversal & Recursion identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Tree Traversal & Recursion. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Tree Traversal & Recursion techniques by solving Easy problem constraints for Invert Binary Tree Optimization.",
    "whyThisPattern": "When observing binary trees problem conditions, Tree Traversal & Recursion optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta"
    ],
    "companyRelevanceTier": "Medium",
    "leetcode_url": "https://leetcode.com/problems/invert-binary-tree/",
    "leetcode_title": "Invert Binary Tree",
    "leetcode_id": 226,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/invert-binary-tree/",
    "canonicalSlug": "invert-binary-tree",
    "canonicalUrl": "https://leetcode.com/problems/invert-binary-tree/",
    "url": "https://leetcode.com/problems/invert-binary-tree/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Invert Binary Tree Optimization (Tree Traversal & Recursion)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Invert Binary Tree Optimization (Tree Traversal & Recursion)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Invert Binary Tree Optimization (Tree Traversal & Recursion)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Invert Binary Tree Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Invert Binary Tree Optimization (Tree Traversal & Recursion)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Invert Binary Tree Optimization (Tree Traversal & Recursion)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Invert Binary Tree Optimization (Tree Traversal & Recursion)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Invert Binary Tree Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Invert Binary Tree",
      "cpp_optimal": "// Solution for Invert Binary Tree",
      "java_brute": "// Solution for Invert Binary Tree",
      "java_optimal": "// Solution for Invert Binary Tree",
      "python_brute": "# Solution for Invert Binary Tree",
      "python_optimal": "# Solution for Invert Binary Tree"
    },
    "originalOrder": 235,
    "learningOrder": 235
  },
  {
    "id": 652,
    "number": 652,
    "sequence_number": 652,
    "title": "Binary Tree Paths",
    "slug": "binary-tree-paths",
    "difficulty": "Easy",
    "topic": "Trees",
    "subtopic": "Tree Traversal & Recursion",
    "pattern": "Tree Traversal & Recursion",
    "secondary_patterns": [
      "Tree Traversal & Recursion"
    ],
    "stage": "Disjoint Set Union (DSU)",
    "curriculumStage": "Stage 14 — Disjoint Set Union (DSU)",
    "roadmapPhase": "Stage 14 — Disjoint Set Union (DSU)",
    "phase": "Stage 14 — Disjoint Set Union (DSU)",
    "estimatedTime": 15,
    "statement": "Solve the **Binary Tree Paths Optimization** problem using the **Tree Traversal & Recursion** technique. Given input constraints appropriate for Easy level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^4",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Tree Traversal & Recursion identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Tree Traversal & Recursion. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Tree Traversal & Recursion techniques by solving Easy problem constraints for Binary Tree Paths Optimization.",
    "whyThisPattern": "When observing binary trees problem conditions, Tree Traversal & Recursion optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Meta",
      "Apple",
      "Netflix"
    ],
    "companyRelevanceTier": "Medium",
    "leetcode_url": "https://leetcode.com/problems/binary-tree-paths/",
    "leetcode_title": "Binary Tree Paths",
    "leetcode_id": 257,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/binary-tree-paths/",
    "canonicalSlug": "binary-tree-paths",
    "canonicalUrl": "https://leetcode.com/problems/binary-tree-paths/",
    "url": "https://leetcode.com/problems/binary-tree-paths/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Binary Tree Paths Optimization (Tree Traversal & Recursion)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Binary Tree Paths Optimization (Tree Traversal & Recursion)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Binary Tree Paths Optimization (Tree Traversal & Recursion)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Binary Tree Paths Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Binary Tree Paths Optimization (Tree Traversal & Recursion)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Binary Tree Paths Optimization (Tree Traversal & Recursion)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Binary Tree Paths Optimization (Tree Traversal & Recursion)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Binary Tree Paths Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Binary Tree Paths",
      "cpp_optimal": "// Solution for Binary Tree Paths",
      "java_brute": "// Solution for Binary Tree Paths",
      "java_optimal": "// Solution for Binary Tree Paths",
      "python_brute": "# Solution for Binary Tree Paths",
      "python_optimal": "# Solution for Binary Tree Paths"
    },
    "originalOrder": 236,
    "learningOrder": 236
  },
  {
    "id": 653,
    "number": 653,
    "sequence_number": 653,
    "title": "Diameter of Binary Tree",
    "slug": "diameter-of-binary-tree",
    "difficulty": "Easy",
    "topic": "Trees",
    "subtopic": "Tree Traversal & Recursion",
    "pattern": "Tree Traversal & Recursion",
    "secondary_patterns": [
      "Tree Traversal & Recursion"
    ],
    "stage": "Disjoint Set Union (DSU)",
    "curriculumStage": "Stage 14 — Disjoint Set Union (DSU)",
    "roadmapPhase": "Stage 14 — Disjoint Set Union (DSU)",
    "phase": "Stage 14 — Disjoint Set Union (DSU)",
    "estimatedTime": 15,
    "statement": "Solve the **Diameter of Binary Tree Challenge** problem using the **Tree Traversal & Recursion** technique. Given input constraints appropriate for Easy level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^4",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Tree Traversal & Recursion identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Tree Traversal & Recursion. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Tree Traversal & Recursion techniques by solving Easy problem constraints for Diameter of Binary Tree Challenge.",
    "whyThisPattern": "When observing binary trees problem conditions, Tree Traversal & Recursion optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Amazon",
      "Microsoft",
      "Uber"
    ],
    "companyRelevanceTier": "Medium",
    "leetcode_url": "https://leetcode.com/problems/diameter-of-binary-tree/",
    "leetcode_title": "Diameter of Binary Tree",
    "leetcode_id": 543,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/diameter-of-binary-tree/",
    "canonicalSlug": "diameter-of-binary-tree",
    "canonicalUrl": "https://leetcode.com/problems/diameter-of-binary-tree/",
    "url": "https://leetcode.com/problems/diameter-of-binary-tree/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Diameter of Binary Tree Challenge (Tree Traversal & Recursion)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Diameter of Binary Tree Challenge (Tree Traversal & Recursion)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Diameter of Binary Tree Challenge (Tree Traversal & Recursion)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Diameter of Binary Tree Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Diameter of Binary Tree Challenge (Tree Traversal & Recursion)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Diameter of Binary Tree Challenge (Tree Traversal & Recursion)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Diameter of Binary Tree Challenge (Tree Traversal & Recursion)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Diameter of Binary Tree Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Diameter of Binary Tree",
      "cpp_optimal": "// Solution for Diameter of Binary Tree",
      "java_brute": "// Solution for Diameter of Binary Tree",
      "java_optimal": "// Solution for Diameter of Binary Tree",
      "python_brute": "# Solution for Diameter of Binary Tree",
      "python_optimal": "# Solution for Diameter of Binary Tree"
    },
    "originalOrder": 237,
    "learningOrder": 237
  },
  {
    "id": 654,
    "number": 654,
    "sequence_number": 654,
    "title": "Maximum Depth of N-ary Tree",
    "slug": "maximum-depth-of-n-ary-tree",
    "difficulty": "Easy",
    "topic": "Trees",
    "subtopic": "Tree Traversal & Recursion",
    "pattern": "Tree Traversal & Recursion",
    "secondary_patterns": [
      "Tree Traversal & Recursion"
    ],
    "stage": "Disjoint Set Union (DSU)",
    "curriculumStage": "Stage 14 — Disjoint Set Union (DSU)",
    "roadmapPhase": "Stage 14 — Disjoint Set Union (DSU)",
    "phase": "Stage 14 — Disjoint Set Union (DSU)",
    "estimatedTime": 15,
    "statement": "Solve the **Maximum Depth of N-ary Tree Challenge** problem using the **Tree Traversal & Recursion** technique. Given input constraints appropriate for Easy level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^4",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Tree Traversal & Recursion identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Tree Traversal & Recursion. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Tree Traversal & Recursion techniques by solving Easy problem constraints for Maximum Depth of N-ary Tree Challenge.",
    "whyThisPattern": "When observing binary trees problem conditions, Tree Traversal & Recursion optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Meta",
      "Uber",
      "Databricks"
    ],
    "companyRelevanceTier": "Medium",
    "leetcode_url": "https://leetcode.com/problems/maximum-depth-of-n-ary-tree/",
    "leetcode_title": "Maximum Depth of N-ary Tree",
    "leetcode_id": 559,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/maximum-depth-of-n-ary-tree/",
    "canonicalSlug": "maximum-depth-of-n-ary-tree",
    "canonicalUrl": "https://leetcode.com/problems/maximum-depth-of-n-ary-tree/",
    "url": "https://leetcode.com/problems/maximum-depth-of-n-ary-tree/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Maximum Depth of N-ary Tree Challenge (Tree Traversal & Recursion)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Maximum Depth of N-ary Tree Challenge (Tree Traversal & Recursion)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Maximum Depth of N-ary Tree Challenge (Tree Traversal & Recursion)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Maximum Depth of N-ary Tree Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Maximum Depth of N-ary Tree Challenge (Tree Traversal & Recursion)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Maximum Depth of N-ary Tree Challenge (Tree Traversal & Recursion)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Maximum Depth of N-ary Tree Challenge (Tree Traversal & Recursion)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Maximum Depth of N-ary Tree Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Maximum Depth of N-ary Tree",
      "cpp_optimal": "// Solution for Maximum Depth of N-ary Tree",
      "java_brute": "// Solution for Maximum Depth of N-ary Tree",
      "java_optimal": "// Solution for Maximum Depth of N-ary Tree",
      "python_brute": "# Solution for Maximum Depth of N-ary Tree",
      "python_optimal": "# Solution for Maximum Depth of N-ary Tree"
    },
    "originalOrder": 238,
    "learningOrder": 238
  },
  {
    "id": 655,
    "number": 655,
    "sequence_number": 655,
    "title": "Binary Tree Tilt",
    "slug": "binary-tree-tilt",
    "difficulty": "Easy",
    "topic": "Trees",
    "subtopic": "Tree Traversal & Recursion",
    "pattern": "Tree Traversal & Recursion",
    "secondary_patterns": [
      "Tree Traversal & Recursion"
    ],
    "stage": "Disjoint Set Union (DSU)",
    "curriculumStage": "Stage 14 — Disjoint Set Union (DSU)",
    "roadmapPhase": "Stage 14 — Disjoint Set Union (DSU)",
    "phase": "Stage 14 — Disjoint Set Union (DSU)",
    "estimatedTime": 15,
    "statement": "Solve the **Binary Tree Tilt Challenge** problem using the **Tree Traversal & Recursion** technique. Given input constraints appropriate for Easy level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^4",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Tree Traversal & Recursion identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Tree Traversal & Recursion. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Tree Traversal & Recursion techniques by solving Easy problem constraints for Binary Tree Tilt Challenge.",
    "whyThisPattern": "When observing binary trees problem conditions, Tree Traversal & Recursion optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Microsoft",
      "Bloomberg",
      "Adobe"
    ],
    "companyRelevanceTier": "Medium",
    "leetcode_url": "https://leetcode.com/problems/binary-tree-tilt/",
    "leetcode_title": "Binary Tree Tilt",
    "leetcode_id": 563,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/binary-tree-tilt/",
    "canonicalSlug": "binary-tree-tilt",
    "canonicalUrl": "https://leetcode.com/problems/binary-tree-tilt/",
    "url": "https://leetcode.com/problems/binary-tree-tilt/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Binary Tree Tilt Challenge (Tree Traversal & Recursion)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Binary Tree Tilt Challenge (Tree Traversal & Recursion)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Binary Tree Tilt Challenge (Tree Traversal & Recursion)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Binary Tree Tilt Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Binary Tree Tilt Challenge (Tree Traversal & Recursion)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Binary Tree Tilt Challenge (Tree Traversal & Recursion)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Binary Tree Tilt Challenge (Tree Traversal & Recursion)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Binary Tree Tilt Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Binary Tree Tilt",
      "cpp_optimal": "// Solution for Binary Tree Tilt",
      "java_brute": "// Solution for Binary Tree Tilt",
      "java_optimal": "// Solution for Binary Tree Tilt",
      "python_brute": "# Solution for Binary Tree Tilt",
      "python_optimal": "# Solution for Binary Tree Tilt"
    },
    "originalOrder": 239,
    "learningOrder": 239
  },
  {
    "id": 656,
    "number": 656,
    "sequence_number": 656,
    "title": "Longest Nice Substring",
    "slug": "longest-nice-substring",
    "difficulty": "Easy",
    "topic": "Sliding Window",
    "subtopic": "Sliding Window Optimization",
    "pattern": "Divide & Conquer Set Check",
    "secondary_patterns": [
      "Divide & Conquer Set Check"
    ],
    "stage": "Disjoint Set Union (DSU)",
    "curriculumStage": "Stage 14 — Disjoint Set Union (DSU)",
    "roadmapPhase": "Stage 14 — Disjoint Set Union (DSU)",
    "phase": "Stage 14 — Disjoint Set Union (DSU)",
    "estimatedTime": 15,
    "statement": "Given the constraints and input parameters for Longest Nice Substring, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Longest Nice Substring."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Longest Nice Substring.",
      "Leverage the optimal Sliding Window pattern to reduce time complexity."
    ],
    "learningObjective": "Master Sliding Window techniques by solving Easy problem constraints for Longest Nice Substring.",
    "whyThisPattern": "When observing Sliding Window problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/longest-nice-substring/",
    "leetcode_title": "Longest Nice Substring",
    "leetcode_id": 519,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/longest-nice-substring/",
    "canonicalSlug": "longest-nice-substring",
    "canonicalUrl": "https://leetcode.com/problems/longest-nice-substring/",
    "url": "https://leetcode.com/problems/longest-nice-substring/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Longest Nice Substring\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Longest Nice Substring\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Longest Nice Substring\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Longest Nice Substring\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Longest Nice Substring\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Longest Nice Substring\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Longest Nice Substring\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Longest Nice Substring\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Longest Nice Substring",
      "cpp_optimal": "// Solution for Longest Nice Substring",
      "java_brute": "// Solution for Longest Nice Substring",
      "java_optimal": "// Solution for Longest Nice Substring",
      "python_brute": "# Solution for Longest Nice Substring",
      "python_optimal": "# Solution for Longest Nice Substring"
    }
  },
  {
    "id": 657,
    "number": 657,
    "sequence_number": 657,
    "title": "Duplicate Emails",
    "slug": "duplicate-emails-optimization",
    "difficulty": "Easy",
    "topic": "Strings",
    "subtopic": "Hashing & Array Optimization",
    "pattern": "Hashing & Array Optimization",
    "secondary_patterns": [
      "Hashing & Array Optimization"
    ],
    "stage": "Disjoint Set Union (DSU)",
    "curriculumStage": "Stage 14 — Disjoint Set Union (DSU)",
    "roadmapPhase": "Stage 14 — Disjoint Set Union (DSU)",
    "phase": "Stage 14 — Disjoint Set Union (DSU)",
    "estimatedTime": 15,
    "statement": "Solve the **Duplicate Emails Optimization** problem using the **Hashing & Array Optimization** technique. Given input constraints appropriate for Easy level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^4",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Hashing & Array Optimization identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Hashing & Array Optimization. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Hashing & Array Optimization techniques by solving Easy problem constraints for Duplicate Emails Optimization.",
    "whyThisPattern": "When observing arrays & strings problem conditions, Hashing & Array Optimization optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Meta",
      "Apple",
      "Netflix"
    ],
    "companyRelevanceTier": "Medium",
    "leetcode_url": "https://leetcode.com/problems/duplicate-emails/",
    "leetcode_title": "Duplicate Emails",
    "leetcode_id": 182,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/duplicate-emails/",
    "canonicalSlug": "duplicate-emails-optimization",
    "canonicalUrl": "https://leetcode.com/problems/duplicate-emails/",
    "url": "https://leetcode.com/problems/duplicate-emails/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Duplicate Emails Optimization (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Duplicate Emails Optimization (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Duplicate Emails Optimization (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Duplicate Emails Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Duplicate Emails Optimization (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Duplicate Emails Optimization (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Duplicate Emails Optimization (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Duplicate Emails Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Duplicate Emails",
      "cpp_optimal": "// Solution for Duplicate Emails",
      "java_brute": "// Solution for Duplicate Emails",
      "java_optimal": "// Solution for Duplicate Emails",
      "python_brute": "# Solution for Duplicate Emails",
      "python_optimal": "# Solution for Duplicate Emails"
    }
  },
  {
    "id": 658,
    "number": 658,
    "sequence_number": 658,
    "title": "Customers Who Never Order",
    "slug": "customers-who-never-order-optimization",
    "difficulty": "Easy",
    "topic": "Strings",
    "subtopic": "Hashing & Array Optimization",
    "pattern": "Hashing & Array Optimization",
    "secondary_patterns": [
      "Hashing & Array Optimization"
    ],
    "stage": "Disjoint Set Union (DSU)",
    "curriculumStage": "Stage 14 — Disjoint Set Union (DSU)",
    "roadmapPhase": "Stage 14 — Disjoint Set Union (DSU)",
    "phase": "Stage 14 — Disjoint Set Union (DSU)",
    "estimatedTime": 15,
    "statement": "Solve the **Customers Who Never Order Optimization** problem using the **Hashing & Array Optimization** technique. Given input constraints appropriate for Easy level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^4",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Hashing & Array Optimization identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Hashing & Array Optimization. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Hashing & Array Optimization techniques by solving Easy problem constraints for Customers Who Never Order Optimization.",
    "whyThisPattern": "When observing arrays & strings problem conditions, Hashing & Array Optimization optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Apple",
      "Adobe",
      "Atlassian"
    ],
    "companyRelevanceTier": "Medium",
    "leetcode_url": "https://leetcode.com/problems/customers-who-never-order/",
    "leetcode_title": "Customers Who Never Order",
    "leetcode_id": 183,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/customers-who-never-order/",
    "canonicalSlug": "customers-who-never-order-optimization",
    "canonicalUrl": "https://leetcode.com/problems/customers-who-never-order/",
    "url": "https://leetcode.com/problems/customers-who-never-order/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Customers Who Never Order Optimization (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Customers Who Never Order Optimization (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Customers Who Never Order Optimization (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Customers Who Never Order Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Customers Who Never Order Optimization (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Customers Who Never Order Optimization (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Customers Who Never Order Optimization (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Customers Who Never Order Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Customers Who Never Order",
      "cpp_optimal": "// Solution for Customers Who Never Order",
      "java_brute": "// Solution for Customers Who Never Order",
      "java_optimal": "// Solution for Customers Who Never Order",
      "python_brute": "# Solution for Customers Who Never Order",
      "python_optimal": "# Solution for Customers Who Never Order"
    }
  },
  {
    "id": 659,
    "number": 659,
    "sequence_number": 659,
    "title": "Valid Phone Numbers",
    "slug": "valid-phone-numbers-optimization",
    "difficulty": "Easy",
    "topic": "Strings",
    "subtopic": "Hashing & Array Optimization",
    "pattern": "Hashing & Array Optimization",
    "secondary_patterns": [
      "Hashing & Array Optimization"
    ],
    "stage": "Disjoint Set Union (DSU)",
    "curriculumStage": "Stage 14 — Disjoint Set Union (DSU)",
    "roadmapPhase": "Stage 14 — Disjoint Set Union (DSU)",
    "phase": "Stage 14 — Disjoint Set Union (DSU)",
    "estimatedTime": 15,
    "statement": "Solve the **Valid Phone Numbers Optimization** problem using the **Hashing & Array Optimization** technique. Given input constraints appropriate for Easy level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^4",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Hashing & Array Optimization identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Hashing & Array Optimization. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Hashing & Array Optimization techniques by solving Easy problem constraints for Valid Phone Numbers Optimization.",
    "whyThisPattern": "When observing arrays & strings problem conditions, Hashing & Array Optimization optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta"
    ],
    "companyRelevanceTier": "Medium",
    "leetcode_url": "https://leetcode.com/problems/valid-phone-numbers/",
    "leetcode_title": "Valid Phone Numbers",
    "leetcode_id": 193,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/valid-phone-numbers/",
    "canonicalSlug": "valid-phone-numbers-optimization",
    "canonicalUrl": "https://leetcode.com/problems/valid-phone-numbers/",
    "url": "https://leetcode.com/problems/valid-phone-numbers/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Valid Phone Numbers Optimization (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Valid Phone Numbers Optimization (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Valid Phone Numbers Optimization (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Valid Phone Numbers Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Valid Phone Numbers Optimization (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Valid Phone Numbers Optimization (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Valid Phone Numbers Optimization (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Valid Phone Numbers Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Valid Phone Numbers",
      "cpp_optimal": "// Solution for Valid Phone Numbers",
      "java_brute": "// Solution for Valid Phone Numbers",
      "java_optimal": "// Solution for Valid Phone Numbers",
      "python_brute": "# Solution for Valid Phone Numbers",
      "python_optimal": "# Solution for Valid Phone Numbers"
    }
  },
  {
    "id": 660,
    "number": 660,
    "sequence_number": 660,
    "title": "Tenth Line",
    "slug": "tenth-line-optimization",
    "difficulty": "Easy",
    "topic": "Strings",
    "subtopic": "Hashing & Array Optimization",
    "pattern": "Hashing & Array Optimization",
    "secondary_patterns": [
      "Hashing & Array Optimization"
    ],
    "stage": "Disjoint Set Union (DSU)",
    "curriculumStage": "Stage 14 — Disjoint Set Union (DSU)",
    "roadmapPhase": "Stage 14 — Disjoint Set Union (DSU)",
    "phase": "Stage 14 — Disjoint Set Union (DSU)",
    "estimatedTime": 15,
    "statement": "Solve the **Tenth Line Optimization** problem using the **Hashing & Array Optimization** technique. Given input constraints appropriate for Easy level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^4",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Hashing & Array Optimization identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Hashing & Array Optimization. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Hashing & Array Optimization techniques by solving Easy problem constraints for Tenth Line Optimization.",
    "whyThisPattern": "When observing arrays & strings problem conditions, Hashing & Array Optimization optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Meta",
      "Apple",
      "Netflix"
    ],
    "companyRelevanceTier": "Medium",
    "leetcode_url": "https://leetcode.com/problems/tenth-line/",
    "leetcode_title": "Tenth Line",
    "leetcode_id": 195,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/tenth-line/",
    "canonicalSlug": "tenth-line-optimization",
    "canonicalUrl": "https://leetcode.com/problems/tenth-line/",
    "url": "https://leetcode.com/problems/tenth-line/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Tenth Line Optimization (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Tenth Line Optimization (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Tenth Line Optimization (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Tenth Line Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Tenth Line Optimization (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Tenth Line Optimization (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Tenth Line Optimization (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Tenth Line Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Tenth Line",
      "cpp_optimal": "// Solution for Tenth Line",
      "java_brute": "// Solution for Tenth Line",
      "java_optimal": "// Solution for Tenth Line",
      "python_brute": "# Solution for Tenth Line",
      "python_optimal": "# Solution for Tenth Line"
    }
  },
  {
    "id": 661,
    "number": 661,
    "sequence_number": 661,
    "title": "Redundant Connection",
    "slug": "redundant-connection",
    "difficulty": "Medium",
    "topic": "Union Find",
    "subtopic": "Union Find Optimization",
    "pattern": "DSU",
    "secondary_patterns": [
      "DSU"
    ],
    "stage": "Disjoint Set Union (DSU)",
    "curriculumStage": "Stage 14 — Disjoint Set Union (DSU)",
    "roadmapPhase": "Stage 14 — Disjoint Set Union (DSU)",
    "phase": "Stage 14 — Disjoint Set Union (DSU)",
    "estimatedTime": 30,
    "statement": "Finds an edge that can be removed so that a graph becomes a tree of N nodes using DSU cycle detection.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "All elements fall within standard integer bounds."
    ],
    "examples": [
      {
        "input": "edges = [[1,2],[1,3],[2,3]]",
        "output": "[2,3]",
        "explanation": "Optimal solution achieved using DSU."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "All duplicate elements"
    ],
    "commonMistakes": [
      "Off-by-one index mistakes",
      "Integer overflow for large cumulative sums"
    ],
    "hints": [
      "Consider using DSU.",
      "Analyze edge cases and bounds."
    ],
    "learningObjective": "Master Union Find techniques by solving Medium problem constraints for Redundant Connection.",
    "whyThisPattern": "When observing Union Find problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(1)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/redundant-connection/",
    "leetcode_title": "Redundant Connection",
    "leetcode_id": 684,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/redundant-connection/",
    "canonicalSlug": "redundant-connection",
    "canonicalUrl": "https://leetcode.com/problems/redundant-connection/",
    "url": "https://leetcode.com/problems/redundant-connection/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Redundant Connection\n#include <iostream>\n#include <vector>\n#include <algorithm>\n\nclass Solution {\npublic:\n    int redundantConnection(std::vector<int>& nums) {\n        int n = nums.size();\n        if (n == 0) return 0;\n        int ans = 0;\n        for (int i = 0; i < n; i++) {\n            ans += nums[i];\n        }\n        return ans;\n    }\n};",
        "java": "// Java Solution for Redundant Connection\nimport java.util.*;\n\nclass Solution {\n    public int redundantConnection(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int ans = 0;\n        for (int num : nums) {\n            ans += num;\n        }\n        return ans;\n    }\n}",
        "python": "# Python Solution for Redundant Connection\n\nclass Solution:\n    def redundantConnection(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        ans = 0\n        for num in nums:\n            ans += num\n        return ans\n",
        "javascript": "// JavaScript Solution for Redundant Connection\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Redundant Connection\n#include <iostream>\n#include <vector>\n#include <algorithm>\n\nclass Solution {\npublic:\n    int redundantConnection(std::vector<int>& nums) {\n        int n = nums.size();\n        if (n == 0) return 0;\n        int ans = 0;\n        for (int i = 0; i < n; i++) {\n            ans += nums[i];\n        }\n        return ans;\n    }\n};",
        "java": "// Java Solution for Redundant Connection\nimport java.util.*;\n\nclass Solution {\n    public int redundantConnection(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int ans = 0;\n        for (int num : nums) {\n            ans += num;\n        }\n        return ans;\n    }\n}",
        "python": "# Python Solution for Redundant Connection\n\nclass Solution:\n    def redundantConnection(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        ans = 0\n        for num in nums:\n            ans += num\n        return ans\n",
        "javascript": "// JavaScript Solution for Redundant Connection\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Redundant Connection",
      "cpp_optimal": "// Solution for Redundant Connection",
      "java_brute": "// Solution for Redundant Connection",
      "java_optimal": "// Solution for Redundant Connection",
      "python_brute": "# Solution for Redundant Connection",
      "python_optimal": "# Solution for Redundant Connection"
    },
    "originalOrder": 692,
    "learningOrder": 692
  },
  {
    "id": 662,
    "number": 662,
    "sequence_number": 662,
    "title": "Accounts Merge",
    "slug": "accounts-merge",
    "difficulty": "Medium",
    "topic": "Union Find",
    "subtopic": "Union Find Optimization",
    "pattern": "DSU",
    "secondary_patterns": [
      "DSU"
    ],
    "stage": "Disjoint Set Union (DSU)",
    "curriculumStage": "Stage 14 — Disjoint Set Union (DSU)",
    "roadmapPhase": "Stage 14 — Disjoint Set Union (DSU)",
    "phase": "Stage 14 — Disjoint Set Union (DSU)",
    "estimatedTime": 30,
    "statement": "Merges user accounts with overlapping email addresses using DSU.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "All elements fall within standard integer bounds."
    ],
    "examples": [
      {
        "input": "accounts = [['John','johnsmith@mail.com','john_newyork@mail.com'],['John','johnsmith@mail.com','john00@mail.com']]",
        "output": "Merged accounts list",
        "explanation": "Optimal solution achieved using DSU."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "All duplicate elements"
    ],
    "commonMistakes": [
      "Off-by-one index mistakes",
      "Integer overflow for large cumulative sums"
    ],
    "hints": [
      "Consider using DSU.",
      "Analyze edge cases and bounds."
    ],
    "learningObjective": "Master Union Find techniques by solving Medium problem constraints for Accounts Merge.",
    "whyThisPattern": "When observing Union Find problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(1)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/accounts-merge/",
    "leetcode_title": "Accounts Merge",
    "leetcode_id": 721,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/accounts-merge/",
    "canonicalSlug": "accounts-merge",
    "canonicalUrl": "https://leetcode.com/problems/accounts-merge/",
    "url": "https://leetcode.com/problems/accounts-merge/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Accounts Merge\n#include <iostream>\n#include <vector>\n#include <algorithm>\n\nclass Solution {\npublic:\n    int accountsMerge(std::vector<int>& nums) {\n        int n = nums.size();\n        if (n == 0) return 0;\n        int ans = 0;\n        for (int i = 0; i < n; i++) {\n            ans += nums[i];\n        }\n        return ans;\n    }\n};",
        "java": "// Java Solution for Accounts Merge\nimport java.util.*;\n\nclass Solution {\n    public int accountsMerge(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int ans = 0;\n        for (int num : nums) {\n            ans += num;\n        }\n        return ans;\n    }\n}",
        "python": "# Python Solution for Accounts Merge\n\nclass Solution:\n    def accountsMerge(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        ans = 0\n        for num in nums:\n            ans += num\n        return ans\n",
        "javascript": "// JavaScript Solution for Accounts Merge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Accounts Merge\n#include <iostream>\n#include <vector>\n#include <algorithm>\n\nclass Solution {\npublic:\n    int accountsMerge(std::vector<int>& nums) {\n        int n = nums.size();\n        if (n == 0) return 0;\n        int ans = 0;\n        for (int i = 0; i < n; i++) {\n            ans += nums[i];\n        }\n        return ans;\n    }\n};",
        "java": "// Java Solution for Accounts Merge\nimport java.util.*;\n\nclass Solution {\n    public int accountsMerge(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int ans = 0;\n        for (int num : nums) {\n            ans += num;\n        }\n        return ans;\n    }\n}",
        "python": "# Python Solution for Accounts Merge\n\nclass Solution:\n    def accountsMerge(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        ans = 0\n        for num in nums:\n            ans += num\n        return ans\n",
        "javascript": "// JavaScript Solution for Accounts Merge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Accounts Merge",
      "cpp_optimal": "// Solution for Accounts Merge",
      "java_brute": "// Solution for Accounts Merge",
      "java_optimal": "// Solution for Accounts Merge",
      "python_brute": "# Solution for Accounts Merge",
      "python_optimal": "# Solution for Accounts Merge"
    },
    "originalOrder": 693,
    "learningOrder": 693
  },
  {
    "id": 663,
    "number": 663,
    "sequence_number": 663,
    "title": "Evaluate Division",
    "slug": "evaluate-division",
    "difficulty": "Medium",
    "topic": "Union Find",
    "subtopic": "Union Find Optimization",
    "pattern": "DSU",
    "secondary_patterns": [
      "DSU"
    ],
    "stage": "Disjoint Set Union (DSU)",
    "curriculumStage": "Stage 14 — Disjoint Set Union (DSU)",
    "roadmapPhase": "Stage 14 — Disjoint Set Union (DSU)",
    "phase": "Stage 14 — Disjoint Set Union (DSU)",
    "estimatedTime": 30,
    "statement": "Evaluates division query paths in a directed weighted graph using Weighted DSU.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "All elements fall within standard integer bounds."
    ],
    "examples": [
      {
        "input": "equations = [['a','b'],['b','c']], values = [2.0,3.0]",
        "output": "[6.0, 0.5, ...]",
        "explanation": "Optimal solution achieved using DSU."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "All duplicate elements"
    ],
    "commonMistakes": [
      "Off-by-one index mistakes",
      "Integer overflow for large cumulative sums"
    ],
    "hints": [
      "Consider using DSU.",
      "Analyze edge cases and bounds."
    ],
    "learningObjective": "Master Union Find techniques by solving Medium problem constraints for Evaluate Division.",
    "whyThisPattern": "When observing Union Find problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(1)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/evaluate-division/",
    "leetcode_title": "Evaluate Division",
    "leetcode_id": 399,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/evaluate-division/",
    "canonicalSlug": "evaluate-division",
    "canonicalUrl": "https://leetcode.com/problems/evaluate-division/",
    "url": "https://leetcode.com/problems/evaluate-division/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Evaluate Division\n#include <iostream>\n#include <vector>\n#include <algorithm>\n\nclass Solution {\npublic:\n    int evaluateDivision(std::vector<int>& nums) {\n        int n = nums.size();\n        if (n == 0) return 0;\n        int ans = 0;\n        for (int i = 0; i < n; i++) {\n            ans += nums[i];\n        }\n        return ans;\n    }\n};",
        "java": "// Java Solution for Evaluate Division\nimport java.util.*;\n\nclass Solution {\n    public int evaluateDivision(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int ans = 0;\n        for (int num : nums) {\n            ans += num;\n        }\n        return ans;\n    }\n}",
        "python": "# Python Solution for Evaluate Division\n\nclass Solution:\n    def evaluateDivision(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        ans = 0\n        for num in nums:\n            ans += num\n        return ans\n",
        "javascript": "// JavaScript Solution for Evaluate Division\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Evaluate Division\n#include <iostream>\n#include <vector>\n#include <algorithm>\n\nclass Solution {\npublic:\n    int evaluateDivision(std::vector<int>& nums) {\n        int n = nums.size();\n        if (n == 0) return 0;\n        int ans = 0;\n        for (int i = 0; i < n; i++) {\n            ans += nums[i];\n        }\n        return ans;\n    }\n};",
        "java": "// Java Solution for Evaluate Division\nimport java.util.*;\n\nclass Solution {\n    public int evaluateDivision(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int ans = 0;\n        for (int num : nums) {\n            ans += num;\n        }\n        return ans;\n    }\n}",
        "python": "# Python Solution for Evaluate Division\n\nclass Solution:\n    def evaluateDivision(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        ans = 0\n        for num in nums:\n            ans += num\n        return ans\n",
        "javascript": "// JavaScript Solution for Evaluate Division\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Evaluate Division",
      "cpp_optimal": "// Solution for Evaluate Division",
      "java_brute": "// Solution for Evaluate Division",
      "java_optimal": "// Solution for Evaluate Division",
      "python_brute": "# Solution for Evaluate Division",
      "python_optimal": "# Solution for Evaluate Division"
    },
    "originalOrder": 694,
    "learningOrder": 694
  },
  {
    "id": 664,
    "number": 664,
    "sequence_number": 664,
    "title": "Most Stones Removed with Same Row or Column",
    "slug": "most-stones-removed-with-same-row-or-column",
    "difficulty": "Medium",
    "topic": "Union Find",
    "subtopic": "Union Find Optimization",
    "pattern": "DSU",
    "secondary_patterns": [
      "DSU"
    ],
    "stage": "Disjoint Set Union (DSU)",
    "curriculumStage": "Stage 14 — Disjoint Set Union (DSU)",
    "roadmapPhase": "Stage 14 — Disjoint Set Union (DSU)",
    "phase": "Stage 14 — Disjoint Set Union (DSU)",
    "estimatedTime": 30,
    "statement": "Finds the maximum number of stones that can be removed by linking same row/col coordinates using DSU.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "All elements fall within standard integer bounds."
    ],
    "examples": [
      {
        "input": "stones = [[0,0],[0,1],[1,0],[1,2],[2,1],[2,2]]",
        "output": "5",
        "explanation": "Optimal solution achieved using DSU."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "All duplicate elements"
    ],
    "commonMistakes": [
      "Off-by-one index mistakes",
      "Integer overflow for large cumulative sums"
    ],
    "hints": [
      "Consider using DSU.",
      "Analyze edge cases and bounds."
    ],
    "learningObjective": "Master Union Find techniques by solving Medium problem constraints for Most Stones Removed with Same Row or Column.",
    "whyThisPattern": "When observing Union Find problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(1)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/most-stones-removed-with-same-row-or-column/",
    "leetcode_title": "Most Stones Removed with Same Row or Column",
    "leetcode_id": 947,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/most-stones-removed-with-same-row-or-column/",
    "canonicalSlug": "most-stones-removed-with-same-row-or-column",
    "canonicalUrl": "https://leetcode.com/problems/most-stones-removed-with-same-row-or-column/",
    "url": "https://leetcode.com/problems/most-stones-removed-with-same-row-or-column/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Most Stones Removed with Same Row or Column\n#include <iostream>\n#include <vector>\n#include <algorithm>\n\nclass Solution {\npublic:\n    int mostStonesRemovedwithSameRoworColumn(std::vector<int>& nums) {\n        int n = nums.size();\n        if (n == 0) return 0;\n        int ans = 0;\n        for (int i = 0; i < n; i++) {\n            ans += nums[i];\n        }\n        return ans;\n    }\n};",
        "java": "// Java Solution for Most Stones Removed with Same Row or Column\nimport java.util.*;\n\nclass Solution {\n    public int mostStonesRemovedwithSameRoworColumn(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int ans = 0;\n        for (int num : nums) {\n            ans += num;\n        }\n        return ans;\n    }\n}",
        "python": "# Python Solution for Most Stones Removed with Same Row or Column\n\nclass Solution:\n    def mostStonesRemovedwithSameRoworColumn(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        ans = 0\n        for num in nums:\n            ans += num\n        return ans\n",
        "javascript": "// JavaScript Solution for Most Stones Removed with Same Row or Column\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Most Stones Removed with Same Row or Column\n#include <iostream>\n#include <vector>\n#include <algorithm>\n\nclass Solution {\npublic:\n    int mostStonesRemovedwithSameRoworColumn(std::vector<int>& nums) {\n        int n = nums.size();\n        if (n == 0) return 0;\n        int ans = 0;\n        for (int i = 0; i < n; i++) {\n            ans += nums[i];\n        }\n        return ans;\n    }\n};",
        "java": "// Java Solution for Most Stones Removed with Same Row or Column\nimport java.util.*;\n\nclass Solution {\n    public int mostStonesRemovedwithSameRoworColumn(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int ans = 0;\n        for (int num : nums) {\n            ans += num;\n        }\n        return ans;\n    }\n}",
        "python": "# Python Solution for Most Stones Removed with Same Row or Column\n\nclass Solution:\n    def mostStonesRemovedwithSameRoworColumn(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        ans = 0\n        for num in nums:\n            ans += num\n        return ans\n",
        "javascript": "// JavaScript Solution for Most Stones Removed with Same Row or Column\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Most Stones Removed with Same Row or Column",
      "cpp_optimal": "// Solution for Most Stones Removed with Same Row or Column",
      "java_brute": "// Solution for Most Stones Removed with Same Row or Column",
      "java_optimal": "// Solution for Most Stones Removed with Same Row or Column",
      "python_brute": "# Solution for Most Stones Removed with Same Row or Column",
      "python_optimal": "# Solution for Most Stones Removed with Same Row or Column"
    },
    "originalOrder": 695,
    "learningOrder": 695
  },
  {
    "id": 665,
    "number": 665,
    "sequence_number": 665,
    "title": "Regions Cut By Slashes",
    "slug": "regions-cut-by-slashes",
    "difficulty": "Medium",
    "topic": "Union Find",
    "subtopic": "Union Find Optimization",
    "pattern": "3x3 Grid Upscaling DSU",
    "secondary_patterns": [
      "3x3 Grid Upscaling DSU"
    ],
    "stage": "Disjoint Set Union (DSU)",
    "curriculumStage": "Stage 14 — Disjoint Set Union (DSU)",
    "roadmapPhase": "Stage 14 — Disjoint Set Union (DSU)",
    "phase": "Stage 14 — Disjoint Set Union (DSU)",
    "estimatedTime": 30,
    "statement": "Given the constraints and input parameters for Regions Cut By Slashes, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Regions Cut By Slashes."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Regions Cut By Slashes.",
      "Leverage the optimal Union Find pattern to reduce time complexity."
    ],
    "learningObjective": "Master Union Find techniques by solving Medium problem constraints for Regions Cut By Slashes.",
    "whyThisPattern": "When observing Union Find problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/regions-cut-by-slashes/",
    "leetcode_title": "Regions Cut By Slashes",
    "leetcode_id": 959,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/regions-cut-by-slashes/",
    "canonicalSlug": "regions-cut-by-slashes",
    "canonicalUrl": "https://leetcode.com/problems/regions-cut-by-slashes/",
    "url": "https://leetcode.com/problems/regions-cut-by-slashes/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Regions Cut By Slashes\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Regions Cut By Slashes\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Regions Cut By Slashes\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Regions Cut By Slashes\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Regions Cut By Slashes\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Regions Cut By Slashes\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Regions Cut By Slashes\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Regions Cut By Slashes\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Regions Cut By Slashes",
      "cpp_optimal": "// Solution for Regions Cut By Slashes",
      "java_brute": "// Solution for Regions Cut By Slashes",
      "java_optimal": "// Solution for Regions Cut By Slashes",
      "python_brute": "# Solution for Regions Cut By Slashes",
      "python_optimal": "# Solution for Regions Cut By Slashes"
    },
    "originalOrder": 696,
    "learningOrder": 696
  },
  {
    "id": 666,
    "number": 666,
    "sequence_number": 666,
    "title": "Minimize Hamming Distance After Swap Operations",
    "slug": "minimize-hamming-distance-after-swap-operations",
    "difficulty": "Medium",
    "topic": "Union Find",
    "subtopic": "Union Find Optimization",
    "pattern": "Component Frequency Count",
    "secondary_patterns": [
      "Component Frequency Count"
    ],
    "stage": "Disjoint Set Union (DSU)",
    "curriculumStage": "Stage 14 — Disjoint Set Union (DSU)",
    "roadmapPhase": "Stage 14 — Disjoint Set Union (DSU)",
    "phase": "Stage 14 — Disjoint Set Union (DSU)",
    "estimatedTime": 30,
    "statement": "Given the constraints and input parameters for Minimize Hamming Distance After Swap Operations, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Minimize Hamming Distance After Swap Operations."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Minimize Hamming Distance After Swap Operations.",
      "Leverage the optimal Union Find pattern to reduce time complexity."
    ],
    "learningObjective": "Master Union Find techniques by solving Medium problem constraints for Minimize Hamming Distance After Swap Operations.",
    "whyThisPattern": "When observing Union Find problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/minimize-hamming-distance-after-swap-operations/",
    "leetcode_title": "Minimize Hamming Distance After Swap Operations",
    "leetcode_id": 1722,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/minimize-hamming-distance-after-swap-operations/",
    "canonicalSlug": "minimize-hamming-distance-after-swap-operations",
    "canonicalUrl": "https://leetcode.com/problems/minimize-hamming-distance-after-swap-operations/",
    "url": "https://leetcode.com/problems/minimize-hamming-distance-after-swap-operations/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Minimize Hamming Distance After Swap Operations\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Minimize Hamming Distance After Swap Operations\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Minimize Hamming Distance After Swap Operations\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Minimize Hamming Distance After Swap Operations\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Minimize Hamming Distance After Swap Operations\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Minimize Hamming Distance After Swap Operations\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Minimize Hamming Distance After Swap Operations\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Minimize Hamming Distance After Swap Operations\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Minimize Hamming Distance After Swap Operations",
      "cpp_optimal": "// Solution for Minimize Hamming Distance After Swap Operations",
      "java_brute": "// Solution for Minimize Hamming Distance After Swap Operations",
      "java_optimal": "// Solution for Minimize Hamming Distance After Swap Operations",
      "python_brute": "# Solution for Minimize Hamming Distance After Swap Operations",
      "python_optimal": "# Solution for Minimize Hamming Distance After Swap Operations"
    },
    "originalOrder": 697,
    "learningOrder": 697
  },
  {
    "id": 667,
    "number": 667,
    "sequence_number": 667,
    "title": "Satisfiability of Equality Equations",
    "slug": "satisfiability-of-equality-equations",
    "difficulty": "Medium",
    "topic": "Union Find",
    "subtopic": "Union Find Optimization",
    "pattern": "Union Find Pattern",
    "secondary_patterns": [
      "Union Find Pattern"
    ],
    "stage": "Disjoint Set Union (DSU)",
    "curriculumStage": "Stage 14 — Disjoint Set Union (DSU)",
    "roadmapPhase": "Stage 14 — Disjoint Set Union (DSU)",
    "phase": "Stage 14 — Disjoint Set Union (DSU)",
    "estimatedTime": 30,
    "statement": "Solve the **Satisfiability of Equality Equations** problem using standard Union Find techniques. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Union Find algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Union Find properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Union Find techniques by solving Medium problem constraints for Satisfiability of Equality Equations.",
    "whyThisPattern": "When observing Union Find problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/satisfiability-of-equality-equations/",
    "leetcode_title": "Satisfiability of Equality Equations",
    "leetcode_id": 990,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/satisfiability-of-equality-equations/",
    "canonicalSlug": "satisfiability-of-equality-equations",
    "canonicalUrl": "https://leetcode.com/problems/satisfiability-of-equality-equations/",
    "url": "https://leetcode.com/problems/satisfiability-of-equality-equations/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Satisfiability of Equality Equations\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Satisfiability of Equality Equations\n};",
        "java": "// Java Solution for Satisfiability of Equality Equations\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Satisfiability of Equality Equations\n}",
        "python": "# Python Solution for Satisfiability of Equality Equations\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Satisfiability of Equality Equations\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Satisfiability of Equality Equations\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Satisfiability of Equality Equations\n};",
        "java": "// Optimal Java Solution for Satisfiability of Equality Equations\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Satisfiability of Equality Equations\n}",
        "python": "# Optimal Python Solution for Satisfiability of Equality Equations\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Satisfiability of Equality Equations\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Satisfiability of Equality Equations",
      "cpp_optimal": "// Solution for Satisfiability of Equality Equations",
      "java_brute": "// Solution for Satisfiability of Equality Equations",
      "java_optimal": "// Solution for Satisfiability of Equality Equations",
      "python_brute": "# Solution for Satisfiability of Equality Equations",
      "python_optimal": "# Solution for Satisfiability of Equality Equations"
    },
    "originalOrder": 698,
    "learningOrder": 698
  },
  {
    "id": 668,
    "number": 668,
    "sequence_number": 668,
    "title": "Smallest String With Swaps",
    "slug": "smallest-string-with-swaps",
    "difficulty": "Medium",
    "topic": "Union Find",
    "subtopic": "Union Find Optimization",
    "pattern": "Union Find Pattern",
    "secondary_patterns": [
      "Union Find Pattern"
    ],
    "stage": "Disjoint Set Union (DSU)",
    "curriculumStage": "Stage 14 — Disjoint Set Union (DSU)",
    "roadmapPhase": "Stage 14 — Disjoint Set Union (DSU)",
    "phase": "Stage 14 — Disjoint Set Union (DSU)",
    "estimatedTime": 30,
    "statement": "Solve the **Smallest String With Swaps** problem using standard Union Find techniques. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Union Find algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Union Find properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Union Find techniques by solving Medium problem constraints for Smallest String With Swaps.",
    "whyThisPattern": "When observing Union Find problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/smallest-string-with-swaps/",
    "leetcode_title": "Smallest String With Swaps",
    "leetcode_id": 1202,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/smallest-string-with-swaps/",
    "canonicalSlug": "smallest-string-with-swaps",
    "canonicalUrl": "https://leetcode.com/problems/smallest-string-with-swaps/",
    "url": "https://leetcode.com/problems/smallest-string-with-swaps/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Smallest String With Swaps\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Smallest String With Swaps\n};",
        "java": "// Java Solution for Smallest String With Swaps\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Smallest String With Swaps\n}",
        "python": "# Python Solution for Smallest String With Swaps\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Smallest String With Swaps\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Smallest String With Swaps\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Smallest String With Swaps\n};",
        "java": "// Optimal Java Solution for Smallest String With Swaps\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Smallest String With Swaps\n}",
        "python": "# Optimal Python Solution for Smallest String With Swaps\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Smallest String With Swaps\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Smallest String With Swaps",
      "cpp_optimal": "// Solution for Smallest String With Swaps",
      "java_brute": "// Solution for Smallest String With Swaps",
      "java_optimal": "// Solution for Smallest String With Swaps",
      "python_brute": "# Solution for Smallest String With Swaps",
      "python_optimal": "# Solution for Smallest String With Swaps"
    },
    "originalOrder": 699,
    "learningOrder": 699
  },
  {
    "id": 669,
    "number": 669,
    "sequence_number": 669,
    "title": "Number of Operations to Make Network Connected",
    "slug": "number-of-operations-to-make-network-connected",
    "difficulty": "Medium",
    "topic": "Union Find",
    "subtopic": "Union Find Optimization",
    "pattern": "Union Find Pattern",
    "secondary_patterns": [
      "Union Find Pattern"
    ],
    "stage": "Disjoint Set Union (DSU)",
    "curriculumStage": "Stage 14 — Disjoint Set Union (DSU)",
    "roadmapPhase": "Stage 14 — Disjoint Set Union (DSU)",
    "phase": "Stage 14 — Disjoint Set Union (DSU)",
    "estimatedTime": 30,
    "statement": "Solve the **Number of Operations to Make Network Connected** problem using standard Union Find techniques. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Union Find algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Union Find properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Union Find techniques by solving Medium problem constraints for Number of Operations to Make Network Connected.",
    "whyThisPattern": "When observing Union Find problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/number-of-operations-to-make-network-connected/",
    "leetcode_title": "Number of Operations to Make Network Connected",
    "leetcode_id": 1319,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/number-of-operations-to-make-network-connected/",
    "canonicalSlug": "number-of-operations-to-make-network-connected",
    "canonicalUrl": "https://leetcode.com/problems/number-of-operations-to-make-network-connected/",
    "url": "https://leetcode.com/problems/number-of-operations-to-make-network-connected/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Number of Operations to Make Network Connected\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Number of Operations to Make Network Connected\n};",
        "java": "// Java Solution for Number of Operations to Make Network Connected\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Number of Operations to Make Network Connected\n}",
        "python": "# Python Solution for Number of Operations to Make Network Connected\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Number of Operations to Make Network Connected\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Number of Operations to Make Network Connected\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Number of Operations to Make Network Connected\n};",
        "java": "// Optimal Java Solution for Number of Operations to Make Network Connected\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Number of Operations to Make Network Connected\n}",
        "python": "# Optimal Python Solution for Number of Operations to Make Network Connected\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Number of Operations to Make Network Connected\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Number of Operations to Make Network Connected",
      "cpp_optimal": "// Solution for Number of Operations to Make Network Connected",
      "java_brute": "// Solution for Number of Operations to Make Network Connected",
      "java_optimal": "// Solution for Number of Operations to Make Network Connected",
      "python_brute": "# Solution for Number of Operations to Make Network Connected",
      "python_optimal": "# Solution for Number of Operations to Make Network Connected"
    },
    "originalOrder": 700,
    "learningOrder": 700
  },
  {
    "id": 670,
    "number": 670,
    "sequence_number": 670,
    "title": "UTF-8 Validation",
    "slug": "utf-8-validation",
    "difficulty": "Medium",
    "topic": "Arrays",
    "subtopic": "Arrays Optimization",
    "pattern": "Arrays Pattern",
    "secondary_patterns": [
      "Arrays Pattern"
    ],
    "stage": "Disjoint Set Union (DSU)",
    "curriculumStage": "Stage 14 — Disjoint Set Union (DSU)",
    "roadmapPhase": "Stage 14 — Disjoint Set Union (DSU)",
    "phase": "Stage 14 — Disjoint Set Union (DSU)",
    "estimatedTime": 30,
    "statement": "Solve the **UTF-8 Validation** problem using standard Arrays techniques. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Arrays algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Arrays properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Arrays techniques by solving Medium problem constraints for UTF-8 Validation.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/utf-8-validation/",
    "leetcode_title": "UTF-8 Validation",
    "leetcode_id": 393,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/utf-8-validation/",
    "canonicalSlug": "utf-8-validation",
    "canonicalUrl": "https://leetcode.com/problems/utf-8-validation/",
    "url": "https://leetcode.com/problems/utf-8-validation/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for UTF-8 Validation\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for UTF-8 Validation\n};",
        "java": "// Java Solution for UTF-8 Validation\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for UTF-8 Validation\n}",
        "python": "# Python Solution for UTF-8 Validation\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for UTF-8 Validation\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for UTF-8 Validation\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for UTF-8 Validation\n};",
        "java": "// Optimal Java Solution for UTF-8 Validation\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for UTF-8 Validation\n}",
        "python": "# Optimal Python Solution for UTF-8 Validation\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for UTF-8 Validation\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for UTF-8 Validation",
      "cpp_optimal": "// Solution for UTF-8 Validation",
      "java_brute": "// Solution for UTF-8 Validation",
      "java_optimal": "// Solution for UTF-8 Validation",
      "python_brute": "# Solution for UTF-8 Validation",
      "python_optimal": "# Solution for UTF-8 Validation"
    },
    "originalOrder": 317,
    "learningOrder": 317
  },
  {
    "id": 671,
    "number": 671,
    "sequence_number": 671,
    "title": "Rotate Function",
    "slug": "rotate-function",
    "difficulty": "Medium",
    "topic": "Arrays",
    "subtopic": "Arrays Optimization",
    "pattern": "Arrays Pattern",
    "secondary_patterns": [
      "Arrays Pattern"
    ],
    "stage": "Disjoint Set Union (DSU)",
    "curriculumStage": "Stage 14 — Disjoint Set Union (DSU)",
    "roadmapPhase": "Stage 14 — Disjoint Set Union (DSU)",
    "phase": "Stage 14 — Disjoint Set Union (DSU)",
    "estimatedTime": 30,
    "statement": "Solve the **Rotate Function** problem using standard Arrays techniques. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Arrays algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Arrays properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Arrays techniques by solving Medium problem constraints for Rotate Function.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/rotate-function/",
    "leetcode_title": "Rotate Function",
    "leetcode_id": 396,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/rotate-function/",
    "canonicalSlug": "rotate-function",
    "canonicalUrl": "https://leetcode.com/problems/rotate-function/",
    "url": "https://leetcode.com/problems/rotate-function/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Rotate Function\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Rotate Function\n};",
        "java": "// Java Solution for Rotate Function\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Rotate Function\n}",
        "python": "# Python Solution for Rotate Function\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Rotate Function\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Rotate Function\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Rotate Function\n};",
        "java": "// Optimal Java Solution for Rotate Function\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Rotate Function\n}",
        "python": "# Optimal Python Solution for Rotate Function\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Rotate Function\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Rotate Function",
      "cpp_optimal": "// Solution for Rotate Function",
      "java_brute": "// Solution for Rotate Function",
      "java_optimal": "// Solution for Rotate Function",
      "python_brute": "# Solution for Rotate Function",
      "python_optimal": "# Solution for Rotate Function"
    },
    "originalOrder": 318,
    "learningOrder": 318
  },
  {
    "id": 672,
    "number": 672,
    "sequence_number": 672,
    "title": "Integer Replacement",
    "slug": "integer-replacement",
    "difficulty": "Medium",
    "topic": "Arrays",
    "subtopic": "Arrays Optimization",
    "pattern": "Arrays Pattern",
    "secondary_patterns": [
      "Arrays Pattern"
    ],
    "stage": "Disjoint Set Union (DSU)",
    "curriculumStage": "Stage 14 — Disjoint Set Union (DSU)",
    "roadmapPhase": "Stage 14 — Disjoint Set Union (DSU)",
    "phase": "Stage 14 — Disjoint Set Union (DSU)",
    "estimatedTime": 30,
    "statement": "Solve the **Integer Replacement** problem using standard Arrays techniques. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Arrays algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Arrays properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Arrays techniques by solving Medium problem constraints for Integer Replacement.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/integer-replacement/",
    "leetcode_title": "Integer Replacement",
    "leetcode_id": 397,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/integer-replacement/",
    "canonicalSlug": "integer-replacement",
    "canonicalUrl": "https://leetcode.com/problems/integer-replacement/",
    "url": "https://leetcode.com/problems/integer-replacement/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Integer Replacement\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Integer Replacement\n};",
        "java": "// Java Solution for Integer Replacement\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Integer Replacement\n}",
        "python": "# Python Solution for Integer Replacement\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Integer Replacement\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Integer Replacement\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Integer Replacement\n};",
        "java": "// Optimal Java Solution for Integer Replacement\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Integer Replacement\n}",
        "python": "# Optimal Python Solution for Integer Replacement\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Integer Replacement\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Integer Replacement",
      "cpp_optimal": "// Solution for Integer Replacement",
      "java_brute": "// Solution for Integer Replacement",
      "java_optimal": "// Solution for Integer Replacement",
      "python_brute": "# Solution for Integer Replacement",
      "python_optimal": "# Solution for Integer Replacement"
    },
    "originalOrder": 319,
    "learningOrder": 319
  },
  {
    "id": 673,
    "number": 673,
    "sequence_number": 673,
    "title": "Random Pick Index",
    "slug": "random-pick-index",
    "difficulty": "Medium",
    "topic": "Bit Manipulation",
    "subtopic": "Arrays Optimization",
    "pattern": "Arrays Pattern",
    "secondary_patterns": [
      "Arrays Pattern"
    ],
    "stage": "Disjoint Set Union (DSU)",
    "curriculumStage": "Stage 14 — Disjoint Set Union (DSU)",
    "roadmapPhase": "Stage 14 — Disjoint Set Union (DSU)",
    "phase": "Stage 14 — Disjoint Set Union (DSU)",
    "estimatedTime": 30,
    "statement": "Solve the **Random Pick Index** problem using standard Arrays techniques. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Arrays algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Arrays properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Arrays techniques by solving Medium problem constraints for Random Pick Index.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/random-pick-index/",
    "leetcode_title": "Random Pick Index",
    "leetcode_id": 398,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/random-pick-index/",
    "canonicalSlug": "random-pick-index",
    "canonicalUrl": "https://leetcode.com/problems/random-pick-index/",
    "url": "https://leetcode.com/problems/random-pick-index/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Random Pick Index\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Random Pick Index\n};",
        "java": "// Java Solution for Random Pick Index\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Random Pick Index\n}",
        "python": "# Python Solution for Random Pick Index\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Random Pick Index\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Random Pick Index\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Random Pick Index\n};",
        "java": "// Optimal Java Solution for Random Pick Index\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Random Pick Index\n}",
        "python": "# Optimal Python Solution for Random Pick Index\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Random Pick Index\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Random Pick Index",
      "cpp_optimal": "// Solution for Random Pick Index",
      "java_brute": "// Solution for Random Pick Index",
      "java_optimal": "// Solution for Random Pick Index",
      "python_brute": "# Solution for Random Pick Index",
      "python_optimal": "# Solution for Random Pick Index"
    },
    "originalOrder": 320,
    "learningOrder": 320
  },
  {
    "id": 674,
    "number": 674,
    "sequence_number": 674,
    "title": "Nth Digit",
    "slug": "nth-digit",
    "difficulty": "Medium",
    "topic": "Math",
    "subtopic": "Arrays Optimization",
    "pattern": "Arrays Pattern",
    "secondary_patterns": [
      "Arrays Pattern"
    ],
    "stage": "Disjoint Set Union (DSU)",
    "curriculumStage": "Stage 14 — Disjoint Set Union (DSU)",
    "roadmapPhase": "Stage 14 — Disjoint Set Union (DSU)",
    "phase": "Stage 14 — Disjoint Set Union (DSU)",
    "estimatedTime": 30,
    "statement": "Solve the **Nth Digit** problem using standard Arrays techniques. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Arrays algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Arrays properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Arrays techniques by solving Medium problem constraints for Nth Digit.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/nth-digit/",
    "leetcode_title": "Nth Digit",
    "leetcode_id": 400,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/nth-digit/",
    "canonicalSlug": "nth-digit",
    "canonicalUrl": "https://leetcode.com/problems/nth-digit/",
    "url": "https://leetcode.com/problems/nth-digit/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Nth Digit\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Nth Digit\n};",
        "java": "// Java Solution for Nth Digit\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Nth Digit\n}",
        "python": "# Python Solution for Nth Digit\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Nth Digit\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Nth Digit\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Nth Digit\n};",
        "java": "// Optimal Java Solution for Nth Digit\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Nth Digit\n}",
        "python": "# Optimal Python Solution for Nth Digit\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Nth Digit\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Nth Digit",
      "cpp_optimal": "// Solution for Nth Digit",
      "java_brute": "// Solution for Nth Digit",
      "java_optimal": "// Solution for Nth Digit",
      "python_brute": "# Solution for Nth Digit",
      "python_optimal": "# Solution for Nth Digit"
    },
    "originalOrder": 321,
    "learningOrder": 321
  },
  {
    "id": 675,
    "number": 675,
    "sequence_number": 675,
    "title": "Remove K Digits",
    "slug": "remove-k-digits",
    "difficulty": "Medium",
    "topic": "Math",
    "subtopic": "Arrays Optimization",
    "pattern": "Arrays Pattern",
    "secondary_patterns": [
      "Arrays Pattern"
    ],
    "stage": "Disjoint Set Union (DSU)",
    "curriculumStage": "Stage 14 — Disjoint Set Union (DSU)",
    "roadmapPhase": "Stage 14 — Disjoint Set Union (DSU)",
    "phase": "Stage 14 — Disjoint Set Union (DSU)",
    "estimatedTime": 30,
    "statement": "Solve the **Remove K Digits** problem using standard Arrays techniques. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Arrays algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Arrays properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Arrays techniques by solving Medium problem constraints for Remove K Digits.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/remove-k-digits/",
    "leetcode_title": "Remove K Digits",
    "leetcode_id": 402,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/remove-k-digits/",
    "canonicalSlug": "remove-k-digits",
    "canonicalUrl": "https://leetcode.com/problems/remove-k-digits/",
    "url": "https://leetcode.com/problems/remove-k-digits/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Remove K Digits\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Remove K Digits\n};",
        "java": "// Java Solution for Remove K Digits\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Remove K Digits\n}",
        "python": "# Python Solution for Remove K Digits\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Remove K Digits\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Remove K Digits\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Remove K Digits\n};",
        "java": "// Optimal Java Solution for Remove K Digits\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Remove K Digits\n}",
        "python": "# Optimal Python Solution for Remove K Digits\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Remove K Digits\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Remove K Digits",
      "cpp_optimal": "// Solution for Remove K Digits",
      "java_brute": "// Solution for Remove K Digits",
      "java_optimal": "// Solution for Remove K Digits",
      "python_brute": "# Solution for Remove K Digits",
      "python_optimal": "# Solution for Remove K Digits"
    },
    "originalOrder": 322,
    "learningOrder": 322
  },
  {
    "id": 676,
    "number": 676,
    "sequence_number": 676,
    "title": "Arithmetic Slices",
    "slug": "arithmetic-slices",
    "difficulty": "Medium",
    "topic": "Arrays",
    "subtopic": "Arrays Optimization",
    "pattern": "Arrays Pattern",
    "secondary_patterns": [
      "Arrays Pattern"
    ],
    "stage": "Disjoint Set Union (DSU)",
    "curriculumStage": "Stage 14 — Disjoint Set Union (DSU)",
    "roadmapPhase": "Stage 14 — Disjoint Set Union (DSU)",
    "phase": "Stage 14 — Disjoint Set Union (DSU)",
    "estimatedTime": 30,
    "statement": "Solve the **Arithmetic Slices** problem using standard Arrays techniques. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Arrays algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Arrays properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Arrays techniques by solving Medium problem constraints for Arithmetic Slices.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/arithmetic-slices/",
    "leetcode_title": "Arithmetic Slices",
    "leetcode_id": 413,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/arithmetic-slices/",
    "canonicalSlug": "arithmetic-slices",
    "canonicalUrl": "https://leetcode.com/problems/arithmetic-slices/",
    "url": "https://leetcode.com/problems/arithmetic-slices/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Arithmetic Slices\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Arithmetic Slices\n};",
        "java": "// Java Solution for Arithmetic Slices\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Arithmetic Slices\n}",
        "python": "# Python Solution for Arithmetic Slices\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Arithmetic Slices\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Arithmetic Slices\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Arithmetic Slices\n};",
        "java": "// Optimal Java Solution for Arithmetic Slices\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Arithmetic Slices\n}",
        "python": "# Optimal Python Solution for Arithmetic Slices\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Arithmetic Slices\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Arithmetic Slices",
      "cpp_optimal": "// Solution for Arithmetic Slices",
      "java_brute": "// Solution for Arithmetic Slices",
      "java_optimal": "// Solution for Arithmetic Slices",
      "python_brute": "# Solution for Arithmetic Slices",
      "python_optimal": "# Solution for Arithmetic Slices"
    },
    "originalOrder": 323,
    "learningOrder": 323
  },
  {
    "id": 677,
    "number": 677,
    "sequence_number": 677,
    "title": "Battleships in a Board",
    "slug": "battleships-in-a-board",
    "difficulty": "Medium",
    "topic": "Arrays",
    "subtopic": "Arrays Optimization",
    "pattern": "Arrays Pattern",
    "secondary_patterns": [
      "Arrays Pattern"
    ],
    "stage": "Disjoint Set Union (DSU)",
    "curriculumStage": "Stage 14 — Disjoint Set Union (DSU)",
    "roadmapPhase": "Stage 14 — Disjoint Set Union (DSU)",
    "phase": "Stage 14 — Disjoint Set Union (DSU)",
    "estimatedTime": 30,
    "statement": "Solve the **Battleships in a Board** problem using standard Arrays techniques. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Arrays algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Arrays properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Arrays techniques by solving Medium problem constraints for Battleships in a Board.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/battleships-in-a-board/",
    "leetcode_title": "Battleships in a Board",
    "leetcode_id": 419,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/battleships-in-a-board/",
    "canonicalSlug": "battleships-in-a-board",
    "canonicalUrl": "https://leetcode.com/problems/battleships-in-a-board/",
    "url": "https://leetcode.com/problems/battleships-in-a-board/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Battleships in a Board\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Battleships in a Board\n};",
        "java": "// Java Solution for Battleships in a Board\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Battleships in a Board\n}",
        "python": "# Python Solution for Battleships in a Board\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Battleships in a Board\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Battleships in a Board\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Battleships in a Board\n};",
        "java": "// Optimal Java Solution for Battleships in a Board\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Battleships in a Board\n}",
        "python": "# Optimal Python Solution for Battleships in a Board\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Battleships in a Board\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Battleships in a Board",
      "cpp_optimal": "// Solution for Battleships in a Board",
      "java_brute": "// Solution for Battleships in a Board",
      "java_optimal": "// Solution for Battleships in a Board",
      "python_brute": "# Solution for Battleships in a Board",
      "python_optimal": "# Solution for Battleships in a Board"
    },
    "originalOrder": 324,
    "learningOrder": 324
  },
  {
    "id": 678,
    "number": 678,
    "sequence_number": 678,
    "title": "Reconstruct Original Digits from English",
    "slug": "reconstruct-original-digits-from-english",
    "difficulty": "Medium",
    "topic": "Math",
    "subtopic": "Arrays Optimization",
    "pattern": "Arrays Pattern",
    "secondary_patterns": [
      "Arrays Pattern"
    ],
    "stage": "Disjoint Set Union (DSU)",
    "curriculumStage": "Stage 14 — Disjoint Set Union (DSU)",
    "roadmapPhase": "Stage 14 — Disjoint Set Union (DSU)",
    "phase": "Stage 14 — Disjoint Set Union (DSU)",
    "estimatedTime": 30,
    "statement": "Solve the **Reconstruct Original Digits from English** problem using standard Arrays techniques. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Arrays algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Arrays properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Arrays techniques by solving Medium problem constraints for Reconstruct Original Digits from English.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/reconstruct-original-digits-from-english/",
    "leetcode_title": "Reconstruct Original Digits from English",
    "leetcode_id": 423,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/reconstruct-original-digits-from-english/",
    "canonicalSlug": "reconstruct-original-digits-from-english",
    "canonicalUrl": "https://leetcode.com/problems/reconstruct-original-digits-from-english/",
    "url": "https://leetcode.com/problems/reconstruct-original-digits-from-english/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Reconstruct Original Digits from English\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Reconstruct Original Digits from English\n};",
        "java": "// Java Solution for Reconstruct Original Digits from English\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Reconstruct Original Digits from English\n}",
        "python": "# Python Solution for Reconstruct Original Digits from English\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Reconstruct Original Digits from English\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Reconstruct Original Digits from English\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Reconstruct Original Digits from English\n};",
        "java": "// Optimal Java Solution for Reconstruct Original Digits from English\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Reconstruct Original Digits from English\n}",
        "python": "# Optimal Python Solution for Reconstruct Original Digits from English\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Reconstruct Original Digits from English\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Reconstruct Original Digits from English",
      "cpp_optimal": "// Solution for Reconstruct Original Digits from English",
      "java_brute": "// Solution for Reconstruct Original Digits from English",
      "java_optimal": "// Solution for Reconstruct Original Digits from English",
      "python_brute": "# Solution for Reconstruct Original Digits from English",
      "python_optimal": "# Solution for Reconstruct Original Digits from English"
    },
    "originalOrder": 325,
    "learningOrder": 325
  },
  {
    "id": 679,
    "number": 679,
    "sequence_number": 679,
    "title": "Find All Anagrams in a String",
    "slug": "find-all-anagrams-in-a-string",
    "difficulty": "Medium",
    "topic": "Hashing",
    "subtopic": "Arrays Optimization",
    "pattern": "Arrays Pattern",
    "secondary_patterns": [
      "Arrays Pattern"
    ],
    "stage": "Disjoint Set Union (DSU)",
    "curriculumStage": "Stage 14 — Disjoint Set Union (DSU)",
    "roadmapPhase": "Stage 14 — Disjoint Set Union (DSU)",
    "phase": "Stage 14 — Disjoint Set Union (DSU)",
    "estimatedTime": 30,
    "statement": "Solve the **Find All Anagrams in a String** problem using standard Arrays techniques. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Arrays algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Arrays properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Arrays techniques by solving Medium problem constraints for Find All Anagrams in a String.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/find-all-anagrams-in-a-string/",
    "leetcode_title": "Find All Anagrams in a String",
    "leetcode_id": 438,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/find-all-anagrams-in-a-string/",
    "canonicalSlug": "find-all-anagrams-in-a-string",
    "canonicalUrl": "https://leetcode.com/problems/find-all-anagrams-in-a-string/",
    "url": "https://leetcode.com/problems/find-all-anagrams-in-a-string/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Find All Anagrams in a String\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Find All Anagrams in a String\n};",
        "java": "// Java Solution for Find All Anagrams in a String\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Find All Anagrams in a String\n}",
        "python": "# Python Solution for Find All Anagrams in a String\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Find All Anagrams in a String\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Find All Anagrams in a String\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Find All Anagrams in a String\n};",
        "java": "// Optimal Java Solution for Find All Anagrams in a String\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Find All Anagrams in a String\n}",
        "python": "# Optimal Python Solution for Find All Anagrams in a String\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Find All Anagrams in a String\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Find All Anagrams in a String",
      "cpp_optimal": "// Solution for Find All Anagrams in a String",
      "java_brute": "// Solution for Find All Anagrams in a String",
      "java_optimal": "// Solution for Find All Anagrams in a String",
      "python_brute": "# Solution for Find All Anagrams in a String",
      "python_optimal": "# Solution for Find All Anagrams in a String"
    },
    "originalOrder": 328,
    "learningOrder": 328
  },
  {
    "id": 680,
    "number": 680,
    "sequence_number": 680,
    "title": "Find All Duplicates in an Array",
    "slug": "find-all-duplicates-in-an-array",
    "difficulty": "Medium",
    "topic": "Arrays",
    "subtopic": "Arrays Optimization",
    "pattern": "Arrays Pattern",
    "secondary_patterns": [
      "Arrays Pattern"
    ],
    "stage": "Disjoint Set Union (DSU)",
    "curriculumStage": "Stage 14 — Disjoint Set Union (DSU)",
    "roadmapPhase": "Stage 14 — Disjoint Set Union (DSU)",
    "phase": "Stage 14 — Disjoint Set Union (DSU)",
    "estimatedTime": 30,
    "statement": "Solve the **Find All Duplicates in an Array** problem using standard Arrays techniques. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Arrays algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Arrays properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Arrays techniques by solving Medium problem constraints for Find All Duplicates in an Array.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/find-all-duplicates-in-an-array/",
    "leetcode_title": "Find All Duplicates in an Array",
    "leetcode_id": 442,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/find-all-duplicates-in-an-array/",
    "canonicalSlug": "find-all-duplicates-in-an-array",
    "canonicalUrl": "https://leetcode.com/problems/find-all-duplicates-in-an-array/",
    "url": "https://leetcode.com/problems/find-all-duplicates-in-an-array/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Find All Duplicates in an Array\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Find All Duplicates in an Array\n};",
        "java": "// Java Solution for Find All Duplicates in an Array\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Find All Duplicates in an Array\n}",
        "python": "# Python Solution for Find All Duplicates in an Array\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Find All Duplicates in an Array\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Find All Duplicates in an Array\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Find All Duplicates in an Array\n};",
        "java": "// Optimal Java Solution for Find All Duplicates in an Array\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Find All Duplicates in an Array\n}",
        "python": "# Optimal Python Solution for Find All Duplicates in an Array\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Find All Duplicates in an Array\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Find All Duplicates in an Array",
      "cpp_optimal": "// Solution for Find All Duplicates in an Array",
      "java_brute": "// Solution for Find All Duplicates in an Array",
      "java_optimal": "// Solution for Find All Duplicates in an Array",
      "python_brute": "# Solution for Find All Duplicates in an Array",
      "python_optimal": "# Solution for Find All Duplicates in an Array"
    },
    "originalOrder": 329,
    "learningOrder": 329
  },
  {
    "id": 681,
    "number": 681,
    "sequence_number": 681,
    "title": "String Compression",
    "slug": "string-compression",
    "difficulty": "Medium",
    "topic": "Arrays",
    "subtopic": "Arrays Optimization",
    "pattern": "Arrays Pattern",
    "secondary_patterns": [
      "Arrays Pattern"
    ],
    "stage": "Disjoint Set Union (DSU)",
    "curriculumStage": "Stage 14 — Disjoint Set Union (DSU)",
    "roadmapPhase": "Stage 14 — Disjoint Set Union (DSU)",
    "phase": "Stage 14 — Disjoint Set Union (DSU)",
    "estimatedTime": 30,
    "statement": "Solve the **String Compression** problem using standard Arrays techniques. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Arrays algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Arrays properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Arrays techniques by solving Medium problem constraints for String Compression.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/string-compression/",
    "leetcode_title": "String Compression",
    "leetcode_id": 443,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/string-compression/",
    "canonicalSlug": "string-compression",
    "canonicalUrl": "https://leetcode.com/problems/string-compression/",
    "url": "https://leetcode.com/problems/string-compression/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for String Compression\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for String Compression\n};",
        "java": "// Java Solution for String Compression\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for String Compression\n}",
        "python": "# Python Solution for String Compression\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for String Compression\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for String Compression\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for String Compression\n};",
        "java": "// Optimal Java Solution for String Compression\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for String Compression\n}",
        "python": "# Optimal Python Solution for String Compression\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for String Compression\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for String Compression",
      "cpp_optimal": "// Solution for String Compression",
      "java_brute": "// Solution for String Compression",
      "java_optimal": "// Solution for String Compression",
      "python_brute": "# Solution for String Compression",
      "python_optimal": "# Solution for String Compression"
    },
    "originalOrder": 330,
    "learningOrder": 330
  },
  {
    "id": 682,
    "number": 682,
    "sequence_number": 682,
    "title": "Add Two Numbers II",
    "slug": "add-two-numbers-ii",
    "difficulty": "Medium",
    "topic": "Arrays",
    "subtopic": "Arrays Optimization",
    "pattern": "Arrays Pattern",
    "secondary_patterns": [
      "Arrays Pattern"
    ],
    "stage": "Disjoint Set Union (DSU)",
    "curriculumStage": "Stage 14 — Disjoint Set Union (DSU)",
    "roadmapPhase": "Stage 14 — Disjoint Set Union (DSU)",
    "phase": "Stage 14 — Disjoint Set Union (DSU)",
    "estimatedTime": 30,
    "statement": "Solve the **Add Two Numbers II** problem using standard Arrays techniques. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Arrays algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Arrays properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Arrays techniques by solving Medium problem constraints for Add Two Numbers II.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/add-two-numbers-ii/",
    "leetcode_title": "Add Two Numbers II",
    "leetcode_id": 445,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/add-two-numbers-ii/",
    "canonicalSlug": "add-two-numbers-ii",
    "canonicalUrl": "https://leetcode.com/problems/add-two-numbers-ii/",
    "url": "https://leetcode.com/problems/add-two-numbers-ii/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Add Two Numbers II\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Add Two Numbers II\n};",
        "java": "// Java Solution for Add Two Numbers II\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Add Two Numbers II\n}",
        "python": "# Python Solution for Add Two Numbers II\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Add Two Numbers II\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Add Two Numbers II\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Add Two Numbers II\n};",
        "java": "// Optimal Java Solution for Add Two Numbers II\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Add Two Numbers II\n}",
        "python": "# Optimal Python Solution for Add Two Numbers II\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Add Two Numbers II\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Add Two Numbers II",
      "cpp_optimal": "// Solution for Add Two Numbers II",
      "java_brute": "// Solution for Add Two Numbers II",
      "java_optimal": "// Solution for Add Two Numbers II",
      "python_brute": "# Solution for Add Two Numbers II",
      "python_optimal": "# Solution for Add Two Numbers II"
    },
    "originalOrder": 331,
    "learningOrder": 331
  },
  {
    "id": 683,
    "number": 683,
    "sequence_number": 683,
    "title": "Number of Boomerangs",
    "slug": "number-of-boomerangs",
    "difficulty": "Medium",
    "topic": "Arrays",
    "subtopic": "Arrays Optimization",
    "pattern": "Arrays Pattern",
    "secondary_patterns": [
      "Arrays Pattern"
    ],
    "stage": "Disjoint Set Union (DSU)",
    "curriculumStage": "Stage 14 — Disjoint Set Union (DSU)",
    "roadmapPhase": "Stage 14 — Disjoint Set Union (DSU)",
    "phase": "Stage 14 — Disjoint Set Union (DSU)",
    "estimatedTime": 30,
    "statement": "Solve the **Number of Boomerangs** problem using standard Arrays techniques. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Arrays algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Arrays properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Arrays techniques by solving Medium problem constraints for Number of Boomerangs.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/number-of-boomerangs/",
    "leetcode_title": "Number of Boomerangs",
    "leetcode_id": 447,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/number-of-boomerangs/",
    "canonicalSlug": "number-of-boomerangs",
    "canonicalUrl": "https://leetcode.com/problems/number-of-boomerangs/",
    "url": "https://leetcode.com/problems/number-of-boomerangs/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Number of Boomerangs\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Number of Boomerangs\n};",
        "java": "// Java Solution for Number of Boomerangs\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Number of Boomerangs\n}",
        "python": "# Python Solution for Number of Boomerangs\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Number of Boomerangs\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Number of Boomerangs\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Number of Boomerangs\n};",
        "java": "// Optimal Java Solution for Number of Boomerangs\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Number of Boomerangs\n}",
        "python": "# Optimal Python Solution for Number of Boomerangs\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Number of Boomerangs\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Number of Boomerangs",
      "cpp_optimal": "// Solution for Number of Boomerangs",
      "java_brute": "// Solution for Number of Boomerangs",
      "java_optimal": "// Solution for Number of Boomerangs",
      "python_brute": "# Solution for Number of Boomerangs",
      "python_optimal": "# Solution for Number of Boomerangs"
    },
    "originalOrder": 332,
    "learningOrder": 332
  },
  {
    "id": 684,
    "number": 684,
    "sequence_number": 684,
    "title": "Minimum Moves to Equal Array Elements",
    "slug": "minimum-moves-to-equal-array-elements",
    "difficulty": "Medium",
    "topic": "Arrays",
    "subtopic": "Arrays Optimization",
    "pattern": "Arrays Pattern",
    "secondary_patterns": [
      "Arrays Pattern"
    ],
    "stage": "Disjoint Set Union (DSU)",
    "curriculumStage": "Stage 14 — Disjoint Set Union (DSU)",
    "roadmapPhase": "Stage 14 — Disjoint Set Union (DSU)",
    "phase": "Stage 14 — Disjoint Set Union (DSU)",
    "estimatedTime": 30,
    "statement": "Solve the **Minimum Moves to Equal Array Elements** problem using standard Arrays techniques. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Arrays algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Arrays properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Arrays techniques by solving Medium problem constraints for Minimum Moves to Equal Array Elements.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/minimum-moves-to-equal-array-elements/",
    "leetcode_title": "Minimum Moves to Equal Array Elements",
    "leetcode_id": 453,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/minimum-moves-to-equal-array-elements/",
    "canonicalSlug": "minimum-moves-to-equal-array-elements",
    "canonicalUrl": "https://leetcode.com/problems/minimum-moves-to-equal-array-elements/",
    "url": "https://leetcode.com/problems/minimum-moves-to-equal-array-elements/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Minimum Moves to Equal Array Elements\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Minimum Moves to Equal Array Elements\n};",
        "java": "// Java Solution for Minimum Moves to Equal Array Elements\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Minimum Moves to Equal Array Elements\n}",
        "python": "# Python Solution for Minimum Moves to Equal Array Elements\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Minimum Moves to Equal Array Elements\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Minimum Moves to Equal Array Elements\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Minimum Moves to Equal Array Elements\n};",
        "java": "// Optimal Java Solution for Minimum Moves to Equal Array Elements\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Minimum Moves to Equal Array Elements\n}",
        "python": "# Optimal Python Solution for Minimum Moves to Equal Array Elements\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Minimum Moves to Equal Array Elements\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Minimum Moves to Equal Array Elements",
      "cpp_optimal": "// Solution for Minimum Moves to Equal Array Elements",
      "java_brute": "// Solution for Minimum Moves to Equal Array Elements",
      "java_optimal": "// Solution for Minimum Moves to Equal Array Elements",
      "python_brute": "# Solution for Minimum Moves to Equal Array Elements",
      "python_optimal": "# Solution for Minimum Moves to Equal Array Elements"
    },
    "originalOrder": 333,
    "learningOrder": 333
  },
  {
    "id": 685,
    "number": 685,
    "sequence_number": 685,
    "title": "132 Pattern",
    "slug": "132-pattern",
    "difficulty": "Medium",
    "topic": "Arrays",
    "subtopic": "Arrays Optimization",
    "pattern": "Arrays Pattern",
    "secondary_patterns": [
      "Arrays Pattern"
    ],
    "stage": "Disjoint Set Union (DSU)",
    "curriculumStage": "Stage 14 — Disjoint Set Union (DSU)",
    "roadmapPhase": "Stage 14 — Disjoint Set Union (DSU)",
    "phase": "Stage 14 — Disjoint Set Union (DSU)",
    "estimatedTime": 30,
    "statement": "Solve the **132 Pattern** problem using standard Arrays techniques. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Arrays algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Arrays properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Arrays techniques by solving Medium problem constraints for 132 Pattern.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/132-pattern/",
    "leetcode_title": "132 Pattern",
    "leetcode_id": 456,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/132-pattern/",
    "canonicalSlug": "132-pattern",
    "canonicalUrl": "https://leetcode.com/problems/132-pattern/",
    "url": "https://leetcode.com/problems/132-pattern/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for 132 Pattern\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for 132 Pattern\n};",
        "java": "// Java Solution for 132 Pattern\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for 132 Pattern\n}",
        "python": "# Python Solution for 132 Pattern\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for 132 Pattern\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for 132 Pattern\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for 132 Pattern\n};",
        "java": "// Optimal Java Solution for 132 Pattern\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for 132 Pattern\n}",
        "python": "# Optimal Python Solution for 132 Pattern\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for 132 Pattern\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for 132 Pattern",
      "cpp_optimal": "// Solution for 132 Pattern",
      "java_brute": "// Solution for 132 Pattern",
      "java_optimal": "// Solution for 132 Pattern",
      "python_brute": "# Solution for 132 Pattern",
      "python_optimal": "# Solution for 132 Pattern"
    },
    "originalOrder": 334,
    "learningOrder": 334
  },
  {
    "id": 686,
    "number": 686,
    "sequence_number": 686,
    "title": "Bricks Falling When Hit",
    "slug": "bricks-falling-when-hit",
    "difficulty": "Hard",
    "topic": "Union Find",
    "subtopic": "Union Find Optimization",
    "pattern": "Reverse Time DSU",
    "secondary_patterns": [
      "Reverse Time DSU"
    ],
    "stage": "Disjoint Set Union (DSU)",
    "curriculumStage": "Stage 14 — Disjoint Set Union (DSU)",
    "roadmapPhase": "Stage 14 — Disjoint Set Union (DSU)",
    "phase": "Stage 14 — Disjoint Set Union (DSU)",
    "estimatedTime": 45,
    "statement": "Given the constraints and input parameters for Bricks Falling When Hit, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Bricks Falling When Hit."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Bricks Falling When Hit.",
      "Leverage the optimal Union Find pattern to reduce time complexity."
    ],
    "learningObjective": "Master Union Find techniques by solving Hard problem constraints for Bricks Falling When Hit.",
    "whyThisPattern": "When observing Union Find problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/bricks-falling-when-hit/",
    "leetcode_title": "Bricks Falling When Hit",
    "leetcode_id": 803,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/bricks-falling-when-hit/",
    "canonicalSlug": "bricks-falling-when-hit",
    "canonicalUrl": "https://leetcode.com/problems/bricks-falling-when-hit/",
    "url": "https://leetcode.com/problems/bricks-falling-when-hit/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Bricks Falling When Hit\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Bricks Falling When Hit\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Bricks Falling When Hit\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Bricks Falling When Hit\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Bricks Falling When Hit\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Bricks Falling When Hit\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Bricks Falling When Hit\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Bricks Falling When Hit\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Bricks Falling When Hit",
      "cpp_optimal": "// Solution for Bricks Falling When Hit",
      "java_brute": "// Solution for Bricks Falling When Hit",
      "java_optimal": "// Solution for Bricks Falling When Hit",
      "python_brute": "# Solution for Bricks Falling When Hit",
      "python_optimal": "# Solution for Bricks Falling When Hit"
    },
    "originalOrder": 986,
    "learningOrder": 986
  },
  {
    "id": 687,
    "number": 687,
    "sequence_number": 687,
    "title": "Similar String Groups",
    "slug": "similar-string-groups",
    "difficulty": "Hard",
    "topic": "Union Find",
    "subtopic": "Union Find Optimization",
    "pattern": "Word Edge DSU",
    "secondary_patterns": [
      "Word Edge DSU"
    ],
    "stage": "Disjoint Set Union (DSU)",
    "curriculumStage": "Stage 14 — Disjoint Set Union (DSU)",
    "roadmapPhase": "Stage 14 — Disjoint Set Union (DSU)",
    "phase": "Stage 14 — Disjoint Set Union (DSU)",
    "estimatedTime": 45,
    "statement": "Given the constraints and input parameters for Similar String Groups, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Similar String Groups."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Similar String Groups.",
      "Leverage the optimal Union Find pattern to reduce time complexity."
    ],
    "learningObjective": "Master Union Find techniques by solving Hard problem constraints for Similar String Groups.",
    "whyThisPattern": "When observing Union Find problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/similar-string-groups/",
    "leetcode_title": "Similar String Groups",
    "leetcode_id": 839,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/similar-string-groups/",
    "canonicalSlug": "similar-string-groups",
    "canonicalUrl": "https://leetcode.com/problems/similar-string-groups/",
    "url": "https://leetcode.com/problems/similar-string-groups/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Similar String Groups\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Similar String Groups\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Similar String Groups\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Similar String Groups\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Similar String Groups\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Similar String Groups\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Similar String Groups\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Similar String Groups\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Similar String Groups",
      "cpp_optimal": "// Solution for Similar String Groups",
      "java_brute": "// Solution for Similar String Groups",
      "java_optimal": "// Solution for Similar String Groups",
      "python_brute": "# Solution for Similar String Groups",
      "python_optimal": "# Solution for Similar String Groups"
    },
    "originalOrder": 987,
    "learningOrder": 987
  },
  {
    "id": 688,
    "number": 688,
    "sequence_number": 688,
    "title": "Minimize Malware Spread",
    "slug": "minimize-malware-spread",
    "difficulty": "Hard",
    "topic": "Union Find",
    "subtopic": "Union Find Optimization",
    "pattern": "Component Size DSU",
    "secondary_patterns": [
      "Component Size DSU"
    ],
    "stage": "Disjoint Set Union (DSU)",
    "curriculumStage": "Stage 14 — Disjoint Set Union (DSU)",
    "roadmapPhase": "Stage 14 — Disjoint Set Union (DSU)",
    "phase": "Stage 14 — Disjoint Set Union (DSU)",
    "estimatedTime": 45,
    "statement": "Given the constraints and input parameters for Minimize Malware Spread, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Minimize Malware Spread."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Minimize Malware Spread.",
      "Leverage the optimal Union Find pattern to reduce time complexity."
    ],
    "learningObjective": "Master Union Find techniques by solving Hard problem constraints for Minimize Malware Spread.",
    "whyThisPattern": "When observing Union Find problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/minimize-malware-spread/",
    "leetcode_title": "Minimize Malware Spread",
    "leetcode_id": 924,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/minimize-malware-spread/",
    "canonicalSlug": "minimize-malware-spread",
    "canonicalUrl": "https://leetcode.com/problems/minimize-malware-spread/",
    "url": "https://leetcode.com/problems/minimize-malware-spread/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Minimize Malware Spread\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Minimize Malware Spread\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Minimize Malware Spread\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Minimize Malware Spread\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Minimize Malware Spread\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Minimize Malware Spread\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Minimize Malware Spread\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Minimize Malware Spread\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Minimize Malware Spread",
      "cpp_optimal": "// Solution for Minimize Malware Spread",
      "java_brute": "// Solution for Minimize Malware Spread",
      "java_optimal": "// Solution for Minimize Malware Spread",
      "python_brute": "# Solution for Minimize Malware Spread",
      "python_optimal": "# Solution for Minimize Malware Spread"
    },
    "originalOrder": 988,
    "learningOrder": 988
  },
  {
    "id": 689,
    "number": 689,
    "sequence_number": 689,
    "title": "Redundant Connection II",
    "slug": "redundant-connection-ii",
    "difficulty": "Hard",
    "topic": "Union Find",
    "subtopic": "Union Find Optimization",
    "pattern": "Directed Graph Two Parents DSU",
    "secondary_patterns": [
      "Directed Graph Two Parents DSU"
    ],
    "stage": "Disjoint Set Union (DSU)",
    "curriculumStage": "Stage 14 — Disjoint Set Union (DSU)",
    "roadmapPhase": "Stage 14 — Disjoint Set Union (DSU)",
    "phase": "Stage 14 — Disjoint Set Union (DSU)",
    "estimatedTime": 45,
    "statement": "Given the constraints and input parameters for Redundant Connection II, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Redundant Connection II."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Redundant Connection II.",
      "Leverage the optimal Union Find pattern to reduce time complexity."
    ],
    "learningObjective": "Master Union Find techniques by solving Hard problem constraints for Redundant Connection II.",
    "whyThisPattern": "When observing Union Find problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/redundant-connection-ii/",
    "leetcode_title": "Redundant Connection II",
    "leetcode_id": 685,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/redundant-connection-ii/",
    "canonicalSlug": "redundant-connection-ii",
    "canonicalUrl": "https://leetcode.com/problems/redundant-connection-ii/",
    "url": "https://leetcode.com/problems/redundant-connection-ii/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Redundant Connection II\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Redundant Connection II\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Redundant Connection II\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Redundant Connection II\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Redundant Connection II\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Redundant Connection II\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Redundant Connection II\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Redundant Connection II\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Redundant Connection II",
      "cpp_optimal": "// Solution for Redundant Connection II",
      "java_brute": "// Solution for Redundant Connection II",
      "java_optimal": "// Solution for Redundant Connection II",
      "python_brute": "# Solution for Redundant Connection II",
      "python_optimal": "# Solution for Redundant Connection II"
    },
    "originalOrder": 989,
    "learningOrder": 989
  },
  {
    "id": 690,
    "number": 690,
    "sequence_number": 690,
    "title": "Making A Large Island",
    "slug": "making-a-large-island",
    "difficulty": "Hard",
    "topic": "Union Find",
    "subtopic": "Union Find Optimization",
    "pattern": "Grid Component Union ID",
    "secondary_patterns": [
      "Grid Component Union ID"
    ],
    "stage": "Disjoint Set Union (DSU)",
    "curriculumStage": "Stage 14 — Disjoint Set Union (DSU)",
    "roadmapPhase": "Stage 14 — Disjoint Set Union (DSU)",
    "phase": "Stage 14 — Disjoint Set Union (DSU)",
    "estimatedTime": 45,
    "statement": "Given the constraints and input parameters for Making A Large Island, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Making A Large Island."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Making A Large Island.",
      "Leverage the optimal Union Find pattern to reduce time complexity."
    ],
    "learningObjective": "Master Union Find techniques by solving Hard problem constraints for Making A Large Island.",
    "whyThisPattern": "When observing Union Find problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/making-a-large-island/",
    "leetcode_title": "Making A Large Island",
    "leetcode_id": 827,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/making-a-large-island/",
    "canonicalSlug": "making-a-large-island",
    "canonicalUrl": "https://leetcode.com/problems/making-a-large-island/",
    "url": "https://leetcode.com/problems/making-a-large-island/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Making A Large Island\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Making A Large Island\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Making A Large Island\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Making A Large Island\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Making A Large Island\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Making A Large Island\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Making A Large Island\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Making A Large Island\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Making A Large Island",
      "cpp_optimal": "// Solution for Making A Large Island",
      "java_brute": "// Solution for Making A Large Island",
      "java_optimal": "// Solution for Making A Large Island",
      "python_brute": "# Solution for Making A Large Island",
      "python_optimal": "# Solution for Making A Large Island"
    },
    "originalOrder": 990,
    "learningOrder": 990
  },
  {
    "id": 691,
    "number": 691,
    "sequence_number": 691,
    "title": "Minimize Malware Spread II",
    "slug": "minimize-malware-spread-ii",
    "difficulty": "Hard",
    "topic": "Union Find",
    "subtopic": "Union Find Optimization",
    "pattern": "Infection Component DSU",
    "secondary_patterns": [
      "Infection Component DSU"
    ],
    "stage": "Disjoint Set Union (DSU)",
    "curriculumStage": "Stage 14 — Disjoint Set Union (DSU)",
    "roadmapPhase": "Stage 14 — Disjoint Set Union (DSU)",
    "phase": "Stage 14 — Disjoint Set Union (DSU)",
    "estimatedTime": 45,
    "statement": "Given the constraints and input parameters for Minimize Malware Spread II, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Minimize Malware Spread II."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Minimize Malware Spread II.",
      "Leverage the optimal Union Find pattern to reduce time complexity."
    ],
    "learningObjective": "Master Union Find techniques by solving Hard problem constraints for Minimize Malware Spread II.",
    "whyThisPattern": "When observing Union Find problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/minimize-malware-spread-ii/",
    "leetcode_title": "Minimize Malware Spread II",
    "leetcode_id": 928,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/minimize-malware-spread-ii/",
    "canonicalSlug": "minimize-malware-spread-ii",
    "canonicalUrl": "https://leetcode.com/problems/minimize-malware-spread-ii/",
    "url": "https://leetcode.com/problems/minimize-malware-spread-ii/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Minimize Malware Spread II\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Minimize Malware Spread II\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Minimize Malware Spread II\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Minimize Malware Spread II\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Minimize Malware Spread II\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Minimize Malware Spread II\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Minimize Malware Spread II\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Minimize Malware Spread II\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Minimize Malware Spread II",
      "cpp_optimal": "// Solution for Minimize Malware Spread II",
      "java_brute": "// Solution for Minimize Malware Spread II",
      "java_optimal": "// Solution for Minimize Malware Spread II",
      "python_brute": "# Solution for Minimize Malware Spread II",
      "python_optimal": "# Solution for Minimize Malware Spread II"
    },
    "originalOrder": 991,
    "learningOrder": 991
  },
  {
    "id": 692,
    "number": 692,
    "sequence_number": 692,
    "title": "Largest Component Size by Common Factor",
    "slug": "largest-component-size-by-common-factor",
    "difficulty": "Hard",
    "topic": "Union Find",
    "subtopic": "Union Find Optimization",
    "pattern": "Prime Factor DSU",
    "secondary_patterns": [
      "Prime Factor DSU"
    ],
    "stage": "Disjoint Set Union (DSU)",
    "curriculumStage": "Stage 14 — Disjoint Set Union (DSU)",
    "roadmapPhase": "Stage 14 — Disjoint Set Union (DSU)",
    "phase": "Stage 14 — Disjoint Set Union (DSU)",
    "estimatedTime": 45,
    "statement": "Given the constraints and input parameters for Largest Component Size by Common Factor, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Largest Component Size by Common Factor."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Largest Component Size by Common Factor.",
      "Leverage the optimal Union Find pattern to reduce time complexity."
    ],
    "learningObjective": "Master Union Find techniques by solving Hard problem constraints for Largest Component Size by Common Factor.",
    "whyThisPattern": "When observing Union Find problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/largest-component-size-by-common-factor/",
    "leetcode_title": "Largest Component Size by Common Factor",
    "leetcode_id": 952,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/largest-component-size-by-common-factor/",
    "canonicalSlug": "largest-component-size-by-common-factor",
    "canonicalUrl": "https://leetcode.com/problems/largest-component-size-by-common-factor/",
    "url": "https://leetcode.com/problems/largest-component-size-by-common-factor/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Largest Component Size by Common Factor\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Largest Component Size by Common Factor\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Largest Component Size by Common Factor\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Largest Component Size by Common Factor\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Largest Component Size by Common Factor\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Largest Component Size by Common Factor\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Largest Component Size by Common Factor\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Largest Component Size by Common Factor\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Largest Component Size by Common Factor",
      "cpp_optimal": "// Solution for Largest Component Size by Common Factor",
      "java_brute": "// Solution for Largest Component Size by Common Factor",
      "java_optimal": "// Solution for Largest Component Size by Common Factor",
      "python_brute": "# Solution for Largest Component Size by Common Factor",
      "python_optimal": "# Solution for Largest Component Size by Common Factor"
    },
    "originalOrder": 992,
    "learningOrder": 992
  },
  {
    "id": 693,
    "number": 693,
    "sequence_number": 693,
    "title": "Find Critical and Pseudo-Critical Edges in Minimum Spanning Tree",
    "slug": "find-critical-and-pseudo-critical-edges-in-minimum-spanning-tree",
    "difficulty": "Hard",
    "topic": "Union Find",
    "subtopic": "Union Find Optimization",
    "pattern": "Kruskal MST Edge Analysis",
    "secondary_patterns": [
      "Kruskal MST Edge Analysis"
    ],
    "stage": "Disjoint Set Union (DSU)",
    "curriculumStage": "Stage 14 — Disjoint Set Union (DSU)",
    "roadmapPhase": "Stage 14 — Disjoint Set Union (DSU)",
    "phase": "Stage 14 — Disjoint Set Union (DSU)",
    "estimatedTime": 45,
    "statement": "Given the constraints and input parameters for Find Critical and Pseudo-Critical Edges in Minimum Spanning Tree, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Find Critical and Pseudo-Critical Edges in Minimum Spanning Tree."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Find Critical and Pseudo-Critical Edges in Minimum Spanning Tree.",
      "Leverage the optimal Union Find pattern to reduce time complexity."
    ],
    "learningObjective": "Master Union Find techniques by solving Hard problem constraints for Find Critical and Pseudo-Critical Edges in Minimum Spanning Tree.",
    "whyThisPattern": "When observing Union Find problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/find-critical-and-pseudo-critical-edges-in-minimum-spanning-tree/",
    "leetcode_title": "Find Critical and Pseudo-Critical Edges in Minimum Spanning Tree",
    "leetcode_id": 1489,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/find-critical-and-pseudo-critical-edges-in-minimum-spanning-tree/",
    "canonicalSlug": "find-critical-and-pseudo-critical-edges-in-minimum-spanning-tree",
    "canonicalUrl": "https://leetcode.com/problems/find-critical-and-pseudo-critical-edges-in-minimum-spanning-tree/",
    "url": "https://leetcode.com/problems/find-critical-and-pseudo-critical-edges-in-minimum-spanning-tree/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Find Critical and Pseudo-Critical Edges in Minimum Spanning Tree\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Find Critical and Pseudo-Critical Edges in Minimum Spanning Tree\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Find Critical and Pseudo-Critical Edges in Minimum Spanning Tree\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Find Critical and Pseudo-Critical Edges in Minimum Spanning Tree\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Find Critical and Pseudo-Critical Edges in Minimum Spanning Tree\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Find Critical and Pseudo-Critical Edges in Minimum Spanning Tree\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Find Critical and Pseudo-Critical Edges in Minimum Spanning Tree\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Find Critical and Pseudo-Critical Edges in Minimum Spanning Tree\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Find Critical and Pseudo-Critical Edges in Minimum Spanning Tree",
      "cpp_optimal": "// Solution for Find Critical and Pseudo-Critical Edges in Minimum Spanning Tree",
      "java_brute": "// Solution for Find Critical and Pseudo-Critical Edges in Minimum Spanning Tree",
      "java_optimal": "// Solution for Find Critical and Pseudo-Critical Edges in Minimum Spanning Tree",
      "python_brute": "# Solution for Find Critical and Pseudo-Critical Edges in Minimum Spanning Tree",
      "python_optimal": "# Solution for Find Critical and Pseudo-Critical Edges in Minimum Spanning Tree"
    },
    "originalOrder": 993,
    "learningOrder": 993
  },
  {
    "id": 694,
    "number": 694,
    "sequence_number": 694,
    "title": "Couples Holding Hands",
    "slug": "couples-holding-hands",
    "difficulty": "Hard",
    "topic": "Union Find",
    "subtopic": "Union Find Optimization",
    "pattern": "Swap Component Graph",
    "secondary_patterns": [
      "Swap Component Graph"
    ],
    "stage": "Disjoint Set Union (DSU)",
    "curriculumStage": "Stage 14 — Disjoint Set Union (DSU)",
    "roadmapPhase": "Stage 14 — Disjoint Set Union (DSU)",
    "phase": "Stage 14 — Disjoint Set Union (DSU)",
    "estimatedTime": 45,
    "statement": "Given the constraints and input parameters for Couples Holding Hands, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Couples Holding Hands."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Couples Holding Hands.",
      "Leverage the optimal Union Find pattern to reduce time complexity."
    ],
    "learningObjective": "Master Union Find techniques by solving Hard problem constraints for Couples Holding Hands.",
    "whyThisPattern": "When observing Union Find problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/couples-holding-hands/",
    "leetcode_title": "Couples Holding Hands",
    "leetcode_id": 765,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/couples-holding-hands/",
    "canonicalSlug": "couples-holding-hands",
    "canonicalUrl": "https://leetcode.com/problems/couples-holding-hands/",
    "url": "https://leetcode.com/problems/couples-holding-hands/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Couples Holding Hands\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Couples Holding Hands\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Couples Holding Hands\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Couples Holding Hands\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Couples Holding Hands\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Couples Holding Hands\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Couples Holding Hands\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Couples Holding Hands\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Couples Holding Hands",
      "cpp_optimal": "// Solution for Couples Holding Hands",
      "java_brute": "// Solution for Couples Holding Hands",
      "java_optimal": "// Solution for Couples Holding Hands",
      "python_brute": "# Solution for Couples Holding Hands",
      "python_optimal": "# Solution for Couples Holding Hands"
    },
    "originalOrder": 994,
    "learningOrder": 994
  },
  {
    "id": 695,
    "number": 695,
    "sequence_number": 695,
    "title": "Maximum Segment Sum After Removals",
    "slug": "maximum-segment-sum-after-removals",
    "difficulty": "Hard",
    "topic": "Union Find",
    "subtopic": "Union Find Optimization",
    "pattern": "Reverse Time DSU Segment Sum",
    "secondary_patterns": [
      "Reverse Time DSU Segment Sum"
    ],
    "stage": "Disjoint Set Union (DSU)",
    "curriculumStage": "Stage 14 — Disjoint Set Union (DSU)",
    "roadmapPhase": "Stage 14 — Disjoint Set Union (DSU)",
    "phase": "Stage 14 — Disjoint Set Union (DSU)",
    "estimatedTime": 45,
    "statement": "Given the constraints and input parameters for Maximum Segment Sum After Removals, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Maximum Segment Sum After Removals."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Maximum Segment Sum After Removals.",
      "Leverage the optimal Union Find pattern to reduce time complexity."
    ],
    "learningObjective": "Master Union Find techniques by solving Hard problem constraints for Maximum Segment Sum After Removals.",
    "whyThisPattern": "When observing Union Find problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/maximum-segment-sum-after-removals/",
    "leetcode_title": "Maximum Segment Sum After Removals",
    "leetcode_id": 2382,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/maximum-segment-sum-after-removals/",
    "canonicalSlug": "maximum-segment-sum-after-removals",
    "canonicalUrl": "https://leetcode.com/problems/maximum-segment-sum-after-removals/",
    "url": "https://leetcode.com/problems/maximum-segment-sum-after-removals/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Maximum Segment Sum After Removals\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Maximum Segment Sum After Removals\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Maximum Segment Sum After Removals\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Maximum Segment Sum After Removals\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Maximum Segment Sum After Removals\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Maximum Segment Sum After Removals\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Maximum Segment Sum After Removals\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Maximum Segment Sum After Removals\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Maximum Segment Sum After Removals",
      "cpp_optimal": "// Solution for Maximum Segment Sum After Removals",
      "java_brute": "// Solution for Maximum Segment Sum After Removals",
      "java_optimal": "// Solution for Maximum Segment Sum After Removals",
      "python_brute": "# Solution for Maximum Segment Sum After Removals",
      "python_optimal": "# Solution for Maximum Segment Sum After Removals"
    },
    "originalOrder": 995,
    "learningOrder": 995
  },
  {
    "id": 696,
    "number": 696,
    "sequence_number": 696,
    "title": "Remove Max Number of Edges to Keep Graph Fully Traversable",
    "slug": "remove-max-number-of-edges-to-keep-graph-fully-traversable",
    "difficulty": "Hard",
    "topic": "Union Find",
    "subtopic": "Union Find Optimization",
    "pattern": "Two-Person DSU Edge Count",
    "secondary_patterns": [
      "Two-Person DSU Edge Count"
    ],
    "stage": "Disjoint Set Union (DSU)",
    "curriculumStage": "Stage 14 — Disjoint Set Union (DSU)",
    "roadmapPhase": "Stage 14 — Disjoint Set Union (DSU)",
    "phase": "Stage 14 — Disjoint Set Union (DSU)",
    "estimatedTime": 45,
    "statement": "Given the constraints and input parameters for Remove Max Number of Edges to Keep Graph Fully Traversable, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Remove Max Number of Edges to Keep Graph Fully Traversable."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Remove Max Number of Edges to Keep Graph Fully Traversable.",
      "Leverage the optimal Union Find pattern to reduce time complexity."
    ],
    "learningObjective": "Master Union Find techniques by solving Hard problem constraints for Remove Max Number of Edges to Keep Graph Fully Traversable.",
    "whyThisPattern": "When observing Union Find problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/remove-max-number-of-edges-to-keep-graph-fully-traversable/",
    "leetcode_title": "Remove Max Number of Edges to Keep Graph Fully Traversable",
    "leetcode_id": 1579,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/remove-max-number-of-edges-to-keep-graph-fully-traversable/",
    "canonicalSlug": "remove-max-number-of-edges-to-keep-graph-fully-traversable",
    "canonicalUrl": "https://leetcode.com/problems/remove-max-number-of-edges-to-keep-graph-fully-traversable/",
    "url": "https://leetcode.com/problems/remove-max-number-of-edges-to-keep-graph-fully-traversable/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Remove Max Number of Edges to Keep Graph Fully Traversable\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Remove Max Number of Edges to Keep Graph Fully Traversable\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Remove Max Number of Edges to Keep Graph Fully Traversable\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Remove Max Number of Edges to Keep Graph Fully Traversable\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Remove Max Number of Edges to Keep Graph Fully Traversable\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Remove Max Number of Edges to Keep Graph Fully Traversable\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Remove Max Number of Edges to Keep Graph Fully Traversable\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Remove Max Number of Edges to Keep Graph Fully Traversable\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Remove Max Number of Edges to Keep Graph Fully Traversable",
      "cpp_optimal": "// Solution for Remove Max Number of Edges to Keep Graph Fully Traversable",
      "java_brute": "// Solution for Remove Max Number of Edges to Keep Graph Fully Traversable",
      "java_optimal": "// Solution for Remove Max Number of Edges to Keep Graph Fully Traversable",
      "python_brute": "# Solution for Remove Max Number of Edges to Keep Graph Fully Traversable",
      "python_optimal": "# Solution for Remove Max Number of Edges to Keep Graph Fully Traversable"
    },
    "originalOrder": 996,
    "learningOrder": 996
  },
  {
    "id": 697,
    "number": 697,
    "sequence_number": 697,
    "title": "Checking Existence of Edge Length Limited Paths",
    "slug": "checking-existence-of-edge-length-limited-paths",
    "difficulty": "Hard",
    "topic": "Union Find",
    "subtopic": "Union Find Optimization",
    "pattern": "Offline Query DSU",
    "secondary_patterns": [
      "Offline Query DSU"
    ],
    "stage": "Disjoint Set Union (DSU)",
    "curriculumStage": "Stage 14 — Disjoint Set Union (DSU)",
    "roadmapPhase": "Stage 14 — Disjoint Set Union (DSU)",
    "phase": "Stage 14 — Disjoint Set Union (DSU)",
    "estimatedTime": 45,
    "statement": "Given the constraints and input parameters for Checking Existence of Edge Length Limited Paths, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Checking Existence of Edge Length Limited Paths."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Checking Existence of Edge Length Limited Paths.",
      "Leverage the optimal Union Find pattern to reduce time complexity."
    ],
    "learningObjective": "Master Union Find techniques by solving Hard problem constraints for Checking Existence of Edge Length Limited Paths.",
    "whyThisPattern": "When observing Union Find problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/checking-existence-of-edge-length-limited-paths/",
    "leetcode_title": "Checking Existence of Edge Length Limited Paths",
    "leetcode_id": 1697,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/checking-existence-of-edge-length-limited-paths/",
    "canonicalSlug": "checking-existence-of-edge-length-limited-paths",
    "canonicalUrl": "https://leetcode.com/problems/checking-existence-of-edge-length-limited-paths/",
    "url": "https://leetcode.com/problems/checking-existence-of-edge-length-limited-paths/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Checking Existence of Edge Length Limited Paths\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Checking Existence of Edge Length Limited Paths\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Checking Existence of Edge Length Limited Paths\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Checking Existence of Edge Length Limited Paths\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Checking Existence of Edge Length Limited Paths\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Checking Existence of Edge Length Limited Paths\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Checking Existence of Edge Length Limited Paths\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Checking Existence of Edge Length Limited Paths\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Checking Existence of Edge Length Limited Paths",
      "cpp_optimal": "// Solution for Checking Existence of Edge Length Limited Paths",
      "java_brute": "// Solution for Checking Existence of Edge Length Limited Paths",
      "java_optimal": "// Solution for Checking Existence of Edge Length Limited Paths",
      "python_brute": "# Solution for Checking Existence of Edge Length Limited Paths",
      "python_optimal": "# Solution for Checking Existence of Edge Length Limited Paths"
    },
    "originalOrder": 997,
    "learningOrder": 997
  },
  {
    "id": 698,
    "number": 698,
    "sequence_number": 698,
    "title": "Process Restricted Friend Requests",
    "slug": "process-restricted-friend-requests",
    "difficulty": "Hard",
    "topic": "Union Find",
    "subtopic": "Union Find Optimization",
    "pattern": "Restriction Check DSU",
    "secondary_patterns": [
      "Restriction Check DSU"
    ],
    "stage": "Disjoint Set Union (DSU)",
    "curriculumStage": "Stage 14 — Disjoint Set Union (DSU)",
    "roadmapPhase": "Stage 14 — Disjoint Set Union (DSU)",
    "phase": "Stage 14 — Disjoint Set Union (DSU)",
    "estimatedTime": 45,
    "statement": "Given the constraints and input parameters for Process Restricted Friend Requests, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Process Restricted Friend Requests."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Process Restricted Friend Requests.",
      "Leverage the optimal Union Find pattern to reduce time complexity."
    ],
    "learningObjective": "Master Union Find techniques by solving Hard problem constraints for Process Restricted Friend Requests.",
    "whyThisPattern": "When observing Union Find problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/process-restricted-friend-requests/",
    "leetcode_title": "Process Restricted Friend Requests",
    "leetcode_id": 2076,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/process-restricted-friend-requests/",
    "canonicalSlug": "process-restricted-friend-requests",
    "canonicalUrl": "https://leetcode.com/problems/process-restricted-friend-requests/",
    "url": "https://leetcode.com/problems/process-restricted-friend-requests/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Process Restricted Friend Requests\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Process Restricted Friend Requests\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Process Restricted Friend Requests\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Process Restricted Friend Requests\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Process Restricted Friend Requests\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Process Restricted Friend Requests\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Process Restricted Friend Requests\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Process Restricted Friend Requests\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Process Restricted Friend Requests",
      "cpp_optimal": "// Solution for Process Restricted Friend Requests",
      "java_brute": "// Solution for Process Restricted Friend Requests",
      "java_optimal": "// Solution for Process Restricted Friend Requests",
      "python_brute": "# Solution for Process Restricted Friend Requests",
      "python_optimal": "# Solution for Process Restricted Friend Requests"
    },
    "originalOrder": 998,
    "learningOrder": 998
  },
  {
    "id": 699,
    "number": 699,
    "sequence_number": 699,
    "title": "Number of Good Paths",
    "slug": "number-of-good-paths",
    "difficulty": "Hard",
    "topic": "Union Find",
    "subtopic": "Union Find Optimization",
    "pattern": "Sorted Value Edge Union DSU",
    "secondary_patterns": [
      "Sorted Value Edge Union DSU"
    ],
    "stage": "Disjoint Set Union (DSU)",
    "curriculumStage": "Stage 14 — Disjoint Set Union (DSU)",
    "roadmapPhase": "Stage 14 — Disjoint Set Union (DSU)",
    "phase": "Stage 14 — Disjoint Set Union (DSU)",
    "estimatedTime": 45,
    "statement": "Given the constraints and input parameters for Number of Good Paths, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Number of Good Paths."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Number of Good Paths.",
      "Leverage the optimal Union Find pattern to reduce time complexity."
    ],
    "learningObjective": "Master Union Find techniques by solving Hard problem constraints for Number of Good Paths.",
    "whyThisPattern": "When observing Union Find problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/number-of-good-paths/",
    "leetcode_title": "Number of Good Paths",
    "leetcode_id": 2421,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/number-of-good-paths/",
    "canonicalSlug": "number-of-good-paths",
    "canonicalUrl": "https://leetcode.com/problems/number-of-good-paths/",
    "url": "https://leetcode.com/problems/number-of-good-paths/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Number of Good Paths\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Number of Good Paths\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Number of Good Paths\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Number of Good Paths\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Number of Good Paths\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Number of Good Paths\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Number of Good Paths\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Number of Good Paths\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Number of Good Paths",
      "cpp_optimal": "// Solution for Number of Good Paths",
      "java_brute": "// Solution for Number of Good Paths",
      "java_optimal": "// Solution for Number of Good Paths",
      "python_brute": "# Solution for Number of Good Paths",
      "python_optimal": "# Solution for Number of Good Paths"
    },
    "originalOrder": 999,
    "learningOrder": 999
  },
  {
    "id": 700,
    "number": 700,
    "sequence_number": 700,
    "title": "Find the String with LCP",
    "slug": "find-the-string-with-lcp",
    "difficulty": "Hard",
    "topic": "Union Find",
    "subtopic": "Union Find Optimization",
    "pattern": "LCP Matrix DSU Reconstruct",
    "secondary_patterns": [
      "LCP Matrix DSU Reconstruct"
    ],
    "stage": "Disjoint Set Union (DSU)",
    "curriculumStage": "Stage 14 — Disjoint Set Union (DSU)",
    "roadmapPhase": "Stage 14 — Disjoint Set Union (DSU)",
    "phase": "Stage 14 — Disjoint Set Union (DSU)",
    "estimatedTime": 45,
    "statement": "Given the constraints and input parameters for Find the String with LCP, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Find the String with LCP."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Find the String with LCP.",
      "Leverage the optimal Union Find pattern to reduce time complexity."
    ],
    "learningObjective": "Master Union Find techniques by solving Hard problem constraints for Find the String with LCP.",
    "whyThisPattern": "When observing Union Find problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/find-the-string-with-lcp/",
    "leetcode_title": "Find the String with LCP",
    "leetcode_id": 2573,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/find-the-string-with-lcp/",
    "canonicalSlug": "find-the-string-with-lcp",
    "canonicalUrl": "https://leetcode.com/problems/find-the-string-with-lcp/",
    "url": "https://leetcode.com/problems/find-the-string-with-lcp/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Find the String with LCP\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Find the String with LCP\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Find the String with LCP\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Find the String with LCP\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Find the String with LCP\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Find the String with LCP\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Find the String with LCP\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Find the String with LCP\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Find the String with LCP",
      "cpp_optimal": "// Solution for Find the String with LCP",
      "java_brute": "// Solution for Find the String with LCP",
      "java_optimal": "// Solution for Find the String with LCP",
      "python_brute": "# Solution for Find the String with LCP",
      "python_optimal": "# Solution for Find the String with LCP"
    },
    "originalOrder": 1000,
    "learningOrder": 1000
  },
  {
    "id": 701,
    "number": 701,
    "sequence_number": 701,
    "title": "Assign Cookies",
    "slug": "assign-cookies",
    "difficulty": "Easy",
    "topic": "Greedy",
    "subtopic": "Hashing & Array Optimization",
    "pattern": "Hashing & Array Optimization",
    "secondary_patterns": [
      "Hashing & Array Optimization"
    ],
    "stage": "Greedy Algorithms & Intervals",
    "curriculumStage": "Stage 15 — Greedy Algorithms & Intervals",
    "roadmapPhase": "Stage 15 — Greedy Algorithms & Intervals",
    "phase": "Stage 15 — Greedy Algorithms & Intervals",
    "estimatedTime": 15,
    "statement": "Solve the **Assign Cookies Optimization** problem using the **Hashing & Array Optimization** technique. Given input constraints appropriate for Easy level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^4",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Hashing & Array Optimization identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Hashing & Array Optimization. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Hashing & Array Optimization techniques by solving Easy problem constraints for Assign Cookies Optimization.",
    "whyThisPattern": "When observing arrays & strings problem conditions, Hashing & Array Optimization optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Meta",
      "Apple",
      "Netflix"
    ],
    "companyRelevanceTier": "Medium",
    "leetcode_url": "https://leetcode.com/problems/assign-cookies/",
    "leetcode_title": "Assign Cookies",
    "leetcode_id": 455,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/assign-cookies/",
    "canonicalSlug": "assign-cookies",
    "canonicalUrl": "https://leetcode.com/problems/assign-cookies/",
    "url": "https://leetcode.com/problems/assign-cookies/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Assign Cookies Optimization (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Assign Cookies Optimization (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Assign Cookies Optimization (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Assign Cookies Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Assign Cookies Optimization (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Assign Cookies Optimization (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Assign Cookies Optimization (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Assign Cookies Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Assign Cookies",
      "cpp_optimal": "// Solution for Assign Cookies",
      "java_brute": "// Solution for Assign Cookies",
      "java_optimal": "// Solution for Assign Cookies",
      "python_brute": "# Solution for Assign Cookies",
      "python_optimal": "# Solution for Assign Cookies"
    },
    "originalOrder": 147,
    "learningOrder": 147
  },
  {
    "id": 702,
    "number": 702,
    "sequence_number": 702,
    "title": "Lemonade Change",
    "slug": "lemonade-change",
    "difficulty": "Easy",
    "topic": "Greedy",
    "subtopic": "Hashing & Array Optimization",
    "pattern": "Hashing & Array Optimization",
    "secondary_patterns": [
      "Hashing & Array Optimization"
    ],
    "stage": "Greedy Algorithms & Intervals",
    "curriculumStage": "Stage 15 — Greedy Algorithms & Intervals",
    "roadmapPhase": "Stage 15 — Greedy Algorithms & Intervals",
    "phase": "Stage 15 — Greedy Algorithms & Intervals",
    "estimatedTime": 15,
    "statement": "Solve the **Lemonade Change Optimization** problem using the **Hashing & Array Optimization** technique. Given input constraints appropriate for Easy level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^4",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Hashing & Array Optimization identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Hashing & Array Optimization. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Hashing & Array Optimization techniques by solving Easy problem constraints for Lemonade Change Optimization.",
    "whyThisPattern": "When observing arrays & strings problem conditions, Hashing & Array Optimization optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Apple",
      "Adobe",
      "Atlassian"
    ],
    "companyRelevanceTier": "Medium",
    "leetcode_url": "https://leetcode.com/problems/lemonade-change/",
    "leetcode_title": "Lemonade Change",
    "leetcode_id": 860,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/lemonade-change/",
    "canonicalSlug": "lemonade-change",
    "canonicalUrl": "https://leetcode.com/problems/lemonade-change/",
    "url": "https://leetcode.com/problems/lemonade-change/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Lemonade Change Optimization (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Lemonade Change Optimization (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Lemonade Change Optimization (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Lemonade Change Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Lemonade Change Optimization (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Lemonade Change Optimization (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Lemonade Change Optimization (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Lemonade Change Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Lemonade Change",
      "cpp_optimal": "// Solution for Lemonade Change",
      "java_brute": "// Solution for Lemonade Change",
      "java_optimal": "// Solution for Lemonade Change",
      "python_brute": "# Solution for Lemonade Change",
      "python_optimal": "# Solution for Lemonade Change"
    },
    "originalOrder": 148,
    "learningOrder": 148
  },
  {
    "id": 703,
    "number": 703,
    "sequence_number": 703,
    "title": "Fair Candy Swap",
    "slug": "fair-candy-swap",
    "difficulty": "Easy",
    "topic": "Greedy",
    "subtopic": "Hashing & Array Optimization",
    "pattern": "Hashing & Array Optimization",
    "secondary_patterns": [
      "Hashing & Array Optimization"
    ],
    "stage": "Greedy Algorithms & Intervals",
    "curriculumStage": "Stage 15 — Greedy Algorithms & Intervals",
    "roadmapPhase": "Stage 15 — Greedy Algorithms & Intervals",
    "phase": "Stage 15 — Greedy Algorithms & Intervals",
    "estimatedTime": 15,
    "statement": "Solve the **Fair Candy Swap Challenge** problem using the **Hashing & Array Optimization** technique. Given input constraints appropriate for Easy level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^4",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Hashing & Array Optimization identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Hashing & Array Optimization. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Hashing & Array Optimization techniques by solving Easy problem constraints for Fair Candy Swap Challenge.",
    "whyThisPattern": "When observing arrays & strings problem conditions, Hashing & Array Optimization optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Microsoft",
      "Bloomberg",
      "Adobe"
    ],
    "companyRelevanceTier": "Medium",
    "leetcode_url": "https://leetcode.com/problems/fair-candy-swap/",
    "leetcode_title": "Fair Candy Swap",
    "leetcode_id": 888,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/fair-candy-swap/",
    "canonicalSlug": "fair-candy-swap",
    "canonicalUrl": "https://leetcode.com/problems/fair-candy-swap/",
    "url": "https://leetcode.com/problems/fair-candy-swap/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Fair Candy Swap Challenge (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Fair Candy Swap Challenge (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Fair Candy Swap Challenge (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Fair Candy Swap Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Fair Candy Swap Challenge (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Fair Candy Swap Challenge (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Fair Candy Swap Challenge (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Fair Candy Swap Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Fair Candy Swap",
      "cpp_optimal": "// Solution for Fair Candy Swap",
      "java_brute": "// Solution for Fair Candy Swap",
      "java_optimal": "// Solution for Fair Candy Swap",
      "python_brute": "# Solution for Fair Candy Swap",
      "python_optimal": "# Solution for Fair Candy Swap"
    },
    "originalOrder": 149,
    "learningOrder": 149
  },
  {
    "id": 704,
    "number": 704,
    "sequence_number": 704,
    "title": "Maximize Sum Of Array After K Negations",
    "slug": "maximize-sum-of-array-after-k-negations",
    "difficulty": "Easy",
    "topic": "Greedy",
    "subtopic": "Greedy Optimization",
    "pattern": "Sort & Flip Smallest",
    "secondary_patterns": [
      "Sort & Flip Smallest"
    ],
    "stage": "Greedy Algorithms & Intervals",
    "curriculumStage": "Stage 15 — Greedy Algorithms & Intervals",
    "roadmapPhase": "Stage 15 — Greedy Algorithms & Intervals",
    "phase": "Stage 15 — Greedy Algorithms & Intervals",
    "estimatedTime": 15,
    "statement": "Given the constraints and input parameters for Maximize Sum Of Array After K Negations, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Maximize Sum Of Array After K Negations."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Maximize Sum Of Array After K Negations.",
      "Leverage the optimal Greedy pattern to reduce time complexity."
    ],
    "learningObjective": "Master Greedy techniques by solving Easy problem constraints for Maximize Sum Of Array After K Negations.",
    "whyThisPattern": "When observing Greedy problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/maximize-sum-of-array-after-k-negations/",
    "leetcode_title": "Maximize Sum Of Array After K Negations",
    "leetcode_id": 1005,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/maximize-sum-of-array-after-k-negations/",
    "canonicalSlug": "maximize-sum-of-array-after-k-negations",
    "canonicalUrl": "https://leetcode.com/problems/maximize-sum-of-array-after-k-negations/",
    "url": "https://leetcode.com/problems/maximize-sum-of-array-after-k-negations/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Maximize Sum Of Array After K Negations\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Maximize Sum Of Array After K Negations\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Maximize Sum Of Array After K Negations\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Maximize Sum Of Array After K Negations\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Maximize Sum Of Array After K Negations\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Maximize Sum Of Array After K Negations\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Maximize Sum Of Array After K Negations\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Maximize Sum Of Array After K Negations\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Maximize Sum Of Array After K Negations",
      "cpp_optimal": "// Solution for Maximize Sum Of Array After K Negations",
      "java_brute": "// Solution for Maximize Sum Of Array After K Negations",
      "java_optimal": "// Solution for Maximize Sum Of Array After K Negations",
      "python_brute": "# Solution for Maximize Sum Of Array After K Negations",
      "python_optimal": "# Solution for Maximize Sum Of Array After K Negations"
    },
    "originalOrder": 150,
    "learningOrder": 150
  },
  {
    "id": 705,
    "number": 705,
    "sequence_number": 705,
    "title": "Delete Duplicate Emails",
    "slug": "delete-duplicate-emails-challenge",
    "difficulty": "Easy",
    "topic": "Strings",
    "subtopic": "Hashing & Array Optimization",
    "pattern": "Hashing & Array Optimization",
    "secondary_patterns": [
      "Hashing & Array Optimization"
    ],
    "stage": "Greedy Algorithms & Intervals",
    "curriculumStage": "Stage 15 — Greedy Algorithms & Intervals",
    "roadmapPhase": "Stage 15 — Greedy Algorithms & Intervals",
    "phase": "Stage 15 — Greedy Algorithms & Intervals",
    "estimatedTime": 15,
    "statement": "Solve the **Delete Duplicate Emails Challenge** problem using the **Hashing & Array Optimization** technique. Given input constraints appropriate for Easy level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^4",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Hashing & Array Optimization identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Hashing & Array Optimization. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Hashing & Array Optimization techniques by solving Easy problem constraints for Delete Duplicate Emails Challenge.",
    "whyThisPattern": "When observing arrays & strings problem conditions, Hashing & Array Optimization optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Microsoft",
      "Bloomberg"
    ],
    "companyRelevanceTier": "Medium",
    "leetcode_url": "https://leetcode.com/problems/delete-duplicate-emails/",
    "leetcode_title": "Delete Duplicate Emails",
    "leetcode_id": 196,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/delete-duplicate-emails/",
    "canonicalSlug": "delete-duplicate-emails-challenge",
    "canonicalUrl": "https://leetcode.com/problems/delete-duplicate-emails/",
    "url": "https://leetcode.com/problems/delete-duplicate-emails/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Delete Duplicate Emails Challenge (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Delete Duplicate Emails Challenge (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Delete Duplicate Emails Challenge (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Delete Duplicate Emails Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Delete Duplicate Emails Challenge (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Delete Duplicate Emails Challenge (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Delete Duplicate Emails Challenge (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Delete Duplicate Emails Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Delete Duplicate Emails",
      "cpp_optimal": "// Solution for Delete Duplicate Emails",
      "java_brute": "// Solution for Delete Duplicate Emails",
      "java_optimal": "// Solution for Delete Duplicate Emails",
      "python_brute": "# Solution for Delete Duplicate Emails",
      "python_optimal": "# Solution for Delete Duplicate Emails"
    }
  },
  {
    "id": 706,
    "number": 706,
    "sequence_number": 706,
    "title": "Distribute Candies to People",
    "slug": "distribute-candies-to-people",
    "difficulty": "Easy",
    "topic": "Bit Manipulation",
    "subtopic": "Arrays Optimization",
    "pattern": "Round-Robin Simulation",
    "secondary_patterns": [
      "Round-Robin Simulation"
    ],
    "stage": "Greedy Algorithms & Intervals",
    "curriculumStage": "Stage 15 — Greedy Algorithms & Intervals",
    "roadmapPhase": "Stage 15 — Greedy Algorithms & Intervals",
    "phase": "Stage 15 — Greedy Algorithms & Intervals",
    "estimatedTime": 15,
    "statement": "Given the constraints and input parameters for Distribute Candies to People, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Distribute Candies to People."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Distribute Candies to People.",
      "Leverage the optimal Arrays pattern to reduce time complexity."
    ],
    "learningObjective": "Master Arrays techniques by solving Easy problem constraints for Distribute Candies to People.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/distribute-candies-to-people/",
    "leetcode_title": "Distribute Candies to People",
    "leetcode_id": 1103,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/distribute-candies-to-people/",
    "canonicalSlug": "distribute-candies-to-people",
    "canonicalUrl": "https://leetcode.com/problems/distribute-candies-to-people/",
    "url": "https://leetcode.com/problems/distribute-candies-to-people/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Distribute Candies to People\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Distribute Candies to People\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Distribute Candies to People\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Distribute Candies to People\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Distribute Candies to People\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Distribute Candies to People\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Distribute Candies to People\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Distribute Candies to People\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Distribute Candies to People",
      "cpp_optimal": "// Solution for Distribute Candies to People",
      "java_brute": "// Solution for Distribute Candies to People",
      "java_optimal": "// Solution for Distribute Candies to People",
      "python_brute": "# Solution for Distribute Candies to People",
      "python_optimal": "# Solution for Distribute Candies to People"
    },
    "originalOrder": 105,
    "learningOrder": 105
  },
  {
    "id": 707,
    "number": 707,
    "sequence_number": 707,
    "title": "Kids With the Greatest Number of Candies",
    "slug": "kids-with-the-greatest-number-of-candies",
    "difficulty": "Easy",
    "topic": "Bit Manipulation",
    "subtopic": "Arrays Optimization",
    "pattern": "Max Comparison",
    "secondary_patterns": [
      "Max Comparison"
    ],
    "stage": "Greedy Algorithms & Intervals",
    "curriculumStage": "Stage 15 — Greedy Algorithms & Intervals",
    "roadmapPhase": "Stage 15 — Greedy Algorithms & Intervals",
    "phase": "Stage 15 — Greedy Algorithms & Intervals",
    "estimatedTime": 15,
    "statement": "Given the constraints and input parameters for Kids With the Greatest Number of Candies, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Kids With the Greatest Number of Candies."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Kids With the Greatest Number of Candies.",
      "Leverage the optimal Arrays pattern to reduce time complexity."
    ],
    "learningObjective": "Master Arrays techniques by solving Easy problem constraints for Kids With the Greatest Number of Candies.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/kids-with-the-greatest-number-of-candies/",
    "leetcode_title": "Kids With the Greatest Number of Candies",
    "leetcode_id": 1431,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/kids-with-the-greatest-number-of-candies/",
    "canonicalSlug": "kids-with-the-greatest-number-of-candies",
    "canonicalUrl": "https://leetcode.com/problems/kids-with-the-greatest-number-of-candies/",
    "url": "https://leetcode.com/problems/kids-with-the-greatest-number-of-candies/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Kids With the Greatest Number of Candies\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Kids With the Greatest Number of Candies\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Kids With the Greatest Number of Candies\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Kids With the Greatest Number of Candies\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Kids With the Greatest Number of Candies\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Kids With the Greatest Number of Candies\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Kids With the Greatest Number of Candies\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Kids With the Greatest Number of Candies\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Kids With the Greatest Number of Candies",
      "cpp_optimal": "// Solution for Kids With the Greatest Number of Candies",
      "java_brute": "// Solution for Kids With the Greatest Number of Candies",
      "java_optimal": "// Solution for Kids With the Greatest Number of Candies",
      "python_brute": "# Solution for Kids With the Greatest Number of Candies",
      "python_optimal": "# Solution for Kids With the Greatest Number of Candies"
    },
    "originalOrder": 109,
    "learningOrder": 109
  },
  {
    "id": 708,
    "number": 708,
    "sequence_number": 708,
    "title": "Linked List Cycle",
    "slug": "linked-list-cycle",
    "difficulty": "Easy",
    "topic": "Dynamic Programming",
    "subtopic": "Pointer Manipulation",
    "pattern": "Pointer Manipulation",
    "secondary_patterns": [
      "Pointer Manipulation"
    ],
    "stage": "Greedy Algorithms & Intervals",
    "curriculumStage": "Stage 15 — Greedy Algorithms & Intervals",
    "roadmapPhase": "Stage 15 — Greedy Algorithms & Intervals",
    "phase": "Stage 15 — Greedy Algorithms & Intervals",
    "estimatedTime": 15,
    "statement": "Solve the **Linked List Cycle Optimization** problem using the **Pointer Manipulation** technique. Given input constraints appropriate for Easy level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^4",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Pointer Manipulation identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Pointer Manipulation. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Pointer Manipulation techniques by solving Easy problem constraints for Linked List Cycle Optimization.",
    "whyThisPattern": "When observing linked lists problem conditions, Pointer Manipulation optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Apple",
      "Adobe",
      "Atlassian"
    ],
    "companyRelevanceTier": "Medium",
    "leetcode_url": "https://leetcode.com/problems/linked-list-cycle/",
    "leetcode_title": "Linked List Cycle",
    "leetcode_id": 141,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/linked-list-cycle/",
    "canonicalSlug": "linked-list-cycle",
    "canonicalUrl": "https://leetcode.com/problems/linked-list-cycle/",
    "url": "https://leetcode.com/problems/linked-list-cycle/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Linked List Cycle Optimization (Pointer Manipulation)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Linked List Cycle Optimization (Pointer Manipulation)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Linked List Cycle Optimization (Pointer Manipulation)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Linked List Cycle Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Linked List Cycle Optimization (Pointer Manipulation)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Linked List Cycle Optimization (Pointer Manipulation)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Linked List Cycle Optimization (Pointer Manipulation)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Linked List Cycle Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Linked List Cycle",
      "cpp_optimal": "// Solution for Linked List Cycle",
      "java_brute": "// Solution for Linked List Cycle",
      "java_optimal": "// Solution for Linked List Cycle",
      "python_brute": "# Solution for Linked List Cycle",
      "python_optimal": "# Solution for Linked List Cycle"
    },
    "originalOrder": 141,
    "learningOrder": 141
  },
  {
    "id": 709,
    "number": 709,
    "sequence_number": 709,
    "title": "Intersection of Two Linked Lists",
    "slug": "intersection-of-two-linked-lists",
    "difficulty": "Easy",
    "topic": "Dynamic Programming",
    "subtopic": "Pointer Manipulation",
    "pattern": "Pointer Manipulation",
    "secondary_patterns": [
      "Pointer Manipulation"
    ],
    "stage": "Greedy Algorithms & Intervals",
    "curriculumStage": "Stage 15 — Greedy Algorithms & Intervals",
    "roadmapPhase": "Stage 15 — Greedy Algorithms & Intervals",
    "phase": "Stage 15 — Greedy Algorithms & Intervals",
    "estimatedTime": 15,
    "statement": "Solve the **Intersection of Two Linked Lists Challenge** problem using the **Pointer Manipulation** technique. Given input constraints appropriate for Easy level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^4",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Pointer Manipulation identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Pointer Manipulation. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Pointer Manipulation techniques by solving Easy problem constraints for Intersection of Two Linked Lists Challenge.",
    "whyThisPattern": "When observing linked lists problem conditions, Pointer Manipulation optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Amazon",
      "Microsoft",
      "Uber"
    ],
    "companyRelevanceTier": "Medium",
    "leetcode_url": "https://leetcode.com/problems/intersection-of-two-linked-lists/",
    "leetcode_title": "Intersection of Two Linked Lists",
    "leetcode_id": 160,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/intersection-of-two-linked-lists/",
    "canonicalSlug": "intersection-of-two-linked-lists",
    "canonicalUrl": "https://leetcode.com/problems/intersection-of-two-linked-lists/",
    "url": "https://leetcode.com/problems/intersection-of-two-linked-lists/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Intersection of Two Linked Lists Challenge (Pointer Manipulation)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Intersection of Two Linked Lists Challenge (Pointer Manipulation)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Intersection of Two Linked Lists Challenge (Pointer Manipulation)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Intersection of Two Linked Lists Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Intersection of Two Linked Lists Challenge (Pointer Manipulation)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Intersection of Two Linked Lists Challenge (Pointer Manipulation)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Intersection of Two Linked Lists Challenge (Pointer Manipulation)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Intersection of Two Linked Lists Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Intersection of Two Linked Lists",
      "cpp_optimal": "// Solution for Intersection of Two Linked Lists",
      "java_brute": "// Solution for Intersection of Two Linked Lists",
      "java_optimal": "// Solution for Intersection of Two Linked Lists",
      "python_brute": "# Solution for Intersection of Two Linked Lists",
      "python_optimal": "# Solution for Intersection of Two Linked Lists"
    },
    "originalOrder": 142,
    "learningOrder": 142
  },
  {
    "id": 710,
    "number": 710,
    "sequence_number": 710,
    "title": "Power of Two",
    "slug": "power-of-two",
    "difficulty": "Easy",
    "topic": "Math",
    "subtopic": "Hashing & Array Optimization",
    "pattern": "Hashing & Array Optimization",
    "secondary_patterns": [
      "Hashing & Array Optimization"
    ],
    "stage": "Greedy Algorithms & Intervals",
    "curriculumStage": "Stage 15 — Greedy Algorithms & Intervals",
    "roadmapPhase": "Stage 15 — Greedy Algorithms & Intervals",
    "phase": "Stage 15 — Greedy Algorithms & Intervals",
    "estimatedTime": 15,
    "statement": "Solve the **Power of Two Optimization** problem using the **Hashing & Array Optimization** technique. Given input constraints appropriate for Easy level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^4",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Hashing & Array Optimization identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Hashing & Array Optimization. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Hashing & Array Optimization techniques by solving Easy problem constraints for Power of Two Optimization.",
    "whyThisPattern": "When observing arrays & strings problem conditions, Hashing & Array Optimization optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Apple",
      "Adobe",
      "Atlassian"
    ],
    "companyRelevanceTier": "Medium",
    "leetcode_url": "https://leetcode.com/problems/power-of-two/",
    "leetcode_title": "Power of Two",
    "leetcode_id": 231,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/power-of-two/",
    "canonicalSlug": "power-of-two",
    "canonicalUrl": "https://leetcode.com/problems/power-of-two/",
    "url": "https://leetcode.com/problems/power-of-two/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Power of Two Optimization (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Power of Two Optimization (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Power of Two Optimization (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Power of Two Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Power of Two Optimization (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Power of Two Optimization (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Power of Two Optimization (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Power of Two Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Power of Two",
      "cpp_optimal": "// Solution for Power of Two",
      "java_brute": "// Solution for Power of Two",
      "java_optimal": "// Solution for Power of Two",
      "python_brute": "# Solution for Power of Two",
      "python_optimal": "# Solution for Power of Two"
    },
    "originalOrder": 152,
    "learningOrder": 152
  },
  {
    "id": 711,
    "number": 711,
    "sequence_number": 711,
    "title": "Minimum Moves to Equal Array Elements II",
    "slug": "minimum-moves-to-equal-array-elements-ii",
    "difficulty": "Medium",
    "topic": "Arrays",
    "subtopic": "Arrays Optimization",
    "pattern": "Arrays Pattern",
    "secondary_patterns": [
      "Arrays Pattern"
    ],
    "stage": "Greedy Algorithms & Intervals",
    "curriculumStage": "Stage 15 — Greedy Algorithms & Intervals",
    "roadmapPhase": "Stage 15 — Greedy Algorithms & Intervals",
    "phase": "Stage 15 — Greedy Algorithms & Intervals",
    "estimatedTime": 30,
    "statement": "Solve the **Minimum Moves to Equal Array Elements II** problem using standard Arrays techniques. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Arrays algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Arrays properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Arrays techniques by solving Medium problem constraints for Minimum Moves to Equal Array Elements II.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/minimum-moves-to-equal-array-elements-ii/",
    "leetcode_title": "Minimum Moves to Equal Array Elements II",
    "leetcode_id": 462,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/minimum-moves-to-equal-array-elements-ii/",
    "canonicalSlug": "minimum-moves-to-equal-array-elements-ii",
    "canonicalUrl": "https://leetcode.com/problems/minimum-moves-to-equal-array-elements-ii/",
    "url": "https://leetcode.com/problems/minimum-moves-to-equal-array-elements-ii/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Minimum Moves to Equal Array Elements II\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Minimum Moves to Equal Array Elements II\n};",
        "java": "// Java Solution for Minimum Moves to Equal Array Elements II\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Minimum Moves to Equal Array Elements II\n}",
        "python": "# Python Solution for Minimum Moves to Equal Array Elements II\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Minimum Moves to Equal Array Elements II\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Minimum Moves to Equal Array Elements II\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Minimum Moves to Equal Array Elements II\n};",
        "java": "// Optimal Java Solution for Minimum Moves to Equal Array Elements II\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Minimum Moves to Equal Array Elements II\n}",
        "python": "# Optimal Python Solution for Minimum Moves to Equal Array Elements II\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Minimum Moves to Equal Array Elements II\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Minimum Moves to Equal Array Elements II",
      "cpp_optimal": "// Solution for Minimum Moves to Equal Array Elements II",
      "java_brute": "// Solution for Minimum Moves to Equal Array Elements II",
      "java_optimal": "// Solution for Minimum Moves to Equal Array Elements II",
      "python_brute": "# Solution for Minimum Moves to Equal Array Elements II",
      "python_optimal": "# Solution for Minimum Moves to Equal Array Elements II"
    },
    "originalOrder": 336,
    "learningOrder": 336
  },
  {
    "id": 712,
    "number": 712,
    "sequence_number": 712,
    "title": "Can I Win",
    "slug": "can-i-win",
    "difficulty": "Medium",
    "topic": "Arrays",
    "subtopic": "Arrays Optimization",
    "pattern": "Arrays Pattern",
    "secondary_patterns": [
      "Arrays Pattern"
    ],
    "stage": "Greedy Algorithms & Intervals",
    "curriculumStage": "Stage 15 — Greedy Algorithms & Intervals",
    "roadmapPhase": "Stage 15 — Greedy Algorithms & Intervals",
    "phase": "Stage 15 — Greedy Algorithms & Intervals",
    "estimatedTime": 30,
    "statement": "Solve the **Can I Win** problem using standard Arrays techniques. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Arrays algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Arrays properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Arrays techniques by solving Medium problem constraints for Can I Win.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/can-i-win/",
    "leetcode_title": "Can I Win",
    "leetcode_id": 464,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/can-i-win/",
    "canonicalSlug": "can-i-win",
    "canonicalUrl": "https://leetcode.com/problems/can-i-win/",
    "url": "https://leetcode.com/problems/can-i-win/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Can I Win\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Can I Win\n};",
        "java": "// Java Solution for Can I Win\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Can I Win\n}",
        "python": "# Python Solution for Can I Win\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Can I Win\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Can I Win\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Can I Win\n};",
        "java": "// Optimal Java Solution for Can I Win\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Can I Win\n}",
        "python": "# Optimal Python Solution for Can I Win\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Can I Win\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Can I Win",
      "cpp_optimal": "// Solution for Can I Win",
      "java_brute": "// Solution for Can I Win",
      "java_optimal": "// Solution for Can I Win",
      "python_brute": "# Solution for Can I Win",
      "python_optimal": "# Solution for Can I Win"
    },
    "originalOrder": 337,
    "learningOrder": 337
  },
  {
    "id": 713,
    "number": 713,
    "sequence_number": 713,
    "title": "Validate IP Address",
    "slug": "validate-ip-address",
    "difficulty": "Medium",
    "topic": "Arrays",
    "subtopic": "Arrays Optimization",
    "pattern": "Arrays Pattern",
    "secondary_patterns": [
      "Arrays Pattern"
    ],
    "stage": "Greedy Algorithms & Intervals",
    "curriculumStage": "Stage 15 — Greedy Algorithms & Intervals",
    "roadmapPhase": "Stage 15 — Greedy Algorithms & Intervals",
    "phase": "Stage 15 — Greedy Algorithms & Intervals",
    "estimatedTime": 30,
    "statement": "Solve the **Validate IP Address** problem using standard Arrays techniques. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Arrays algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Arrays properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Arrays techniques by solving Medium problem constraints for Validate IP Address.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/validate-ip-address/",
    "leetcode_title": "Validate IP Address",
    "leetcode_id": 468,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/validate-ip-address/",
    "canonicalSlug": "validate-ip-address",
    "canonicalUrl": "https://leetcode.com/problems/validate-ip-address/",
    "url": "https://leetcode.com/problems/validate-ip-address/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Validate IP Address\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Validate IP Address\n};",
        "java": "// Java Solution for Validate IP Address\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Validate IP Address\n}",
        "python": "# Python Solution for Validate IP Address\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Validate IP Address\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Validate IP Address\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Validate IP Address\n};",
        "java": "// Optimal Java Solution for Validate IP Address\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Validate IP Address\n}",
        "python": "# Optimal Python Solution for Validate IP Address\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Validate IP Address\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Validate IP Address",
      "cpp_optimal": "// Solution for Validate IP Address",
      "java_brute": "// Solution for Validate IP Address",
      "java_optimal": "// Solution for Validate IP Address",
      "python_brute": "# Solution for Validate IP Address",
      "python_optimal": "# Solution for Validate IP Address"
    },
    "originalOrder": 338,
    "learningOrder": 338
  },
  {
    "id": 714,
    "number": 714,
    "sequence_number": 714,
    "title": "Heaters",
    "slug": "heaters",
    "difficulty": "Medium",
    "topic": "Arrays",
    "subtopic": "Arrays Optimization",
    "pattern": "Arrays Pattern",
    "secondary_patterns": [
      "Arrays Pattern"
    ],
    "stage": "Greedy Algorithms & Intervals",
    "curriculumStage": "Stage 15 — Greedy Algorithms & Intervals",
    "roadmapPhase": "Stage 15 — Greedy Algorithms & Intervals",
    "phase": "Stage 15 — Greedy Algorithms & Intervals",
    "estimatedTime": 30,
    "statement": "Solve the **Heaters** problem using standard Arrays techniques. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Arrays algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Arrays properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Arrays techniques by solving Medium problem constraints for Heaters.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/heaters/",
    "leetcode_title": "Heaters",
    "leetcode_id": 475,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/heaters/",
    "canonicalSlug": "heaters",
    "canonicalUrl": "https://leetcode.com/problems/heaters/",
    "url": "https://leetcode.com/problems/heaters/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Heaters\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Heaters\n};",
        "java": "// Java Solution for Heaters\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Heaters\n}",
        "python": "# Python Solution for Heaters\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Heaters\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Heaters\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Heaters\n};",
        "java": "// Optimal Java Solution for Heaters\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Heaters\n}",
        "python": "# Optimal Python Solution for Heaters\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Heaters\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Heaters",
      "cpp_optimal": "// Solution for Heaters",
      "java_brute": "// Solution for Heaters",
      "java_optimal": "// Solution for Heaters",
      "python_brute": "# Solution for Heaters",
      "python_optimal": "# Solution for Heaters"
    },
    "originalOrder": 341,
    "learningOrder": 341
  },
  {
    "id": 715,
    "number": 715,
    "sequence_number": 715,
    "title": "Total Hamming Distance",
    "slug": "total-hamming-distance",
    "difficulty": "Medium",
    "topic": "Arrays",
    "subtopic": "Arrays Optimization",
    "pattern": "Arrays Pattern",
    "secondary_patterns": [
      "Arrays Pattern"
    ],
    "stage": "Greedy Algorithms & Intervals",
    "curriculumStage": "Stage 15 — Greedy Algorithms & Intervals",
    "roadmapPhase": "Stage 15 — Greedy Algorithms & Intervals",
    "phase": "Stage 15 — Greedy Algorithms & Intervals",
    "estimatedTime": 30,
    "statement": "Solve the **Total Hamming Distance** problem using standard Arrays techniques. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Arrays algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Arrays properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Arrays techniques by solving Medium problem constraints for Total Hamming Distance.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/total-hamming-distance/",
    "leetcode_title": "Total Hamming Distance",
    "leetcode_id": 477,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/total-hamming-distance/",
    "canonicalSlug": "total-hamming-distance",
    "canonicalUrl": "https://leetcode.com/problems/total-hamming-distance/",
    "url": "https://leetcode.com/problems/total-hamming-distance/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Total Hamming Distance\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Total Hamming Distance\n};",
        "java": "// Java Solution for Total Hamming Distance\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Total Hamming Distance\n}",
        "python": "# Python Solution for Total Hamming Distance\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Total Hamming Distance\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Total Hamming Distance\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Total Hamming Distance\n};",
        "java": "// Optimal Java Solution for Total Hamming Distance\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Total Hamming Distance\n}",
        "python": "# Optimal Python Solution for Total Hamming Distance\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Total Hamming Distance\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Total Hamming Distance",
      "cpp_optimal": "// Solution for Total Hamming Distance",
      "java_brute": "// Solution for Total Hamming Distance",
      "java_optimal": "// Solution for Total Hamming Distance",
      "python_brute": "# Solution for Total Hamming Distance",
      "python_optimal": "# Solution for Total Hamming Distance"
    },
    "originalOrder": 342,
    "learningOrder": 342
  },
  {
    "id": 716,
    "number": 716,
    "sequence_number": 716,
    "title": "Magical String",
    "slug": "magical-string",
    "difficulty": "Medium",
    "topic": "Arrays",
    "subtopic": "Arrays Optimization",
    "pattern": "Arrays Pattern",
    "secondary_patterns": [
      "Arrays Pattern"
    ],
    "stage": "Greedy Algorithms & Intervals",
    "curriculumStage": "Stage 15 — Greedy Algorithms & Intervals",
    "roadmapPhase": "Stage 15 — Greedy Algorithms & Intervals",
    "phase": "Stage 15 — Greedy Algorithms & Intervals",
    "estimatedTime": 30,
    "statement": "Solve the **Magical String** problem using standard Arrays techniques. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Arrays algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Arrays properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Arrays techniques by solving Medium problem constraints for Magical String.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/magical-string/",
    "leetcode_title": "Magical String",
    "leetcode_id": 481,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/magical-string/",
    "canonicalSlug": "magical-string",
    "canonicalUrl": "https://leetcode.com/problems/magical-string/",
    "url": "https://leetcode.com/problems/magical-string/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Magical String\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Magical String\n};",
        "java": "// Java Solution for Magical String\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Magical String\n}",
        "python": "# Python Solution for Magical String\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Magical String\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Magical String\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Magical String\n};",
        "java": "// Optimal Java Solution for Magical String\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Magical String\n}",
        "python": "# Optimal Python Solution for Magical String\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Magical String\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Magical String",
      "cpp_optimal": "// Solution for Magical String",
      "java_brute": "// Solution for Magical String",
      "java_optimal": "// Solution for Magical String",
      "python_brute": "# Solution for Magical String",
      "python_optimal": "# Solution for Magical String"
    },
    "originalOrder": 343,
    "learningOrder": 343
  },
  {
    "id": 717,
    "number": 717,
    "sequence_number": 717,
    "title": "Predict the Winner",
    "slug": "predict-the-winner",
    "difficulty": "Medium",
    "topic": "Arrays",
    "subtopic": "Arrays Optimization",
    "pattern": "Arrays Pattern",
    "secondary_patterns": [
      "Arrays Pattern"
    ],
    "stage": "Greedy Algorithms & Intervals",
    "curriculumStage": "Stage 15 — Greedy Algorithms & Intervals",
    "roadmapPhase": "Stage 15 — Greedy Algorithms & Intervals",
    "phase": "Stage 15 — Greedy Algorithms & Intervals",
    "estimatedTime": 30,
    "statement": "Solve the **Predict the Winner** problem using standard Arrays techniques. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Arrays algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Arrays properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Arrays techniques by solving Medium problem constraints for Predict the Winner.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/predict-the-winner/",
    "leetcode_title": "Predict the Winner",
    "leetcode_id": 486,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/predict-the-winner/",
    "canonicalSlug": "predict-the-winner",
    "canonicalUrl": "https://leetcode.com/problems/predict-the-winner/",
    "url": "https://leetcode.com/problems/predict-the-winner/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Predict the Winner\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Predict the Winner\n};",
        "java": "// Java Solution for Predict the Winner\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Predict the Winner\n}",
        "python": "# Python Solution for Predict the Winner\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Predict the Winner\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Predict the Winner\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Predict the Winner\n};",
        "java": "// Optimal Java Solution for Predict the Winner\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Predict the Winner\n}",
        "python": "# Optimal Python Solution for Predict the Winner\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Predict the Winner\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Predict the Winner",
      "cpp_optimal": "// Solution for Predict the Winner",
      "java_brute": "// Solution for Predict the Winner",
      "java_optimal": "// Solution for Predict the Winner",
      "python_brute": "# Solution for Predict the Winner",
      "python_optimal": "# Solution for Predict the Winner"
    },
    "originalOrder": 344,
    "learningOrder": 344
  },
  {
    "id": 718,
    "number": 718,
    "sequence_number": 718,
    "title": "Non-decreasing Subsequences",
    "slug": "non-decreasing-subsequences",
    "difficulty": "Medium",
    "topic": "Arrays",
    "subtopic": "Arrays Optimization",
    "pattern": "Arrays Pattern",
    "secondary_patterns": [
      "Arrays Pattern"
    ],
    "stage": "Greedy Algorithms & Intervals",
    "curriculumStage": "Stage 15 — Greedy Algorithms & Intervals",
    "roadmapPhase": "Stage 15 — Greedy Algorithms & Intervals",
    "phase": "Stage 15 — Greedy Algorithms & Intervals",
    "estimatedTime": 30,
    "statement": "Solve the **Non-decreasing Subsequences** problem using standard Arrays techniques. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Arrays algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Arrays properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Arrays techniques by solving Medium problem constraints for Non-decreasing Subsequences.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/non-decreasing-subsequences/",
    "leetcode_title": "Non-decreasing Subsequences",
    "leetcode_id": 491,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/non-decreasing-subsequences/",
    "canonicalSlug": "non-decreasing-subsequences",
    "canonicalUrl": "https://leetcode.com/problems/non-decreasing-subsequences/",
    "url": "https://leetcode.com/problems/non-decreasing-subsequences/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Non-decreasing Subsequences\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Non-decreasing Subsequences\n};",
        "java": "// Java Solution for Non-decreasing Subsequences\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Non-decreasing Subsequences\n}",
        "python": "# Python Solution for Non-decreasing Subsequences\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Non-decreasing Subsequences\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Non-decreasing Subsequences\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Non-decreasing Subsequences\n};",
        "java": "// Optimal Java Solution for Non-decreasing Subsequences\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Non-decreasing Subsequences\n}",
        "python": "# Optimal Python Solution for Non-decreasing Subsequences\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Non-decreasing Subsequences\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Non-decreasing Subsequences",
      "cpp_optimal": "// Solution for Non-decreasing Subsequences",
      "java_brute": "// Solution for Non-decreasing Subsequences",
      "java_optimal": "// Solution for Non-decreasing Subsequences",
      "python_brute": "# Solution for Non-decreasing Subsequences",
      "python_optimal": "# Solution for Non-decreasing Subsequences"
    },
    "originalOrder": 345,
    "learningOrder": 345
  },
  {
    "id": 719,
    "number": 719,
    "sequence_number": 719,
    "title": "Diagonal Traverse",
    "slug": "diagonal-traverse",
    "difficulty": "Medium",
    "topic": "Arrays",
    "subtopic": "Arrays Optimization",
    "pattern": "Arrays Pattern",
    "secondary_patterns": [
      "Arrays Pattern"
    ],
    "stage": "Greedy Algorithms & Intervals",
    "curriculumStage": "Stage 15 — Greedy Algorithms & Intervals",
    "roadmapPhase": "Stage 15 — Greedy Algorithms & Intervals",
    "phase": "Stage 15 — Greedy Algorithms & Intervals",
    "estimatedTime": 30,
    "statement": "Solve the **Diagonal Traverse** problem using standard Arrays techniques. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Arrays algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Arrays properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Arrays techniques by solving Medium problem constraints for Diagonal Traverse.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/diagonal-traverse/",
    "leetcode_title": "Diagonal Traverse",
    "leetcode_id": 498,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/diagonal-traverse/",
    "canonicalSlug": "diagonal-traverse",
    "canonicalUrl": "https://leetcode.com/problems/diagonal-traverse/",
    "url": "https://leetcode.com/problems/diagonal-traverse/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Diagonal Traverse\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Diagonal Traverse\n};",
        "java": "// Java Solution for Diagonal Traverse\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Diagonal Traverse\n}",
        "python": "# Python Solution for Diagonal Traverse\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Diagonal Traverse\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Diagonal Traverse\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Diagonal Traverse\n};",
        "java": "// Optimal Java Solution for Diagonal Traverse\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Diagonal Traverse\n}",
        "python": "# Optimal Python Solution for Diagonal Traverse\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Diagonal Traverse\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Diagonal Traverse",
      "cpp_optimal": "// Solution for Diagonal Traverse",
      "java_brute": "// Solution for Diagonal Traverse",
      "java_optimal": "// Solution for Diagonal Traverse",
      "python_brute": "# Solution for Diagonal Traverse",
      "python_optimal": "# Solution for Diagonal Traverse"
    },
    "originalOrder": 346,
    "learningOrder": 346
  },
  {
    "id": 720,
    "number": 720,
    "sequence_number": 720,
    "title": "Longest Palindromic Subsequence",
    "slug": "longest-palindromic-subsequence",
    "difficulty": "Medium",
    "topic": "Arrays",
    "subtopic": "Arrays Optimization",
    "pattern": "Arrays Pattern",
    "secondary_patterns": [
      "Arrays Pattern"
    ],
    "stage": "Greedy Algorithms & Intervals",
    "curriculumStage": "Stage 15 — Greedy Algorithms & Intervals",
    "roadmapPhase": "Stage 15 — Greedy Algorithms & Intervals",
    "phase": "Stage 15 — Greedy Algorithms & Intervals",
    "estimatedTime": 30,
    "statement": "Solve the **Longest Palindromic Subsequence** problem using standard Arrays techniques. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Arrays algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Arrays properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Arrays techniques by solving Medium problem constraints for Longest Palindromic Subsequence.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/longest-palindromic-subsequence/",
    "leetcode_title": "Longest Palindromic Subsequence",
    "leetcode_id": 516,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/longest-palindromic-subsequence/",
    "canonicalSlug": "longest-palindromic-subsequence",
    "canonicalUrl": "https://leetcode.com/problems/longest-palindromic-subsequence/",
    "url": "https://leetcode.com/problems/longest-palindromic-subsequence/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Longest Palindromic Subsequence\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Longest Palindromic Subsequence\n};",
        "java": "// Java Solution for Longest Palindromic Subsequence\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Longest Palindromic Subsequence\n}",
        "python": "# Python Solution for Longest Palindromic Subsequence\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Longest Palindromic Subsequence\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Longest Palindromic Subsequence\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Longest Palindromic Subsequence\n};",
        "java": "// Optimal Java Solution for Longest Palindromic Subsequence\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Longest Palindromic Subsequence\n}",
        "python": "# Optimal Python Solution for Longest Palindromic Subsequence\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Longest Palindromic Subsequence\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Longest Palindromic Subsequence",
      "cpp_optimal": "// Solution for Longest Palindromic Subsequence",
      "java_brute": "// Solution for Longest Palindromic Subsequence",
      "java_optimal": "// Solution for Longest Palindromic Subsequence",
      "python_brute": "# Solution for Longest Palindromic Subsequence",
      "python_optimal": "# Solution for Longest Palindromic Subsequence"
    },
    "originalOrder": 347,
    "learningOrder": 347
  },
  {
    "id": 721,
    "number": 721,
    "sequence_number": 721,
    "title": "Coin Change II",
    "slug": "coin-change-ii",
    "difficulty": "Medium",
    "topic": "Arrays",
    "subtopic": "Arrays Optimization",
    "pattern": "Arrays Pattern",
    "secondary_patterns": [
      "Arrays Pattern"
    ],
    "stage": "Greedy Algorithms & Intervals",
    "curriculumStage": "Stage 15 — Greedy Algorithms & Intervals",
    "roadmapPhase": "Stage 15 — Greedy Algorithms & Intervals",
    "phase": "Stage 15 — Greedy Algorithms & Intervals",
    "estimatedTime": 30,
    "statement": "Solve the **Coin Change II** problem using standard Arrays techniques. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Arrays algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Arrays properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Arrays techniques by solving Medium problem constraints for Coin Change II.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/coin-change-ii/",
    "leetcode_title": "Coin Change II",
    "leetcode_id": 518,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/coin-change-ii/",
    "canonicalSlug": "coin-change-ii",
    "canonicalUrl": "https://leetcode.com/problems/coin-change-ii/",
    "url": "https://leetcode.com/problems/coin-change-ii/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Coin Change II\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Coin Change II\n};",
        "java": "// Java Solution for Coin Change II\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Coin Change II\n}",
        "python": "# Python Solution for Coin Change II\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Coin Change II\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Coin Change II\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Coin Change II\n};",
        "java": "// Optimal Java Solution for Coin Change II\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Coin Change II\n}",
        "python": "# Optimal Python Solution for Coin Change II\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Coin Change II\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Coin Change II",
      "cpp_optimal": "// Solution for Coin Change II",
      "java_brute": "// Solution for Coin Change II",
      "java_optimal": "// Solution for Coin Change II",
      "python_brute": "# Solution for Coin Change II",
      "python_optimal": "# Solution for Coin Change II"
    },
    "originalOrder": 348,
    "learningOrder": 348
  },
  {
    "id": 722,
    "number": 722,
    "sequence_number": 722,
    "title": "Longest Uncommon Subsequence II",
    "slug": "longest-uncommon-subsequence-ii",
    "difficulty": "Medium",
    "topic": "Arrays",
    "subtopic": "Arrays Optimization",
    "pattern": "Arrays Pattern",
    "secondary_patterns": [
      "Arrays Pattern"
    ],
    "stage": "Greedy Algorithms & Intervals",
    "curriculumStage": "Stage 15 — Greedy Algorithms & Intervals",
    "roadmapPhase": "Stage 15 — Greedy Algorithms & Intervals",
    "phase": "Stage 15 — Greedy Algorithms & Intervals",
    "estimatedTime": 30,
    "statement": "Solve the **Longest Uncommon Subsequence II** problem using standard Arrays techniques. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Arrays algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Arrays properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Arrays techniques by solving Medium problem constraints for Longest Uncommon Subsequence II.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/longest-uncommon-subsequence-ii/",
    "leetcode_title": "Longest Uncommon Subsequence II",
    "leetcode_id": 522,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/longest-uncommon-subsequence-ii/",
    "canonicalSlug": "longest-uncommon-subsequence-ii",
    "canonicalUrl": "https://leetcode.com/problems/longest-uncommon-subsequence-ii/",
    "url": "https://leetcode.com/problems/longest-uncommon-subsequence-ii/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Longest Uncommon Subsequence II\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Longest Uncommon Subsequence II\n};",
        "java": "// Java Solution for Longest Uncommon Subsequence II\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Longest Uncommon Subsequence II\n}",
        "python": "# Python Solution for Longest Uncommon Subsequence II\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Longest Uncommon Subsequence II\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Longest Uncommon Subsequence II\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Longest Uncommon Subsequence II\n};",
        "java": "// Optimal Java Solution for Longest Uncommon Subsequence II\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Longest Uncommon Subsequence II\n}",
        "python": "# Optimal Python Solution for Longest Uncommon Subsequence II\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Longest Uncommon Subsequence II\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Longest Uncommon Subsequence II",
      "cpp_optimal": "// Solution for Longest Uncommon Subsequence II",
      "java_brute": "// Solution for Longest Uncommon Subsequence II",
      "java_optimal": "// Solution for Longest Uncommon Subsequence II",
      "python_brute": "# Solution for Longest Uncommon Subsequence II",
      "python_optimal": "# Solution for Longest Uncommon Subsequence II"
    },
    "originalOrder": 349,
    "learningOrder": 349
  },
  {
    "id": 723,
    "number": 723,
    "sequence_number": 723,
    "title": "Continuous Subarray Sum",
    "slug": "continuous-subarray-sum",
    "difficulty": "Medium",
    "topic": "Arrays",
    "subtopic": "Arrays Optimization",
    "pattern": "Arrays Pattern",
    "secondary_patterns": [
      "Arrays Pattern"
    ],
    "stage": "Greedy Algorithms & Intervals",
    "curriculumStage": "Stage 15 — Greedy Algorithms & Intervals",
    "roadmapPhase": "Stage 15 — Greedy Algorithms & Intervals",
    "phase": "Stage 15 — Greedy Algorithms & Intervals",
    "estimatedTime": 30,
    "statement": "Solve the **Continuous Subarray Sum** problem using standard Arrays techniques. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Arrays algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Arrays properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Arrays techniques by solving Medium problem constraints for Continuous Subarray Sum.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/continuous-subarray-sum/",
    "leetcode_title": "Continuous Subarray Sum",
    "leetcode_id": 523,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/continuous-subarray-sum/",
    "canonicalSlug": "continuous-subarray-sum",
    "canonicalUrl": "https://leetcode.com/problems/continuous-subarray-sum/",
    "url": "https://leetcode.com/problems/continuous-subarray-sum/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Continuous Subarray Sum\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Continuous Subarray Sum\n};",
        "java": "// Java Solution for Continuous Subarray Sum\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Continuous Subarray Sum\n}",
        "python": "# Python Solution for Continuous Subarray Sum\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Continuous Subarray Sum\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Continuous Subarray Sum\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Continuous Subarray Sum\n};",
        "java": "// Optimal Java Solution for Continuous Subarray Sum\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Continuous Subarray Sum\n}",
        "python": "# Optimal Python Solution for Continuous Subarray Sum\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Continuous Subarray Sum\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Continuous Subarray Sum",
      "cpp_optimal": "// Solution for Continuous Subarray Sum",
      "java_brute": "// Solution for Continuous Subarray Sum",
      "java_optimal": "// Solution for Continuous Subarray Sum",
      "python_brute": "# Solution for Continuous Subarray Sum",
      "python_optimal": "# Solution for Continuous Subarray Sum"
    },
    "originalOrder": 350,
    "learningOrder": 350
  },
  {
    "id": 724,
    "number": 724,
    "sequence_number": 724,
    "title": "Contiguous Array",
    "slug": "contiguous-array",
    "difficulty": "Medium",
    "topic": "Arrays",
    "subtopic": "Arrays Optimization",
    "pattern": "Arrays Pattern",
    "secondary_patterns": [
      "Arrays Pattern"
    ],
    "stage": "Greedy Algorithms & Intervals",
    "curriculumStage": "Stage 15 — Greedy Algorithms & Intervals",
    "roadmapPhase": "Stage 15 — Greedy Algorithms & Intervals",
    "phase": "Stage 15 — Greedy Algorithms & Intervals",
    "estimatedTime": 30,
    "statement": "Solve the **Contiguous Array** problem using standard Arrays techniques. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Arrays algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Arrays properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Arrays techniques by solving Medium problem constraints for Contiguous Array.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/contiguous-array/",
    "leetcode_title": "Contiguous Array",
    "leetcode_id": 525,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/contiguous-array/",
    "canonicalSlug": "contiguous-array",
    "canonicalUrl": "https://leetcode.com/problems/contiguous-array/",
    "url": "https://leetcode.com/problems/contiguous-array/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Contiguous Array\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Contiguous Array\n};",
        "java": "// Java Solution for Contiguous Array\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Contiguous Array\n}",
        "python": "# Python Solution for Contiguous Array\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Contiguous Array\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Contiguous Array\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Contiguous Array\n};",
        "java": "// Optimal Java Solution for Contiguous Array\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Contiguous Array\n}",
        "python": "# Optimal Python Solution for Contiguous Array\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Contiguous Array\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Contiguous Array",
      "cpp_optimal": "// Solution for Contiguous Array",
      "java_brute": "// Solution for Contiguous Array",
      "java_optimal": "// Solution for Contiguous Array",
      "python_brute": "# Solution for Contiguous Array",
      "python_optimal": "# Solution for Contiguous Array"
    },
    "originalOrder": 351,
    "learningOrder": 351
  },
  {
    "id": 725,
    "number": 725,
    "sequence_number": 725,
    "title": "Beautiful Arrangement",
    "slug": "beautiful-arrangement",
    "difficulty": "Medium",
    "topic": "Arrays",
    "subtopic": "Arrays Optimization",
    "pattern": "Arrays Pattern",
    "secondary_patterns": [
      "Arrays Pattern"
    ],
    "stage": "Greedy Algorithms & Intervals",
    "curriculumStage": "Stage 15 — Greedy Algorithms & Intervals",
    "roadmapPhase": "Stage 15 — Greedy Algorithms & Intervals",
    "phase": "Stage 15 — Greedy Algorithms & Intervals",
    "estimatedTime": 30,
    "statement": "Solve the **Beautiful Arrangement** problem using standard Arrays techniques. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Arrays algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Arrays properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Arrays techniques by solving Medium problem constraints for Beautiful Arrangement.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/beautiful-arrangement/",
    "leetcode_title": "Beautiful Arrangement",
    "leetcode_id": 526,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/beautiful-arrangement/",
    "canonicalSlug": "beautiful-arrangement",
    "canonicalUrl": "https://leetcode.com/problems/beautiful-arrangement/",
    "url": "https://leetcode.com/problems/beautiful-arrangement/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Beautiful Arrangement\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Beautiful Arrangement\n};",
        "java": "// Java Solution for Beautiful Arrangement\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Beautiful Arrangement\n}",
        "python": "# Python Solution for Beautiful Arrangement\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Beautiful Arrangement\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Beautiful Arrangement\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Beautiful Arrangement\n};",
        "java": "// Optimal Java Solution for Beautiful Arrangement\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Beautiful Arrangement\n}",
        "python": "# Optimal Python Solution for Beautiful Arrangement\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Beautiful Arrangement\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Beautiful Arrangement",
      "cpp_optimal": "// Solution for Beautiful Arrangement",
      "java_brute": "// Solution for Beautiful Arrangement",
      "java_optimal": "// Solution for Beautiful Arrangement",
      "python_brute": "# Solution for Beautiful Arrangement",
      "python_optimal": "# Solution for Beautiful Arrangement"
    },
    "originalOrder": 352,
    "learningOrder": 352
  },
  {
    "id": 726,
    "number": 726,
    "sequence_number": 726,
    "title": "Minesweeper",
    "slug": "minesweeper",
    "difficulty": "Medium",
    "topic": "Arrays",
    "subtopic": "Arrays Optimization",
    "pattern": "Arrays Pattern",
    "secondary_patterns": [
      "Arrays Pattern"
    ],
    "stage": "Greedy Algorithms & Intervals",
    "curriculumStage": "Stage 15 — Greedy Algorithms & Intervals",
    "roadmapPhase": "Stage 15 — Greedy Algorithms & Intervals",
    "phase": "Stage 15 — Greedy Algorithms & Intervals",
    "estimatedTime": 30,
    "statement": "Solve the **Minesweeper** problem using standard Arrays techniques. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Arrays algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Arrays properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Arrays techniques by solving Medium problem constraints for Minesweeper.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/minesweeper/",
    "leetcode_title": "Minesweeper",
    "leetcode_id": 529,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/minesweeper/",
    "canonicalSlug": "minesweeper",
    "canonicalUrl": "https://leetcode.com/problems/minesweeper/",
    "url": "https://leetcode.com/problems/minesweeper/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Minesweeper\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Minesweeper\n};",
        "java": "// Java Solution for Minesweeper\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Minesweeper\n}",
        "python": "# Python Solution for Minesweeper\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Minesweeper\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Minesweeper\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Minesweeper\n};",
        "java": "// Optimal Java Solution for Minesweeper\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Minesweeper\n}",
        "python": "# Optimal Python Solution for Minesweeper\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Minesweeper\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Minesweeper",
      "cpp_optimal": "// Solution for Minesweeper",
      "java_brute": "// Solution for Minesweeper",
      "java_optimal": "// Solution for Minesweeper",
      "python_brute": "# Solution for Minesweeper",
      "python_optimal": "# Solution for Minesweeper"
    },
    "originalOrder": 354,
    "learningOrder": 354
  },
  {
    "id": 727,
    "number": 727,
    "sequence_number": 727,
    "title": "K-diff Pairs in an Array",
    "slug": "k-diff-pairs-in-an-array",
    "difficulty": "Medium",
    "topic": "Arrays",
    "subtopic": "Arrays Optimization",
    "pattern": "Arrays Pattern",
    "secondary_patterns": [
      "Arrays Pattern"
    ],
    "stage": "Greedy Algorithms & Intervals",
    "curriculumStage": "Stage 15 — Greedy Algorithms & Intervals",
    "roadmapPhase": "Stage 15 — Greedy Algorithms & Intervals",
    "phase": "Stage 15 — Greedy Algorithms & Intervals",
    "estimatedTime": 30,
    "statement": "Solve the **K-diff Pairs in an Array** problem using standard Arrays techniques. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Arrays algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Arrays properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Arrays techniques by solving Medium problem constraints for K-diff Pairs in an Array.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/k-diff-pairs-in-an-array/",
    "leetcode_title": "K-diff Pairs in an Array",
    "leetcode_id": 532,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/k-diff-pairs-in-an-array/",
    "canonicalSlug": "k-diff-pairs-in-an-array",
    "canonicalUrl": "https://leetcode.com/problems/k-diff-pairs-in-an-array/",
    "url": "https://leetcode.com/problems/k-diff-pairs-in-an-array/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for K-diff Pairs in an Array\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for K-diff Pairs in an Array\n};",
        "java": "// Java Solution for K-diff Pairs in an Array\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for K-diff Pairs in an Array\n}",
        "python": "# Python Solution for K-diff Pairs in an Array\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for K-diff Pairs in an Array\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for K-diff Pairs in an Array\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for K-diff Pairs in an Array\n};",
        "java": "// Optimal Java Solution for K-diff Pairs in an Array\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for K-diff Pairs in an Array\n}",
        "python": "# Optimal Python Solution for K-diff Pairs in an Array\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for K-diff Pairs in an Array\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for K-diff Pairs in an Array",
      "cpp_optimal": "// Solution for K-diff Pairs in an Array",
      "java_brute": "// Solution for K-diff Pairs in an Array",
      "java_optimal": "// Solution for K-diff Pairs in an Array",
      "python_brute": "# Solution for K-diff Pairs in an Array",
      "python_optimal": "# Solution for K-diff Pairs in an Array"
    },
    "originalOrder": 355,
    "learningOrder": 355
  },
  {
    "id": 728,
    "number": 728,
    "sequence_number": 728,
    "title": "Complex Number Multiplication",
    "slug": "complex-number-multiplication",
    "difficulty": "Medium",
    "topic": "Arrays",
    "subtopic": "Arrays Optimization",
    "pattern": "Arrays Pattern",
    "secondary_patterns": [
      "Arrays Pattern"
    ],
    "stage": "Greedy Algorithms & Intervals",
    "curriculumStage": "Stage 15 — Greedy Algorithms & Intervals",
    "roadmapPhase": "Stage 15 — Greedy Algorithms & Intervals",
    "phase": "Stage 15 — Greedy Algorithms & Intervals",
    "estimatedTime": 30,
    "statement": "Solve the **Complex Number Multiplication** problem using standard Arrays techniques. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Arrays algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Arrays properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Arrays techniques by solving Medium problem constraints for Complex Number Multiplication.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/complex-number-multiplication/",
    "leetcode_title": "Complex Number Multiplication",
    "leetcode_id": 537,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/complex-number-multiplication/",
    "canonicalSlug": "complex-number-multiplication",
    "canonicalUrl": "https://leetcode.com/problems/complex-number-multiplication/",
    "url": "https://leetcode.com/problems/complex-number-multiplication/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Complex Number Multiplication\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Complex Number Multiplication\n};",
        "java": "// Java Solution for Complex Number Multiplication\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Complex Number Multiplication\n}",
        "python": "# Python Solution for Complex Number Multiplication\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Complex Number Multiplication\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Complex Number Multiplication\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Complex Number Multiplication\n};",
        "java": "// Optimal Java Solution for Complex Number Multiplication\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Complex Number Multiplication\n}",
        "python": "# Optimal Python Solution for Complex Number Multiplication\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Complex Number Multiplication\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Complex Number Multiplication",
      "cpp_optimal": "// Solution for Complex Number Multiplication",
      "java_brute": "// Solution for Complex Number Multiplication",
      "java_optimal": "// Solution for Complex Number Multiplication",
      "python_brute": "# Solution for Complex Number Multiplication",
      "python_optimal": "# Solution for Complex Number Multiplication"
    },
    "originalOrder": 357,
    "learningOrder": 357
  },
  {
    "id": 729,
    "number": 729,
    "sequence_number": 729,
    "title": "Minimum Time Difference",
    "slug": "minimum-time-difference",
    "difficulty": "Medium",
    "topic": "Arrays",
    "subtopic": "Arrays Optimization",
    "pattern": "Arrays Pattern",
    "secondary_patterns": [
      "Arrays Pattern"
    ],
    "stage": "Greedy Algorithms & Intervals",
    "curriculumStage": "Stage 15 — Greedy Algorithms & Intervals",
    "roadmapPhase": "Stage 15 — Greedy Algorithms & Intervals",
    "phase": "Stage 15 — Greedy Algorithms & Intervals",
    "estimatedTime": 30,
    "statement": "Solve the **Minimum Time Difference** problem using standard Arrays techniques. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Arrays algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Arrays properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Arrays techniques by solving Medium problem constraints for Minimum Time Difference.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/minimum-time-difference/",
    "leetcode_title": "Minimum Time Difference",
    "leetcode_id": 539,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/minimum-time-difference/",
    "canonicalSlug": "minimum-time-difference",
    "canonicalUrl": "https://leetcode.com/problems/minimum-time-difference/",
    "url": "https://leetcode.com/problems/minimum-time-difference/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Minimum Time Difference\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Minimum Time Difference\n};",
        "java": "// Java Solution for Minimum Time Difference\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Minimum Time Difference\n}",
        "python": "# Python Solution for Minimum Time Difference\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Minimum Time Difference\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Minimum Time Difference\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Minimum Time Difference\n};",
        "java": "// Optimal Java Solution for Minimum Time Difference\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Minimum Time Difference\n}",
        "python": "# Optimal Python Solution for Minimum Time Difference\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Minimum Time Difference\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Minimum Time Difference",
      "cpp_optimal": "// Solution for Minimum Time Difference",
      "java_brute": "// Solution for Minimum Time Difference",
      "java_optimal": "// Solution for Minimum Time Difference",
      "python_brute": "# Solution for Minimum Time Difference",
      "python_optimal": "# Solution for Minimum Time Difference"
    },
    "originalOrder": 358,
    "learningOrder": 358
  },
  {
    "id": 730,
    "number": 730,
    "sequence_number": 730,
    "title": "Number of Provinces",
    "slug": "number-of-provinces",
    "difficulty": "Medium",
    "topic": "Arrays",
    "subtopic": "Arrays Optimization",
    "pattern": "Arrays Pattern",
    "secondary_patterns": [
      "Arrays Pattern"
    ],
    "stage": "Greedy Algorithms & Intervals",
    "curriculumStage": "Stage 15 — Greedy Algorithms & Intervals",
    "roadmapPhase": "Stage 15 — Greedy Algorithms & Intervals",
    "phase": "Stage 15 — Greedy Algorithms & Intervals",
    "estimatedTime": 30,
    "statement": "Solve the **Number of Provinces** problem using standard Arrays techniques. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Arrays algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Arrays properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Arrays techniques by solving Medium problem constraints for Number of Provinces.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/number-of-provinces/",
    "leetcode_title": "Number of Provinces",
    "leetcode_id": 547,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/number-of-provinces/",
    "canonicalSlug": "number-of-provinces",
    "canonicalUrl": "https://leetcode.com/problems/number-of-provinces/",
    "url": "https://leetcode.com/problems/number-of-provinces/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Number of Provinces\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Number of Provinces\n};",
        "java": "// Java Solution for Number of Provinces\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Number of Provinces\n}",
        "python": "# Python Solution for Number of Provinces\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Number of Provinces\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Number of Provinces\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Number of Provinces\n};",
        "java": "// Optimal Java Solution for Number of Provinces\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Number of Provinces\n}",
        "python": "# Optimal Python Solution for Number of Provinces\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Number of Provinces\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Number of Provinces",
      "cpp_optimal": "// Solution for Number of Provinces",
      "java_brute": "// Solution for Number of Provinces",
      "java_optimal": "// Solution for Number of Provinces",
      "python_brute": "# Solution for Number of Provinces",
      "python_optimal": "# Solution for Number of Provinces"
    },
    "originalOrder": 359,
    "learningOrder": 359
  },
  {
    "id": 731,
    "number": 731,
    "sequence_number": 731,
    "title": "Game Play Analysis IV",
    "slug": "game-play-analysis-iv",
    "difficulty": "Medium",
    "topic": "Arrays",
    "subtopic": "Arrays Optimization",
    "pattern": "Arrays Pattern",
    "secondary_patterns": [
      "Arrays Pattern"
    ],
    "stage": "Greedy Algorithms & Intervals",
    "curriculumStage": "Stage 15 — Greedy Algorithms & Intervals",
    "roadmapPhase": "Stage 15 — Greedy Algorithms & Intervals",
    "phase": "Stage 15 — Greedy Algorithms & Intervals",
    "estimatedTime": 30,
    "statement": "Solve the **Game Play Analysis IV** problem using standard Arrays techniques. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Arrays algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Arrays properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Arrays techniques by solving Medium problem constraints for Game Play Analysis IV.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/game-play-analysis-iv/",
    "leetcode_title": "Game Play Analysis IV",
    "leetcode_id": 550,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/game-play-analysis-iv/",
    "canonicalSlug": "game-play-analysis-iv",
    "canonicalUrl": "https://leetcode.com/problems/game-play-analysis-iv/",
    "url": "https://leetcode.com/problems/game-play-analysis-iv/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Game Play Analysis IV\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Game Play Analysis IV\n};",
        "java": "// Java Solution for Game Play Analysis IV\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Game Play Analysis IV\n}",
        "python": "# Python Solution for Game Play Analysis IV\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Game Play Analysis IV\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Game Play Analysis IV\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Game Play Analysis IV\n};",
        "java": "// Optimal Java Solution for Game Play Analysis IV\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Game Play Analysis IV\n}",
        "python": "# Optimal Python Solution for Game Play Analysis IV\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Game Play Analysis IV\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Game Play Analysis IV",
      "cpp_optimal": "// Solution for Game Play Analysis IV",
      "java_brute": "// Solution for Game Play Analysis IV",
      "java_optimal": "// Solution for Game Play Analysis IV",
      "python_brute": "# Solution for Game Play Analysis IV",
      "python_optimal": "# Solution for Game Play Analysis IV"
    },
    "originalOrder": 360,
    "learningOrder": 360
  },
  {
    "id": 732,
    "number": 732,
    "sequence_number": 732,
    "title": "Optimal Division",
    "slug": "optimal-division",
    "difficulty": "Medium",
    "topic": "Arrays",
    "subtopic": "Arrays Optimization",
    "pattern": "Arrays Pattern",
    "secondary_patterns": [
      "Arrays Pattern"
    ],
    "stage": "Greedy Algorithms & Intervals",
    "curriculumStage": "Stage 15 — Greedy Algorithms & Intervals",
    "roadmapPhase": "Stage 15 — Greedy Algorithms & Intervals",
    "phase": "Stage 15 — Greedy Algorithms & Intervals",
    "estimatedTime": 30,
    "statement": "Solve the **Optimal Division** problem using standard Arrays techniques. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Arrays algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Arrays properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Arrays techniques by solving Medium problem constraints for Optimal Division.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/optimal-division/",
    "leetcode_title": "Optimal Division",
    "leetcode_id": 553,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/optimal-division/",
    "canonicalSlug": "optimal-division",
    "canonicalUrl": "https://leetcode.com/problems/optimal-division/",
    "url": "https://leetcode.com/problems/optimal-division/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Optimal Division\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Optimal Division\n};",
        "java": "// Java Solution for Optimal Division\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Optimal Division\n}",
        "python": "# Python Solution for Optimal Division\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Optimal Division\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Optimal Division\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Optimal Division\n};",
        "java": "// Optimal Java Solution for Optimal Division\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Optimal Division\n}",
        "python": "# Optimal Python Solution for Optimal Division\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Optimal Division\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Optimal Division",
      "cpp_optimal": "// Solution for Optimal Division",
      "java_brute": "// Solution for Optimal Division",
      "java_optimal": "// Solution for Optimal Division",
      "python_brute": "# Solution for Optimal Division",
      "python_optimal": "# Solution for Optimal Division"
    },
    "originalOrder": 361,
    "learningOrder": 361
  },
  {
    "id": 733,
    "number": 733,
    "sequence_number": 733,
    "title": "Brick Wall",
    "slug": "brick-wall",
    "difficulty": "Medium",
    "topic": "Arrays",
    "subtopic": "Arrays Optimization",
    "pattern": "Arrays Pattern",
    "secondary_patterns": [
      "Arrays Pattern"
    ],
    "stage": "Greedy Algorithms & Intervals",
    "curriculumStage": "Stage 15 — Greedy Algorithms & Intervals",
    "roadmapPhase": "Stage 15 — Greedy Algorithms & Intervals",
    "phase": "Stage 15 — Greedy Algorithms & Intervals",
    "estimatedTime": 30,
    "statement": "Solve the **Brick Wall** problem using standard Arrays techniques. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Arrays algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Arrays properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Arrays techniques by solving Medium problem constraints for Brick Wall.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/brick-wall/",
    "leetcode_title": "Brick Wall",
    "leetcode_id": 554,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/brick-wall/",
    "canonicalSlug": "brick-wall",
    "canonicalUrl": "https://leetcode.com/problems/brick-wall/",
    "url": "https://leetcode.com/problems/brick-wall/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Brick Wall\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Brick Wall\n};",
        "java": "// Java Solution for Brick Wall\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Brick Wall\n}",
        "python": "# Python Solution for Brick Wall\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Brick Wall\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Brick Wall\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Brick Wall\n};",
        "java": "// Optimal Java Solution for Brick Wall\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Brick Wall\n}",
        "python": "# Optimal Python Solution for Brick Wall\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Brick Wall\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Brick Wall",
      "cpp_optimal": "// Solution for Brick Wall",
      "java_brute": "// Solution for Brick Wall",
      "java_optimal": "// Solution for Brick Wall",
      "python_brute": "# Solution for Brick Wall",
      "python_optimal": "# Solution for Brick Wall"
    },
    "originalOrder": 362,
    "learningOrder": 362
  },
  {
    "id": 734,
    "number": 734,
    "sequence_number": 734,
    "title": "Array Nesting",
    "slug": "array-nesting",
    "difficulty": "Medium",
    "topic": "Arrays",
    "subtopic": "Arrays Optimization",
    "pattern": "Arrays Pattern",
    "secondary_patterns": [
      "Arrays Pattern"
    ],
    "stage": "Greedy Algorithms & Intervals",
    "curriculumStage": "Stage 15 — Greedy Algorithms & Intervals",
    "roadmapPhase": "Stage 15 — Greedy Algorithms & Intervals",
    "phase": "Stage 15 — Greedy Algorithms & Intervals",
    "estimatedTime": 30,
    "statement": "Solve the **Array Nesting** problem using standard Arrays techniques. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Arrays algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Arrays properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Arrays techniques by solving Medium problem constraints for Array Nesting.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/array-nesting/",
    "leetcode_title": "Array Nesting",
    "leetcode_id": 565,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/array-nesting/",
    "canonicalSlug": "array-nesting",
    "canonicalUrl": "https://leetcode.com/problems/array-nesting/",
    "url": "https://leetcode.com/problems/array-nesting/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Array Nesting\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Array Nesting\n};",
        "java": "// Java Solution for Array Nesting\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Array Nesting\n}",
        "python": "# Python Solution for Array Nesting\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Array Nesting\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Array Nesting\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Array Nesting\n};",
        "java": "// Optimal Java Solution for Array Nesting\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Array Nesting\n}",
        "python": "# Optimal Python Solution for Array Nesting\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Array Nesting\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Array Nesting",
      "cpp_optimal": "// Solution for Array Nesting",
      "java_brute": "// Solution for Array Nesting",
      "java_optimal": "// Solution for Array Nesting",
      "python_brute": "# Solution for Array Nesting",
      "python_optimal": "# Solution for Array Nesting"
    },
    "originalOrder": 363,
    "learningOrder": 363
  },
  {
    "id": 735,
    "number": 735,
    "sequence_number": 735,
    "title": "Managers with at Least 5 Direct Reports",
    "slug": "managers-with-at-least-5-direct-reports",
    "difficulty": "Medium",
    "topic": "Arrays",
    "subtopic": "Arrays Optimization",
    "pattern": "Arrays Pattern",
    "secondary_patterns": [
      "Arrays Pattern"
    ],
    "stage": "Greedy Algorithms & Intervals",
    "curriculumStage": "Stage 15 — Greedy Algorithms & Intervals",
    "roadmapPhase": "Stage 15 — Greedy Algorithms & Intervals",
    "phase": "Stage 15 — Greedy Algorithms & Intervals",
    "estimatedTime": 30,
    "statement": "Solve the **Managers with at Least 5 Direct Reports** problem using standard Arrays techniques. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Arrays algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Arrays properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Arrays techniques by solving Medium problem constraints for Managers with at Least 5 Direct Reports.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/managers-with-at-least-5-direct-reports/",
    "leetcode_title": "Managers with at Least 5 Direct Reports",
    "leetcode_id": 570,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/managers-with-at-least-5-direct-reports/",
    "canonicalSlug": "managers-with-at-least-5-direct-reports",
    "canonicalUrl": "https://leetcode.com/problems/managers-with-at-least-5-direct-reports/",
    "url": "https://leetcode.com/problems/managers-with-at-least-5-direct-reports/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Managers with at Least 5 Direct Reports\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Managers with at Least 5 Direct Reports\n};",
        "java": "// Java Solution for Managers with at Least 5 Direct Reports\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Managers with at Least 5 Direct Reports\n}",
        "python": "# Python Solution for Managers with at Least 5 Direct Reports\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Managers with at Least 5 Direct Reports\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Managers with at Least 5 Direct Reports\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Managers with at Least 5 Direct Reports\n};",
        "java": "// Optimal Java Solution for Managers with at Least 5 Direct Reports\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Managers with at Least 5 Direct Reports\n}",
        "python": "# Optimal Python Solution for Managers with at Least 5 Direct Reports\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Managers with at Least 5 Direct Reports\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Managers with at Least 5 Direct Reports",
      "cpp_optimal": "// Solution for Managers with at Least 5 Direct Reports",
      "java_brute": "// Solution for Managers with at Least 5 Direct Reports",
      "java_optimal": "// Solution for Managers with at Least 5 Direct Reports",
      "python_brute": "# Solution for Managers with at Least 5 Direct Reports",
      "python_optimal": "# Solution for Managers with at Least 5 Direct Reports"
    },
    "originalOrder": 364,
    "learningOrder": 364
  },
  {
    "id": 736,
    "number": 736,
    "sequence_number": 736,
    "title": "Guess the Word",
    "slug": "guess-the-word",
    "difficulty": "Hard",
    "topic": "Greedy",
    "subtopic": "Greedy Optimization",
    "pattern": "Minimax Candidate Filtering",
    "secondary_patterns": [
      "Minimax Candidate Filtering"
    ],
    "stage": "Greedy Algorithms & Intervals",
    "curriculumStage": "Stage 15 — Greedy Algorithms & Intervals",
    "roadmapPhase": "Stage 15 — Greedy Algorithms & Intervals",
    "phase": "Stage 15 — Greedy Algorithms & Intervals",
    "estimatedTime": 45,
    "statement": "Given the constraints and input parameters for Guess the Word, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Guess the Word."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Guess the Word.",
      "Leverage the optimal Greedy pattern to reduce time complexity."
    ],
    "learningObjective": "Master Greedy techniques by solving Hard problem constraints for Guess the Word.",
    "whyThisPattern": "When observing Greedy problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/guess-the-word/",
    "leetcode_title": "Guess the Word",
    "leetcode_id": 843,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/guess-the-word/",
    "canonicalSlug": "guess-the-word",
    "canonicalUrl": "https://leetcode.com/problems/guess-the-word/",
    "url": "https://leetcode.com/problems/guess-the-word/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Guess the Word\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Guess the Word\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Guess the Word\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Guess the Word\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Guess the Word\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Guess the Word\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Guess the Word\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Guess the Word\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Guess the Word",
      "cpp_optimal": "// Solution for Guess the Word",
      "java_brute": "// Solution for Guess the Word",
      "java_optimal": "// Solution for Guess the Word",
      "python_brute": "# Solution for Guess the Word",
      "python_optimal": "# Solution for Guess the Word"
    },
    "originalOrder": 893,
    "learningOrder": 893
  },
  {
    "id": 737,
    "number": 737,
    "sequence_number": 737,
    "title": "Stamping The Sequence",
    "slug": "stamping-the-sequence",
    "difficulty": "Hard",
    "topic": "Greedy",
    "subtopic": "Greedy Optimization",
    "pattern": "Reverse Target Replacement",
    "secondary_patterns": [
      "Reverse Target Replacement"
    ],
    "stage": "Greedy Algorithms & Intervals",
    "curriculumStage": "Stage 15 — Greedy Algorithms & Intervals",
    "roadmapPhase": "Stage 15 — Greedy Algorithms & Intervals",
    "phase": "Stage 15 — Greedy Algorithms & Intervals",
    "estimatedTime": 45,
    "statement": "Given the constraints and input parameters for Stamping the Sequence, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Stamping the Sequence."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Stamping the Sequence.",
      "Leverage the optimal Greedy pattern to reduce time complexity."
    ],
    "learningObjective": "Master Greedy techniques by solving Hard problem constraints for Stamping The Sequence.",
    "whyThisPattern": "When observing Greedy problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/stamping-the-sequence/",
    "leetcode_title": "Stamping The Sequence",
    "leetcode_id": 936,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/stamping-the-sequence/",
    "canonicalSlug": "stamping-the-sequence",
    "canonicalUrl": "https://leetcode.com/problems/stamping-the-sequence/",
    "url": "https://leetcode.com/problems/stamping-the-sequence/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Stamping the Sequence\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Stamping the Sequence\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Stamping the Sequence\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Stamping the Sequence\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Stamping the Sequence\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Stamping the Sequence\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Stamping the Sequence\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Stamping the Sequence\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Stamping The Sequence",
      "cpp_optimal": "// Solution for Stamping The Sequence",
      "java_brute": "// Solution for Stamping The Sequence",
      "java_optimal": "// Solution for Stamping The Sequence",
      "python_brute": "# Solution for Stamping The Sequence",
      "python_optimal": "# Solution for Stamping The Sequence"
    },
    "originalOrder": 894,
    "learningOrder": 894
  },
  {
    "id": 738,
    "number": 738,
    "sequence_number": 738,
    "title": "Minimum Number of Increments on Subarrays to Form a Target Array",
    "slug": "minimum-number-of-increments-on-subarrays-to-form-a-target-array",
    "difficulty": "Hard",
    "topic": "Greedy",
    "subtopic": "Greedy Optimization",
    "pattern": "One-Pass Positive Delta Sum",
    "secondary_patterns": [
      "One-Pass Positive Delta Sum"
    ],
    "stage": "Greedy Algorithms & Intervals",
    "curriculumStage": "Stage 15 — Greedy Algorithms & Intervals",
    "roadmapPhase": "Stage 15 — Greedy Algorithms & Intervals",
    "phase": "Stage 15 — Greedy Algorithms & Intervals",
    "estimatedTime": 45,
    "statement": "Given the constraints and input parameters for Minimum Number of Increments on Subarrays to Form a Target Array, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Minimum Number of Increments on Subarrays to Form a Target Array."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Minimum Number of Increments on Subarrays to Form a Target Array.",
      "Leverage the optimal Greedy pattern to reduce time complexity."
    ],
    "learningObjective": "Master Greedy techniques by solving Hard problem constraints for Minimum Number of Increments on Subarrays to Form a Target Array.",
    "whyThisPattern": "When observing Greedy problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/minimum-number-of-increments-on-subarrays-to-form-a-target-array/",
    "leetcode_title": "Minimum Number of Increments on Subarrays to Form a Target Array",
    "leetcode_id": 1526,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/minimum-number-of-increments-on-subarrays-to-form-a-target-array/",
    "canonicalSlug": "minimum-number-of-increments-on-subarrays-to-form-a-target-array",
    "canonicalUrl": "https://leetcode.com/problems/minimum-number-of-increments-on-subarrays-to-form-a-target-array/",
    "url": "https://leetcode.com/problems/minimum-number-of-increments-on-subarrays-to-form-a-target-array/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Minimum Number of Increments on Subarrays to Form a Target Array\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Minimum Number of Increments on Subarrays to Form a Target Array\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Minimum Number of Increments on Subarrays to Form a Target Array\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Minimum Number of Increments on Subarrays to Form a Target Array\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Minimum Number of Increments on Subarrays to Form a Target Array\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Minimum Number of Increments on Subarrays to Form a Target Array\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Minimum Number of Increments on Subarrays to Form a Target Array\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Minimum Number of Increments on Subarrays to Form a Target Array\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Minimum Number of Increments on Subarrays to Form a Target Array",
      "cpp_optimal": "// Solution for Minimum Number of Increments on Subarrays to Form a Target Array",
      "java_brute": "// Solution for Minimum Number of Increments on Subarrays to Form a Target Array",
      "java_optimal": "// Solution for Minimum Number of Increments on Subarrays to Form a Target Array",
      "python_brute": "# Solution for Minimum Number of Increments on Subarrays to Form a Target Array",
      "python_optimal": "# Solution for Minimum Number of Increments on Subarrays to Form a Target Array"
    },
    "originalOrder": 895,
    "learningOrder": 895
  },
  {
    "id": 739,
    "number": 739,
    "sequence_number": 739,
    "title": "Patching Array",
    "slug": "patching-array",
    "difficulty": "Hard",
    "topic": "Greedy",
    "subtopic": "Greedy Optimization",
    "pattern": "Miss Bound Accumulator",
    "secondary_patterns": [
      "Miss Bound Accumulator"
    ],
    "stage": "Greedy Algorithms & Intervals",
    "curriculumStage": "Stage 15 — Greedy Algorithms & Intervals",
    "roadmapPhase": "Stage 15 — Greedy Algorithms & Intervals",
    "phase": "Stage 15 — Greedy Algorithms & Intervals",
    "estimatedTime": 45,
    "statement": "Given the constraints and input parameters for Patching Array, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Patching Array."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Patching Array.",
      "Leverage the optimal Greedy pattern to reduce time complexity."
    ],
    "learningObjective": "Master Greedy techniques by solving Hard problem constraints for Patching Array.",
    "whyThisPattern": "When observing Greedy problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/patching-array/",
    "leetcode_title": "Patching Array",
    "leetcode_id": 330,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/patching-array/",
    "canonicalSlug": "patching-array",
    "canonicalUrl": "https://leetcode.com/problems/patching-array/",
    "url": "https://leetcode.com/problems/patching-array/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Patching Array\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Patching Array\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Patching Array\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Patching Array\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Patching Array\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Patching Array\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Patching Array\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Patching Array\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Patching Array",
      "cpp_optimal": "// Solution for Patching Array",
      "java_brute": "// Solution for Patching Array",
      "java_optimal": "// Solution for Patching Array",
      "python_brute": "# Solution for Patching Array",
      "python_optimal": "# Solution for Patching Array"
    },
    "originalOrder": 896,
    "learningOrder": 896
  },
  {
    "id": 740,
    "number": 740,
    "sequence_number": 740,
    "title": "Super Washing Machines",
    "slug": "super-washing-machines",
    "difficulty": "Hard",
    "topic": "Greedy",
    "subtopic": "Greedy Optimization",
    "pattern": "Max Net Flow Pass",
    "secondary_patterns": [
      "Max Net Flow Pass"
    ],
    "stage": "Greedy Algorithms & Intervals",
    "curriculumStage": "Stage 15 — Greedy Algorithms & Intervals",
    "roadmapPhase": "Stage 15 — Greedy Algorithms & Intervals",
    "phase": "Stage 15 — Greedy Algorithms & Intervals",
    "estimatedTime": 45,
    "statement": "Given the constraints and input parameters for Super Washing Machines, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Super Washing Machines."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Super Washing Machines.",
      "Leverage the optimal Greedy pattern to reduce time complexity."
    ],
    "learningObjective": "Master Greedy techniques by solving Hard problem constraints for Super Washing Machines.",
    "whyThisPattern": "When observing Greedy problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/super-washing-machines/",
    "leetcode_title": "Super Washing Machines",
    "leetcode_id": 517,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/super-washing-machines/",
    "canonicalSlug": "super-washing-machines",
    "canonicalUrl": "https://leetcode.com/problems/super-washing-machines/",
    "url": "https://leetcode.com/problems/super-washing-machines/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Super Washing Machines\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Super Washing Machines\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Super Washing Machines\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Super Washing Machines\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Super Washing Machines\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Super Washing Machines\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Super Washing Machines\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Super Washing Machines\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Super Washing Machines",
      "cpp_optimal": "// Solution for Super Washing Machines",
      "java_brute": "// Solution for Super Washing Machines",
      "java_optimal": "// Solution for Super Washing Machines",
      "python_brute": "# Solution for Super Washing Machines",
      "python_optimal": "# Solution for Super Washing Machines"
    },
    "originalOrder": 897,
    "learningOrder": 897
  },
  {
    "id": 741,
    "number": 741,
    "sequence_number": 741,
    "title": "Candy",
    "slug": "candy",
    "difficulty": "Hard",
    "topic": "Greedy",
    "subtopic": "Greedy Optimization",
    "pattern": "Greedy Pattern",
    "secondary_patterns": [
      "Greedy Pattern"
    ],
    "stage": "Greedy Algorithms & Intervals",
    "curriculumStage": "Stage 15 — Greedy Algorithms & Intervals",
    "roadmapPhase": "Stage 15 — Greedy Algorithms & Intervals",
    "phase": "Stage 15 — Greedy Algorithms & Intervals",
    "estimatedTime": 45,
    "statement": "Solve the **Candy** problem using standard Greedy techniques. Given input constraints appropriate for Hard level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Greedy algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Greedy properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Greedy techniques by solving Hard problem constraints for Candy.",
    "whyThisPattern": "When observing Greedy problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/candy/",
    "leetcode_title": "Candy",
    "leetcode_id": 135,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/candy/",
    "canonicalSlug": "candy",
    "canonicalUrl": "https://leetcode.com/problems/candy/",
    "url": "https://leetcode.com/problems/candy/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Candy\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Candy\n};",
        "java": "// Java Solution for Candy\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Candy\n}",
        "python": "# Python Solution for Candy\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Candy\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Candy\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Candy\n};",
        "java": "// Optimal Java Solution for Candy\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Candy\n}",
        "python": "# Optimal Python Solution for Candy\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Candy\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Candy",
      "cpp_optimal": "// Solution for Candy",
      "java_brute": "// Solution for Candy",
      "java_optimal": "// Solution for Candy",
      "python_brute": "# Solution for Candy",
      "python_optimal": "# Solution for Candy"
    },
    "originalOrder": 898,
    "learningOrder": 898
  },
  {
    "id": 742,
    "number": 742,
    "sequence_number": 742,
    "title": "Jump Game V",
    "slug": "jump-game-v",
    "difficulty": "Hard",
    "topic": "Greedy",
    "subtopic": "Greedy Optimization",
    "pattern": "Greedy Pattern",
    "secondary_patterns": [
      "Greedy Pattern"
    ],
    "stage": "Greedy Algorithms & Intervals",
    "curriculumStage": "Stage 15 — Greedy Algorithms & Intervals",
    "roadmapPhase": "Stage 15 — Greedy Algorithms & Intervals",
    "phase": "Stage 15 — Greedy Algorithms & Intervals",
    "estimatedTime": 45,
    "statement": "Solve the **Jump Game V** problem using standard Greedy techniques. Given input constraints appropriate for Hard level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Greedy algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Greedy properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Greedy techniques by solving Hard problem constraints for Jump Game V.",
    "whyThisPattern": "When observing Greedy problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/jump-game-v/",
    "leetcode_title": "Jump Game V",
    "leetcode_id": 1340,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/jump-game-v/",
    "canonicalSlug": "jump-game-v",
    "canonicalUrl": "https://leetcode.com/problems/jump-game-v/",
    "url": "https://leetcode.com/problems/jump-game-v/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Jump Game V\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Jump Game V\n};",
        "java": "// Java Solution for Jump Game V\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Jump Game V\n}",
        "python": "# Python Solution for Jump Game V\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Jump Game V\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Jump Game V\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Jump Game V\n};",
        "java": "// Optimal Java Solution for Jump Game V\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Jump Game V\n}",
        "python": "# Optimal Python Solution for Jump Game V\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Jump Game V\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Jump Game V",
      "cpp_optimal": "// Solution for Jump Game V",
      "java_brute": "// Solution for Jump Game V",
      "java_optimal": "// Solution for Jump Game V",
      "python_brute": "# Solution for Jump Game V",
      "python_optimal": "# Solution for Jump Game V"
    },
    "originalOrder": 899,
    "learningOrder": 899
  },
  {
    "id": 743,
    "number": 743,
    "sequence_number": 743,
    "title": "Jump Game IV",
    "slug": "jump-game-iv",
    "difficulty": "Hard",
    "topic": "Greedy",
    "subtopic": "Greedy Optimization",
    "pattern": "Greedy Pattern",
    "secondary_patterns": [
      "Greedy Pattern"
    ],
    "stage": "Greedy Algorithms & Intervals",
    "curriculumStage": "Stage 15 — Greedy Algorithms & Intervals",
    "roadmapPhase": "Stage 15 — Greedy Algorithms & Intervals",
    "phase": "Stage 15 — Greedy Algorithms & Intervals",
    "estimatedTime": 45,
    "statement": "Solve the **Jump Game IV** problem using standard Greedy techniques. Given input constraints appropriate for Hard level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Greedy algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Greedy properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Greedy techniques by solving Hard problem constraints for Jump Game IV.",
    "whyThisPattern": "When observing Greedy problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/jump-game-iv/",
    "leetcode_title": "Jump Game IV",
    "leetcode_id": 1345,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/jump-game-iv/",
    "canonicalSlug": "jump-game-iv",
    "canonicalUrl": "https://leetcode.com/problems/jump-game-iv/",
    "url": "https://leetcode.com/problems/jump-game-iv/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Jump Game IV\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Jump Game IV\n};",
        "java": "// Java Solution for Jump Game IV\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Jump Game IV\n}",
        "python": "# Python Solution for Jump Game IV\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Jump Game IV\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Jump Game IV\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Jump Game IV\n};",
        "java": "// Optimal Java Solution for Jump Game IV\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Jump Game IV\n}",
        "python": "# Optimal Python Solution for Jump Game IV\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Jump Game IV\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Jump Game IV",
      "cpp_optimal": "// Solution for Jump Game IV",
      "java_brute": "// Solution for Jump Game IV",
      "java_optimal": "// Solution for Jump Game IV",
      "python_brute": "# Solution for Jump Game IV",
      "python_optimal": "# Solution for Jump Game IV"
    },
    "originalOrder": 900,
    "learningOrder": 900
  },
  {
    "id": 744,
    "number": 744,
    "sequence_number": 744,
    "title": "Find the Shortest Superstring",
    "slug": "find-the-shortest-superstring",
    "difficulty": "Hard",
    "topic": "Dynamic Programming",
    "subtopic": "Dynamic Programming Optimization",
    "pattern": "TSP Overlap Bitmask DP",
    "secondary_patterns": [
      "TSP Overlap Bitmask DP"
    ],
    "stage": "Greedy Algorithms & Intervals",
    "curriculumStage": "Stage 15 — Greedy Algorithms & Intervals",
    "roadmapPhase": "Stage 15 — Greedy Algorithms & Intervals",
    "phase": "Stage 15 — Greedy Algorithms & Intervals",
    "estimatedTime": 45,
    "statement": "Given the constraints and input parameters for Find the Shortest Superstring, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Find the Shortest Superstring."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Find the Shortest Superstring.",
      "Leverage the optimal Dynamic Programming pattern to reduce time complexity."
    ],
    "learningObjective": "Master Dynamic Programming techniques by solving Hard problem constraints for Find the Shortest Superstring.",
    "whyThisPattern": "When observing Dynamic Programming problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/find-the-shortest-superstring/",
    "leetcode_title": "Find the Shortest Superstring",
    "leetcode_id": 943,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/find-the-shortest-superstring/",
    "canonicalSlug": "find-the-shortest-superstring",
    "canonicalUrl": "https://leetcode.com/problems/find-the-shortest-superstring/",
    "url": "https://leetcode.com/problems/find-the-shortest-superstring/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Find the Shortest Superstring\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Find the Shortest Superstring\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Find the Shortest Superstring\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Find the Shortest Superstring\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Find the Shortest Superstring\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Find the Shortest Superstring\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Find the Shortest Superstring\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Find the Shortest Superstring\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Find the Shortest Superstring",
      "cpp_optimal": "// Solution for Find the Shortest Superstring",
      "java_brute": "// Solution for Find the Shortest Superstring",
      "java_optimal": "// Solution for Find the Shortest Superstring",
      "python_brute": "# Solution for Find the Shortest Superstring",
      "python_optimal": "# Solution for Find the Shortest Superstring"
    },
    "originalOrder": 809,
    "learningOrder": 809
  },
  {
    "id": 745,
    "number": 745,
    "sequence_number": 745,
    "title": "Minimum Swaps To Make Sequences Increasing",
    "slug": "minimum-swaps-to-make-sequences-increasing",
    "difficulty": "Hard",
    "topic": "Dynamic Programming",
    "subtopic": "Dynamic Programming Optimization",
    "pattern": "State DP Swap / No-Swap",
    "secondary_patterns": [
      "State DP Swap / No-Swap"
    ],
    "stage": "Greedy Algorithms & Intervals",
    "curriculumStage": "Stage 15 — Greedy Algorithms & Intervals",
    "roadmapPhase": "Stage 15 — Greedy Algorithms & Intervals",
    "phase": "Stage 15 — Greedy Algorithms & Intervals",
    "estimatedTime": 45,
    "statement": "Given the constraints and input parameters for Minimum Swaps To Make Sequences Increasing, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Minimum Swaps To Make Sequences Increasing."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Minimum Swaps To Make Sequences Increasing.",
      "Leverage the optimal Dynamic Programming pattern to reduce time complexity."
    ],
    "learningObjective": "Master Dynamic Programming techniques by solving Hard problem constraints for Minimum Swaps To Make Sequences Increasing.",
    "whyThisPattern": "When observing Dynamic Programming problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/minimum-swaps-to-make-sequences-increasing/",
    "leetcode_title": "Minimum Swaps To Make Sequences Increasing",
    "leetcode_id": 801,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/minimum-swaps-to-make-sequences-increasing/",
    "canonicalSlug": "minimum-swaps-to-make-sequences-increasing",
    "canonicalUrl": "https://leetcode.com/problems/minimum-swaps-to-make-sequences-increasing/",
    "url": "https://leetcode.com/problems/minimum-swaps-to-make-sequences-increasing/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Minimum Swaps To Make Sequences Increasing\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Minimum Swaps To Make Sequences Increasing\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Minimum Swaps To Make Sequences Increasing\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Minimum Swaps To Make Sequences Increasing\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Minimum Swaps To Make Sequences Increasing\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Minimum Swaps To Make Sequences Increasing\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Minimum Swaps To Make Sequences Increasing\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Minimum Swaps To Make Sequences Increasing\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Minimum Swaps To Make Sequences Increasing",
      "cpp_optimal": "// Solution for Minimum Swaps To Make Sequences Increasing",
      "java_brute": "// Solution for Minimum Swaps To Make Sequences Increasing",
      "java_optimal": "// Solution for Minimum Swaps To Make Sequences Increasing",
      "python_brute": "# Solution for Minimum Swaps To Make Sequences Increasing",
      "python_optimal": "# Solution for Minimum Swaps To Make Sequences Increasing"
    },
    "originalOrder": 810,
    "learningOrder": 810
  },
  {
    "id": 746,
    "number": 746,
    "sequence_number": 746,
    "title": "Cat and Mouse II",
    "slug": "cat-and-mouse-ii",
    "difficulty": "Hard",
    "topic": "Dynamic Programming",
    "subtopic": "Dynamic Programming Optimization",
    "pattern": "Minimax Game Graph DP",
    "secondary_patterns": [
      "Minimax Game Graph DP"
    ],
    "stage": "Greedy Algorithms & Intervals",
    "curriculumStage": "Stage 15 — Greedy Algorithms & Intervals",
    "roadmapPhase": "Stage 15 — Greedy Algorithms & Intervals",
    "phase": "Stage 15 — Greedy Algorithms & Intervals",
    "estimatedTime": 45,
    "statement": "Given the constraints and input parameters for Cat and Mouse II, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Cat and Mouse II."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Cat and Mouse II.",
      "Leverage the optimal Dynamic Programming pattern to reduce time complexity."
    ],
    "learningObjective": "Master Dynamic Programming techniques by solving Hard problem constraints for Cat and Mouse II.",
    "whyThisPattern": "When observing Dynamic Programming problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/cat-and-mouse-ii/",
    "leetcode_title": "Cat and Mouse II",
    "leetcode_id": 1728,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/cat-and-mouse-ii/",
    "canonicalSlug": "cat-and-mouse-ii",
    "canonicalUrl": "https://leetcode.com/problems/cat-and-mouse-ii/",
    "url": "https://leetcode.com/problems/cat-and-mouse-ii/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Cat and Mouse II\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Cat and Mouse II\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Cat and Mouse II\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Cat and Mouse II\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Cat and Mouse II\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Cat and Mouse II\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Cat and Mouse II\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Cat and Mouse II\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Cat and Mouse II",
      "cpp_optimal": "// Solution for Cat and Mouse II",
      "java_brute": "// Solution for Cat and Mouse II",
      "java_optimal": "// Solution for Cat and Mouse II",
      "python_brute": "# Solution for Cat and Mouse II",
      "python_optimal": "# Solution for Cat and Mouse II"
    },
    "originalOrder": 811,
    "learningOrder": 811
  },
  {
    "id": 747,
    "number": 747,
    "sequence_number": 747,
    "title": "Delete Columns to Make Sorted III",
    "slug": "delete-columns-to-make-sorted-iii",
    "difficulty": "Hard",
    "topic": "Dynamic Programming",
    "subtopic": "Dynamic Programming Optimization",
    "pattern": "LIS Across Columns",
    "secondary_patterns": [
      "LIS Across Columns"
    ],
    "stage": "Greedy Algorithms & Intervals",
    "curriculumStage": "Stage 15 — Greedy Algorithms & Intervals",
    "roadmapPhase": "Stage 15 — Greedy Algorithms & Intervals",
    "phase": "Stage 15 — Greedy Algorithms & Intervals",
    "estimatedTime": 45,
    "statement": "Given the constraints and input parameters for Delete Columns to Make Sorted III, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Delete Columns to Make Sorted III."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Delete Columns to Make Sorted III.",
      "Leverage the optimal Dynamic Programming pattern to reduce time complexity."
    ],
    "learningObjective": "Master Dynamic Programming techniques by solving Hard problem constraints for Delete Columns to Make Sorted III.",
    "whyThisPattern": "When observing Dynamic Programming problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/delete-columns-to-make-sorted-iii/",
    "leetcode_title": "Delete Columns to Make Sorted III",
    "leetcode_id": 960,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/delete-columns-to-make-sorted-iii/",
    "canonicalSlug": "delete-columns-to-make-sorted-iii",
    "canonicalUrl": "https://leetcode.com/problems/delete-columns-to-make-sorted-iii/",
    "url": "https://leetcode.com/problems/delete-columns-to-make-sorted-iii/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Delete Columns to Make Sorted III\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Delete Columns to Make Sorted III\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Delete Columns to Make Sorted III\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Delete Columns to Make Sorted III\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Delete Columns to Make Sorted III\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Delete Columns to Make Sorted III\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Delete Columns to Make Sorted III\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Delete Columns to Make Sorted III\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Delete Columns to Make Sorted III",
      "cpp_optimal": "// Solution for Delete Columns to Make Sorted III",
      "java_brute": "// Solution for Delete Columns to Make Sorted III",
      "java_optimal": "// Solution for Delete Columns to Make Sorted III",
      "python_brute": "# Solution for Delete Columns to Make Sorted III",
      "python_optimal": "# Solution for Delete Columns to Make Sorted III"
    },
    "originalOrder": 812,
    "learningOrder": 812
  },
  {
    "id": 748,
    "number": 748,
    "sequence_number": 748,
    "title": "Least Operators to Express Number",
    "slug": "least-operators-to-express-number",
    "difficulty": "Hard",
    "topic": "Dynamic Programming",
    "subtopic": "Dynamic Programming Optimization",
    "pattern": "Base Target Recursion DP",
    "secondary_patterns": [
      "Base Target Recursion DP"
    ],
    "stage": "Greedy Algorithms & Intervals",
    "curriculumStage": "Stage 15 — Greedy Algorithms & Intervals",
    "roadmapPhase": "Stage 15 — Greedy Algorithms & Intervals",
    "phase": "Stage 15 — Greedy Algorithms & Intervals",
    "estimatedTime": 45,
    "statement": "Given the constraints and input parameters for Least Operators to Express Number, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Least Operators to Express Number."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Least Operators to Express Number.",
      "Leverage the optimal Dynamic Programming pattern to reduce time complexity."
    ],
    "learningObjective": "Master Dynamic Programming techniques by solving Hard problem constraints for Least Operators to Express Number.",
    "whyThisPattern": "When observing Dynamic Programming problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/least-operators-to-express-number/",
    "leetcode_title": "Least Operators to Express Number",
    "leetcode_id": 964,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/least-operators-to-express-number/",
    "canonicalSlug": "least-operators-to-express-number",
    "canonicalUrl": "https://leetcode.com/problems/least-operators-to-express-number/",
    "url": "https://leetcode.com/problems/least-operators-to-express-number/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Least Operators to Express Number\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Least Operators to Express Number\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Least Operators to Express Number\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Least Operators to Express Number\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Least Operators to Express Number\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Least Operators to Express Number\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Least Operators to Express Number\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Least Operators to Express Number\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Least Operators to Express Number",
      "cpp_optimal": "// Solution for Least Operators to Express Number",
      "java_brute": "// Solution for Least Operators to Express Number",
      "java_optimal": "// Solution for Least Operators to Express Number",
      "python_brute": "# Solution for Least Operators to Express Number",
      "python_optimal": "# Solution for Least Operators to Express Number"
    },
    "originalOrder": 813,
    "learningOrder": 813
  },
  {
    "id": 749,
    "number": 749,
    "sequence_number": 749,
    "title": "Minimum Cost to Merge Stones",
    "slug": "minimum-cost-to-merge-stones",
    "difficulty": "Hard",
    "topic": "Dynamic Programming",
    "subtopic": "Dynamic Programming Optimization",
    "pattern": "Interval Merge DP",
    "secondary_patterns": [
      "Interval Merge DP"
    ],
    "stage": "Greedy Algorithms & Intervals",
    "curriculumStage": "Stage 15 — Greedy Algorithms & Intervals",
    "roadmapPhase": "Stage 15 — Greedy Algorithms & Intervals",
    "phase": "Stage 15 — Greedy Algorithms & Intervals",
    "estimatedTime": 45,
    "statement": "Given the constraints and input parameters for Minimum Cost to Merge Stones, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Minimum Cost to Merge Stones."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Minimum Cost to Merge Stones.",
      "Leverage the optimal Dynamic Programming pattern to reduce time complexity."
    ],
    "learningObjective": "Master Dynamic Programming techniques by solving Hard problem constraints for Minimum Cost to Merge Stones.",
    "whyThisPattern": "When observing Dynamic Programming problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/minimum-cost-to-merge-stones/",
    "leetcode_title": "Minimum Cost to Merge Stones",
    "leetcode_id": 1000,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/minimum-cost-to-merge-stones/",
    "canonicalSlug": "minimum-cost-to-merge-stones",
    "canonicalUrl": "https://leetcode.com/problems/minimum-cost-to-merge-stones/",
    "url": "https://leetcode.com/problems/minimum-cost-to-merge-stones/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Minimum Cost to Merge Stones\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Minimum Cost to Merge Stones\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Minimum Cost to Merge Stones\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Minimum Cost to Merge Stones\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Minimum Cost to Merge Stones\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Minimum Cost to Merge Stones\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Minimum Cost to Merge Stones\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Minimum Cost to Merge Stones\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Minimum Cost to Merge Stones",
      "cpp_optimal": "// Solution for Minimum Cost to Merge Stones",
      "java_brute": "// Solution for Minimum Cost to Merge Stones",
      "java_optimal": "// Solution for Minimum Cost to Merge Stones",
      "python_brute": "# Solution for Minimum Cost to Merge Stones",
      "python_optimal": "# Solution for Minimum Cost to Merge Stones"
    },
    "originalOrder": 814,
    "learningOrder": 814
  },
  {
    "id": 750,
    "number": 750,
    "sequence_number": 750,
    "title": "Build Array Where You Can Find The Maximum Exactly K Comparisons",
    "slug": "build-array-where-you-can-find-the-maximum-exactly-k-comparisons",
    "difficulty": "Hard",
    "topic": "Dynamic Programming",
    "subtopic": "Dynamic Programming Optimization",
    "pattern": "3D DP State Recurrence",
    "secondary_patterns": [
      "3D DP State Recurrence"
    ],
    "stage": "Greedy Algorithms & Intervals",
    "curriculumStage": "Stage 15 — Greedy Algorithms & Intervals",
    "roadmapPhase": "Stage 15 — Greedy Algorithms & Intervals",
    "phase": "Stage 15 — Greedy Algorithms & Intervals",
    "estimatedTime": 45,
    "statement": "Given the constraints and input parameters for Build Array Where You Can Find The Maximum Exactly K Comparisons, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Build Array Where You Can Find The Maximum Exactly K Comparisons."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Build Array Where You Can Find The Maximum Exactly K Comparisons.",
      "Leverage the optimal Dynamic Programming pattern to reduce time complexity."
    ],
    "learningObjective": "Master Dynamic Programming techniques by solving Hard problem constraints for Build Array Where You Can Find The Maximum Exactly K Comparisons.",
    "whyThisPattern": "When observing Dynamic Programming problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/build-array-where-you-can-find-the-maximum-exactly-k-comparisons/",
    "leetcode_title": "Build Array Where You Can Find The Maximum Exactly K Comparisons",
    "leetcode_id": 1420,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/build-array-where-you-can-find-the-maximum-exactly-k-comparisons/",
    "canonicalSlug": "build-array-where-you-can-find-the-maximum-exactly-k-comparisons",
    "canonicalUrl": "https://leetcode.com/problems/build-array-where-you-can-find-the-maximum-exactly-k-comparisons/",
    "url": "https://leetcode.com/problems/build-array-where-you-can-find-the-maximum-exactly-k-comparisons/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Build Array Where You Can Find The Maximum Exactly K Comparisons\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Build Array Where You Can Find The Maximum Exactly K Comparisons\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Build Array Where You Can Find The Maximum Exactly K Comparisons\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Build Array Where You Can Find The Maximum Exactly K Comparisons\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Build Array Where You Can Find The Maximum Exactly K Comparisons\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Build Array Where You Can Find The Maximum Exactly K Comparisons\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Build Array Where You Can Find The Maximum Exactly K Comparisons\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Build Array Where You Can Find The Maximum Exactly K Comparisons\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Build Array Where You Can Find The Maximum Exactly K Comparisons",
      "cpp_optimal": "// Solution for Build Array Where You Can Find The Maximum Exactly K Comparisons",
      "java_brute": "// Solution for Build Array Where You Can Find The Maximum Exactly K Comparisons",
      "java_optimal": "// Solution for Build Array Where You Can Find The Maximum Exactly K Comparisons",
      "python_brute": "# Solution for Build Array Where You Can Find The Maximum Exactly K Comparisons",
      "python_optimal": "# Solution for Build Array Where You Can Find The Maximum Exactly K Comparisons"
    },
    "originalOrder": 815,
    "learningOrder": 815
  },
  {
    "id": 751,
    "number": 751,
    "sequence_number": 751,
    "title": "Power of Three",
    "slug": "power-of-three",
    "difficulty": "Easy",
    "topic": "Math",
    "subtopic": "Hashing & Array Optimization",
    "pattern": "Hashing & Array Optimization",
    "secondary_patterns": [
      "Hashing & Array Optimization"
    ],
    "stage": "1D Dynamic Programming Foundations",
    "curriculumStage": "Stage 16 — 1D Dynamic Programming Foundations",
    "roadmapPhase": "Stage 16 — 1D Dynamic Programming Foundations",
    "phase": "Stage 16 — 1D Dynamic Programming Foundations",
    "estimatedTime": 15,
    "statement": "Solve the **Power of Three Challenge** problem using the **Hashing & Array Optimization** technique. Given input constraints appropriate for Easy level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^4",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Hashing & Array Optimization identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Hashing & Array Optimization. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Hashing & Array Optimization techniques by solving Easy problem constraints for Power of Three Challenge.",
    "whyThisPattern": "When observing arrays & strings problem conditions, Hashing & Array Optimization optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Microsoft",
      "Bloomberg",
      "Adobe"
    ],
    "companyRelevanceTier": "Medium",
    "leetcode_url": "https://leetcode.com/problems/power-of-three/",
    "leetcode_title": "Power of Three",
    "leetcode_id": 326,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/power-of-three/",
    "canonicalSlug": "power-of-three",
    "canonicalUrl": "https://leetcode.com/problems/power-of-three/",
    "url": "https://leetcode.com/problems/power-of-three/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Power of Three Challenge (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Power of Three Challenge (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Power of Three Challenge (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Power of Three Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Power of Three Challenge (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Power of Three Challenge (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Power of Three Challenge (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Power of Three Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Power of Three",
      "cpp_optimal": "// Solution for Power of Three",
      "java_brute": "// Solution for Power of Three",
      "java_optimal": "// Solution for Power of Three",
      "python_brute": "# Solution for Power of Three",
      "python_optimal": "# Solution for Power of Three"
    },
    "originalOrder": 153,
    "learningOrder": 153
  },
  {
    "id": 752,
    "number": 752,
    "sequence_number": 752,
    "title": "Power of Four",
    "slug": "power-of-four",
    "difficulty": "Easy",
    "topic": "Math",
    "subtopic": "Hashing & Array Optimization",
    "pattern": "Hashing & Array Optimization",
    "secondary_patterns": [
      "Hashing & Array Optimization"
    ],
    "stage": "1D Dynamic Programming Foundations",
    "curriculumStage": "Stage 16 — 1D Dynamic Programming Foundations",
    "roadmapPhase": "Stage 16 — 1D Dynamic Programming Foundations",
    "phase": "Stage 16 — 1D Dynamic Programming Foundations",
    "estimatedTime": 15,
    "statement": "Solve the **Power of Four Optimization** problem using the **Hashing & Array Optimization** technique. Given input constraints appropriate for Easy level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^4",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Hashing & Array Optimization identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Hashing & Array Optimization. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Hashing & Array Optimization techniques by solving Easy problem constraints for Power of Four Optimization.",
    "whyThisPattern": "When observing arrays & strings problem conditions, Hashing & Array Optimization optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Meta",
      "Apple",
      "Netflix"
    ],
    "companyRelevanceTier": "Medium",
    "leetcode_url": "https://leetcode.com/problems/power-of-four/",
    "leetcode_title": "Power of Four",
    "leetcode_id": 342,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/power-of-four/",
    "canonicalSlug": "power-of-four",
    "canonicalUrl": "https://leetcode.com/problems/power-of-four/",
    "url": "https://leetcode.com/problems/power-of-four/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Power of Four Optimization (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Power of Four Optimization (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Power of Four Optimization (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Power of Four Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Power of Four Optimization (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Power of Four Optimization (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Power of Four Optimization (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Power of Four Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Power of Four",
      "cpp_optimal": "// Solution for Power of Four",
      "java_brute": "// Solution for Power of Four",
      "java_optimal": "// Solution for Power of Four",
      "python_brute": "# Solution for Power of Four",
      "python_optimal": "# Solution for Power of Four"
    },
    "originalOrder": 154,
    "learningOrder": 154
  },
  {
    "id": 753,
    "number": 753,
    "sequence_number": 753,
    "title": "Fizz Buzz",
    "slug": "fizz-buzz",
    "difficulty": "Easy",
    "topic": "Simulation",
    "subtopic": "Hashing & Array Optimization",
    "pattern": "Hashing & Array Optimization",
    "secondary_patterns": [
      "Hashing & Array Optimization"
    ],
    "stage": "1D Dynamic Programming Foundations",
    "curriculumStage": "Stage 16 — 1D Dynamic Programming Foundations",
    "roadmapPhase": "Stage 16 — 1D Dynamic Programming Foundations",
    "phase": "Stage 16 — 1D Dynamic Programming Foundations",
    "estimatedTime": 15,
    "statement": "Solve the **Fizz Buzz Optimization** problem using the **Hashing & Array Optimization** technique. Given input constraints appropriate for Easy level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^4",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Hashing & Array Optimization identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Hashing & Array Optimization. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Hashing & Array Optimization techniques by solving Easy problem constraints for Fizz Buzz Optimization.",
    "whyThisPattern": "When observing arrays & strings problem conditions, Hashing & Array Optimization optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta"
    ],
    "companyRelevanceTier": "Medium",
    "leetcode_url": "https://leetcode.com/problems/fizz-buzz/",
    "leetcode_title": "Fizz Buzz",
    "leetcode_id": 412,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/fizz-buzz/",
    "canonicalSlug": "fizz-buzz",
    "canonicalUrl": "https://leetcode.com/problems/fizz-buzz/",
    "url": "https://leetcode.com/problems/fizz-buzz/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Fizz Buzz Optimization (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Fizz Buzz Optimization (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Fizz Buzz Optimization (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Fizz Buzz Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Fizz Buzz Optimization (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Fizz Buzz Optimization (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Fizz Buzz Optimization (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Fizz Buzz Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Fizz Buzz",
      "cpp_optimal": "// Solution for Fizz Buzz",
      "java_brute": "// Solution for Fizz Buzz",
      "java_optimal": "// Solution for Fizz Buzz",
      "python_brute": "# Solution for Fizz Buzz",
      "python_optimal": "# Solution for Fizz Buzz"
    },
    "originalOrder": 158,
    "learningOrder": 158
  },
  {
    "id": 754,
    "number": 754,
    "sequence_number": 754,
    "title": "Happy Number",
    "slug": "happy-number",
    "difficulty": "Easy",
    "topic": "Strings",
    "subtopic": "Hashing & Array Optimization",
    "pattern": "Hashing & Array Optimization",
    "secondary_patterns": [
      "Hashing & Array Optimization"
    ],
    "stage": "1D Dynamic Programming Foundations",
    "curriculumStage": "Stage 16 — 1D Dynamic Programming Foundations",
    "roadmapPhase": "Stage 16 — 1D Dynamic Programming Foundations",
    "phase": "Stage 16 — 1D Dynamic Programming Foundations",
    "estimatedTime": 15,
    "statement": "Solve the **Happy Number Optimization** problem using the **Hashing & Array Optimization** technique. Given input constraints appropriate for Easy level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^4",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Hashing & Array Optimization identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Hashing & Array Optimization. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Hashing & Array Optimization techniques by solving Easy problem constraints for Happy Number Optimization.",
    "whyThisPattern": "When observing arrays & strings problem conditions, Hashing & Array Optimization optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "LinkedIn",
      "Amazon"
    ],
    "companyRelevanceTier": "Medium",
    "leetcode_url": "https://leetcode.com/problems/happy-number/",
    "leetcode_title": "Happy Number",
    "leetcode_id": 202,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/happy-number/",
    "canonicalSlug": "happy-number",
    "canonicalUrl": "https://leetcode.com/problems/happy-number/",
    "url": "https://leetcode.com/problems/happy-number/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Happy Number Optimization (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Happy Number Optimization (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Happy Number Optimization (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Happy Number Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Happy Number Optimization (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Happy Number Optimization (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Happy Number Optimization (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Happy Number Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Happy Number",
      "cpp_optimal": "// Solution for Happy Number",
      "java_brute": "// Solution for Happy Number",
      "java_optimal": "// Solution for Happy Number",
      "python_brute": "# Solution for Happy Number",
      "python_optimal": "# Solution for Happy Number"
    },
    "originalOrder": 169,
    "learningOrder": 169
  },
  {
    "id": 755,
    "number": 755,
    "sequence_number": 755,
    "title": "Summary Ranges",
    "slug": "summary-ranges",
    "difficulty": "Easy",
    "topic": "Strings",
    "subtopic": "Hashing & Array Optimization",
    "pattern": "Hashing & Array Optimization",
    "secondary_patterns": [
      "Hashing & Array Optimization"
    ],
    "stage": "1D Dynamic Programming Foundations",
    "curriculumStage": "Stage 16 — 1D Dynamic Programming Foundations",
    "roadmapPhase": "Stage 16 — 1D Dynamic Programming Foundations",
    "phase": "Stage 16 — 1D Dynamic Programming Foundations",
    "estimatedTime": 15,
    "statement": "Solve the **Summary Ranges Optimization** problem using the **Hashing & Array Optimization** technique. Given input constraints appropriate for Easy level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^4",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Hashing & Array Optimization identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Hashing & Array Optimization. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Hashing & Array Optimization techniques by solving Easy problem constraints for Summary Ranges Optimization.",
    "whyThisPattern": "When observing arrays & strings problem conditions, Hashing & Array Optimization optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Meta",
      "Apple",
      "Netflix"
    ],
    "companyRelevanceTier": "Medium",
    "leetcode_url": "https://leetcode.com/problems/summary-ranges/",
    "leetcode_title": "Summary Ranges",
    "leetcode_id": 228,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/summary-ranges/",
    "canonicalSlug": "summary-ranges",
    "canonicalUrl": "https://leetcode.com/problems/summary-ranges/",
    "url": "https://leetcode.com/problems/summary-ranges/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Summary Ranges Optimization (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Summary Ranges Optimization (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Summary Ranges Optimization (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Summary Ranges Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Summary Ranges Optimization (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Summary Ranges Optimization (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Summary Ranges Optimization (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Summary Ranges Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Summary Ranges",
      "cpp_optimal": "// Solution for Summary Ranges",
      "java_brute": "// Solution for Summary Ranges",
      "java_optimal": "// Solution for Summary Ranges",
      "python_brute": "# Solution for Summary Ranges",
      "python_optimal": "# Solution for Summary Ranges"
    },
    "originalOrder": 170,
    "learningOrder": 170
  },
  {
    "id": 756,
    "number": 756,
    "sequence_number": 756,
    "title": "Valid Anagram",
    "slug": "valid-anagram",
    "difficulty": "Easy",
    "topic": "Strings",
    "subtopic": "Hashing & Array Optimization",
    "pattern": "Hashing & Array Optimization",
    "secondary_patterns": [
      "Hashing & Array Optimization"
    ],
    "stage": "1D Dynamic Programming Foundations",
    "curriculumStage": "Stage 16 — 1D Dynamic Programming Foundations",
    "roadmapPhase": "Stage 16 — 1D Dynamic Programming Foundations",
    "phase": "Stage 16 — 1D Dynamic Programming Foundations",
    "estimatedTime": 15,
    "statement": "Solve the **Valid Anagram Optimization** problem using the **Hashing & Array Optimization** technique. Given input constraints appropriate for Easy level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^4",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Hashing & Array Optimization identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Hashing & Array Optimization. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Hashing & Array Optimization techniques by solving Easy problem constraints for Valid Anagram Optimization.",
    "whyThisPattern": "When observing arrays & strings problem conditions, Hashing & Array Optimization optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta"
    ],
    "companyRelevanceTier": "Medium",
    "leetcode_url": "https://leetcode.com/problems/valid-anagram/",
    "leetcode_title": "Valid Anagram",
    "leetcode_id": 242,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/valid-anagram/",
    "canonicalSlug": "valid-anagram",
    "canonicalUrl": "https://leetcode.com/problems/valid-anagram/",
    "url": "https://leetcode.com/problems/valid-anagram/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Valid Anagram Optimization (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Valid Anagram Optimization (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Valid Anagram Optimization (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Valid Anagram Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Valid Anagram Optimization (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Valid Anagram Optimization (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Valid Anagram Optimization (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Valid Anagram Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Valid Anagram",
      "cpp_optimal": "// Solution for Valid Anagram",
      "java_brute": "// Solution for Valid Anagram",
      "java_optimal": "// Solution for Valid Anagram",
      "python_brute": "# Solution for Valid Anagram",
      "python_optimal": "# Solution for Valid Anagram"
    },
    "originalOrder": 171,
    "learningOrder": 171
  },
  {
    "id": 757,
    "number": 757,
    "sequence_number": 757,
    "title": "Add Digits",
    "slug": "add-digits",
    "difficulty": "Easy",
    "topic": "Strings",
    "subtopic": "Hashing & Array Optimization",
    "pattern": "Hashing & Array Optimization",
    "secondary_patterns": [
      "Hashing & Array Optimization"
    ],
    "stage": "1D Dynamic Programming Foundations",
    "curriculumStage": "Stage 16 — 1D Dynamic Programming Foundations",
    "roadmapPhase": "Stage 16 — 1D Dynamic Programming Foundations",
    "phase": "Stage 16 — 1D Dynamic Programming Foundations",
    "estimatedTime": 15,
    "statement": "Solve the **Add Digits Challenge** problem using the **Hashing & Array Optimization** technique. Given input constraints appropriate for Easy level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^4",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Hashing & Array Optimization identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Hashing & Array Optimization. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Hashing & Array Optimization techniques by solving Easy problem constraints for Add Digits Challenge.",
    "whyThisPattern": "When observing arrays & strings problem conditions, Hashing & Array Optimization optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Microsoft",
      "Bloomberg"
    ],
    "companyRelevanceTier": "Medium",
    "leetcode_url": "https://leetcode.com/problems/add-digits/",
    "leetcode_title": "Add Digits",
    "leetcode_id": 258,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/add-digits/",
    "canonicalSlug": "add-digits",
    "canonicalUrl": "https://leetcode.com/problems/add-digits/",
    "url": "https://leetcode.com/problems/add-digits/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Add Digits Challenge (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Add Digits Challenge (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Add Digits Challenge (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Add Digits Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Add Digits Challenge (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Add Digits Challenge (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Add Digits Challenge (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Add Digits Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Add Digits",
      "cpp_optimal": "// Solution for Add Digits",
      "java_brute": "// Solution for Add Digits",
      "java_optimal": "// Solution for Add Digits",
      "python_brute": "# Solution for Add Digits",
      "python_optimal": "# Solution for Add Digits"
    },
    "originalOrder": 172,
    "learningOrder": 172
  },
  {
    "id": 758,
    "number": 758,
    "sequence_number": 758,
    "title": "Ugly Number",
    "slug": "ugly-number",
    "difficulty": "Easy",
    "topic": "Strings",
    "subtopic": "Hashing & Array Optimization",
    "pattern": "Hashing & Array Optimization",
    "secondary_patterns": [
      "Hashing & Array Optimization"
    ],
    "stage": "1D Dynamic Programming Foundations",
    "curriculumStage": "Stage 16 — 1D Dynamic Programming Foundations",
    "roadmapPhase": "Stage 16 — 1D Dynamic Programming Foundations",
    "phase": "Stage 16 — 1D Dynamic Programming Foundations",
    "estimatedTime": 15,
    "statement": "Solve the **Ugly Number Optimization** problem using the **Hashing & Array Optimization** technique. Given input constraints appropriate for Easy level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^4",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Hashing & Array Optimization identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Hashing & Array Optimization. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Hashing & Array Optimization techniques by solving Easy problem constraints for Ugly Number Optimization.",
    "whyThisPattern": "When observing arrays & strings problem conditions, Hashing & Array Optimization optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Apple",
      "Adobe",
      "Atlassian"
    ],
    "companyRelevanceTier": "Medium",
    "leetcode_url": "https://leetcode.com/problems/ugly-number/",
    "leetcode_title": "Ugly Number",
    "leetcode_id": 263,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/ugly-number/",
    "canonicalSlug": "ugly-number",
    "canonicalUrl": "https://leetcode.com/problems/ugly-number/",
    "url": "https://leetcode.com/problems/ugly-number/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Ugly Number Optimization (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Ugly Number Optimization (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Ugly Number Optimization (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Ugly Number Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Ugly Number Optimization (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Ugly Number Optimization (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Ugly Number Optimization (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Ugly Number Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Ugly Number",
      "cpp_optimal": "// Solution for Ugly Number",
      "java_brute": "// Solution for Ugly Number",
      "java_optimal": "// Solution for Ugly Number",
      "python_brute": "# Solution for Ugly Number",
      "python_optimal": "# Solution for Ugly Number"
    },
    "originalOrder": 173,
    "learningOrder": 173
  },
  {
    "id": 759,
    "number": 759,
    "sequence_number": 759,
    "title": "First Bad Version",
    "slug": "first-bad-version",
    "difficulty": "Easy",
    "topic": "Strings",
    "subtopic": "Hashing & Array Optimization",
    "pattern": "Hashing & Array Optimization",
    "secondary_patterns": [
      "Hashing & Array Optimization"
    ],
    "stage": "1D Dynamic Programming Foundations",
    "curriculumStage": "Stage 16 — 1D Dynamic Programming Foundations",
    "roadmapPhase": "Stage 16 — 1D Dynamic Programming Foundations",
    "phase": "Stage 16 — 1D Dynamic Programming Foundations",
    "estimatedTime": 15,
    "statement": "Solve the **First Bad Version Optimization** problem using the **Hashing & Array Optimization** technique. Given input constraints appropriate for Easy level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^4",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Hashing & Array Optimization identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Hashing & Array Optimization. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Hashing & Array Optimization techniques by solving Easy problem constraints for First Bad Version Optimization.",
    "whyThisPattern": "When observing arrays & strings problem conditions, Hashing & Array Optimization optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta"
    ],
    "companyRelevanceTier": "Medium",
    "leetcode_url": "https://leetcode.com/problems/first-bad-version/",
    "leetcode_title": "First Bad Version",
    "leetcode_id": 278,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/first-bad-version/",
    "canonicalSlug": "first-bad-version",
    "canonicalUrl": "https://leetcode.com/problems/first-bad-version/",
    "url": "https://leetcode.com/problems/first-bad-version/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for First Bad Version Optimization (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for First Bad Version Optimization (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for First Bad Version Optimization (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for First Bad Version Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for First Bad Version Optimization (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for First Bad Version Optimization (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for First Bad Version Optimization (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for First Bad Version Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for First Bad Version",
      "cpp_optimal": "// Solution for First Bad Version",
      "java_brute": "// Solution for First Bad Version",
      "java_optimal": "// Solution for First Bad Version",
      "python_brute": "# Solution for First Bad Version",
      "python_optimal": "# Solution for First Bad Version"
    },
    "originalOrder": 174,
    "learningOrder": 174
  },
  {
    "id": 760,
    "number": 760,
    "sequence_number": 760,
    "title": "Nim Game",
    "slug": "nim-game",
    "difficulty": "Easy",
    "topic": "Strings",
    "subtopic": "Hashing & Array Optimization",
    "pattern": "Hashing & Array Optimization",
    "secondary_patterns": [
      "Hashing & Array Optimization"
    ],
    "stage": "1D Dynamic Programming Foundations",
    "curriculumStage": "Stage 16 — 1D Dynamic Programming Foundations",
    "roadmapPhase": "Stage 16 — 1D Dynamic Programming Foundations",
    "phase": "Stage 16 — 1D Dynamic Programming Foundations",
    "estimatedTime": 15,
    "statement": "Solve the **Nim Game Optimization** problem using the **Hashing & Array Optimization** technique. Given input constraints appropriate for Easy level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^4",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Hashing & Array Optimization identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Hashing & Array Optimization. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Hashing & Array Optimization techniques by solving Easy problem constraints for Nim Game Optimization.",
    "whyThisPattern": "When observing arrays & strings problem conditions, Hashing & Array Optimization optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Apple",
      "Adobe",
      "Atlassian"
    ],
    "companyRelevanceTier": "Medium",
    "leetcode_url": "https://leetcode.com/problems/nim-game/",
    "leetcode_title": "Nim Game",
    "leetcode_id": 292,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/nim-game/",
    "canonicalSlug": "nim-game",
    "canonicalUrl": "https://leetcode.com/problems/nim-game/",
    "url": "https://leetcode.com/problems/nim-game/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Nim Game Optimization (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Nim Game Optimization (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Nim Game Optimization (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Nim Game Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Nim Game Optimization (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Nim Game Optimization (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Nim Game Optimization (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Nim Game Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Nim Game",
      "cpp_optimal": "// Solution for Nim Game",
      "java_brute": "// Solution for Nim Game",
      "java_optimal": "// Solution for Nim Game",
      "python_brute": "# Solution for Nim Game",
      "python_optimal": "# Solution for Nim Game"
    },
    "originalOrder": 175,
    "learningOrder": 175
  },
  {
    "id": 761,
    "number": 761,
    "sequence_number": 761,
    "title": "Length of Longest Fibonacci Subsequence",
    "slug": "length-of-longest-fibonacci-subsequence",
    "difficulty": "Medium",
    "topic": "Dynamic Programming",
    "subtopic": "Dynamic Programming Optimization",
    "pattern": "2D DP Pair Transitions",
    "secondary_patterns": [
      "2D DP Pair Transitions"
    ],
    "stage": "1D Dynamic Programming Foundations",
    "curriculumStage": "Stage 16 — 1D Dynamic Programming Foundations",
    "roadmapPhase": "Stage 16 — 1D Dynamic Programming Foundations",
    "phase": "Stage 16 — 1D Dynamic Programming Foundations",
    "estimatedTime": 30,
    "statement": "Given the constraints and input parameters for Length of Longest Fibonacci Subsequence, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Length of Longest Fibonacci Subsequence."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Length of Longest Fibonacci Subsequence.",
      "Leverage the optimal Dynamic Programming pattern to reduce time complexity."
    ],
    "learningObjective": "Master Dynamic Programming techniques by solving Medium problem constraints for Length of Longest Fibonacci Subsequence.",
    "whyThisPattern": "When observing Dynamic Programming problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/length-of-longest-fibonacci-subsequence/",
    "leetcode_title": "Length of Longest Fibonacci Subsequence",
    "leetcode_id": 873,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/length-of-longest-fibonacci-subsequence/",
    "canonicalSlug": "length-of-longest-fibonacci-subsequence",
    "canonicalUrl": "https://leetcode.com/problems/length-of-longest-fibonacci-subsequence/",
    "url": "https://leetcode.com/problems/length-of-longest-fibonacci-subsequence/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Length of Longest Fibonacci Subsequence\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Length of Longest Fibonacci Subsequence\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Length of Longest Fibonacci Subsequence\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Length of Longest Fibonacci Subsequence\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Length of Longest Fibonacci Subsequence\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Length of Longest Fibonacci Subsequence\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Length of Longest Fibonacci Subsequence\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Length of Longest Fibonacci Subsequence\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Length of Longest Fibonacci Subsequence",
      "cpp_optimal": "// Solution for Length of Longest Fibonacci Subsequence",
      "java_brute": "// Solution for Length of Longest Fibonacci Subsequence",
      "java_optimal": "// Solution for Length of Longest Fibonacci Subsequence",
      "python_brute": "# Solution for Length of Longest Fibonacci Subsequence",
      "python_optimal": "# Solution for Length of Longest Fibonacci Subsequence"
    },
    "originalOrder": 452,
    "learningOrder": 452
  },
  {
    "id": 762,
    "number": 762,
    "sequence_number": 762,
    "title": "Knight Dialer",
    "slug": "knight-dialer",
    "difficulty": "Medium",
    "topic": "Dynamic Programming",
    "subtopic": "Dynamic Programming Optimization",
    "pattern": "Transition DP Matrix",
    "secondary_patterns": [
      "Transition DP Matrix"
    ],
    "stage": "1D Dynamic Programming Foundations",
    "curriculumStage": "Stage 16 — 1D Dynamic Programming Foundations",
    "roadmapPhase": "Stage 16 — 1D Dynamic Programming Foundations",
    "phase": "Stage 16 — 1D Dynamic Programming Foundations",
    "estimatedTime": 30,
    "statement": "Given the constraints and input parameters for Knight Dialer, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Knight Dialer."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Knight Dialer.",
      "Leverage the optimal Dynamic Programming pattern to reduce time complexity."
    ],
    "learningObjective": "Master Dynamic Programming techniques by solving Medium problem constraints for Knight Dialer.",
    "whyThisPattern": "When observing Dynamic Programming problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/knight-dialer/",
    "leetcode_title": "Knight Dialer",
    "leetcode_id": 935,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/knight-dialer/",
    "canonicalSlug": "knight-dialer",
    "canonicalUrl": "https://leetcode.com/problems/knight-dialer/",
    "url": "https://leetcode.com/problems/knight-dialer/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Knight Dialer\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Knight Dialer\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Knight Dialer\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Knight Dialer\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Knight Dialer\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Knight Dialer\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Knight Dialer\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Knight Dialer\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Knight Dialer",
      "cpp_optimal": "// Solution for Knight Dialer",
      "java_brute": "// Solution for Knight Dialer",
      "java_optimal": "// Solution for Knight Dialer",
      "python_brute": "# Solution for Knight Dialer",
      "python_optimal": "# Solution for Knight Dialer"
    },
    "originalOrder": 453,
    "learningOrder": 453
  },
  {
    "id": 763,
    "number": 763,
    "sequence_number": 763,
    "title": "Minimum Falling Path Sum",
    "slug": "minimum-falling-path-sum",
    "difficulty": "Medium",
    "topic": "Dynamic Programming",
    "subtopic": "Dynamic Programming Optimization",
    "pattern": "2D Grid Path Min",
    "secondary_patterns": [
      "2D Grid Path Min"
    ],
    "stage": "1D Dynamic Programming Foundations",
    "curriculumStage": "Stage 16 — 1D Dynamic Programming Foundations",
    "roadmapPhase": "Stage 16 — 1D Dynamic Programming Foundations",
    "phase": "Stage 16 — 1D Dynamic Programming Foundations",
    "estimatedTime": 30,
    "statement": "Given the constraints and input parameters for Minimum Falling Path Sum, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Minimum Falling Path Sum."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Minimum Falling Path Sum.",
      "Leverage the optimal Dynamic Programming pattern to reduce time complexity."
    ],
    "learningObjective": "Master Dynamic Programming techniques by solving Medium problem constraints for Minimum Falling Path Sum.",
    "whyThisPattern": "When observing Dynamic Programming problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/minimum-falling-path-sum/",
    "leetcode_title": "Minimum Falling Path Sum",
    "leetcode_id": 931,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/minimum-falling-path-sum/",
    "canonicalSlug": "minimum-falling-path-sum",
    "canonicalUrl": "https://leetcode.com/problems/minimum-falling-path-sum/",
    "url": "https://leetcode.com/problems/minimum-falling-path-sum/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Minimum Falling Path Sum\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Minimum Falling Path Sum\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Minimum Falling Path Sum\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Minimum Falling Path Sum\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Minimum Falling Path Sum\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Minimum Falling Path Sum\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Minimum Falling Path Sum\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Minimum Falling Path Sum\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Minimum Falling Path Sum",
      "cpp_optimal": "// Solution for Minimum Falling Path Sum",
      "java_brute": "// Solution for Minimum Falling Path Sum",
      "java_optimal": "// Solution for Minimum Falling Path Sum",
      "python_brute": "# Solution for Minimum Falling Path Sum",
      "python_optimal": "# Solution for Minimum Falling Path Sum"
    },
    "originalOrder": 454,
    "learningOrder": 454
  },
  {
    "id": 764,
    "number": 764,
    "sequence_number": 764,
    "title": "New 21 Game",
    "slug": "new-21-game",
    "difficulty": "Medium",
    "topic": "Dynamic Programming",
    "subtopic": "Dynamic Programming Optimization",
    "pattern": "Sliding Window DP Probability",
    "secondary_patterns": [
      "Sliding Window DP Probability"
    ],
    "stage": "1D Dynamic Programming Foundations",
    "curriculumStage": "Stage 16 — 1D Dynamic Programming Foundations",
    "roadmapPhase": "Stage 16 — 1D Dynamic Programming Foundations",
    "phase": "Stage 16 — 1D Dynamic Programming Foundations",
    "estimatedTime": 30,
    "statement": "Given the constraints and input parameters for New 21 Game, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for New 21 Game."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for New 21 Game.",
      "Leverage the optimal Dynamic Programming pattern to reduce time complexity."
    ],
    "learningObjective": "Master Dynamic Programming techniques by solving Medium problem constraints for New 21 Game.",
    "whyThisPattern": "When observing Dynamic Programming problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/new-21-game/",
    "leetcode_title": "New 21 Game",
    "leetcode_id": 837,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/new-21-game/",
    "canonicalSlug": "new-21-game",
    "canonicalUrl": "https://leetcode.com/problems/new-21-game/",
    "url": "https://leetcode.com/problems/new-21-game/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for New 21 Game\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for New 21 Game\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for New 21 Game\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for New 21 Game\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for New 21 Game\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for New 21 Game\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for New 21 Game\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for New 21 Game\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for New 21 Game",
      "cpp_optimal": "// Solution for New 21 Game",
      "java_brute": "// Solution for New 21 Game",
      "java_optimal": "// Solution for New 21 Game",
      "python_brute": "# Solution for New 21 Game",
      "python_optimal": "# Solution for New 21 Game"
    },
    "originalOrder": 455,
    "learningOrder": 455
  },
  {
    "id": 765,
    "number": 765,
    "sequence_number": 765,
    "title": "Flip String to Monotone Increasing",
    "slug": "flip-string-to-monotone-increasing",
    "difficulty": "Medium",
    "topic": "Dynamic Programming",
    "subtopic": "Dynamic Programming Optimization",
    "pattern": "0/1 Flip Min DP",
    "secondary_patterns": [
      "0/1 Flip Min DP"
    ],
    "stage": "1D Dynamic Programming Foundations",
    "curriculumStage": "Stage 16 — 1D Dynamic Programming Foundations",
    "roadmapPhase": "Stage 16 — 1D Dynamic Programming Foundations",
    "phase": "Stage 16 — 1D Dynamic Programming Foundations",
    "estimatedTime": 30,
    "statement": "Given the constraints and input parameters for Flip String to Monotone Increasing, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Flip String to Monotone Increasing."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Flip String to Monotone Increasing.",
      "Leverage the optimal Dynamic Programming pattern to reduce time complexity."
    ],
    "learningObjective": "Master Dynamic Programming techniques by solving Medium problem constraints for Flip String to Monotone Increasing.",
    "whyThisPattern": "When observing Dynamic Programming problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/flip-string-to-monotone-increasing/",
    "leetcode_title": "Flip String to Monotone Increasing",
    "leetcode_id": 926,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/flip-string-to-monotone-increasing/",
    "canonicalSlug": "flip-string-to-monotone-increasing",
    "canonicalUrl": "https://leetcode.com/problems/flip-string-to-monotone-increasing/",
    "url": "https://leetcode.com/problems/flip-string-to-monotone-increasing/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Flip String to Monotone Increasing\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Flip String to Monotone Increasing\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Flip String to Monotone Increasing\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Flip String to Monotone Increasing\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Flip String to Monotone Increasing\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Flip String to Monotone Increasing\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Flip String to Monotone Increasing\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Flip String to Monotone Increasing\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Flip String to Monotone Increasing",
      "cpp_optimal": "// Solution for Flip String to Monotone Increasing",
      "java_brute": "// Solution for Flip String to Monotone Increasing",
      "java_optimal": "// Solution for Flip String to Monotone Increasing",
      "python_brute": "# Solution for Flip String to Monotone Increasing",
      "python_optimal": "# Solution for Flip String to Monotone Increasing"
    },
    "originalOrder": 456,
    "learningOrder": 456
  },
  {
    "id": 766,
    "number": 766,
    "sequence_number": 766,
    "title": "Find Two Non-overlapping Sub-arrays Each With Target Sum",
    "slug": "find-two-non-overlapping-sub-arrays-each-with-target-sum",
    "difficulty": "Medium",
    "topic": "Dynamic Programming",
    "subtopic": "Dynamic Programming Optimization",
    "pattern": "Prefix Suffix Min Window DP",
    "secondary_patterns": [
      "Prefix Suffix Min Window DP"
    ],
    "stage": "1D Dynamic Programming Foundations",
    "curriculumStage": "Stage 16 — 1D Dynamic Programming Foundations",
    "roadmapPhase": "Stage 16 — 1D Dynamic Programming Foundations",
    "phase": "Stage 16 — 1D Dynamic Programming Foundations",
    "estimatedTime": 30,
    "statement": "Given the constraints and input parameters for Find Two Non-overlapping Sub-arrays Each With Target Sum, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Find Two Non-overlapping Sub-arrays Each With Target Sum."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Find Two Non-overlapping Sub-arrays Each With Target Sum.",
      "Leverage the optimal Dynamic Programming pattern to reduce time complexity."
    ],
    "learningObjective": "Master Dynamic Programming techniques by solving Medium problem constraints for Find Two Non-overlapping Sub-arrays Each With Target Sum.",
    "whyThisPattern": "When observing Dynamic Programming problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/find-two-non-overlapping-sub-arrays-each-with-target-sum/",
    "leetcode_title": "Find Two Non-overlapping Sub-arrays Each With Target Sum",
    "leetcode_id": 1477,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/find-two-non-overlapping-sub-arrays-each-with-target-sum/",
    "canonicalSlug": "find-two-non-overlapping-sub-arrays-each-with-target-sum",
    "canonicalUrl": "https://leetcode.com/problems/find-two-non-overlapping-sub-arrays-each-with-target-sum/",
    "url": "https://leetcode.com/problems/find-two-non-overlapping-sub-arrays-each-with-target-sum/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Find Two Non-overlapping Sub-arrays Each With Target Sum\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Find Two Non-overlapping Sub-arrays Each With Target Sum\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Find Two Non-overlapping Sub-arrays Each With Target Sum\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Find Two Non-overlapping Sub-arrays Each With Target Sum\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Find Two Non-overlapping Sub-arrays Each With Target Sum\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Find Two Non-overlapping Sub-arrays Each With Target Sum\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Find Two Non-overlapping Sub-arrays Each With Target Sum\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Find Two Non-overlapping Sub-arrays Each With Target Sum\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Find Two Non-overlapping Sub-arrays Each With Target Sum",
      "cpp_optimal": "// Solution for Find Two Non-overlapping Sub-arrays Each With Target Sum",
      "java_brute": "// Solution for Find Two Non-overlapping Sub-arrays Each With Target Sum",
      "java_optimal": "// Solution for Find Two Non-overlapping Sub-arrays Each With Target Sum",
      "python_brute": "# Solution for Find Two Non-overlapping Sub-arrays Each With Target Sum",
      "python_optimal": "# Solution for Find Two Non-overlapping Sub-arrays Each With Target Sum"
    },
    "originalOrder": 457,
    "learningOrder": 457
  },
  {
    "id": 767,
    "number": 767,
    "sequence_number": 767,
    "title": "Minimum Deletions to Make String Balanced",
    "slug": "minimum-deletions-to-make-string-balanced",
    "difficulty": "Medium",
    "topic": "Dynamic Programming",
    "subtopic": "Dynamic Programming Optimization",
    "pattern": "b-Count / Deletion DP",
    "secondary_patterns": [
      "b-Count / Deletion DP"
    ],
    "stage": "1D Dynamic Programming Foundations",
    "curriculumStage": "Stage 16 — 1D Dynamic Programming Foundations",
    "roadmapPhase": "Stage 16 — 1D Dynamic Programming Foundations",
    "phase": "Stage 16 — 1D Dynamic Programming Foundations",
    "estimatedTime": 30,
    "statement": "Given the constraints and input parameters for Minimum Deletions to Make String Balanced, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Minimum Deletions to Make String Balanced."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Minimum Deletions to Make String Balanced.",
      "Leverage the optimal Dynamic Programming pattern to reduce time complexity."
    ],
    "learningObjective": "Master Dynamic Programming techniques by solving Medium problem constraints for Minimum Deletions to Make String Balanced.",
    "whyThisPattern": "When observing Dynamic Programming problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/minimum-deletions-to-make-string-balanced/",
    "leetcode_title": "Minimum Deletions to Make String Balanced",
    "leetcode_id": 1653,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/minimum-deletions-to-make-string-balanced/",
    "canonicalSlug": "minimum-deletions-to-make-string-balanced",
    "canonicalUrl": "https://leetcode.com/problems/minimum-deletions-to-make-string-balanced/",
    "url": "https://leetcode.com/problems/minimum-deletions-to-make-string-balanced/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Minimum Deletions to Make String Balanced\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Minimum Deletions to Make String Balanced\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Minimum Deletions to Make String Balanced\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Minimum Deletions to Make String Balanced\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Minimum Deletions to Make String Balanced\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Minimum Deletions to Make String Balanced\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Minimum Deletions to Make String Balanced\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Minimum Deletions to Make String Balanced\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Minimum Deletions to Make String Balanced",
      "cpp_optimal": "// Solution for Minimum Deletions to Make String Balanced",
      "java_brute": "// Solution for Minimum Deletions to Make String Balanced",
      "java_optimal": "// Solution for Minimum Deletions to Make String Balanced",
      "python_brute": "# Solution for Minimum Deletions to Make String Balanced",
      "python_optimal": "# Solution for Minimum Deletions to Make String Balanced"
    },
    "originalOrder": 458,
    "learningOrder": 458
  },
  {
    "id": 768,
    "number": 768,
    "sequence_number": 768,
    "title": "Maximum Non Negative Product in a Matrix",
    "slug": "maximum-non-negative-product-in-a-matrix",
    "difficulty": "Medium",
    "topic": "Dynamic Programming",
    "subtopic": "Dynamic Programming Optimization",
    "pattern": "2D Min-Max Product DP",
    "secondary_patterns": [
      "2D Min-Max Product DP"
    ],
    "stage": "1D Dynamic Programming Foundations",
    "curriculumStage": "Stage 16 — 1D Dynamic Programming Foundations",
    "roadmapPhase": "Stage 16 — 1D Dynamic Programming Foundations",
    "phase": "Stage 16 — 1D Dynamic Programming Foundations",
    "estimatedTime": 30,
    "statement": "Given the constraints and input parameters for Maximum Non Negative Product in a Matrix, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Maximum Non Negative Product in a Matrix."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Maximum Non Negative Product in a Matrix.",
      "Leverage the optimal Dynamic Programming pattern to reduce time complexity."
    ],
    "learningObjective": "Master Dynamic Programming techniques by solving Medium problem constraints for Maximum Non Negative Product in a Matrix.",
    "whyThisPattern": "When observing Dynamic Programming problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/maximum-non-negative-product-in-a-matrix/",
    "leetcode_title": "Maximum Non Negative Product in a Matrix",
    "leetcode_id": 1594,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/maximum-non-negative-product-in-a-matrix/",
    "canonicalSlug": "maximum-non-negative-product-in-a-matrix",
    "canonicalUrl": "https://leetcode.com/problems/maximum-non-negative-product-in-a-matrix/",
    "url": "https://leetcode.com/problems/maximum-non-negative-product-in-a-matrix/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Maximum Non Negative Product in a Matrix\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Maximum Non Negative Product in a Matrix\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Maximum Non Negative Product in a Matrix\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Maximum Non Negative Product in a Matrix\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Maximum Non Negative Product in a Matrix\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Maximum Non Negative Product in a Matrix\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Maximum Non Negative Product in a Matrix\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Maximum Non Negative Product in a Matrix\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Maximum Non Negative Product in a Matrix",
      "cpp_optimal": "// Solution for Maximum Non Negative Product in a Matrix",
      "java_brute": "// Solution for Maximum Non Negative Product in a Matrix",
      "java_optimal": "// Solution for Maximum Non Negative Product in a Matrix",
      "python_brute": "# Solution for Maximum Non Negative Product in a Matrix",
      "python_optimal": "# Solution for Maximum Non Negative Product in a Matrix"
    },
    "originalOrder": 459,
    "learningOrder": 459
  },
  {
    "id": 769,
    "number": 769,
    "sequence_number": 769,
    "title": "Maximum Length of Subarray With Positive Product",
    "slug": "maximum-length-of-subarray-with-positive-product",
    "difficulty": "Medium",
    "topic": "Dynamic Programming",
    "subtopic": "Dynamic Programming Optimization",
    "pattern": "Pos/Neg Dynamic State",
    "secondary_patterns": [
      "Pos/Neg Dynamic State"
    ],
    "stage": "1D Dynamic Programming Foundations",
    "curriculumStage": "Stage 16 — 1D Dynamic Programming Foundations",
    "roadmapPhase": "Stage 16 — 1D Dynamic Programming Foundations",
    "phase": "Stage 16 — 1D Dynamic Programming Foundations",
    "estimatedTime": 30,
    "statement": "Given the constraints and input parameters for Maximum Length of Subarray With Positive Product, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Maximum Length of Subarray With Positive Product."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Maximum Length of Subarray With Positive Product.",
      "Leverage the optimal Dynamic Programming pattern to reduce time complexity."
    ],
    "learningObjective": "Master Dynamic Programming techniques by solving Medium problem constraints for Maximum Length of Subarray With Positive Product.",
    "whyThisPattern": "When observing Dynamic Programming problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/maximum-length-of-subarray-with-positive-product/",
    "leetcode_title": "Maximum Length of Subarray With Positive Product",
    "leetcode_id": 1567,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/maximum-length-of-subarray-with-positive-product/",
    "canonicalSlug": "maximum-length-of-subarray-with-positive-product",
    "canonicalUrl": "https://leetcode.com/problems/maximum-length-of-subarray-with-positive-product/",
    "url": "https://leetcode.com/problems/maximum-length-of-subarray-with-positive-product/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Maximum Length of Subarray With Positive Product\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Maximum Length of Subarray With Positive Product\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Maximum Length of Subarray With Positive Product\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Maximum Length of Subarray With Positive Product\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Maximum Length of Subarray With Positive Product\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Maximum Length of Subarray With Positive Product\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Maximum Length of Subarray With Positive Product\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Maximum Length of Subarray With Positive Product\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Maximum Length of Subarray With Positive Product",
      "cpp_optimal": "// Solution for Maximum Length of Subarray With Positive Product",
      "java_brute": "// Solution for Maximum Length of Subarray With Positive Product",
      "java_optimal": "// Solution for Maximum Length of Subarray With Positive Product",
      "python_brute": "# Solution for Maximum Length of Subarray With Positive Product",
      "python_optimal": "# Solution for Maximum Length of Subarray With Positive Product"
    },
    "originalOrder": 460,
    "learningOrder": 460
  },
  {
    "id": 770,
    "number": 770,
    "sequence_number": 770,
    "title": "Unique Paths II",
    "slug": "unique-paths-ii",
    "difficulty": "Medium",
    "topic": "Dynamic Programming",
    "subtopic": "Dynamic Programming Optimization",
    "pattern": "2D Grid Obstacle DP",
    "secondary_patterns": [
      "2D Grid Obstacle DP"
    ],
    "stage": "1D Dynamic Programming Foundations",
    "curriculumStage": "Stage 16 — 1D Dynamic Programming Foundations",
    "roadmapPhase": "Stage 16 — 1D Dynamic Programming Foundations",
    "phase": "Stage 16 — 1D Dynamic Programming Foundations",
    "estimatedTime": 30,
    "statement": "Given the constraints and input parameters for Unique Paths II, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Unique Paths II."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Unique Paths II.",
      "Leverage the optimal Dynamic Programming pattern to reduce time complexity."
    ],
    "learningObjective": "Master Dynamic Programming techniques by solving Medium problem constraints for Unique Paths II.",
    "whyThisPattern": "When observing Dynamic Programming problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/unique-paths-ii/",
    "leetcode_title": "Unique Paths II",
    "leetcode_id": 63,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/unique-paths-ii/",
    "canonicalSlug": "unique-paths-ii",
    "canonicalUrl": "https://leetcode.com/problems/unique-paths-ii/",
    "url": "https://leetcode.com/problems/unique-paths-ii/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Unique Paths II\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Unique Paths II\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Unique Paths II\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Unique Paths II\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Unique Paths II\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Unique Paths II\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Unique Paths II\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Unique Paths II\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Unique Paths II",
      "cpp_optimal": "// Solution for Unique Paths II",
      "java_brute": "// Solution for Unique Paths II",
      "java_optimal": "// Solution for Unique Paths II",
      "python_brute": "# Solution for Unique Paths II",
      "python_optimal": "# Solution for Unique Paths II"
    },
    "originalOrder": 461,
    "learningOrder": 461
  },
  {
    "id": 771,
    "number": 771,
    "sequence_number": 771,
    "title": "Minimum Path Sum",
    "slug": "minimum-path-sum",
    "difficulty": "Medium",
    "topic": "Dynamic Programming",
    "subtopic": "Dynamic Programming Optimization",
    "pattern": "2D Grid Min Path DP",
    "secondary_patterns": [
      "2D Grid Min Path DP"
    ],
    "stage": "1D Dynamic Programming Foundations",
    "curriculumStage": "Stage 16 — 1D Dynamic Programming Foundations",
    "roadmapPhase": "Stage 16 — 1D Dynamic Programming Foundations",
    "phase": "Stage 16 — 1D Dynamic Programming Foundations",
    "estimatedTime": 30,
    "statement": "Given the constraints and input parameters for Minimum Path Sum, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Minimum Path Sum."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Minimum Path Sum.",
      "Leverage the optimal Dynamic Programming pattern to reduce time complexity."
    ],
    "learningObjective": "Master Dynamic Programming techniques by solving Medium problem constraints for Minimum Path Sum.",
    "whyThisPattern": "When observing Dynamic Programming problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/minimum-path-sum/",
    "leetcode_title": "Minimum Path Sum",
    "leetcode_id": 64,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/minimum-path-sum/",
    "canonicalSlug": "minimum-path-sum",
    "canonicalUrl": "https://leetcode.com/problems/minimum-path-sum/",
    "url": "https://leetcode.com/problems/minimum-path-sum/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Minimum Path Sum\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Minimum Path Sum\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Minimum Path Sum\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Minimum Path Sum\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Minimum Path Sum\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Minimum Path Sum\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Minimum Path Sum\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Minimum Path Sum\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Minimum Path Sum",
      "cpp_optimal": "// Solution for Minimum Path Sum",
      "java_brute": "// Solution for Minimum Path Sum",
      "java_optimal": "// Solution for Minimum Path Sum",
      "python_brute": "# Solution for Minimum Path Sum",
      "python_optimal": "# Solution for Minimum Path Sum"
    },
    "originalOrder": 462,
    "learningOrder": 462
  },
  {
    "id": 772,
    "number": 772,
    "sequence_number": 772,
    "title": "Triangle",
    "slug": "triangle",
    "difficulty": "Medium",
    "topic": "Dynamic Programming",
    "subtopic": "Dynamic Programming Optimization",
    "pattern": "Bottom-Up Row Min DP",
    "secondary_patterns": [
      "Bottom-Up Row Min DP"
    ],
    "stage": "1D Dynamic Programming Foundations",
    "curriculumStage": "Stage 16 — 1D Dynamic Programming Foundations",
    "roadmapPhase": "Stage 16 — 1D Dynamic Programming Foundations",
    "phase": "Stage 16 — 1D Dynamic Programming Foundations",
    "estimatedTime": 30,
    "statement": "Given the constraints and input parameters for Triangle, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Triangle."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Triangle.",
      "Leverage the optimal Dynamic Programming pattern to reduce time complexity."
    ],
    "learningObjective": "Master Dynamic Programming techniques by solving Medium problem constraints for Triangle.",
    "whyThisPattern": "When observing Dynamic Programming problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/triangle/",
    "leetcode_title": "Triangle",
    "leetcode_id": 120,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/triangle/",
    "canonicalSlug": "triangle",
    "canonicalUrl": "https://leetcode.com/problems/triangle/",
    "url": "https://leetcode.com/problems/triangle/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Triangle\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Triangle\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Triangle\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Triangle\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Triangle\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Triangle\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Triangle\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Triangle\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Triangle",
      "cpp_optimal": "// Solution for Triangle",
      "java_brute": "// Solution for Triangle",
      "java_optimal": "// Solution for Triangle",
      "python_brute": "# Solution for Triangle",
      "python_optimal": "# Solution for Triangle"
    },
    "originalOrder": 463,
    "learningOrder": 463
  },
  {
    "id": 773,
    "number": 773,
    "sequence_number": 773,
    "title": "Target Sum",
    "slug": "target-sum",
    "difficulty": "Medium",
    "topic": "Dynamic Programming",
    "subtopic": "Dynamic Programming Optimization",
    "pattern": "Subset Sum Offset DP",
    "secondary_patterns": [
      "Subset Sum Offset DP"
    ],
    "stage": "1D Dynamic Programming Foundations",
    "curriculumStage": "Stage 16 — 1D Dynamic Programming Foundations",
    "roadmapPhase": "Stage 16 — 1D Dynamic Programming Foundations",
    "phase": "Stage 16 — 1D Dynamic Programming Foundations",
    "estimatedTime": 30,
    "statement": "Given the constraints and input parameters for Target Sum, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Target Sum."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Target Sum.",
      "Leverage the optimal Dynamic Programming pattern to reduce time complexity."
    ],
    "learningObjective": "Master Dynamic Programming techniques by solving Medium problem constraints for Target Sum.",
    "whyThisPattern": "When observing Dynamic Programming problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/target-sum/",
    "leetcode_title": "Target Sum",
    "leetcode_id": 494,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/target-sum/",
    "canonicalSlug": "target-sum",
    "canonicalUrl": "https://leetcode.com/problems/target-sum/",
    "url": "https://leetcode.com/problems/target-sum/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Target Sum\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Target Sum\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Target Sum\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Target Sum\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Target Sum\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Target Sum\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Target Sum\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Target Sum\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Target Sum",
      "cpp_optimal": "// Solution for Target Sum",
      "java_brute": "// Solution for Target Sum",
      "java_optimal": "// Solution for Target Sum",
      "python_brute": "# Solution for Target Sum",
      "python_optimal": "# Solution for Target Sum"
    },
    "originalOrder": 464,
    "learningOrder": 464
  },
  {
    "id": 774,
    "number": 774,
    "sequence_number": 774,
    "title": "Decode Ways",
    "slug": "decode-ways",
    "difficulty": "Medium",
    "topic": "Dynamic Programming",
    "subtopic": "Dynamic Programming Optimization",
    "pattern": "1D String Parsing DP",
    "secondary_patterns": [
      "1D String Parsing DP"
    ],
    "stage": "1D Dynamic Programming Foundations",
    "curriculumStage": "Stage 16 — 1D Dynamic Programming Foundations",
    "roadmapPhase": "Stage 16 — 1D Dynamic Programming Foundations",
    "phase": "Stage 16 — 1D Dynamic Programming Foundations",
    "estimatedTime": 30,
    "statement": "Given the constraints and input parameters for Decode Ways, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Decode Ways."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Decode Ways.",
      "Leverage the optimal Dynamic Programming pattern to reduce time complexity."
    ],
    "learningObjective": "Master Dynamic Programming techniques by solving Medium problem constraints for Decode Ways.",
    "whyThisPattern": "When observing Dynamic Programming problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/decode-ways/",
    "leetcode_title": "Decode Ways",
    "leetcode_id": 91,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/decode-ways/",
    "canonicalSlug": "decode-ways",
    "canonicalUrl": "https://leetcode.com/problems/decode-ways/",
    "url": "https://leetcode.com/problems/decode-ways/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Decode Ways\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Decode Ways\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Decode Ways\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Decode Ways\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Decode Ways\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Decode Ways\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Decode Ways\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Decode Ways\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Decode Ways",
      "cpp_optimal": "// Solution for Decode Ways",
      "java_brute": "// Solution for Decode Ways",
      "java_optimal": "// Solution for Decode Ways",
      "python_brute": "# Solution for Decode Ways",
      "python_optimal": "# Solution for Decode Ways"
    },
    "originalOrder": 465,
    "learningOrder": 465
  },
  {
    "id": 775,
    "number": 775,
    "sequence_number": 775,
    "title": "House Robber",
    "slug": "house-robber",
    "difficulty": "Medium",
    "topic": "Dynamic Programming",
    "subtopic": "Dynamic Programming Optimization",
    "pattern": "1D DP Skip Neighbor",
    "secondary_patterns": [
      "1D DP Skip Neighbor"
    ],
    "stage": "1D Dynamic Programming Foundations",
    "curriculumStage": "Stage 16 — 1D Dynamic Programming Foundations",
    "roadmapPhase": "Stage 16 — 1D Dynamic Programming Foundations",
    "phase": "Stage 16 — 1D Dynamic Programming Foundations",
    "estimatedTime": 30,
    "statement": "Given the constraints and input parameters for House Robber, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for House Robber."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for House Robber.",
      "Leverage the optimal Dynamic Programming pattern to reduce time complexity."
    ],
    "learningObjective": "Master Dynamic Programming techniques by solving Medium problem constraints for House Robber.",
    "whyThisPattern": "When observing Dynamic Programming problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/house-robber/",
    "leetcode_title": "House Robber",
    "leetcode_id": 198,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/house-robber/",
    "canonicalSlug": "house-robber",
    "canonicalUrl": "https://leetcode.com/problems/house-robber/",
    "url": "https://leetcode.com/problems/house-robber/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for House Robber\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for House Robber\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for House Robber\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for House Robber\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for House Robber\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for House Robber\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for House Robber\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for House Robber\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for House Robber",
      "cpp_optimal": "// Solution for House Robber",
      "java_brute": "// Solution for House Robber",
      "java_optimal": "// Solution for House Robber",
      "python_brute": "# Solution for House Robber",
      "python_optimal": "# Solution for House Robber"
    },
    "originalOrder": 466,
    "learningOrder": 466
  },
  {
    "id": 776,
    "number": 776,
    "sequence_number": 776,
    "title": "House Robber II",
    "slug": "house-robber-ii",
    "difficulty": "Medium",
    "topic": "Dynamic Programming",
    "subtopic": "Dynamic Programming Optimization",
    "pattern": "Circular Row DP",
    "secondary_patterns": [
      "Circular Row DP"
    ],
    "stage": "1D Dynamic Programming Foundations",
    "curriculumStage": "Stage 16 — 1D Dynamic Programming Foundations",
    "roadmapPhase": "Stage 16 — 1D Dynamic Programming Foundations",
    "phase": "Stage 16 — 1D Dynamic Programming Foundations",
    "estimatedTime": 30,
    "statement": "Given the constraints and input parameters for House Robber II, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for House Robber II."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for House Robber II.",
      "Leverage the optimal Dynamic Programming pattern to reduce time complexity."
    ],
    "learningObjective": "Master Dynamic Programming techniques by solving Medium problem constraints for House Robber II.",
    "whyThisPattern": "When observing Dynamic Programming problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/house-robber-ii/",
    "leetcode_title": "House Robber II",
    "leetcode_id": 213,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/house-robber-ii/",
    "canonicalSlug": "house-robber-ii",
    "canonicalUrl": "https://leetcode.com/problems/house-robber-ii/",
    "url": "https://leetcode.com/problems/house-robber-ii/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for House Robber II\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for House Robber II\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for House Robber II\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for House Robber II\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for House Robber II\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for House Robber II\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for House Robber II\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for House Robber II\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for House Robber II",
      "cpp_optimal": "// Solution for House Robber II",
      "java_brute": "// Solution for House Robber II",
      "java_optimal": "// Solution for House Robber II",
      "python_brute": "# Solution for House Robber II",
      "python_optimal": "# Solution for House Robber II"
    },
    "originalOrder": 467,
    "learningOrder": 467
  },
  {
    "id": 777,
    "number": 777,
    "sequence_number": 777,
    "title": "Coin Change",
    "slug": "coin-change",
    "difficulty": "Medium",
    "topic": "Dynamic Programming",
    "subtopic": "Dynamic Programming Optimization",
    "pattern": "Unbounded Knapsack Min Coins",
    "secondary_patterns": [
      "Unbounded Knapsack Min Coins"
    ],
    "stage": "1D Dynamic Programming Foundations",
    "curriculumStage": "Stage 16 — 1D Dynamic Programming Foundations",
    "roadmapPhase": "Stage 16 — 1D Dynamic Programming Foundations",
    "phase": "Stage 16 — 1D Dynamic Programming Foundations",
    "estimatedTime": 30,
    "statement": "Given the constraints and input parameters for Coin Change, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Coin Change."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Coin Change.",
      "Leverage the optimal Dynamic Programming pattern to reduce time complexity."
    ],
    "learningObjective": "Master Dynamic Programming techniques by solving Medium problem constraints for Coin Change.",
    "whyThisPattern": "When observing Dynamic Programming problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/coin-change/",
    "leetcode_title": "Coin Change",
    "leetcode_id": 322,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/coin-change/",
    "canonicalSlug": "coin-change",
    "canonicalUrl": "https://leetcode.com/problems/coin-change/",
    "url": "https://leetcode.com/problems/coin-change/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Coin Change\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Coin Change\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Coin Change\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Coin Change\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Coin Change\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Coin Change\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Coin Change\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Coin Change\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Coin Change",
      "cpp_optimal": "// Solution for Coin Change",
      "java_brute": "// Solution for Coin Change",
      "java_optimal": "// Solution for Coin Change",
      "python_brute": "# Solution for Coin Change",
      "python_optimal": "# Solution for Coin Change"
    },
    "originalOrder": 468,
    "learningOrder": 468
  },
  {
    "id": 778,
    "number": 778,
    "sequence_number": 778,
    "title": "Longest Increasing Subsequence",
    "slug": "longest-increasing-subsequence",
    "difficulty": "Medium",
    "topic": "Dynamic Programming",
    "subtopic": "Dynamic Programming Optimization",
    "pattern": "Patience Sorting / LIS DP",
    "secondary_patterns": [
      "Patience Sorting / LIS DP"
    ],
    "stage": "1D Dynamic Programming Foundations",
    "curriculumStage": "Stage 16 — 1D Dynamic Programming Foundations",
    "roadmapPhase": "Stage 16 — 1D Dynamic Programming Foundations",
    "phase": "Stage 16 — 1D Dynamic Programming Foundations",
    "estimatedTime": 30,
    "statement": "Given the constraints and input parameters for Longest Increasing Subsequence, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Longest Increasing Subsequence."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Longest Increasing Subsequence.",
      "Leverage the optimal Dynamic Programming pattern to reduce time complexity."
    ],
    "learningObjective": "Master Dynamic Programming techniques by solving Medium problem constraints for Longest Increasing Subsequence.",
    "whyThisPattern": "When observing Dynamic Programming problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/longest-increasing-subsequence/",
    "leetcode_title": "Longest Increasing Subsequence",
    "leetcode_id": 300,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/longest-increasing-subsequence/",
    "canonicalSlug": "longest-increasing-subsequence",
    "canonicalUrl": "https://leetcode.com/problems/longest-increasing-subsequence/",
    "url": "https://leetcode.com/problems/longest-increasing-subsequence/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Longest Increasing Subsequence\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Longest Increasing Subsequence\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Longest Increasing Subsequence\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Longest Increasing Subsequence\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Longest Increasing Subsequence\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Longest Increasing Subsequence\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Longest Increasing Subsequence\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Longest Increasing Subsequence\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Longest Increasing Subsequence",
      "cpp_optimal": "// Solution for Longest Increasing Subsequence",
      "java_brute": "// Solution for Longest Increasing Subsequence",
      "java_optimal": "// Solution for Longest Increasing Subsequence",
      "python_brute": "# Solution for Longest Increasing Subsequence",
      "python_optimal": "# Solution for Longest Increasing Subsequence"
    },
    "originalOrder": 469,
    "learningOrder": 469
  },
  {
    "id": 779,
    "number": 779,
    "sequence_number": 779,
    "title": "Partition Equal Subset Sum",
    "slug": "partition-equal-subset-sum",
    "difficulty": "Medium",
    "topic": "Dynamic Programming",
    "subtopic": "Dynamic Programming Optimization",
    "pattern": "0/1 Knapsack Target Sum DP",
    "secondary_patterns": [
      "0/1 Knapsack Target Sum DP"
    ],
    "stage": "1D Dynamic Programming Foundations",
    "curriculumStage": "Stage 16 — 1D Dynamic Programming Foundations",
    "roadmapPhase": "Stage 16 — 1D Dynamic Programming Foundations",
    "phase": "Stage 16 — 1D Dynamic Programming Foundations",
    "estimatedTime": 30,
    "statement": "Given the constraints and input parameters for Partition Equal Subset Sum, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Partition Equal Subset Sum."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Partition Equal Subset Sum.",
      "Leverage the optimal Dynamic Programming pattern to reduce time complexity."
    ],
    "learningObjective": "Master Dynamic Programming techniques by solving Medium problem constraints for Partition Equal Subset Sum.",
    "whyThisPattern": "When observing Dynamic Programming problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/partition-equal-subset-sum/",
    "leetcode_title": "Partition Equal Subset Sum",
    "leetcode_id": 416,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/partition-equal-subset-sum/",
    "canonicalSlug": "partition-equal-subset-sum",
    "canonicalUrl": "https://leetcode.com/problems/partition-equal-subset-sum/",
    "url": "https://leetcode.com/problems/partition-equal-subset-sum/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Partition Equal Subset Sum\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Partition Equal Subset Sum\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Partition Equal Subset Sum\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Partition Equal Subset Sum\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Partition Equal Subset Sum\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Partition Equal Subset Sum\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Partition Equal Subset Sum\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Partition Equal Subset Sum\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Partition Equal Subset Sum",
      "cpp_optimal": "// Solution for Partition Equal Subset Sum",
      "java_brute": "// Solution for Partition Equal Subset Sum",
      "java_optimal": "// Solution for Partition Equal Subset Sum",
      "python_brute": "# Solution for Partition Equal Subset Sum",
      "python_optimal": "# Solution for Partition Equal Subset Sum"
    },
    "originalOrder": 470,
    "learningOrder": 470
  },
  {
    "id": 780,
    "number": 780,
    "sequence_number": 780,
    "title": "Word Break",
    "slug": "word-break",
    "difficulty": "Medium",
    "topic": "Dynamic Programming",
    "subtopic": "Dynamic Programming Optimization",
    "pattern": "1D Prefix DP",
    "secondary_patterns": [
      "1D Prefix DP"
    ],
    "stage": "1D Dynamic Programming Foundations",
    "curriculumStage": "Stage 16 — 1D Dynamic Programming Foundations",
    "roadmapPhase": "Stage 16 — 1D Dynamic Programming Foundations",
    "phase": "Stage 16 — 1D Dynamic Programming Foundations",
    "estimatedTime": 30,
    "statement": "Given the constraints and input parameters for Word Break, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Word Break."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Word Break.",
      "Leverage the optimal Dynamic Programming pattern to reduce time complexity."
    ],
    "learningObjective": "Master Dynamic Programming techniques by solving Medium problem constraints for Word Break.",
    "whyThisPattern": "When observing Dynamic Programming problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/word-break/",
    "leetcode_title": "Word Break",
    "leetcode_id": 139,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/word-break/",
    "canonicalSlug": "word-break",
    "canonicalUrl": "https://leetcode.com/problems/word-break/",
    "url": "https://leetcode.com/problems/word-break/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Word Break\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Word Break\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Word Break\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Word Break\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Word Break\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Word Break\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Word Break\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Word Break\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Word Break",
      "cpp_optimal": "// Solution for Word Break",
      "java_brute": "// Solution for Word Break",
      "java_optimal": "// Solution for Word Break",
      "python_brute": "# Solution for Word Break",
      "python_optimal": "# Solution for Word Break"
    },
    "originalOrder": 471,
    "learningOrder": 471
  },
  {
    "id": 781,
    "number": 781,
    "sequence_number": 781,
    "title": "Simplified Fractions",
    "slug": "simplified-fractions",
    "difficulty": "Medium",
    "topic": "Math",
    "subtopic": "Math Optimization",
    "pattern": "GCD Fraction Filter",
    "secondary_patterns": [
      "GCD Fraction Filter"
    ],
    "stage": "1D Dynamic Programming Foundations",
    "curriculumStage": "Stage 16 — 1D Dynamic Programming Foundations",
    "roadmapPhase": "Stage 16 — 1D Dynamic Programming Foundations",
    "phase": "Stage 16 — 1D Dynamic Programming Foundations",
    "estimatedTime": 30,
    "statement": "Given the constraints and input parameters for Simplified Fractions, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Simplified Fractions."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Simplified Fractions.",
      "Leverage the optimal Math pattern to reduce time complexity."
    ],
    "learningObjective": "Master Math techniques by solving Medium problem constraints for Simplified Fractions.",
    "whyThisPattern": "When observing Math problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/simplified-fractions/",
    "leetcode_title": "Simplified Fractions",
    "leetcode_id": 1447,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/simplified-fractions/",
    "canonicalSlug": "simplified-fractions",
    "canonicalUrl": "https://leetcode.com/problems/simplified-fractions/",
    "url": "https://leetcode.com/problems/simplified-fractions/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Simplified Fractions\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Simplified Fractions\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Simplified Fractions\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Simplified Fractions\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Simplified Fractions\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Simplified Fractions\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Simplified Fractions\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Simplified Fractions\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Simplified Fractions",
      "cpp_optimal": "// Solution for Simplified Fractions",
      "java_brute": "// Solution for Simplified Fractions",
      "java_optimal": "// Solution for Simplified Fractions",
      "python_brute": "# Solution for Simplified Fractions",
      "python_optimal": "# Solution for Simplified Fractions"
    },
    "originalOrder": 562,
    "learningOrder": 562
  },
  {
    "id": 782,
    "number": 782,
    "sequence_number": 782,
    "title": "Pow(x, n)",
    "slug": "powx-n",
    "difficulty": "Medium",
    "topic": "Math",
    "subtopic": "Math Optimization",
    "pattern": "Binary Exponentiation",
    "secondary_patterns": [
      "Binary Exponentiation"
    ],
    "stage": "1D Dynamic Programming Foundations",
    "curriculumStage": "Stage 16 — 1D Dynamic Programming Foundations",
    "roadmapPhase": "Stage 16 — 1D Dynamic Programming Foundations",
    "phase": "Stage 16 — 1D Dynamic Programming Foundations",
    "estimatedTime": 30,
    "statement": "Given the constraints and input parameters for Pow(x, n), implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Pow(x, n)."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Pow(x, n).",
      "Leverage the optimal Math pattern to reduce time complexity."
    ],
    "learningObjective": "Master Math techniques by solving Medium problem constraints for Pow(x, n).",
    "whyThisPattern": "When observing Math problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/powx-n/",
    "leetcode_title": "Pow(x, n)",
    "leetcode_id": 50,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/powx-n/",
    "canonicalSlug": "powx-n",
    "canonicalUrl": "https://leetcode.com/problems/powx-n/",
    "url": "https://leetcode.com/problems/powx-n/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Pow(x, n)\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Pow(x, n)\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Pow(x, n)\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Pow(x, n)\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Pow(x, n)\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Pow(x, n)\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Pow(x, n)\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Pow(x, n)\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Pow(x, n)",
      "cpp_optimal": "// Solution for Pow(x, n)",
      "java_brute": "// Solution for Pow(x, n)",
      "java_optimal": "// Solution for Pow(x, n)",
      "python_brute": "# Solution for Pow(x, n)",
      "python_optimal": "# Solution for Pow(x, n)"
    },
    "originalOrder": 563,
    "learningOrder": 563
  },
  {
    "id": 783,
    "number": 783,
    "sequence_number": 783,
    "title": "Integer to Roman",
    "slug": "integer-to-roman",
    "difficulty": "Medium",
    "topic": "Math",
    "subtopic": "Math Optimization",
    "pattern": "Math Pattern",
    "secondary_patterns": [
      "Math Pattern"
    ],
    "stage": "1D Dynamic Programming Foundations",
    "curriculumStage": "Stage 16 — 1D Dynamic Programming Foundations",
    "roadmapPhase": "Stage 16 — 1D Dynamic Programming Foundations",
    "phase": "Stage 16 — 1D Dynamic Programming Foundations",
    "estimatedTime": 30,
    "statement": "Solve the **Integer to Roman** problem using standard Math techniques. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Math algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Math properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Math techniques by solving Medium problem constraints for Integer to Roman.",
    "whyThisPattern": "When observing Math problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/integer-to-roman/",
    "leetcode_title": "Integer to Roman",
    "leetcode_id": 12,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/integer-to-roman/",
    "canonicalSlug": "integer-to-roman",
    "canonicalUrl": "https://leetcode.com/problems/integer-to-roman/",
    "url": "https://leetcode.com/problems/integer-to-roman/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Integer to Roman\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Integer to Roman\n};",
        "java": "// Java Solution for Integer to Roman\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Integer to Roman\n}",
        "python": "# Python Solution for Integer to Roman\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Integer to Roman\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Integer to Roman\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Integer to Roman\n};",
        "java": "// Optimal Java Solution for Integer to Roman\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Integer to Roman\n}",
        "python": "# Optimal Python Solution for Integer to Roman\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Integer to Roman\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Integer to Roman",
      "cpp_optimal": "// Solution for Integer to Roman",
      "java_brute": "// Solution for Integer to Roman",
      "java_optimal": "// Solution for Integer to Roman",
      "python_brute": "# Solution for Integer to Roman",
      "python_optimal": "# Solution for Integer to Roman"
    },
    "originalOrder": 564,
    "learningOrder": 564
  },
  {
    "id": 784,
    "number": 784,
    "sequence_number": 784,
    "title": "Fraction to Recurring Decimal",
    "slug": "fraction-to-recurring-decimal",
    "difficulty": "Medium",
    "topic": "Math",
    "subtopic": "Math Optimization",
    "pattern": "Math Pattern",
    "secondary_patterns": [
      "Math Pattern"
    ],
    "stage": "1D Dynamic Programming Foundations",
    "curriculumStage": "Stage 16 — 1D Dynamic Programming Foundations",
    "roadmapPhase": "Stage 16 — 1D Dynamic Programming Foundations",
    "phase": "Stage 16 — 1D Dynamic Programming Foundations",
    "estimatedTime": 30,
    "statement": "Solve the **Fraction to Recurring Decimal** problem using standard Math techniques. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Math algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Math properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Math techniques by solving Medium problem constraints for Fraction to Recurring Decimal.",
    "whyThisPattern": "When observing Math problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/fraction-to-recurring-decimal/",
    "leetcode_title": "Fraction to Recurring Decimal",
    "leetcode_id": 166,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/fraction-to-recurring-decimal/",
    "canonicalSlug": "fraction-to-recurring-decimal",
    "canonicalUrl": "https://leetcode.com/problems/fraction-to-recurring-decimal/",
    "url": "https://leetcode.com/problems/fraction-to-recurring-decimal/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Fraction to Recurring Decimal\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Fraction to Recurring Decimal\n};",
        "java": "// Java Solution for Fraction to Recurring Decimal\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Fraction to Recurring Decimal\n}",
        "python": "# Python Solution for Fraction to Recurring Decimal\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Fraction to Recurring Decimal\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Fraction to Recurring Decimal\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Fraction to Recurring Decimal\n};",
        "java": "// Optimal Java Solution for Fraction to Recurring Decimal\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Fraction to Recurring Decimal\n}",
        "python": "# Optimal Python Solution for Fraction to Recurring Decimal\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Fraction to Recurring Decimal\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Fraction to Recurring Decimal",
      "cpp_optimal": "// Solution for Fraction to Recurring Decimal",
      "java_brute": "// Solution for Fraction to Recurring Decimal",
      "java_optimal": "// Solution for Fraction to Recurring Decimal",
      "python_brute": "# Solution for Fraction to Recurring Decimal",
      "python_optimal": "# Solution for Fraction to Recurring Decimal"
    },
    "originalOrder": 565,
    "learningOrder": 565
  },
  {
    "id": 785,
    "number": 785,
    "sequence_number": 785,
    "title": "Factorial Trailing Zeroes",
    "slug": "factorial-trailing-zeroes",
    "difficulty": "Medium",
    "topic": "Math",
    "subtopic": "Math Optimization",
    "pattern": "Math Pattern",
    "secondary_patterns": [
      "Math Pattern"
    ],
    "stage": "1D Dynamic Programming Foundations",
    "curriculumStage": "Stage 16 — 1D Dynamic Programming Foundations",
    "roadmapPhase": "Stage 16 — 1D Dynamic Programming Foundations",
    "phase": "Stage 16 — 1D Dynamic Programming Foundations",
    "estimatedTime": 30,
    "statement": "Solve the **Factorial Trailing Zeroes** problem using standard Math techniques. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Math algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Math properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Math techniques by solving Medium problem constraints for Factorial Trailing Zeroes.",
    "whyThisPattern": "When observing Math problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/factorial-trailing-zeroes/",
    "leetcode_title": "Factorial Trailing Zeroes",
    "leetcode_id": 172,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/factorial-trailing-zeroes/",
    "canonicalSlug": "factorial-trailing-zeroes",
    "canonicalUrl": "https://leetcode.com/problems/factorial-trailing-zeroes/",
    "url": "https://leetcode.com/problems/factorial-trailing-zeroes/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Factorial Trailing Zeroes\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Factorial Trailing Zeroes\n};",
        "java": "// Java Solution for Factorial Trailing Zeroes\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Factorial Trailing Zeroes\n}",
        "python": "# Python Solution for Factorial Trailing Zeroes\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Factorial Trailing Zeroes\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Factorial Trailing Zeroes\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Factorial Trailing Zeroes\n};",
        "java": "// Optimal Java Solution for Factorial Trailing Zeroes\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Factorial Trailing Zeroes\n}",
        "python": "# Optimal Python Solution for Factorial Trailing Zeroes\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Factorial Trailing Zeroes\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Factorial Trailing Zeroes",
      "cpp_optimal": "// Solution for Factorial Trailing Zeroes",
      "java_brute": "// Solution for Factorial Trailing Zeroes",
      "java_optimal": "// Solution for Factorial Trailing Zeroes",
      "python_brute": "# Solution for Factorial Trailing Zeroes",
      "python_optimal": "# Solution for Factorial Trailing Zeroes"
    },
    "originalOrder": 566,
    "learningOrder": 566
  },
  {
    "id": 786,
    "number": 786,
    "sequence_number": 786,
    "title": "Number of Ways to Wear Different Hats to Each Other",
    "slug": "number-of-ways-to-wear-different-hats-to-each-other",
    "difficulty": "Hard",
    "topic": "Dynamic Programming",
    "subtopic": "Dynamic Programming Optimization",
    "pattern": "Bitmask Hat Assignment DP",
    "secondary_patterns": [
      "Bitmask Hat Assignment DP"
    ],
    "stage": "1D Dynamic Programming Foundations",
    "curriculumStage": "Stage 16 — 1D Dynamic Programming Foundations",
    "roadmapPhase": "Stage 16 — 1D Dynamic Programming Foundations",
    "phase": "Stage 16 — 1D Dynamic Programming Foundations",
    "estimatedTime": 45,
    "statement": "Given the constraints and input parameters for Number of Ways to Wear Different Hats to Each Other, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Number of Ways to Wear Different Hats to Each Other."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Number of Ways to Wear Different Hats to Each Other.",
      "Leverage the optimal Dynamic Programming pattern to reduce time complexity."
    ],
    "learningObjective": "Master Dynamic Programming techniques by solving Hard problem constraints for Number of Ways to Wear Different Hats to Each Other.",
    "whyThisPattern": "When observing Dynamic Programming problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/number-of-ways-to-wear-different-hats-to-each-other/",
    "leetcode_title": "Number of Ways to Wear Different Hats to Each Other",
    "leetcode_id": 1434,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/number-of-ways-to-wear-different-hats-to-each-other/",
    "canonicalSlug": "number-of-ways-to-wear-different-hats-to-each-other",
    "canonicalUrl": "https://leetcode.com/problems/number-of-ways-to-wear-different-hats-to-each-other/",
    "url": "https://leetcode.com/problems/number-of-ways-to-wear-different-hats-to-each-other/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Number of Ways to Wear Different Hats to Each Other\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Number of Ways to Wear Different Hats to Each Other\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Number of Ways to Wear Different Hats to Each Other\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Number of Ways to Wear Different Hats to Each Other\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Number of Ways to Wear Different Hats to Each Other\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Number of Ways to Wear Different Hats to Each Other\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Number of Ways to Wear Different Hats to Each Other\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Number of Ways to Wear Different Hats to Each Other\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Number of Ways to Wear Different Hats to Each Other",
      "cpp_optimal": "// Solution for Number of Ways to Wear Different Hats to Each Other",
      "java_brute": "// Solution for Number of Ways to Wear Different Hats to Each Other",
      "java_optimal": "// Solution for Number of Ways to Wear Different Hats to Each Other",
      "python_brute": "# Solution for Number of Ways to Wear Different Hats to Each Other",
      "python_optimal": "# Solution for Number of Ways to Wear Different Hats to Each Other"
    },
    "originalOrder": 816,
    "learningOrder": 816
  },
  {
    "id": 787,
    "number": 787,
    "sequence_number": 787,
    "title": "Number of Ways of Cutting a Pizza",
    "slug": "number-of-ways-of-cutting-a-pizza",
    "difficulty": "Hard",
    "topic": "Dynamic Programming",
    "subtopic": "Dynamic Programming Optimization",
    "pattern": "2D Suffix Apple DP",
    "secondary_patterns": [
      "2D Suffix Apple DP"
    ],
    "stage": "1D Dynamic Programming Foundations",
    "curriculumStage": "Stage 16 — 1D Dynamic Programming Foundations",
    "roadmapPhase": "Stage 16 — 1D Dynamic Programming Foundations",
    "phase": "Stage 16 — 1D Dynamic Programming Foundations",
    "estimatedTime": 45,
    "statement": "Given the constraints and input parameters for Number of Ways of Cutting a Pizza, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Number of Ways of Cutting a Pizza."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Number of Ways of Cutting a Pizza.",
      "Leverage the optimal Dynamic Programming pattern to reduce time complexity."
    ],
    "learningObjective": "Master Dynamic Programming techniques by solving Hard problem constraints for Number of Ways of Cutting a Pizza.",
    "whyThisPattern": "When observing Dynamic Programming problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/number-of-ways-of-cutting-a-pizza/",
    "leetcode_title": "Number of Ways of Cutting a Pizza",
    "leetcode_id": 1444,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/number-of-ways-of-cutting-a-pizza/",
    "canonicalSlug": "number-of-ways-of-cutting-a-pizza",
    "canonicalUrl": "https://leetcode.com/problems/number-of-ways-of-cutting-a-pizza/",
    "url": "https://leetcode.com/problems/number-of-ways-of-cutting-a-pizza/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Number of Ways of Cutting a Pizza\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Number of Ways of Cutting a Pizza\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Number of Ways of Cutting a Pizza\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Number of Ways of Cutting a Pizza\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Number of Ways of Cutting a Pizza\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Number of Ways of Cutting a Pizza\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Number of Ways of Cutting a Pizza\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Number of Ways of Cutting a Pizza\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Number of Ways of Cutting a Pizza",
      "cpp_optimal": "// Solution for Number of Ways of Cutting a Pizza",
      "java_brute": "// Solution for Number of Ways of Cutting a Pizza",
      "java_optimal": "// Solution for Number of Ways of Cutting a Pizza",
      "python_brute": "# Solution for Number of Ways of Cutting a Pizza",
      "python_optimal": "# Solution for Number of Ways of Cutting a Pizza"
    },
    "originalOrder": 817,
    "learningOrder": 817
  },
  {
    "id": 788,
    "number": 788,
    "sequence_number": 788,
    "title": "Find All Good Strings",
    "slug": "find-all-good-strings",
    "difficulty": "Hard",
    "topic": "Dynamic Programming",
    "subtopic": "Dynamic Programming Optimization",
    "pattern": "KMP + Digit DP State",
    "secondary_patterns": [
      "KMP + Digit DP State"
    ],
    "stage": "1D Dynamic Programming Foundations",
    "curriculumStage": "Stage 16 — 1D Dynamic Programming Foundations",
    "roadmapPhase": "Stage 16 — 1D Dynamic Programming Foundations",
    "phase": "Stage 16 — 1D Dynamic Programming Foundations",
    "estimatedTime": 45,
    "statement": "Given the constraints and input parameters for Find All Good Strings, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Find All Good Strings."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Find All Good Strings.",
      "Leverage the optimal Dynamic Programming pattern to reduce time complexity."
    ],
    "learningObjective": "Master Dynamic Programming techniques by solving Hard problem constraints for Find All Good Strings.",
    "whyThisPattern": "When observing Dynamic Programming problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/find-all-good-strings/",
    "leetcode_title": "Find All Good Strings",
    "leetcode_id": 1397,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/find-all-good-strings/",
    "canonicalSlug": "find-all-good-strings",
    "canonicalUrl": "https://leetcode.com/problems/find-all-good-strings/",
    "url": "https://leetcode.com/problems/find-all-good-strings/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Find All Good Strings\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Find All Good Strings\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Find All Good Strings\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Find All Good Strings\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Find All Good Strings\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Find All Good Strings\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Find All Good Strings\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Find All Good Strings\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Find All Good Strings",
      "cpp_optimal": "// Solution for Find All Good Strings",
      "java_brute": "// Solution for Find All Good Strings",
      "java_optimal": "// Solution for Find All Good Strings",
      "python_brute": "# Solution for Find All Good Strings",
      "python_optimal": "# Solution for Find All Good Strings"
    },
    "originalOrder": 818,
    "learningOrder": 818
  },
  {
    "id": 789,
    "number": 789,
    "sequence_number": 789,
    "title": "Form Largest Integer With Digits That Add up to Target",
    "slug": "form-largest-integer-with-digits-that-add-up-to-target",
    "difficulty": "Hard",
    "topic": "Dynamic Programming",
    "subtopic": "Dynamic Programming Optimization",
    "pattern": "Unbounded Knapsack String DP",
    "secondary_patterns": [
      "Unbounded Knapsack String DP"
    ],
    "stage": "1D Dynamic Programming Foundations",
    "curriculumStage": "Stage 16 — 1D Dynamic Programming Foundations",
    "roadmapPhase": "Stage 16 — 1D Dynamic Programming Foundations",
    "phase": "Stage 16 — 1D Dynamic Programming Foundations",
    "estimatedTime": 45,
    "statement": "Given the constraints and input parameters for Form Largest Integer With Digits That Add up to Target, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Form Largest Integer With Digits That Add up to Target."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Form Largest Integer With Digits That Add up to Target.",
      "Leverage the optimal Dynamic Programming pattern to reduce time complexity."
    ],
    "learningObjective": "Master Dynamic Programming techniques by solving Hard problem constraints for Form Largest Integer With Digits That Add up to Target.",
    "whyThisPattern": "When observing Dynamic Programming problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/form-largest-integer-with-digits-that-add-up-to-target/",
    "leetcode_title": "Form Largest Integer With Digits That Add up to Target",
    "leetcode_id": 1449,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/form-largest-integer-with-digits-that-add-up-to-target/",
    "canonicalSlug": "form-largest-integer-with-digits-that-add-up-to-target",
    "canonicalUrl": "https://leetcode.com/problems/form-largest-integer-with-digits-that-add-up-to-target/",
    "url": "https://leetcode.com/problems/form-largest-integer-with-digits-that-add-up-to-target/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Form Largest Integer With Digits That Add up to Target\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Form Largest Integer With Digits That Add up to Target\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Form Largest Integer With Digits That Add up to Target\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Form Largest Integer With Digits That Add up to Target\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Form Largest Integer With Digits That Add up to Target\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Form Largest Integer With Digits That Add up to Target\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Form Largest Integer With Digits That Add up to Target\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Form Largest Integer With Digits That Add up to Target\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Form Largest Integer With Digits That Add up to Target",
      "cpp_optimal": "// Solution for Form Largest Integer With Digits That Add up to Target",
      "java_brute": "// Solution for Form Largest Integer With Digits That Add up to Target",
      "java_optimal": "// Solution for Form Largest Integer With Digits That Add up to Target",
      "python_brute": "# Solution for Form Largest Integer With Digits That Add up to Target",
      "python_optimal": "# Solution for Form Largest Integer With Digits That Add up to Target"
    },
    "originalOrder": 819,
    "learningOrder": 819
  },
  {
    "id": 790,
    "number": 790,
    "sequence_number": 790,
    "title": "Cherry Pickup II",
    "slug": "cherry-pickup-ii",
    "difficulty": "Hard",
    "topic": "Dynamic Programming",
    "subtopic": "Dynamic Programming Optimization",
    "pattern": "3D Grid Two Robot DP",
    "secondary_patterns": [
      "3D Grid Two Robot DP"
    ],
    "stage": "1D Dynamic Programming Foundations",
    "curriculumStage": "Stage 16 — 1D Dynamic Programming Foundations",
    "roadmapPhase": "Stage 16 — 1D Dynamic Programming Foundations",
    "phase": "Stage 16 — 1D Dynamic Programming Foundations",
    "estimatedTime": 45,
    "statement": "Given the constraints and input parameters for Cherry Pickup II, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Cherry Pickup II."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Cherry Pickup II.",
      "Leverage the optimal Dynamic Programming pattern to reduce time complexity."
    ],
    "learningObjective": "Master Dynamic Programming techniques by solving Hard problem constraints for Cherry Pickup II.",
    "whyThisPattern": "When observing Dynamic Programming problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/cherry-pickup-ii/",
    "leetcode_title": "Cherry Pickup II",
    "leetcode_id": 1463,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/cherry-pickup-ii/",
    "canonicalSlug": "cherry-pickup-ii",
    "canonicalUrl": "https://leetcode.com/problems/cherry-pickup-ii/",
    "url": "https://leetcode.com/problems/cherry-pickup-ii/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Cherry Pickup II\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Cherry Pickup II\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Cherry Pickup II\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Cherry Pickup II\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Cherry Pickup II\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Cherry Pickup II\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Cherry Pickup II\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Cherry Pickup II\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Cherry Pickup II",
      "cpp_optimal": "// Solution for Cherry Pickup II",
      "java_brute": "// Solution for Cherry Pickup II",
      "java_optimal": "// Solution for Cherry Pickup II",
      "python_brute": "# Solution for Cherry Pickup II",
      "python_optimal": "# Solution for Cherry Pickup II"
    },
    "originalOrder": 820,
    "learningOrder": 820
  },
  {
    "id": 791,
    "number": 791,
    "sequence_number": 791,
    "title": "Parallel Courses II",
    "slug": "parallel-courses-ii",
    "difficulty": "Hard",
    "topic": "Dynamic Programming",
    "subtopic": "Dynamic Programming Optimization",
    "pattern": "Bitmask Subgraph DP",
    "secondary_patterns": [
      "Bitmask Subgraph DP"
    ],
    "stage": "1D Dynamic Programming Foundations",
    "curriculumStage": "Stage 16 — 1D Dynamic Programming Foundations",
    "roadmapPhase": "Stage 16 — 1D Dynamic Programming Foundations",
    "phase": "Stage 16 — 1D Dynamic Programming Foundations",
    "estimatedTime": 45,
    "statement": "Given the constraints and input parameters for Parallel Courses II, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Parallel Courses II."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Parallel Courses II.",
      "Leverage the optimal Dynamic Programming pattern to reduce time complexity."
    ],
    "learningObjective": "Master Dynamic Programming techniques by solving Hard problem constraints for Parallel Courses II.",
    "whyThisPattern": "When observing Dynamic Programming problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/parallel-courses-ii/",
    "leetcode_title": "Parallel Courses II",
    "leetcode_id": 1494,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/parallel-courses-ii/",
    "canonicalSlug": "parallel-courses-ii",
    "canonicalUrl": "https://leetcode.com/problems/parallel-courses-ii/",
    "url": "https://leetcode.com/problems/parallel-courses-ii/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Parallel Courses II\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Parallel Courses II\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Parallel Courses II\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Parallel Courses II\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Parallel Courses II\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Parallel Courses II\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Parallel Courses II\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Parallel Courses II\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Parallel Courses II",
      "cpp_optimal": "// Solution for Parallel Courses II",
      "java_brute": "// Solution for Parallel Courses II",
      "java_optimal": "// Solution for Parallel Courses II",
      "python_brute": "# Solution for Parallel Courses II",
      "python_optimal": "# Solution for Parallel Courses II"
    },
    "originalOrder": 821,
    "learningOrder": 821
  },
  {
    "id": 792,
    "number": 792,
    "sequence_number": 792,
    "title": "Allocate Mailboxes",
    "slug": "allocate-mailboxes",
    "difficulty": "Hard",
    "topic": "Dynamic Programming",
    "subtopic": "Dynamic Programming Optimization",
    "pattern": "1D Partition Distance DP",
    "secondary_patterns": [
      "1D Partition Distance DP"
    ],
    "stage": "1D Dynamic Programming Foundations",
    "curriculumStage": "Stage 16 — 1D Dynamic Programming Foundations",
    "roadmapPhase": "Stage 16 — 1D Dynamic Programming Foundations",
    "phase": "Stage 16 — 1D Dynamic Programming Foundations",
    "estimatedTime": 45,
    "statement": "Given the constraints and input parameters for Allocate Mailboxes, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Allocate Mailboxes."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Allocate Mailboxes.",
      "Leverage the optimal Dynamic Programming pattern to reduce time complexity."
    ],
    "learningObjective": "Master Dynamic Programming techniques by solving Hard problem constraints for Allocate Mailboxes.",
    "whyThisPattern": "When observing Dynamic Programming problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/allocate-mailboxes/",
    "leetcode_title": "Allocate Mailboxes",
    "leetcode_id": 1478,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/allocate-mailboxes/",
    "canonicalSlug": "allocate-mailboxes",
    "canonicalUrl": "https://leetcode.com/problems/allocate-mailboxes/",
    "url": "https://leetcode.com/problems/allocate-mailboxes/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Allocate Mailboxes\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Allocate Mailboxes\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Allocate Mailboxes\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Allocate Mailboxes\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Allocate Mailboxes\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Allocate Mailboxes\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Allocate Mailboxes\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Allocate Mailboxes\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Allocate Mailboxes",
      "cpp_optimal": "// Solution for Allocate Mailboxes",
      "java_brute": "// Solution for Allocate Mailboxes",
      "java_optimal": "// Solution for Allocate Mailboxes",
      "python_brute": "# Solution for Allocate Mailboxes",
      "python_optimal": "# Solution for Allocate Mailboxes"
    },
    "originalOrder": 822,
    "learningOrder": 822
  },
  {
    "id": 793,
    "number": 793,
    "sequence_number": 793,
    "title": "Dungeon Game",
    "slug": "dungeon-game",
    "difficulty": "Hard",
    "topic": "Dynamic Programming",
    "subtopic": "Dynamic Programming Optimization",
    "pattern": "Bottom-Up Minimum Health DP",
    "secondary_patterns": [
      "Bottom-Up Minimum Health DP"
    ],
    "stage": "1D Dynamic Programming Foundations",
    "curriculumStage": "Stage 16 — 1D Dynamic Programming Foundations",
    "roadmapPhase": "Stage 16 — 1D Dynamic Programming Foundations",
    "phase": "Stage 16 — 1D Dynamic Programming Foundations",
    "estimatedTime": 45,
    "statement": "Given the constraints and input parameters for Dungeon Game, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Dungeon Game."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Dungeon Game.",
      "Leverage the optimal Dynamic Programming pattern to reduce time complexity."
    ],
    "learningObjective": "Master Dynamic Programming techniques by solving Hard problem constraints for Dungeon Game.",
    "whyThisPattern": "When observing Dynamic Programming problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/dungeon-game/",
    "leetcode_title": "Dungeon Game",
    "leetcode_id": 174,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/dungeon-game/",
    "canonicalSlug": "dungeon-game",
    "canonicalUrl": "https://leetcode.com/problems/dungeon-game/",
    "url": "https://leetcode.com/problems/dungeon-game/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Dungeon Game\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Dungeon Game\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Dungeon Game\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Dungeon Game\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Dungeon Game\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Dungeon Game\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Dungeon Game\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Dungeon Game\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Dungeon Game",
      "cpp_optimal": "// Solution for Dungeon Game",
      "java_brute": "// Solution for Dungeon Game",
      "java_optimal": "// Solution for Dungeon Game",
      "python_brute": "# Solution for Dungeon Game",
      "python_optimal": "# Solution for Dungeon Game"
    },
    "originalOrder": 823,
    "learningOrder": 823
  },
  {
    "id": 794,
    "number": 794,
    "sequence_number": 794,
    "title": "String Compression II",
    "slug": "string-compression-ii",
    "difficulty": "Hard",
    "topic": "Dynamic Programming",
    "subtopic": "Dynamic Programming Optimization",
    "pattern": "2D Run-Length Deletion DP",
    "secondary_patterns": [
      "2D Run-Length Deletion DP"
    ],
    "stage": "1D Dynamic Programming Foundations",
    "curriculumStage": "Stage 16 — 1D Dynamic Programming Foundations",
    "roadmapPhase": "Stage 16 — 1D Dynamic Programming Foundations",
    "phase": "Stage 16 — 1D Dynamic Programming Foundations",
    "estimatedTime": 45,
    "statement": "Given the constraints and input parameters for String Compression II, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for String Compression II."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for String Compression II.",
      "Leverage the optimal Dynamic Programming pattern to reduce time complexity."
    ],
    "learningObjective": "Master Dynamic Programming techniques by solving Hard problem constraints for String Compression II.",
    "whyThisPattern": "When observing Dynamic Programming problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/string-compression-ii/",
    "leetcode_title": "String Compression II",
    "leetcode_id": 1531,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/string-compression-ii/",
    "canonicalSlug": "string-compression-ii",
    "canonicalUrl": "https://leetcode.com/problems/string-compression-ii/",
    "url": "https://leetcode.com/problems/string-compression-ii/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for String Compression II\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for String Compression II\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for String Compression II\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for String Compression II\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for String Compression II\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for String Compression II\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for String Compression II\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for String Compression II\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for String Compression II",
      "cpp_optimal": "// Solution for String Compression II",
      "java_brute": "// Solution for String Compression II",
      "java_optimal": "// Solution for String Compression II",
      "python_brute": "# Solution for String Compression II",
      "python_optimal": "# Solution for String Compression II"
    },
    "originalOrder": 824,
    "learningOrder": 824
  },
  {
    "id": 795,
    "number": 795,
    "sequence_number": 795,
    "title": "Minimum Cost to Cut a Stick",
    "slug": "minimum-cost-to-cut-a-stick",
    "difficulty": "Hard",
    "topic": "Dynamic Programming",
    "subtopic": "Dynamic Programming Optimization",
    "pattern": "Interval Cut DP",
    "secondary_patterns": [
      "Interval Cut DP"
    ],
    "stage": "1D Dynamic Programming Foundations",
    "curriculumStage": "Stage 16 — 1D Dynamic Programming Foundations",
    "roadmapPhase": "Stage 16 — 1D Dynamic Programming Foundations",
    "phase": "Stage 16 — 1D Dynamic Programming Foundations",
    "estimatedTime": 45,
    "statement": "Given the constraints and input parameters for Minimum Cost to Cut a Stick, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Minimum Cost to Cut a Stick."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Minimum Cost to Cut a Stick.",
      "Leverage the optimal Dynamic Programming pattern to reduce time complexity."
    ],
    "learningObjective": "Master Dynamic Programming techniques by solving Hard problem constraints for Minimum Cost to Cut a Stick.",
    "whyThisPattern": "When observing Dynamic Programming problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/minimum-cost-to-cut-a-stick/",
    "leetcode_title": "Minimum Cost to Cut a Stick",
    "leetcode_id": 1547,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/minimum-cost-to-cut-a-stick/",
    "canonicalSlug": "minimum-cost-to-cut-a-stick",
    "canonicalUrl": "https://leetcode.com/problems/minimum-cost-to-cut-a-stick/",
    "url": "https://leetcode.com/problems/minimum-cost-to-cut-a-stick/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Minimum Cost to Cut a Stick\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Minimum Cost to Cut a Stick\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Minimum Cost to Cut a Stick\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Minimum Cost to Cut a Stick\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Minimum Cost to Cut a Stick\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Minimum Cost to Cut a Stick\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Minimum Cost to Cut a Stick\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Minimum Cost to Cut a Stick\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Minimum Cost to Cut a Stick",
      "cpp_optimal": "// Solution for Minimum Cost to Cut a Stick",
      "java_brute": "// Solution for Minimum Cost to Cut a Stick",
      "java_optimal": "// Solution for Minimum Cost to Cut a Stick",
      "python_brute": "# Solution for Minimum Cost to Cut a Stick",
      "python_optimal": "# Solution for Minimum Cost to Cut a Stick"
    },
    "originalOrder": 825,
    "learningOrder": 825
  },
  {
    "id": 796,
    "number": 796,
    "sequence_number": 796,
    "title": "Stone Game V",
    "slug": "stone-game-v",
    "difficulty": "Hard",
    "topic": "Dynamic Programming",
    "subtopic": "Dynamic Programming Optimization",
    "pattern": "Interval Prefix Sum DP",
    "secondary_patterns": [
      "Interval Prefix Sum DP"
    ],
    "stage": "1D Dynamic Programming Foundations",
    "curriculumStage": "Stage 16 — 1D Dynamic Programming Foundations",
    "roadmapPhase": "Stage 16 — 1D Dynamic Programming Foundations",
    "phase": "Stage 16 — 1D Dynamic Programming Foundations",
    "estimatedTime": 45,
    "statement": "Given the constraints and input parameters for Stone Game V, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Stone Game V."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Stone Game V.",
      "Leverage the optimal Dynamic Programming pattern to reduce time complexity."
    ],
    "learningObjective": "Master Dynamic Programming techniques by solving Hard problem constraints for Stone Game V.",
    "whyThisPattern": "When observing Dynamic Programming problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/stone-game-v/",
    "leetcode_title": "Stone Game V",
    "leetcode_id": 1563,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/stone-game-v/",
    "canonicalSlug": "stone-game-v",
    "canonicalUrl": "https://leetcode.com/problems/stone-game-v/",
    "url": "https://leetcode.com/problems/stone-game-v/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Stone Game V\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Stone Game V\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Stone Game V\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Stone Game V\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Stone Game V\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Stone Game V\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Stone Game V\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Stone Game V\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Stone Game V",
      "cpp_optimal": "// Solution for Stone Game V",
      "java_brute": "// Solution for Stone Game V",
      "java_optimal": "// Solution for Stone Game V",
      "python_brute": "# Solution for Stone Game V",
      "python_optimal": "# Solution for Stone Game V"
    },
    "originalOrder": 826,
    "learningOrder": 826
  },
  {
    "id": 797,
    "number": 797,
    "sequence_number": 797,
    "title": "Minimum Number of Days to Eat N Oranges",
    "slug": "minimum-number-of-days-to-eat-n-oranges",
    "difficulty": "Hard",
    "topic": "Dynamic Programming",
    "subtopic": "Dynamic Programming Optimization",
    "pattern": "BFS / Memoized Division DP",
    "secondary_patterns": [
      "BFS / Memoized Division DP"
    ],
    "stage": "1D Dynamic Programming Foundations",
    "curriculumStage": "Stage 16 — 1D Dynamic Programming Foundations",
    "roadmapPhase": "Stage 16 — 1D Dynamic Programming Foundations",
    "phase": "Stage 16 — 1D Dynamic Programming Foundations",
    "estimatedTime": 45,
    "statement": "Given the constraints and input parameters for Minimum Number of Days to Eat N Oranges, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Minimum Number of Days to Eat N Oranges."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Minimum Number of Days to Eat N Oranges.",
      "Leverage the optimal Dynamic Programming pattern to reduce time complexity."
    ],
    "learningObjective": "Master Dynamic Programming techniques by solving Hard problem constraints for Minimum Number of Days to Eat N Oranges.",
    "whyThisPattern": "When observing Dynamic Programming problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/minimum-number-of-days-to-eat-n-oranges/",
    "leetcode_title": "Minimum Number of Days to Eat N Oranges",
    "leetcode_id": 1553,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/minimum-number-of-days-to-eat-n-oranges/",
    "canonicalSlug": "minimum-number-of-days-to-eat-n-oranges",
    "canonicalUrl": "https://leetcode.com/problems/minimum-number-of-days-to-eat-n-oranges/",
    "url": "https://leetcode.com/problems/minimum-number-of-days-to-eat-n-oranges/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Minimum Number of Days to Eat N Oranges\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Minimum Number of Days to Eat N Oranges\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Minimum Number of Days to Eat N Oranges\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Minimum Number of Days to Eat N Oranges\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Minimum Number of Days to Eat N Oranges\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Minimum Number of Days to Eat N Oranges\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Minimum Number of Days to Eat N Oranges\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Minimum Number of Days to Eat N Oranges\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Minimum Number of Days to Eat N Oranges",
      "cpp_optimal": "// Solution for Minimum Number of Days to Eat N Oranges",
      "java_brute": "// Solution for Minimum Number of Days to Eat N Oranges",
      "java_optimal": "// Solution for Minimum Number of Days to Eat N Oranges",
      "python_brute": "# Solution for Minimum Number of Days to Eat N Oranges",
      "python_optimal": "# Solution for Minimum Number of Days to Eat N Oranges"
    },
    "originalOrder": 827,
    "learningOrder": 827
  },
  {
    "id": 798,
    "number": 798,
    "sequence_number": 798,
    "title": "Strange Printer",
    "slug": "strange-printer",
    "difficulty": "Hard",
    "topic": "Dynamic Programming",
    "subtopic": "Dynamic Programming Optimization",
    "pattern": "Interval Character Match DP",
    "secondary_patterns": [
      "Interval Character Match DP"
    ],
    "stage": "1D Dynamic Programming Foundations",
    "curriculumStage": "Stage 16 — 1D Dynamic Programming Foundations",
    "roadmapPhase": "Stage 16 — 1D Dynamic Programming Foundations",
    "phase": "Stage 16 — 1D Dynamic Programming Foundations",
    "estimatedTime": 45,
    "statement": "Given the constraints and input parameters for Strange Printer, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Strange Printer."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Strange Printer.",
      "Leverage the optimal Dynamic Programming pattern to reduce time complexity."
    ],
    "learningObjective": "Master Dynamic Programming techniques by solving Hard problem constraints for Strange Printer.",
    "whyThisPattern": "When observing Dynamic Programming problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/strange-printer/",
    "leetcode_title": "Strange Printer",
    "leetcode_id": 664,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/strange-printer/",
    "canonicalSlug": "strange-printer",
    "canonicalUrl": "https://leetcode.com/problems/strange-printer/",
    "url": "https://leetcode.com/problems/strange-printer/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Strange Printer\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Strange Printer\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Strange Printer\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Strange Printer\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Strange Printer\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Strange Printer\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Strange Printer\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Strange Printer\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Strange Printer",
      "cpp_optimal": "// Solution for Strange Printer",
      "java_brute": "// Solution for Strange Printer",
      "java_optimal": "// Solution for Strange Printer",
      "python_brute": "# Solution for Strange Printer",
      "python_optimal": "# Solution for Strange Printer"
    },
    "originalOrder": 828,
    "learningOrder": 828
  },
  {
    "id": 799,
    "number": 799,
    "sequence_number": 799,
    "title": "Remove Boxes",
    "slug": "remove-boxes",
    "difficulty": "Hard",
    "topic": "Dynamic Programming",
    "subtopic": "Dynamic Programming Optimization",
    "pattern": "3D Interval Streak DP",
    "secondary_patterns": [
      "3D Interval Streak DP"
    ],
    "stage": "1D Dynamic Programming Foundations",
    "curriculumStage": "Stage 16 — 1D Dynamic Programming Foundations",
    "roadmapPhase": "Stage 16 — 1D Dynamic Programming Foundations",
    "phase": "Stage 16 — 1D Dynamic Programming Foundations",
    "estimatedTime": 45,
    "statement": "Given the constraints and input parameters for Remove Boxes, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Remove Boxes."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Remove Boxes.",
      "Leverage the optimal Dynamic Programming pattern to reduce time complexity."
    ],
    "learningObjective": "Master Dynamic Programming techniques by solving Hard problem constraints for Remove Boxes.",
    "whyThisPattern": "When observing Dynamic Programming problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/remove-boxes/",
    "leetcode_title": "Remove Boxes",
    "leetcode_id": 546,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/remove-boxes/",
    "canonicalSlug": "remove-boxes",
    "canonicalUrl": "https://leetcode.com/problems/remove-boxes/",
    "url": "https://leetcode.com/problems/remove-boxes/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Remove Boxes\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Remove Boxes\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Remove Boxes\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Remove Boxes\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Remove Boxes\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Remove Boxes\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Remove Boxes\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Remove Boxes\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Remove Boxes",
      "cpp_optimal": "// Solution for Remove Boxes",
      "java_brute": "// Solution for Remove Boxes",
      "java_optimal": "// Solution for Remove Boxes",
      "python_brute": "# Solution for Remove Boxes",
      "python_optimal": "# Solution for Remove Boxes"
    },
    "originalOrder": 829,
    "learningOrder": 829
  },
  {
    "id": 800,
    "number": 800,
    "sequence_number": 800,
    "title": "Count Different Palindromic Subsequences",
    "slug": "count-different-palindromic-subsequences",
    "difficulty": "Hard",
    "topic": "Dynamic Programming",
    "subtopic": "Dynamic Programming Optimization",
    "pattern": "Interval 4-Char DP",
    "secondary_patterns": [
      "Interval 4-Char DP"
    ],
    "stage": "1D Dynamic Programming Foundations",
    "curriculumStage": "Stage 16 — 1D Dynamic Programming Foundations",
    "roadmapPhase": "Stage 16 — 1D Dynamic Programming Foundations",
    "phase": "Stage 16 — 1D Dynamic Programming Foundations",
    "estimatedTime": 45,
    "statement": "Given the constraints and input parameters for Count Different Palindromic Subsequences, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Count Different Palindromic Subsequences."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Count Different Palindromic Subsequences.",
      "Leverage the optimal Dynamic Programming pattern to reduce time complexity."
    ],
    "learningObjective": "Master Dynamic Programming techniques by solving Hard problem constraints for Count Different Palindromic Subsequences.",
    "whyThisPattern": "When observing Dynamic Programming problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/count-different-palindromic-subsequences/",
    "leetcode_title": "Count Different Palindromic Subsequences",
    "leetcode_id": 730,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/count-different-palindromic-subsequences/",
    "canonicalSlug": "count-different-palindromic-subsequences",
    "canonicalUrl": "https://leetcode.com/problems/count-different-palindromic-subsequences/",
    "url": "https://leetcode.com/problems/count-different-palindromic-subsequences/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Count Different Palindromic Subsequences\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Count Different Palindromic Subsequences\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Count Different Palindromic Subsequences\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Count Different Palindromic Subsequences\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Count Different Palindromic Subsequences\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Count Different Palindromic Subsequences\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Count Different Palindromic Subsequences\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Count Different Palindromic Subsequences\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Count Different Palindromic Subsequences",
      "cpp_optimal": "// Solution for Count Different Palindromic Subsequences",
      "java_brute": "// Solution for Count Different Palindromic Subsequences",
      "java_optimal": "// Solution for Count Different Palindromic Subsequences",
      "python_brute": "# Solution for Count Different Palindromic Subsequences",
      "python_optimal": "# Solution for Count Different Palindromic Subsequences"
    },
    "originalOrder": 830,
    "learningOrder": 830
  },
  {
    "id": 801,
    "number": 801,
    "sequence_number": 801,
    "title": "Reverse String",
    "slug": "reverse-string",
    "difficulty": "Easy",
    "topic": "Strings",
    "subtopic": "Hashing & Array Optimization",
    "pattern": "Hashing & Array Optimization",
    "secondary_patterns": [
      "Hashing & Array Optimization"
    ],
    "stage": "2D & Grid Dynamic Programming",
    "curriculumStage": "Stage 17 — 2D & Grid Dynamic Programming",
    "roadmapPhase": "Stage 17 — 2D & Grid Dynamic Programming",
    "phase": "Stage 17 — 2D & Grid Dynamic Programming",
    "estimatedTime": 15,
    "statement": "Solve the **Reverse String Optimization** problem using the **Hashing & Array Optimization** technique. Given input constraints appropriate for Easy level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^4",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Hashing & Array Optimization identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Hashing & Array Optimization. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Hashing & Array Optimization techniques by solving Easy problem constraints for Reverse String Optimization.",
    "whyThisPattern": "When observing arrays & strings problem conditions, Hashing & Array Optimization optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Apple",
      "Adobe",
      "Atlassian"
    ],
    "companyRelevanceTier": "Medium",
    "leetcode_url": "https://leetcode.com/problems/reverse-string/",
    "leetcode_title": "Reverse String",
    "leetcode_id": 344,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/reverse-string/",
    "canonicalSlug": "reverse-string",
    "canonicalUrl": "https://leetcode.com/problems/reverse-string/",
    "url": "https://leetcode.com/problems/reverse-string/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Reverse String Optimization (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Reverse String Optimization (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Reverse String Optimization (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Reverse String Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Reverse String Optimization (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Reverse String Optimization (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Reverse String Optimization (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Reverse String Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Reverse String",
      "cpp_optimal": "// Solution for Reverse String",
      "java_brute": "// Solution for Reverse String",
      "java_optimal": "// Solution for Reverse String",
      "python_brute": "# Solution for Reverse String",
      "python_optimal": "# Solution for Reverse String"
    },
    "originalOrder": 176,
    "learningOrder": 176
  },
  {
    "id": 802,
    "number": 802,
    "sequence_number": 802,
    "title": "Reverse Vowels of a String",
    "slug": "reverse-vowels-of-a-string",
    "difficulty": "Easy",
    "topic": "Strings",
    "subtopic": "Hashing & Array Optimization",
    "pattern": "Hashing & Array Optimization",
    "secondary_patterns": [
      "Hashing & Array Optimization"
    ],
    "stage": "2D & Grid Dynamic Programming",
    "curriculumStage": "Stage 17 — 2D & Grid Dynamic Programming",
    "roadmapPhase": "Stage 17 — 2D & Grid Dynamic Programming",
    "phase": "Stage 17 — 2D & Grid Dynamic Programming",
    "estimatedTime": 15,
    "statement": "Solve the **Reverse Vowels of a String Challenge** problem using the **Hashing & Array Optimization** technique. Given input constraints appropriate for Easy level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^4",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Hashing & Array Optimization identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Hashing & Array Optimization. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Hashing & Array Optimization techniques by solving Easy problem constraints for Reverse Vowels of a String Challenge.",
    "whyThisPattern": "When observing arrays & strings problem conditions, Hashing & Array Optimization optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Meta",
      "Uber",
      "Databricks"
    ],
    "companyRelevanceTier": "Medium",
    "leetcode_url": "https://leetcode.com/problems/reverse-vowels-of-a-string/",
    "leetcode_title": "Reverse Vowels of a String",
    "leetcode_id": 345,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/reverse-vowels-of-a-string/",
    "canonicalSlug": "reverse-vowels-of-a-string",
    "canonicalUrl": "https://leetcode.com/problems/reverse-vowels-of-a-string/",
    "url": "https://leetcode.com/problems/reverse-vowels-of-a-string/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Reverse Vowels of a String Challenge (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Reverse Vowels of a String Challenge (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Reverse Vowels of a String Challenge (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Reverse Vowels of a String Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Reverse Vowels of a String Challenge (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Reverse Vowels of a String Challenge (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Reverse Vowels of a String Challenge (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Reverse Vowels of a String Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Reverse Vowels of a String",
      "cpp_optimal": "// Solution for Reverse Vowels of a String",
      "java_brute": "// Solution for Reverse Vowels of a String",
      "java_optimal": "// Solution for Reverse Vowels of a String",
      "python_brute": "# Solution for Reverse Vowels of a String",
      "python_optimal": "# Solution for Reverse Vowels of a String"
    },
    "originalOrder": 177,
    "learningOrder": 177
  },
  {
    "id": 803,
    "number": 803,
    "sequence_number": 803,
    "title": "Valid Perfect Square",
    "slug": "valid-perfect-square",
    "difficulty": "Easy",
    "topic": "Strings",
    "subtopic": "Hashing & Array Optimization",
    "pattern": "Hashing & Array Optimization",
    "secondary_patterns": [
      "Hashing & Array Optimization"
    ],
    "stage": "2D & Grid Dynamic Programming",
    "curriculumStage": "Stage 17 — 2D & Grid Dynamic Programming",
    "roadmapPhase": "Stage 17 — 2D & Grid Dynamic Programming",
    "phase": "Stage 17 — 2D & Grid Dynamic Programming",
    "estimatedTime": 15,
    "statement": "Solve the **Valid Perfect Square Optimization** problem using the **Hashing & Array Optimization** technique. Given input constraints appropriate for Easy level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^4",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Hashing & Array Optimization identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Hashing & Array Optimization. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Hashing & Array Optimization techniques by solving Easy problem constraints for Valid Perfect Square Optimization.",
    "whyThisPattern": "When observing arrays & strings problem conditions, Hashing & Array Optimization optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Meta",
      "Apple",
      "Netflix"
    ],
    "companyRelevanceTier": "Medium",
    "leetcode_url": "https://leetcode.com/problems/valid-perfect-square/",
    "leetcode_title": "Valid Perfect Square",
    "leetcode_id": 367,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/valid-perfect-square/",
    "canonicalSlug": "valid-perfect-square",
    "canonicalUrl": "https://leetcode.com/problems/valid-perfect-square/",
    "url": "https://leetcode.com/problems/valid-perfect-square/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Valid Perfect Square Optimization (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Valid Perfect Square Optimization (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Valid Perfect Square Optimization (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Valid Perfect Square Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Valid Perfect Square Optimization (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Valid Perfect Square Optimization (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Valid Perfect Square Optimization (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Valid Perfect Square Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Valid Perfect Square",
      "cpp_optimal": "// Solution for Valid Perfect Square",
      "java_brute": "// Solution for Valid Perfect Square",
      "java_optimal": "// Solution for Valid Perfect Square",
      "python_brute": "# Solution for Valid Perfect Square",
      "python_optimal": "# Solution for Valid Perfect Square"
    },
    "originalOrder": 178,
    "learningOrder": 178
  },
  {
    "id": 804,
    "number": 804,
    "sequence_number": 804,
    "title": "Guess Number Higher or Lower",
    "slug": "guess-number-higher-or-lower",
    "difficulty": "Easy",
    "topic": "Strings",
    "subtopic": "Hashing & Array Optimization",
    "pattern": "Hashing & Array Optimization",
    "secondary_patterns": [
      "Hashing & Array Optimization"
    ],
    "stage": "2D & Grid Dynamic Programming",
    "curriculumStage": "Stage 17 — 2D & Grid Dynamic Programming",
    "roadmapPhase": "Stage 17 — 2D & Grid Dynamic Programming",
    "phase": "Stage 17 — 2D & Grid Dynamic Programming",
    "estimatedTime": 15,
    "statement": "Solve the **Guess Number Higher or Lower Challenge** problem using the **Hashing & Array Optimization** technique. Given input constraints appropriate for Easy level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^4",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Hashing & Array Optimization identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Hashing & Array Optimization. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Hashing & Array Optimization techniques by solving Easy problem constraints for Guess Number Higher or Lower Challenge.",
    "whyThisPattern": "When observing arrays & strings problem conditions, Hashing & Array Optimization optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Microsoft",
      "Bloomberg"
    ],
    "companyRelevanceTier": "Medium",
    "leetcode_url": "https://leetcode.com/problems/guess-number-higher-or-lower/",
    "leetcode_title": "Guess Number Higher or Lower",
    "leetcode_id": 374,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/guess-number-higher-or-lower/",
    "canonicalSlug": "guess-number-higher-or-lower",
    "canonicalUrl": "https://leetcode.com/problems/guess-number-higher-or-lower/",
    "url": "https://leetcode.com/problems/guess-number-higher-or-lower/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Guess Number Higher or Lower Challenge (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Guess Number Higher or Lower Challenge (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Guess Number Higher or Lower Challenge (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Guess Number Higher or Lower Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Guess Number Higher or Lower Challenge (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Guess Number Higher or Lower Challenge (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Guess Number Higher or Lower Challenge (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Guess Number Higher or Lower Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Guess Number Higher or Lower",
      "cpp_optimal": "// Solution for Guess Number Higher or Lower",
      "java_brute": "// Solution for Guess Number Higher or Lower",
      "java_optimal": "// Solution for Guess Number Higher or Lower",
      "python_brute": "# Solution for Guess Number Higher or Lower",
      "python_optimal": "# Solution for Guess Number Higher or Lower"
    },
    "originalOrder": 179,
    "learningOrder": 179
  },
  {
    "id": 805,
    "number": 805,
    "sequence_number": 805,
    "title": "Ransom Note",
    "slug": "ransom-note",
    "difficulty": "Easy",
    "topic": "Strings",
    "subtopic": "Hashing & Array Optimization",
    "pattern": "Hashing & Array Optimization",
    "secondary_patterns": [
      "Hashing & Array Optimization"
    ],
    "stage": "2D & Grid Dynamic Programming",
    "curriculumStage": "Stage 17 — 2D & Grid Dynamic Programming",
    "roadmapPhase": "Stage 17 — 2D & Grid Dynamic Programming",
    "phase": "Stage 17 — 2D & Grid Dynamic Programming",
    "estimatedTime": 15,
    "statement": "Solve the **Ransom Note Optimization** problem using the **Hashing & Array Optimization** technique. Given input constraints appropriate for Easy level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^4",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Hashing & Array Optimization identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Hashing & Array Optimization. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Hashing & Array Optimization techniques by solving Easy problem constraints for Ransom Note Optimization.",
    "whyThisPattern": "When observing arrays & strings problem conditions, Hashing & Array Optimization optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Apple",
      "Adobe",
      "Atlassian"
    ],
    "companyRelevanceTier": "Medium",
    "leetcode_url": "https://leetcode.com/problems/ransom-note/",
    "leetcode_title": "Ransom Note",
    "leetcode_id": 383,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/ransom-note/",
    "canonicalSlug": "ransom-note",
    "canonicalUrl": "https://leetcode.com/problems/ransom-note/",
    "url": "https://leetcode.com/problems/ransom-note/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Ransom Note Optimization (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Ransom Note Optimization (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Ransom Note Optimization (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Ransom Note Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Ransom Note Optimization (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Ransom Note Optimization (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Ransom Note Optimization (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Ransom Note Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Ransom Note",
      "cpp_optimal": "// Solution for Ransom Note",
      "java_brute": "// Solution for Ransom Note",
      "java_optimal": "// Solution for Ransom Note",
      "python_brute": "# Solution for Ransom Note",
      "python_optimal": "# Solution for Ransom Note"
    },
    "originalOrder": 180,
    "learningOrder": 180
  },
  {
    "id": 806,
    "number": 806,
    "sequence_number": 806,
    "title": "First Unique Character in a String",
    "slug": "first-unique-character-in-a-string",
    "difficulty": "Easy",
    "topic": "Strings",
    "subtopic": "Hashing & Array Optimization",
    "pattern": "Hashing & Array Optimization",
    "secondary_patterns": [
      "Hashing & Array Optimization"
    ],
    "stage": "2D & Grid Dynamic Programming",
    "curriculumStage": "Stage 17 — 2D & Grid Dynamic Programming",
    "roadmapPhase": "Stage 17 — 2D & Grid Dynamic Programming",
    "phase": "Stage 17 — 2D & Grid Dynamic Programming",
    "estimatedTime": 15,
    "statement": "Solve the **First Unique Character in a String Optimization** problem using the **Hashing & Array Optimization** technique. Given input constraints appropriate for Easy level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^4",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Hashing & Array Optimization identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Hashing & Array Optimization. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Hashing & Array Optimization techniques by solving Easy problem constraints for First Unique Character in a String Optimization.",
    "whyThisPattern": "When observing arrays & strings problem conditions, Hashing & Array Optimization optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "LinkedIn",
      "Amazon"
    ],
    "companyRelevanceTier": "Medium",
    "leetcode_url": "https://leetcode.com/problems/first-unique-character-in-a-string/",
    "leetcode_title": "First Unique Character in a String",
    "leetcode_id": 387,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/first-unique-character-in-a-string/",
    "canonicalSlug": "first-unique-character-in-a-string",
    "canonicalUrl": "https://leetcode.com/problems/first-unique-character-in-a-string/",
    "url": "https://leetcode.com/problems/first-unique-character-in-a-string/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for First Unique Character in a String Optimization (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for First Unique Character in a String Optimization (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for First Unique Character in a String Optimization (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for First Unique Character in a String Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for First Unique Character in a String Optimization (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for First Unique Character in a String Optimization (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for First Unique Character in a String Optimization (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for First Unique Character in a String Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for First Unique Character in a String",
      "cpp_optimal": "// Solution for First Unique Character in a String",
      "java_brute": "// Solution for First Unique Character in a String",
      "java_optimal": "// Solution for First Unique Character in a String",
      "python_brute": "# Solution for First Unique Character in a String",
      "python_optimal": "# Solution for First Unique Character in a String"
    },
    "originalOrder": 181,
    "learningOrder": 181
  },
  {
    "id": 807,
    "number": 807,
    "sequence_number": 807,
    "title": "Find the Difference",
    "slug": "find-the-difference",
    "difficulty": "Easy",
    "topic": "Strings",
    "subtopic": "Hashing & Array Optimization",
    "pattern": "Hashing & Array Optimization",
    "secondary_patterns": [
      "Hashing & Array Optimization"
    ],
    "stage": "2D & Grid Dynamic Programming",
    "curriculumStage": "Stage 17 — 2D & Grid Dynamic Programming",
    "roadmapPhase": "Stage 17 — 2D & Grid Dynamic Programming",
    "phase": "Stage 17 — 2D & Grid Dynamic Programming",
    "estimatedTime": 15,
    "statement": "Solve the **Find the Difference Optimization** problem using the **Hashing & Array Optimization** technique. Given input constraints appropriate for Easy level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^4",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Hashing & Array Optimization identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Hashing & Array Optimization. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Hashing & Array Optimization techniques by solving Easy problem constraints for Find the Difference Optimization.",
    "whyThisPattern": "When observing arrays & strings problem conditions, Hashing & Array Optimization optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta"
    ],
    "companyRelevanceTier": "Medium",
    "leetcode_url": "https://leetcode.com/problems/find-the-difference/",
    "leetcode_title": "Find the Difference",
    "leetcode_id": 389,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/find-the-difference/",
    "canonicalSlug": "find-the-difference",
    "canonicalUrl": "https://leetcode.com/problems/find-the-difference/",
    "url": "https://leetcode.com/problems/find-the-difference/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Find the Difference Optimization (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Find the Difference Optimization (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Find the Difference Optimization (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Find the Difference Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Find the Difference Optimization (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Find the Difference Optimization (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Find the Difference Optimization (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Find the Difference Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Find the Difference",
      "cpp_optimal": "// Solution for Find the Difference",
      "java_brute": "// Solution for Find the Difference",
      "java_optimal": "// Solution for Find the Difference",
      "python_brute": "# Solution for Find the Difference",
      "python_optimal": "# Solution for Find the Difference"
    },
    "originalOrder": 182,
    "learningOrder": 182
  },
  {
    "id": 808,
    "number": 808,
    "sequence_number": 808,
    "title": "Binary Watch",
    "slug": "binary-watch",
    "difficulty": "Easy",
    "topic": "Strings",
    "subtopic": "Hashing & Array Optimization",
    "pattern": "Hashing & Array Optimization",
    "secondary_patterns": [
      "Hashing & Array Optimization"
    ],
    "stage": "2D & Grid Dynamic Programming",
    "curriculumStage": "Stage 17 — 2D & Grid Dynamic Programming",
    "roadmapPhase": "Stage 17 — 2D & Grid Dynamic Programming",
    "phase": "Stage 17 — 2D & Grid Dynamic Programming",
    "estimatedTime": 15,
    "statement": "Solve the **Binary Watch Optimization** problem using the **Hashing & Array Optimization** technique. Given input constraints appropriate for Easy level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^4",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Hashing & Array Optimization identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Hashing & Array Optimization. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Hashing & Array Optimization techniques by solving Easy problem constraints for Binary Watch Optimization.",
    "whyThisPattern": "When observing arrays & strings problem conditions, Hashing & Array Optimization optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Meta",
      "Apple",
      "Netflix"
    ],
    "companyRelevanceTier": "Medium",
    "leetcode_url": "https://leetcode.com/problems/binary-watch/",
    "leetcode_title": "Binary Watch",
    "leetcode_id": 401,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/binary-watch/",
    "canonicalSlug": "binary-watch",
    "canonicalUrl": "https://leetcode.com/problems/binary-watch/",
    "url": "https://leetcode.com/problems/binary-watch/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Binary Watch Optimization (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Binary Watch Optimization (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Binary Watch Optimization (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Binary Watch Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Binary Watch Optimization (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Binary Watch Optimization (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Binary Watch Optimization (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Binary Watch Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Binary Watch",
      "cpp_optimal": "// Solution for Binary Watch",
      "java_brute": "// Solution for Binary Watch",
      "java_optimal": "// Solution for Binary Watch",
      "python_brute": "# Solution for Binary Watch",
      "python_optimal": "# Solution for Binary Watch"
    },
    "originalOrder": 183,
    "learningOrder": 183
  },
  {
    "id": 809,
    "number": 809,
    "sequence_number": 809,
    "title": "Sum of Left Leaves",
    "slug": "sum-of-left-leaves",
    "difficulty": "Easy",
    "topic": "Strings",
    "subtopic": "Hashing & Array Optimization",
    "pattern": "Hashing & Array Optimization",
    "secondary_patterns": [
      "Hashing & Array Optimization"
    ],
    "stage": "2D & Grid Dynamic Programming",
    "curriculumStage": "Stage 17 — 2D & Grid Dynamic Programming",
    "roadmapPhase": "Stage 17 — 2D & Grid Dynamic Programming",
    "phase": "Stage 17 — 2D & Grid Dynamic Programming",
    "estimatedTime": 15,
    "statement": "Solve the **Sum of Left Leaves Optimization** problem using the **Hashing & Array Optimization** technique. Given input constraints appropriate for Easy level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^4",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Hashing & Array Optimization identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Hashing & Array Optimization. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Hashing & Array Optimization techniques by solving Easy problem constraints for Sum of Left Leaves Optimization.",
    "whyThisPattern": "When observing arrays & strings problem conditions, Hashing & Array Optimization optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Apple",
      "Adobe",
      "Atlassian"
    ],
    "companyRelevanceTier": "Medium",
    "leetcode_url": "https://leetcode.com/problems/sum-of-left-leaves/",
    "leetcode_title": "Sum of Left Leaves",
    "leetcode_id": 404,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/sum-of-left-leaves/",
    "canonicalSlug": "sum-of-left-leaves",
    "canonicalUrl": "https://leetcode.com/problems/sum-of-left-leaves/",
    "url": "https://leetcode.com/problems/sum-of-left-leaves/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Sum of Left Leaves Optimization (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Sum of Left Leaves Optimization (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Sum of Left Leaves Optimization (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Sum of Left Leaves Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Sum of Left Leaves Optimization (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Sum of Left Leaves Optimization (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Sum of Left Leaves Optimization (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Sum of Left Leaves Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Sum of Left Leaves",
      "cpp_optimal": "// Solution for Sum of Left Leaves",
      "java_brute": "// Solution for Sum of Left Leaves",
      "java_optimal": "// Solution for Sum of Left Leaves",
      "python_brute": "# Solution for Sum of Left Leaves",
      "python_optimal": "# Solution for Sum of Left Leaves"
    },
    "originalOrder": 184,
    "learningOrder": 184
  },
  {
    "id": 810,
    "number": 810,
    "sequence_number": 810,
    "title": "Convert a Number to Hexadecimal",
    "slug": "convert-a-number-to-hexadecimal",
    "difficulty": "Easy",
    "topic": "Strings",
    "subtopic": "Hashing & Array Optimization",
    "pattern": "Hashing & Array Optimization",
    "secondary_patterns": [
      "Hashing & Array Optimization"
    ],
    "stage": "2D & Grid Dynamic Programming",
    "curriculumStage": "Stage 17 — 2D & Grid Dynamic Programming",
    "roadmapPhase": "Stage 17 — 2D & Grid Dynamic Programming",
    "phase": "Stage 17 — 2D & Grid Dynamic Programming",
    "estimatedTime": 15,
    "statement": "Solve the **Convert a Number to Hexadecimal Optimization** problem using the **Hashing & Array Optimization** technique. Given input constraints appropriate for Easy level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^4",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Hashing & Array Optimization identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Hashing & Array Optimization. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Hashing & Array Optimization techniques by solving Easy problem constraints for Convert a Number to Hexadecimal Optimization.",
    "whyThisPattern": "When observing arrays & strings problem conditions, Hashing & Array Optimization optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "LinkedIn",
      "Amazon"
    ],
    "companyRelevanceTier": "Medium",
    "leetcode_url": "https://leetcode.com/problems/convert-a-number-to-hexadecimal/",
    "leetcode_title": "Convert a Number to Hexadecimal",
    "leetcode_id": 405,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/convert-a-number-to-hexadecimal/",
    "canonicalSlug": "convert-a-number-to-hexadecimal",
    "canonicalUrl": "https://leetcode.com/problems/convert-a-number-to-hexadecimal/",
    "url": "https://leetcode.com/problems/convert-a-number-to-hexadecimal/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Convert a Number to Hexadecimal Optimization (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Convert a Number to Hexadecimal Optimization (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Convert a Number to Hexadecimal Optimization (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Convert a Number to Hexadecimal Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Convert a Number to Hexadecimal Optimization (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Convert a Number to Hexadecimal Optimization (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Convert a Number to Hexadecimal Optimization (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Convert a Number to Hexadecimal Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Convert a Number to Hexadecimal",
      "cpp_optimal": "// Solution for Convert a Number to Hexadecimal",
      "java_brute": "// Solution for Convert a Number to Hexadecimal",
      "java_optimal": "// Solution for Convert a Number to Hexadecimal",
      "python_brute": "# Solution for Convert a Number to Hexadecimal",
      "python_optimal": "# Solution for Convert a Number to Hexadecimal"
    },
    "originalOrder": 185,
    "learningOrder": 185
  },
  {
    "id": 811,
    "number": 811,
    "sequence_number": 811,
    "title": "Out of Boundary Paths",
    "slug": "out-of-boundary-paths",
    "difficulty": "Medium",
    "topic": "Arrays",
    "subtopic": "Arrays Optimization",
    "pattern": "Arrays Pattern",
    "secondary_patterns": [
      "Arrays Pattern"
    ],
    "stage": "2D & Grid Dynamic Programming",
    "curriculumStage": "Stage 17 — 2D & Grid Dynamic Programming",
    "roadmapPhase": "Stage 17 — 2D & Grid Dynamic Programming",
    "phase": "Stage 17 — 2D & Grid Dynamic Programming",
    "estimatedTime": 30,
    "statement": "Solve the **Out of Boundary Paths** problem using standard Arrays techniques. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Arrays algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Arrays properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Arrays techniques by solving Medium problem constraints for Out of Boundary Paths.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/out-of-boundary-paths/",
    "leetcode_title": "Out of Boundary Paths",
    "leetcode_id": 576,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/out-of-boundary-paths/",
    "canonicalSlug": "out-of-boundary-paths",
    "canonicalUrl": "https://leetcode.com/problems/out-of-boundary-paths/",
    "url": "https://leetcode.com/problems/out-of-boundary-paths/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Out of Boundary Paths\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Out of Boundary Paths\n};",
        "java": "// Java Solution for Out of Boundary Paths\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Out of Boundary Paths\n}",
        "python": "# Python Solution for Out of Boundary Paths\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Out of Boundary Paths\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Out of Boundary Paths\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Out of Boundary Paths\n};",
        "java": "// Optimal Java Solution for Out of Boundary Paths\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Out of Boundary Paths\n}",
        "python": "# Optimal Python Solution for Out of Boundary Paths\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Out of Boundary Paths\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Out of Boundary Paths",
      "cpp_optimal": "// Solution for Out of Boundary Paths",
      "java_brute": "// Solution for Out of Boundary Paths",
      "java_optimal": "// Solution for Out of Boundary Paths",
      "python_brute": "# Solution for Out of Boundary Paths",
      "python_optimal": "# Solution for Out of Boundary Paths"
    },
    "originalOrder": 365,
    "learningOrder": 365
  },
  {
    "id": 812,
    "number": 812,
    "sequence_number": 812,
    "title": "Delete Operation for Two Strings",
    "slug": "delete-operation-for-two-strings",
    "difficulty": "Medium",
    "topic": "Arrays",
    "subtopic": "Arrays Optimization",
    "pattern": "Arrays Pattern",
    "secondary_patterns": [
      "Arrays Pattern"
    ],
    "stage": "2D & Grid Dynamic Programming",
    "curriculumStage": "Stage 17 — 2D & Grid Dynamic Programming",
    "roadmapPhase": "Stage 17 — 2D & Grid Dynamic Programming",
    "phase": "Stage 17 — 2D & Grid Dynamic Programming",
    "estimatedTime": 30,
    "statement": "Solve the **Delete Operation for Two Strings** problem using standard Arrays techniques. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Arrays algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Arrays properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Arrays techniques by solving Medium problem constraints for Delete Operation for Two Strings.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/delete-operation-for-two-strings/",
    "leetcode_title": "Delete Operation for Two Strings",
    "leetcode_id": 583,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/delete-operation-for-two-strings/",
    "canonicalSlug": "delete-operation-for-two-strings",
    "canonicalUrl": "https://leetcode.com/problems/delete-operation-for-two-strings/",
    "url": "https://leetcode.com/problems/delete-operation-for-two-strings/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Delete Operation for Two Strings\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Delete Operation for Two Strings\n};",
        "java": "// Java Solution for Delete Operation for Two Strings\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Delete Operation for Two Strings\n}",
        "python": "# Python Solution for Delete Operation for Two Strings\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Delete Operation for Two Strings\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Delete Operation for Two Strings\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Delete Operation for Two Strings\n};",
        "java": "// Optimal Java Solution for Delete Operation for Two Strings\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Delete Operation for Two Strings\n}",
        "python": "# Optimal Python Solution for Delete Operation for Two Strings\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Delete Operation for Two Strings\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Delete Operation for Two Strings",
      "cpp_optimal": "// Solution for Delete Operation for Two Strings",
      "java_brute": "// Solution for Delete Operation for Two Strings",
      "java_optimal": "// Solution for Delete Operation for Two Strings",
      "python_brute": "# Solution for Delete Operation for Two Strings",
      "python_optimal": "# Solution for Delete Operation for Two Strings"
    },
    "originalOrder": 366,
    "learningOrder": 366
  },
  {
    "id": 813,
    "number": 813,
    "sequence_number": 813,
    "title": "Investments in 2016",
    "slug": "investments-in-2016",
    "difficulty": "Medium",
    "topic": "Arrays",
    "subtopic": "Arrays Optimization",
    "pattern": "Arrays Pattern",
    "secondary_patterns": [
      "Arrays Pattern"
    ],
    "stage": "2D & Grid Dynamic Programming",
    "curriculumStage": "Stage 17 — 2D & Grid Dynamic Programming",
    "roadmapPhase": "Stage 17 — 2D & Grid Dynamic Programming",
    "phase": "Stage 17 — 2D & Grid Dynamic Programming",
    "estimatedTime": 30,
    "statement": "Solve the **Investments in 2016** problem using standard Arrays techniques. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Arrays algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Arrays properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Arrays techniques by solving Medium problem constraints for Investments in 2016.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/investments-in-2016/",
    "leetcode_title": "Investments in 2016",
    "leetcode_id": 585,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/investments-in-2016/",
    "canonicalSlug": "investments-in-2016",
    "canonicalUrl": "https://leetcode.com/problems/investments-in-2016/",
    "url": "https://leetcode.com/problems/investments-in-2016/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Investments in 2016\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Investments in 2016\n};",
        "java": "// Java Solution for Investments in 2016\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Investments in 2016\n}",
        "python": "# Python Solution for Investments in 2016\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Investments in 2016\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Investments in 2016\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Investments in 2016\n};",
        "java": "// Optimal Java Solution for Investments in 2016\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Investments in 2016\n}",
        "python": "# Optimal Python Solution for Investments in 2016\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Investments in 2016\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Investments in 2016",
      "cpp_optimal": "// Solution for Investments in 2016",
      "java_brute": "// Solution for Investments in 2016",
      "java_optimal": "// Solution for Investments in 2016",
      "python_brute": "# Solution for Investments in 2016",
      "python_optimal": "# Solution for Investments in 2016"
    },
    "originalOrder": 367,
    "learningOrder": 367
  },
  {
    "id": 814,
    "number": 814,
    "sequence_number": 814,
    "title": "Valid Square",
    "slug": "valid-square",
    "difficulty": "Medium",
    "topic": "Arrays",
    "subtopic": "Arrays Optimization",
    "pattern": "Arrays Pattern",
    "secondary_patterns": [
      "Arrays Pattern"
    ],
    "stage": "2D & Grid Dynamic Programming",
    "curriculumStage": "Stage 17 — 2D & Grid Dynamic Programming",
    "roadmapPhase": "Stage 17 — 2D & Grid Dynamic Programming",
    "phase": "Stage 17 — 2D & Grid Dynamic Programming",
    "estimatedTime": 30,
    "statement": "Solve the **Valid Square** problem using standard Arrays techniques. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Arrays algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Arrays properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Arrays techniques by solving Medium problem constraints for Valid Square.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/valid-square/",
    "leetcode_title": "Valid Square",
    "leetcode_id": 593,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/valid-square/",
    "canonicalSlug": "valid-square",
    "canonicalUrl": "https://leetcode.com/problems/valid-square/",
    "url": "https://leetcode.com/problems/valid-square/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Valid Square\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Valid Square\n};",
        "java": "// Java Solution for Valid Square\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Valid Square\n}",
        "python": "# Python Solution for Valid Square\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Valid Square\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Valid Square\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Valid Square\n};",
        "java": "// Optimal Java Solution for Valid Square\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Valid Square\n}",
        "python": "# Optimal Python Solution for Valid Square\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Valid Square\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Valid Square",
      "cpp_optimal": "// Solution for Valid Square",
      "java_brute": "// Solution for Valid Square",
      "java_optimal": "// Solution for Valid Square",
      "python_brute": "# Solution for Valid Square",
      "python_optimal": "# Solution for Valid Square"
    },
    "originalOrder": 368,
    "learningOrder": 368
  },
  {
    "id": 815,
    "number": 815,
    "sequence_number": 815,
    "title": "Friend Requests II: Who Has the Most Friends",
    "slug": "friend-requests-ii-who-has-the-most-friends",
    "difficulty": "Medium",
    "topic": "Arrays",
    "subtopic": "Arrays Optimization",
    "pattern": "Arrays Pattern",
    "secondary_patterns": [
      "Arrays Pattern"
    ],
    "stage": "2D & Grid Dynamic Programming",
    "curriculumStage": "Stage 17 — 2D & Grid Dynamic Programming",
    "roadmapPhase": "Stage 17 — 2D & Grid Dynamic Programming",
    "phase": "Stage 17 — 2D & Grid Dynamic Programming",
    "estimatedTime": 30,
    "statement": "Solve the **Friend Requests II: Who Has the Most Friends** problem using standard Arrays techniques. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Arrays algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Arrays properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Arrays techniques by solving Medium problem constraints for Friend Requests II: Who Has the Most Friends.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/friend-requests-ii-who-has-the-most-friends/",
    "leetcode_title": "Friend Requests II: Who Has the Most Friends",
    "leetcode_id": 602,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/friend-requests-ii-who-has-the-most-friends/",
    "canonicalSlug": "friend-requests-ii-who-has-the-most-friends",
    "canonicalUrl": "https://leetcode.com/problems/friend-requests-ii-who-has-the-most-friends/",
    "url": "https://leetcode.com/problems/friend-requests-ii-who-has-the-most-friends/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Friend Requests II: Who Has the Most Friends\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Friend Requests II: Who Has the Most Friends\n};",
        "java": "// Java Solution for Friend Requests II: Who Has the Most Friends\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Friend Requests II: Who Has the Most Friends\n}",
        "python": "# Python Solution for Friend Requests II: Who Has the Most Friends\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Friend Requests II: Who Has the Most Friends\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Friend Requests II: Who Has the Most Friends\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Friend Requests II: Who Has the Most Friends\n};",
        "java": "// Optimal Java Solution for Friend Requests II: Who Has the Most Friends\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Friend Requests II: Who Has the Most Friends\n}",
        "python": "# Optimal Python Solution for Friend Requests II: Who Has the Most Friends\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Friend Requests II: Who Has the Most Friends\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Friend Requests II: Who Has the Most Friends",
      "cpp_optimal": "// Solution for Friend Requests II: Who Has the Most Friends",
      "java_brute": "// Solution for Friend Requests II: Who Has the Most Friends",
      "java_optimal": "// Solution for Friend Requests II: Who Has the Most Friends",
      "python_brute": "# Solution for Friend Requests II: Who Has the Most Friends",
      "python_optimal": "# Solution for Friend Requests II: Who Has the Most Friends"
    },
    "originalOrder": 369,
    "learningOrder": 369
  },
  {
    "id": 816,
    "number": 816,
    "sequence_number": 816,
    "title": "Find Duplicate File in System",
    "slug": "find-duplicate-file-in-system",
    "difficulty": "Medium",
    "topic": "Arrays",
    "subtopic": "Arrays Optimization",
    "pattern": "Arrays Pattern",
    "secondary_patterns": [
      "Arrays Pattern"
    ],
    "stage": "2D & Grid Dynamic Programming",
    "curriculumStage": "Stage 17 — 2D & Grid Dynamic Programming",
    "roadmapPhase": "Stage 17 — 2D & Grid Dynamic Programming",
    "phase": "Stage 17 — 2D & Grid Dynamic Programming",
    "estimatedTime": 30,
    "statement": "Solve the **Find Duplicate File in System** problem using standard Arrays techniques. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Arrays algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Arrays properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Arrays techniques by solving Medium problem constraints for Find Duplicate File in System.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/find-duplicate-file-in-system/",
    "leetcode_title": "Find Duplicate File in System",
    "leetcode_id": 609,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/find-duplicate-file-in-system/",
    "canonicalSlug": "find-duplicate-file-in-system",
    "canonicalUrl": "https://leetcode.com/problems/find-duplicate-file-in-system/",
    "url": "https://leetcode.com/problems/find-duplicate-file-in-system/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Find Duplicate File in System\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Find Duplicate File in System\n};",
        "java": "// Java Solution for Find Duplicate File in System\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Find Duplicate File in System\n}",
        "python": "# Python Solution for Find Duplicate File in System\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Find Duplicate File in System\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Find Duplicate File in System\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Find Duplicate File in System\n};",
        "java": "// Optimal Java Solution for Find Duplicate File in System\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Find Duplicate File in System\n}",
        "python": "# Optimal Python Solution for Find Duplicate File in System\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Find Duplicate File in System\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Find Duplicate File in System",
      "cpp_optimal": "// Solution for Find Duplicate File in System",
      "java_brute": "// Solution for Find Duplicate File in System",
      "java_optimal": "// Solution for Find Duplicate File in System",
      "python_brute": "# Solution for Find Duplicate File in System",
      "python_optimal": "# Solution for Find Duplicate File in System"
    },
    "originalOrder": 370,
    "learningOrder": 370
  },
  {
    "id": 817,
    "number": 817,
    "sequence_number": 817,
    "title": "Maximum Distance in Arrays",
    "slug": "maximum-distance-in-arrays",
    "difficulty": "Medium",
    "topic": "Arrays",
    "subtopic": "Arrays Optimization",
    "pattern": "Arrays Pattern",
    "secondary_patterns": [
      "Arrays Pattern"
    ],
    "stage": "2D & Grid Dynamic Programming",
    "curriculumStage": "Stage 17 — 2D & Grid Dynamic Programming",
    "roadmapPhase": "Stage 17 — 2D & Grid Dynamic Programming",
    "phase": "Stage 17 — 2D & Grid Dynamic Programming",
    "estimatedTime": 30,
    "statement": "Solve the **Maximum Distance in Arrays** problem using standard Arrays techniques. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Arrays algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Arrays properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Arrays techniques by solving Medium problem constraints for Maximum Distance in Arrays.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/maximum-distance-in-arrays/",
    "leetcode_title": "Maximum Distance in Arrays",
    "leetcode_id": 624,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/maximum-distance-in-arrays/",
    "canonicalSlug": "maximum-distance-in-arrays",
    "canonicalUrl": "https://leetcode.com/problems/maximum-distance-in-arrays/",
    "url": "https://leetcode.com/problems/maximum-distance-in-arrays/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Maximum Distance in Arrays\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Maximum Distance in Arrays\n};",
        "java": "// Java Solution for Maximum Distance in Arrays\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Maximum Distance in Arrays\n}",
        "python": "# Python Solution for Maximum Distance in Arrays\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Maximum Distance in Arrays\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Maximum Distance in Arrays\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Maximum Distance in Arrays\n};",
        "java": "// Optimal Java Solution for Maximum Distance in Arrays\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Maximum Distance in Arrays\n}",
        "python": "# Optimal Python Solution for Maximum Distance in Arrays\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Maximum Distance in Arrays\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Maximum Distance in Arrays",
      "cpp_optimal": "// Solution for Maximum Distance in Arrays",
      "java_brute": "// Solution for Maximum Distance in Arrays",
      "java_optimal": "// Solution for Maximum Distance in Arrays",
      "python_brute": "# Solution for Maximum Distance in Arrays",
      "python_optimal": "# Solution for Maximum Distance in Arrays"
    },
    "originalOrder": 371,
    "learningOrder": 371
  },
  {
    "id": 818,
    "number": 818,
    "sequence_number": 818,
    "title": "Exchange Seats",
    "slug": "exchange-seats",
    "difficulty": "Medium",
    "topic": "Arrays",
    "subtopic": "Arrays Optimization",
    "pattern": "Arrays Pattern",
    "secondary_patterns": [
      "Arrays Pattern"
    ],
    "stage": "2D & Grid Dynamic Programming",
    "curriculumStage": "Stage 17 — 2D & Grid Dynamic Programming",
    "roadmapPhase": "Stage 17 — 2D & Grid Dynamic Programming",
    "phase": "Stage 17 — 2D & Grid Dynamic Programming",
    "estimatedTime": 30,
    "statement": "Solve the **Exchange Seats** problem using standard Arrays techniques. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Arrays algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Arrays properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Arrays techniques by solving Medium problem constraints for Exchange Seats.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/exchange-seats/",
    "leetcode_title": "Exchange Seats",
    "leetcode_id": 626,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/exchange-seats/",
    "canonicalSlug": "exchange-seats",
    "canonicalUrl": "https://leetcode.com/problems/exchange-seats/",
    "url": "https://leetcode.com/problems/exchange-seats/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Exchange Seats\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Exchange Seats\n};",
        "java": "// Java Solution for Exchange Seats\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Exchange Seats\n}",
        "python": "# Python Solution for Exchange Seats\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Exchange Seats\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Exchange Seats\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Exchange Seats\n};",
        "java": "// Optimal Java Solution for Exchange Seats\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Exchange Seats\n}",
        "python": "# Optimal Python Solution for Exchange Seats\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Exchange Seats\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Exchange Seats",
      "cpp_optimal": "// Solution for Exchange Seats",
      "java_brute": "// Solution for Exchange Seats",
      "java_optimal": "// Solution for Exchange Seats",
      "python_brute": "# Solution for Exchange Seats",
      "python_optimal": "# Solution for Exchange Seats"
    },
    "originalOrder": 372,
    "learningOrder": 372
  },
  {
    "id": 819,
    "number": 819,
    "sequence_number": 819,
    "title": "Sum of Square Numbers",
    "slug": "sum-of-square-numbers",
    "difficulty": "Medium",
    "topic": "Arrays",
    "subtopic": "Arrays Optimization",
    "pattern": "Arrays Pattern",
    "secondary_patterns": [
      "Arrays Pattern"
    ],
    "stage": "2D & Grid Dynamic Programming",
    "curriculumStage": "Stage 17 — 2D & Grid Dynamic Programming",
    "roadmapPhase": "Stage 17 — 2D & Grid Dynamic Programming",
    "phase": "Stage 17 — 2D & Grid Dynamic Programming",
    "estimatedTime": 30,
    "statement": "Solve the **Sum of Square Numbers** problem using standard Arrays techniques. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Arrays algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Arrays properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Arrays techniques by solving Medium problem constraints for Sum of Square Numbers.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/sum-of-square-numbers/",
    "leetcode_title": "Sum of Square Numbers",
    "leetcode_id": 633,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/sum-of-square-numbers/",
    "canonicalSlug": "sum-of-square-numbers",
    "canonicalUrl": "https://leetcode.com/problems/sum-of-square-numbers/",
    "url": "https://leetcode.com/problems/sum-of-square-numbers/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Sum of Square Numbers\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Sum of Square Numbers\n};",
        "java": "// Java Solution for Sum of Square Numbers\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Sum of Square Numbers\n}",
        "python": "# Python Solution for Sum of Square Numbers\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Sum of Square Numbers\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Sum of Square Numbers\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Sum of Square Numbers\n};",
        "java": "// Optimal Java Solution for Sum of Square Numbers\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Sum of Square Numbers\n}",
        "python": "# Optimal Python Solution for Sum of Square Numbers\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Sum of Square Numbers\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Sum of Square Numbers",
      "cpp_optimal": "// Solution for Sum of Square Numbers",
      "java_brute": "// Solution for Sum of Square Numbers",
      "java_optimal": "// Solution for Sum of Square Numbers",
      "python_brute": "# Solution for Sum of Square Numbers",
      "python_optimal": "# Solution for Sum of Square Numbers"
    },
    "originalOrder": 373,
    "learningOrder": 373
  },
  {
    "id": 820,
    "number": 820,
    "sequence_number": 820,
    "title": "Exclusive Time of Functions",
    "slug": "exclusive-time-of-functions",
    "difficulty": "Medium",
    "topic": "Arrays",
    "subtopic": "Arrays Optimization",
    "pattern": "Arrays Pattern",
    "secondary_patterns": [
      "Arrays Pattern"
    ],
    "stage": "2D & Grid Dynamic Programming",
    "curriculumStage": "Stage 17 — 2D & Grid Dynamic Programming",
    "roadmapPhase": "Stage 17 — 2D & Grid Dynamic Programming",
    "phase": "Stage 17 — 2D & Grid Dynamic Programming",
    "estimatedTime": 30,
    "statement": "Solve the **Exclusive Time of Functions** problem using standard Arrays techniques. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Arrays algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Arrays properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Arrays techniques by solving Medium problem constraints for Exclusive Time of Functions.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/exclusive-time-of-functions/",
    "leetcode_title": "Exclusive Time of Functions",
    "leetcode_id": 636,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/exclusive-time-of-functions/",
    "canonicalSlug": "exclusive-time-of-functions",
    "canonicalUrl": "https://leetcode.com/problems/exclusive-time-of-functions/",
    "url": "https://leetcode.com/problems/exclusive-time-of-functions/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Exclusive Time of Functions\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Exclusive Time of Functions\n};",
        "java": "// Java Solution for Exclusive Time of Functions\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Exclusive Time of Functions\n}",
        "python": "# Python Solution for Exclusive Time of Functions\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Exclusive Time of Functions\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Exclusive Time of Functions\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Exclusive Time of Functions\n};",
        "java": "// Optimal Java Solution for Exclusive Time of Functions\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Exclusive Time of Functions\n}",
        "python": "# Optimal Python Solution for Exclusive Time of Functions\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Exclusive Time of Functions\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Exclusive Time of Functions",
      "cpp_optimal": "// Solution for Exclusive Time of Functions",
      "java_brute": "// Solution for Exclusive Time of Functions",
      "java_optimal": "// Solution for Exclusive Time of Functions",
      "python_brute": "# Solution for Exclusive Time of Functions",
      "python_optimal": "# Solution for Exclusive Time of Functions"
    },
    "originalOrder": 374,
    "learningOrder": 374
  },
  {
    "id": 821,
    "number": 821,
    "sequence_number": 821,
    "title": "Shopping Offers",
    "slug": "shopping-offers",
    "difficulty": "Medium",
    "topic": "Arrays",
    "subtopic": "Arrays Optimization",
    "pattern": "Arrays Pattern",
    "secondary_patterns": [
      "Arrays Pattern"
    ],
    "stage": "2D & Grid Dynamic Programming",
    "curriculumStage": "Stage 17 — 2D & Grid Dynamic Programming",
    "roadmapPhase": "Stage 17 — 2D & Grid Dynamic Programming",
    "phase": "Stage 17 — 2D & Grid Dynamic Programming",
    "estimatedTime": 30,
    "statement": "Solve the **Shopping Offers** problem using standard Arrays techniques. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Arrays algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Arrays properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Arrays techniques by solving Medium problem constraints for Shopping Offers.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/shopping-offers/",
    "leetcode_title": "Shopping Offers",
    "leetcode_id": 638,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/shopping-offers/",
    "canonicalSlug": "shopping-offers",
    "canonicalUrl": "https://leetcode.com/problems/shopping-offers/",
    "url": "https://leetcode.com/problems/shopping-offers/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Shopping Offers\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Shopping Offers\n};",
        "java": "// Java Solution for Shopping Offers\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Shopping Offers\n}",
        "python": "# Python Solution for Shopping Offers\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Shopping Offers\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Shopping Offers\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Shopping Offers\n};",
        "java": "// Optimal Java Solution for Shopping Offers\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Shopping Offers\n}",
        "python": "# Optimal Python Solution for Shopping Offers\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Shopping Offers\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Shopping Offers",
      "cpp_optimal": "// Solution for Shopping Offers",
      "java_brute": "// Solution for Shopping Offers",
      "java_optimal": "// Solution for Shopping Offers",
      "python_brute": "# Solution for Shopping Offers",
      "python_optimal": "# Solution for Shopping Offers"
    },
    "originalOrder": 375,
    "learningOrder": 375
  },
  {
    "id": 822,
    "number": 822,
    "sequence_number": 822,
    "title": "Solve the Equation",
    "slug": "solve-the-equation",
    "difficulty": "Medium",
    "topic": "Arrays",
    "subtopic": "Arrays Optimization",
    "pattern": "Arrays Pattern",
    "secondary_patterns": [
      "Arrays Pattern"
    ],
    "stage": "2D & Grid Dynamic Programming",
    "curriculumStage": "Stage 17 — 2D & Grid Dynamic Programming",
    "roadmapPhase": "Stage 17 — 2D & Grid Dynamic Programming",
    "phase": "Stage 17 — 2D & Grid Dynamic Programming",
    "estimatedTime": 30,
    "statement": "Solve the **Solve the Equation** problem using standard Arrays techniques. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Arrays algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Arrays properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Arrays techniques by solving Medium problem constraints for Solve the Equation.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/solve-the-equation/",
    "leetcode_title": "Solve the Equation",
    "leetcode_id": 640,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/solve-the-equation/",
    "canonicalSlug": "solve-the-equation",
    "canonicalUrl": "https://leetcode.com/problems/solve-the-equation/",
    "url": "https://leetcode.com/problems/solve-the-equation/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Solve the Equation\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Solve the Equation\n};",
        "java": "// Java Solution for Solve the Equation\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Solve the Equation\n}",
        "python": "# Python Solution for Solve the Equation\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Solve the Equation\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Solve the Equation\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Solve the Equation\n};",
        "java": "// Optimal Java Solution for Solve the Equation\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Solve the Equation\n}",
        "python": "# Optimal Python Solution for Solve the Equation\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Solve the Equation\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Solve the Equation",
      "cpp_optimal": "// Solution for Solve the Equation",
      "java_brute": "// Solution for Solve the Equation",
      "java_optimal": "// Solution for Solve the Equation",
      "python_brute": "# Solution for Solve the Equation",
      "python_optimal": "# Solution for Solve the Equation"
    },
    "originalOrder": 376,
    "learningOrder": 376
  },
  {
    "id": 823,
    "number": 823,
    "sequence_number": 823,
    "title": "Maximum Length of Pair Chain",
    "slug": "maximum-length-of-pair-chain",
    "difficulty": "Medium",
    "topic": "Arrays",
    "subtopic": "Arrays Optimization",
    "pattern": "Arrays Pattern",
    "secondary_patterns": [
      "Arrays Pattern"
    ],
    "stage": "2D & Grid Dynamic Programming",
    "curriculumStage": "Stage 17 — 2D & Grid Dynamic Programming",
    "roadmapPhase": "Stage 17 — 2D & Grid Dynamic Programming",
    "phase": "Stage 17 — 2D & Grid Dynamic Programming",
    "estimatedTime": 30,
    "statement": "Solve the **Maximum Length of Pair Chain** problem using standard Arrays techniques. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Arrays algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Arrays properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Arrays techniques by solving Medium problem constraints for Maximum Length of Pair Chain.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/maximum-length-of-pair-chain/",
    "leetcode_title": "Maximum Length of Pair Chain",
    "leetcode_id": 646,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/maximum-length-of-pair-chain/",
    "canonicalSlug": "maximum-length-of-pair-chain",
    "canonicalUrl": "https://leetcode.com/problems/maximum-length-of-pair-chain/",
    "url": "https://leetcode.com/problems/maximum-length-of-pair-chain/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Maximum Length of Pair Chain\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Maximum Length of Pair Chain\n};",
        "java": "// Java Solution for Maximum Length of Pair Chain\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Maximum Length of Pair Chain\n}",
        "python": "# Python Solution for Maximum Length of Pair Chain\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Maximum Length of Pair Chain\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Maximum Length of Pair Chain\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Maximum Length of Pair Chain\n};",
        "java": "// Optimal Java Solution for Maximum Length of Pair Chain\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Maximum Length of Pair Chain\n}",
        "python": "# Optimal Python Solution for Maximum Length of Pair Chain\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Maximum Length of Pair Chain\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Maximum Length of Pair Chain",
      "cpp_optimal": "// Solution for Maximum Length of Pair Chain",
      "java_brute": "// Solution for Maximum Length of Pair Chain",
      "java_optimal": "// Solution for Maximum Length of Pair Chain",
      "python_brute": "# Solution for Maximum Length of Pair Chain",
      "python_optimal": "# Solution for Maximum Length of Pair Chain"
    },
    "originalOrder": 377,
    "learningOrder": 377
  },
  {
    "id": 824,
    "number": 824,
    "sequence_number": 824,
    "title": "2 Keys Keyboard",
    "slug": "2-keys-keyboard",
    "difficulty": "Medium",
    "topic": "Arrays",
    "subtopic": "Arrays Optimization",
    "pattern": "Arrays Pattern",
    "secondary_patterns": [
      "Arrays Pattern"
    ],
    "stage": "2D & Grid Dynamic Programming",
    "curriculumStage": "Stage 17 — 2D & Grid Dynamic Programming",
    "roadmapPhase": "Stage 17 — 2D & Grid Dynamic Programming",
    "phase": "Stage 17 — 2D & Grid Dynamic Programming",
    "estimatedTime": 30,
    "statement": "Solve the **2 Keys Keyboard** problem using standard Arrays techniques. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Arrays algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Arrays properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Arrays techniques by solving Medium problem constraints for 2 Keys Keyboard.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/2-keys-keyboard/",
    "leetcode_title": "2 Keys Keyboard",
    "leetcode_id": 650,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/2-keys-keyboard/",
    "canonicalSlug": "2-keys-keyboard",
    "canonicalUrl": "https://leetcode.com/problems/2-keys-keyboard/",
    "url": "https://leetcode.com/problems/2-keys-keyboard/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for 2 Keys Keyboard\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for 2 Keys Keyboard\n};",
        "java": "// Java Solution for 2 Keys Keyboard\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for 2 Keys Keyboard\n}",
        "python": "# Python Solution for 2 Keys Keyboard\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for 2 Keys Keyboard\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for 2 Keys Keyboard\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for 2 Keys Keyboard\n};",
        "java": "// Optimal Java Solution for 2 Keys Keyboard\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for 2 Keys Keyboard\n}",
        "python": "# Optimal Python Solution for 2 Keys Keyboard\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for 2 Keys Keyboard\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for 2 Keys Keyboard",
      "cpp_optimal": "// Solution for 2 Keys Keyboard",
      "java_brute": "// Solution for 2 Keys Keyboard",
      "java_optimal": "// Solution for 2 Keys Keyboard",
      "python_brute": "# Solution for 2 Keys Keyboard",
      "python_optimal": "# Solution for 2 Keys Keyboard"
    },
    "originalOrder": 378,
    "learningOrder": 378
  },
  {
    "id": 825,
    "number": 825,
    "sequence_number": 825,
    "title": "Implement Rand10() Using Rand7()",
    "slug": "implement-rand10-using-rand7",
    "difficulty": "Medium",
    "topic": "Bit Manipulation",
    "subtopic": "Arrays Optimization",
    "pattern": "Arrays Pattern",
    "secondary_patterns": [
      "Arrays Pattern"
    ],
    "stage": "2D & Grid Dynamic Programming",
    "curriculumStage": "Stage 17 — 2D & Grid Dynamic Programming",
    "roadmapPhase": "Stage 17 — 2D & Grid Dynamic Programming",
    "phase": "Stage 17 — 2D & Grid Dynamic Programming",
    "estimatedTime": 30,
    "statement": "Solve the **Implement Rand10() Using Rand7()** problem using standard Arrays techniques. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Arrays algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Arrays properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Arrays techniques by solving Medium problem constraints for Implement Rand10() Using Rand7().",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/implement-rand10-using-rand7/",
    "leetcode_title": "Implement Rand10() Using Rand7()",
    "leetcode_id": 470,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/implement-rand10-using-rand7/",
    "canonicalSlug": "implement-rand10-using-rand7",
    "canonicalUrl": "https://leetcode.com/problems/implement-rand10-using-rand7/",
    "url": "https://leetcode.com/problems/implement-rand10-using-rand7/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Implement Rand10() Using Rand7()\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Implement Rand10() Using Rand7()\n};",
        "java": "// Java Solution for Implement Rand10() Using Rand7()\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Implement Rand10() Using Rand7()\n}",
        "python": "# Python Solution for Implement Rand10() Using Rand7()\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Implement Rand10() Using Rand7()\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Implement Rand10() Using Rand7()\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Implement Rand10() Using Rand7()\n};",
        "java": "// Optimal Java Solution for Implement Rand10() Using Rand7()\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Implement Rand10() Using Rand7()\n}",
        "python": "# Optimal Python Solution for Implement Rand10() Using Rand7()\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Implement Rand10() Using Rand7()\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Implement Rand10() Using Rand7()",
      "cpp_optimal": "// Solution for Implement Rand10() Using Rand7()",
      "java_brute": "// Solution for Implement Rand10() Using Rand7()",
      "java_optimal": "// Solution for Implement Rand10() Using Rand7()",
      "python_brute": "# Solution for Implement Rand10() Using Rand7()",
      "python_optimal": "# Solution for Implement Rand10() Using Rand7()"
    },
    "originalOrder": 339,
    "learningOrder": 339
  },
  {
    "id": 826,
    "number": 826,
    "sequence_number": 826,
    "title": "Ones and Zeroes",
    "slug": "ones-and-zeroes",
    "difficulty": "Medium",
    "topic": "Bit Manipulation",
    "subtopic": "Arrays Optimization",
    "pattern": "Arrays Pattern",
    "secondary_patterns": [
      "Arrays Pattern"
    ],
    "stage": "2D & Grid Dynamic Programming",
    "curriculumStage": "Stage 17 — 2D & Grid Dynamic Programming",
    "roadmapPhase": "Stage 17 — 2D & Grid Dynamic Programming",
    "phase": "Stage 17 — 2D & Grid Dynamic Programming",
    "estimatedTime": 30,
    "statement": "Solve the **Ones and Zeroes** problem using standard Arrays techniques. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Arrays algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Arrays properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Arrays techniques by solving Medium problem constraints for Ones and Zeroes.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/ones-and-zeroes/",
    "leetcode_title": "Ones and Zeroes",
    "leetcode_id": 474,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/ones-and-zeroes/",
    "canonicalSlug": "ones-and-zeroes",
    "canonicalUrl": "https://leetcode.com/problems/ones-and-zeroes/",
    "url": "https://leetcode.com/problems/ones-and-zeroes/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Ones and Zeroes\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Ones and Zeroes\n};",
        "java": "// Java Solution for Ones and Zeroes\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Ones and Zeroes\n}",
        "python": "# Python Solution for Ones and Zeroes\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Ones and Zeroes\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Ones and Zeroes\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Ones and Zeroes\n};",
        "java": "// Optimal Java Solution for Ones and Zeroes\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Ones and Zeroes\n}",
        "python": "# Optimal Python Solution for Ones and Zeroes\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Ones and Zeroes\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Ones and Zeroes",
      "cpp_optimal": "// Solution for Ones and Zeroes",
      "java_brute": "// Solution for Ones and Zeroes",
      "java_optimal": "// Solution for Ones and Zeroes",
      "python_brute": "# Solution for Ones and Zeroes",
      "python_optimal": "# Solution for Ones and Zeroes"
    },
    "originalOrder": 340,
    "learningOrder": 340
  },
  {
    "id": 827,
    "number": 827,
    "sequence_number": 827,
    "title": "Random Pick with Weight",
    "slug": "random-pick-with-weight",
    "difficulty": "Medium",
    "topic": "Bit Manipulation",
    "subtopic": "Arrays Optimization",
    "pattern": "Arrays Pattern",
    "secondary_patterns": [
      "Arrays Pattern"
    ],
    "stage": "2D & Grid Dynamic Programming",
    "curriculumStage": "Stage 17 — 2D & Grid Dynamic Programming",
    "roadmapPhase": "Stage 17 — 2D & Grid Dynamic Programming",
    "phase": "Stage 17 — 2D & Grid Dynamic Programming",
    "estimatedTime": 30,
    "statement": "Solve the **Random Pick with Weight** problem using standard Arrays techniques. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Arrays algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Arrays properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Arrays techniques by solving Medium problem constraints for Random Pick with Weight.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/random-pick-with-weight/",
    "leetcode_title": "Random Pick with Weight",
    "leetcode_id": 528,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/random-pick-with-weight/",
    "canonicalSlug": "random-pick-with-weight",
    "canonicalUrl": "https://leetcode.com/problems/random-pick-with-weight/",
    "url": "https://leetcode.com/problems/random-pick-with-weight/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Random Pick with Weight\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Random Pick with Weight\n};",
        "java": "// Java Solution for Random Pick with Weight\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Random Pick with Weight\n}",
        "python": "# Python Solution for Random Pick with Weight\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Random Pick with Weight\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Random Pick with Weight\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Random Pick with Weight\n};",
        "java": "// Optimal Java Solution for Random Pick with Weight\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Random Pick with Weight\n}",
        "python": "# Optimal Python Solution for Random Pick with Weight\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Random Pick with Weight\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Random Pick with Weight",
      "cpp_optimal": "// Solution for Random Pick with Weight",
      "java_brute": "// Solution for Random Pick with Weight",
      "java_optimal": "// Solution for Random Pick with Weight",
      "python_brute": "# Solution for Random Pick with Weight",
      "python_optimal": "# Solution for Random Pick with Weight"
    },
    "originalOrder": 353,
    "learningOrder": 353
  },
  {
    "id": 828,
    "number": 828,
    "sequence_number": 828,
    "title": "Encode and Decode TinyURL",
    "slug": "encode-and-decode-tinyurl",
    "difficulty": "Medium",
    "topic": "Bit Manipulation",
    "subtopic": "Arrays Optimization",
    "pattern": "Arrays Pattern",
    "secondary_patterns": [
      "Arrays Pattern"
    ],
    "stage": "2D & Grid Dynamic Programming",
    "curriculumStage": "Stage 17 — 2D & Grid Dynamic Programming",
    "roadmapPhase": "Stage 17 — 2D & Grid Dynamic Programming",
    "phase": "Stage 17 — 2D & Grid Dynamic Programming",
    "estimatedTime": 30,
    "statement": "Solve the **Encode and Decode TinyURL** problem using standard Arrays techniques. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Arrays algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Arrays properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Arrays techniques by solving Medium problem constraints for Encode and Decode TinyURL.",
    "whyThisPattern": "When observing Arrays problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/encode-and-decode-tinyurl/",
    "leetcode_title": "Encode and Decode TinyURL",
    "leetcode_id": 535,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/encode-and-decode-tinyurl/",
    "canonicalSlug": "encode-and-decode-tinyurl",
    "canonicalUrl": "https://leetcode.com/problems/encode-and-decode-tinyurl/",
    "url": "https://leetcode.com/problems/encode-and-decode-tinyurl/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Encode and Decode TinyURL\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Encode and Decode TinyURL\n};",
        "java": "// Java Solution for Encode and Decode TinyURL\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Encode and Decode TinyURL\n}",
        "python": "# Python Solution for Encode and Decode TinyURL\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Encode and Decode TinyURL\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Encode and Decode TinyURL\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Encode and Decode TinyURL\n};",
        "java": "// Optimal Java Solution for Encode and Decode TinyURL\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Encode and Decode TinyURL\n}",
        "python": "# Optimal Python Solution for Encode and Decode TinyURL\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Encode and Decode TinyURL\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Encode and Decode TinyURL",
      "cpp_optimal": "// Solution for Encode and Decode TinyURL",
      "java_brute": "// Solution for Encode and Decode TinyURL",
      "java_optimal": "// Solution for Encode and Decode TinyURL",
      "python_brute": "# Solution for Encode and Decode TinyURL",
      "python_optimal": "# Solution for Encode and Decode TinyURL"
    },
    "originalOrder": 356,
    "learningOrder": 356
  },
  {
    "id": 829,
    "number": 829,
    "sequence_number": 829,
    "title": "Single Number II",
    "slug": "single-number-ii",
    "difficulty": "Medium",
    "topic": "Bit Manipulation",
    "subtopic": "Bit Manipulation Optimization",
    "pattern": "Bitwise Modular Count",
    "secondary_patterns": [
      "Bitwise Modular Count"
    ],
    "stage": "2D & Grid Dynamic Programming",
    "curriculumStage": "Stage 17 — 2D & Grid Dynamic Programming",
    "roadmapPhase": "Stage 17 — 2D & Grid Dynamic Programming",
    "phase": "Stage 17 — 2D & Grid Dynamic Programming",
    "estimatedTime": 30,
    "statement": "Given the constraints and input parameters for Single Number II, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Single Number II."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Single Number II.",
      "Leverage the optimal Bit Manipulation pattern to reduce time complexity."
    ],
    "learningObjective": "Master Bit Manipulation techniques by solving Medium problem constraints for Single Number II.",
    "whyThisPattern": "When observing Bit Manipulation problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/single-number-ii/",
    "leetcode_title": "Single Number II",
    "leetcode_id": 137,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/single-number-ii/",
    "canonicalSlug": "single-number-ii",
    "canonicalUrl": "https://leetcode.com/problems/single-number-ii/",
    "url": "https://leetcode.com/problems/single-number-ii/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Single Number II\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Single Number II\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Single Number II\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Single Number II\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Single Number II\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Single Number II\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Single Number II\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Single Number II\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Single Number II",
      "cpp_optimal": "// Solution for Single Number II",
      "java_brute": "// Solution for Single Number II",
      "java_optimal": "// Solution for Single Number II",
      "python_brute": "# Solution for Single Number II",
      "python_optimal": "# Solution for Single Number II"
    },
    "originalOrder": 428,
    "learningOrder": 428
  },
  {
    "id": 830,
    "number": 830,
    "sequence_number": 830,
    "title": "Single Number III",
    "slug": "single-number-iii",
    "difficulty": "Medium",
    "topic": "Bit Manipulation",
    "subtopic": "Bit Manipulation Optimization",
    "pattern": "XOR Grouping Diff Bit",
    "secondary_patterns": [
      "XOR Grouping Diff Bit"
    ],
    "stage": "2D & Grid Dynamic Programming",
    "curriculumStage": "Stage 17 — 2D & Grid Dynamic Programming",
    "roadmapPhase": "Stage 17 — 2D & Grid Dynamic Programming",
    "phase": "Stage 17 — 2D & Grid Dynamic Programming",
    "estimatedTime": 30,
    "statement": "Given the constraints and input parameters for Single Number III, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Single Number III."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Single Number III.",
      "Leverage the optimal Bit Manipulation pattern to reduce time complexity."
    ],
    "learningObjective": "Master Bit Manipulation techniques by solving Medium problem constraints for Single Number III.",
    "whyThisPattern": "When observing Bit Manipulation problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/single-number-iii/",
    "leetcode_title": "Single Number III",
    "leetcode_id": 260,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/single-number-iii/",
    "canonicalSlug": "single-number-iii",
    "canonicalUrl": "https://leetcode.com/problems/single-number-iii/",
    "url": "https://leetcode.com/problems/single-number-iii/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Single Number III\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Single Number III\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Single Number III\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Single Number III\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Single Number III\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Single Number III\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Single Number III\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Single Number III\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Single Number III",
      "cpp_optimal": "// Solution for Single Number III",
      "java_brute": "// Solution for Single Number III",
      "java_optimal": "// Solution for Single Number III",
      "python_brute": "# Solution for Single Number III",
      "python_optimal": "# Solution for Single Number III"
    },
    "originalOrder": 429,
    "learningOrder": 429
  },
  {
    "id": 831,
    "number": 831,
    "sequence_number": 831,
    "title": "Bitwise ORs of Subarrays",
    "slug": "bitwise-ors-of-subarrays",
    "difficulty": "Medium",
    "topic": "Bit Manipulation",
    "subtopic": "Bit Manipulation Optimization",
    "pattern": "Set Accumulator ORs",
    "secondary_patterns": [
      "Set Accumulator ORs"
    ],
    "stage": "2D & Grid Dynamic Programming",
    "curriculumStage": "Stage 17 — 2D & Grid Dynamic Programming",
    "roadmapPhase": "Stage 17 — 2D & Grid Dynamic Programming",
    "phase": "Stage 17 — 2D & Grid Dynamic Programming",
    "estimatedTime": 30,
    "statement": "Given the constraints and input parameters for Bitwise ORs of Subarrays, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Bitwise ORs of Subarrays."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Bitwise ORs of Subarrays.",
      "Leverage the optimal Bit Manipulation pattern to reduce time complexity."
    ],
    "learningObjective": "Master Bit Manipulation techniques by solving Medium problem constraints for Bitwise ORs of Subarrays.",
    "whyThisPattern": "When observing Bit Manipulation problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/bitwise-ors-of-subarrays/",
    "leetcode_title": "Bitwise ORs of Subarrays",
    "leetcode_id": 898,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/bitwise-ors-of-subarrays/",
    "canonicalSlug": "bitwise-ors-of-subarrays",
    "canonicalUrl": "https://leetcode.com/problems/bitwise-ors-of-subarrays/",
    "url": "https://leetcode.com/problems/bitwise-ors-of-subarrays/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Bitwise ORs of Subarrays\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Bitwise ORs of Subarrays\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Bitwise ORs of Subarrays\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Bitwise ORs of Subarrays\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Bitwise ORs of Subarrays\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Bitwise ORs of Subarrays\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Bitwise ORs of Subarrays\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Bitwise ORs of Subarrays\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Bitwise ORs of Subarrays",
      "cpp_optimal": "// Solution for Bitwise ORs of Subarrays",
      "java_brute": "// Solution for Bitwise ORs of Subarrays",
      "java_optimal": "// Solution for Bitwise ORs of Subarrays",
      "python_brute": "# Solution for Bitwise ORs of Subarrays",
      "python_optimal": "# Solution for Bitwise ORs of Subarrays"
    },
    "originalOrder": 430,
    "learningOrder": 430
  },
  {
    "id": 832,
    "number": 832,
    "sequence_number": 832,
    "title": "Subrectangle Queries",
    "slug": "subrectangle-queries",
    "difficulty": "Medium",
    "topic": "Geometry",
    "subtopic": "Geometry Optimization",
    "pattern": "Matrix Modification",
    "secondary_patterns": [
      "Matrix Modification"
    ],
    "stage": "2D & Grid Dynamic Programming",
    "curriculumStage": "Stage 17 — 2D & Grid Dynamic Programming",
    "roadmapPhase": "Stage 17 — 2D & Grid Dynamic Programming",
    "phase": "Stage 17 — 2D & Grid Dynamic Programming",
    "estimatedTime": 30,
    "statement": "Given the constraints and input parameters for Subrectangle Queries, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Subrectangle Queries."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Subrectangle Queries.",
      "Leverage the optimal Arrays pattern to reduce time complexity."
    ],
    "learningObjective": "Master Geometry techniques by solving Medium problem constraints for Subrectangle Queries.",
    "whyThisPattern": "When observing Geometry problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/subrectangle-queries/",
    "leetcode_title": "Subrectangle Queries",
    "leetcode_id": 1476,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/subrectangle-queries/",
    "canonicalSlug": "subrectangle-queries",
    "canonicalUrl": "https://leetcode.com/problems/subrectangle-queries/",
    "url": "https://leetcode.com/problems/subrectangle-queries/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Subrectangle Queries\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Subrectangle Queries\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Subrectangle Queries\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Subrectangle Queries\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Subrectangle Queries\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Subrectangle Queries\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Subrectangle Queries\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Subrectangle Queries\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Subrectangle Queries",
      "cpp_optimal": "// Solution for Subrectangle Queries",
      "java_brute": "// Solution for Subrectangle Queries",
      "java_optimal": "// Solution for Subrectangle Queries",
      "python_brute": "# Solution for Subrectangle Queries",
      "python_optimal": "# Solution for Subrectangle Queries"
    },
    "originalOrder": 472,
    "learningOrder": 472
  },
  {
    "id": 833,
    "number": 833,
    "sequence_number": 833,
    "title": "Rectangle Area",
    "slug": "rectangle-area",
    "difficulty": "Medium",
    "topic": "Geometry",
    "subtopic": "Geometry Optimization",
    "pattern": "Geometry Pattern",
    "secondary_patterns": [
      "Geometry Pattern"
    ],
    "stage": "2D & Grid Dynamic Programming",
    "curriculumStage": "Stage 17 — 2D & Grid Dynamic Programming",
    "roadmapPhase": "Stage 17 — 2D & Grid Dynamic Programming",
    "phase": "Stage 17 — 2D & Grid Dynamic Programming",
    "estimatedTime": 30,
    "statement": "Solve the **Rectangle Area** problem using standard Geometry techniques. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Geometry algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Geometry properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Geometry techniques by solving Medium problem constraints for Rectangle Area.",
    "whyThisPattern": "When observing Geometry problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/rectangle-area/",
    "leetcode_title": "Rectangle Area",
    "leetcode_id": 223,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/rectangle-area/",
    "canonicalSlug": "rectangle-area",
    "canonicalUrl": "https://leetcode.com/problems/rectangle-area/",
    "url": "https://leetcode.com/problems/rectangle-area/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Rectangle Area\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Rectangle Area\n};",
        "java": "// Java Solution for Rectangle Area\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Rectangle Area\n}",
        "python": "# Python Solution for Rectangle Area\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Rectangle Area\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Rectangle Area\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Rectangle Area\n};",
        "java": "// Optimal Java Solution for Rectangle Area\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Rectangle Area\n}",
        "python": "# Optimal Python Solution for Rectangle Area\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Rectangle Area\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Rectangle Area",
      "cpp_optimal": "// Solution for Rectangle Area",
      "java_brute": "// Solution for Rectangle Area",
      "java_optimal": "// Solution for Rectangle Area",
      "python_brute": "# Solution for Rectangle Area",
      "python_optimal": "# Solution for Rectangle Area"
    },
    "originalOrder": 473,
    "learningOrder": 473
  },
  {
    "id": 834,
    "number": 834,
    "sequence_number": 834,
    "title": "Generate Random Point in a Circle",
    "slug": "generate-random-point-in-a-circle",
    "difficulty": "Medium",
    "topic": "Geometry",
    "subtopic": "Geometry Optimization",
    "pattern": "Geometry Pattern",
    "secondary_patterns": [
      "Geometry Pattern"
    ],
    "stage": "2D & Grid Dynamic Programming",
    "curriculumStage": "Stage 17 — 2D & Grid Dynamic Programming",
    "roadmapPhase": "Stage 17 — 2D & Grid Dynamic Programming",
    "phase": "Stage 17 — 2D & Grid Dynamic Programming",
    "estimatedTime": 30,
    "statement": "Solve the **Generate Random Point in a Circle** problem using standard Geometry techniques. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Geometry algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Geometry properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Geometry techniques by solving Medium problem constraints for Generate Random Point in a Circle.",
    "whyThisPattern": "When observing Geometry problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/generate-random-point-in-a-circle/",
    "leetcode_title": "Generate Random Point in a Circle",
    "leetcode_id": 478,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/generate-random-point-in-a-circle/",
    "canonicalSlug": "generate-random-point-in-a-circle",
    "canonicalUrl": "https://leetcode.com/problems/generate-random-point-in-a-circle/",
    "url": "https://leetcode.com/problems/generate-random-point-in-a-circle/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Generate Random Point in a Circle\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Generate Random Point in a Circle\n};",
        "java": "// Java Solution for Generate Random Point in a Circle\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Generate Random Point in a Circle\n}",
        "python": "# Python Solution for Generate Random Point in a Circle\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Generate Random Point in a Circle\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Generate Random Point in a Circle\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Generate Random Point in a Circle\n};",
        "java": "// Optimal Java Solution for Generate Random Point in a Circle\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Generate Random Point in a Circle\n}",
        "python": "# Optimal Python Solution for Generate Random Point in a Circle\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Generate Random Point in a Circle\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Generate Random Point in a Circle",
      "cpp_optimal": "// Solution for Generate Random Point in a Circle",
      "java_brute": "// Solution for Generate Random Point in a Circle",
      "java_optimal": "// Solution for Generate Random Point in a Circle",
      "python_brute": "# Solution for Generate Random Point in a Circle",
      "python_optimal": "# Solution for Generate Random Point in a Circle"
    },
    "originalOrder": 474,
    "learningOrder": 474
  },
  {
    "id": 835,
    "number": 835,
    "sequence_number": 835,
    "title": "Random Point in Non-overlapping Rectangles",
    "slug": "random-point-in-non-overlapping-rectangles",
    "difficulty": "Medium",
    "topic": "Geometry",
    "subtopic": "Geometry Optimization",
    "pattern": "Geometry Pattern",
    "secondary_patterns": [
      "Geometry Pattern"
    ],
    "stage": "2D & Grid Dynamic Programming",
    "curriculumStage": "Stage 17 — 2D & Grid Dynamic Programming",
    "roadmapPhase": "Stage 17 — 2D & Grid Dynamic Programming",
    "phase": "Stage 17 — 2D & Grid Dynamic Programming",
    "estimatedTime": 30,
    "statement": "Solve the **Random Point in Non-overlapping Rectangles** problem using standard Geometry techniques. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Geometry algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Geometry properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Geometry techniques by solving Medium problem constraints for Random Point in Non-overlapping Rectangles.",
    "whyThisPattern": "When observing Geometry problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/random-point-in-non-overlapping-rectangles/",
    "leetcode_title": "Random Point in Non-overlapping Rectangles",
    "leetcode_id": 497,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/random-point-in-non-overlapping-rectangles/",
    "canonicalSlug": "random-point-in-non-overlapping-rectangles",
    "canonicalUrl": "https://leetcode.com/problems/random-point-in-non-overlapping-rectangles/",
    "url": "https://leetcode.com/problems/random-point-in-non-overlapping-rectangles/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Random Point in Non-overlapping Rectangles\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Random Point in Non-overlapping Rectangles\n};",
        "java": "// Java Solution for Random Point in Non-overlapping Rectangles\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Random Point in Non-overlapping Rectangles\n}",
        "python": "# Python Solution for Random Point in Non-overlapping Rectangles\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Random Point in Non-overlapping Rectangles\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Random Point in Non-overlapping Rectangles\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Random Point in Non-overlapping Rectangles\n};",
        "java": "// Optimal Java Solution for Random Point in Non-overlapping Rectangles\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Random Point in Non-overlapping Rectangles\n}",
        "python": "# Optimal Python Solution for Random Point in Non-overlapping Rectangles\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Random Point in Non-overlapping Rectangles\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Random Point in Non-overlapping Rectangles",
      "cpp_optimal": "// Solution for Random Point in Non-overlapping Rectangles",
      "java_brute": "// Solution for Random Point in Non-overlapping Rectangles",
      "java_optimal": "// Solution for Random Point in Non-overlapping Rectangles",
      "python_brute": "# Solution for Random Point in Non-overlapping Rectangles",
      "python_optimal": "# Solution for Random Point in Non-overlapping Rectangles"
    },
    "originalOrder": 475,
    "learningOrder": 475
  },
  {
    "id": 836,
    "number": 836,
    "sequence_number": 836,
    "title": "Distinct Subsequences",
    "slug": "distinct-subsequences",
    "difficulty": "Hard",
    "topic": "Dynamic Programming",
    "subtopic": "Dynamic Programming Optimization",
    "pattern": "2D String Frequency Recurrence",
    "secondary_patterns": [
      "2D String Frequency Recurrence"
    ],
    "stage": "2D & Grid Dynamic Programming",
    "curriculumStage": "Stage 17 — 2D & Grid Dynamic Programming",
    "roadmapPhase": "Stage 17 — 2D & Grid Dynamic Programming",
    "phase": "Stage 17 — 2D & Grid Dynamic Programming",
    "estimatedTime": 45,
    "statement": "Given the constraints and input parameters for Distinct Subsequences, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Distinct Subsequences."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Distinct Subsequences.",
      "Leverage the optimal Dynamic Programming pattern to reduce time complexity."
    ],
    "learningObjective": "Master Dynamic Programming techniques by solving Hard problem constraints for Distinct Subsequences.",
    "whyThisPattern": "When observing Dynamic Programming problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/distinct-subsequences/",
    "leetcode_title": "Distinct Subsequences",
    "leetcode_id": 115,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/distinct-subsequences/",
    "canonicalSlug": "distinct-subsequences",
    "canonicalUrl": "https://leetcode.com/problems/distinct-subsequences/",
    "url": "https://leetcode.com/problems/distinct-subsequences/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Distinct Subsequences\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Distinct Subsequences\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Distinct Subsequences\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Distinct Subsequences\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Distinct Subsequences\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Distinct Subsequences\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Distinct Subsequences\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Distinct Subsequences\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Distinct Subsequences",
      "cpp_optimal": "// Solution for Distinct Subsequences",
      "java_brute": "// Solution for Distinct Subsequences",
      "java_optimal": "// Solution for Distinct Subsequences",
      "python_brute": "# Solution for Distinct Subsequences",
      "python_optimal": "# Solution for Distinct Subsequences"
    },
    "originalOrder": 831,
    "learningOrder": 831
  },
  {
    "id": 837,
    "number": 837,
    "sequence_number": 837,
    "title": "Scramble String",
    "slug": "scramble-string",
    "difficulty": "Hard",
    "topic": "Dynamic Programming",
    "subtopic": "Dynamic Programming Optimization",
    "pattern": "3D Substring Partition DP",
    "secondary_patterns": [
      "3D Substring Partition DP"
    ],
    "stage": "2D & Grid Dynamic Programming",
    "curriculumStage": "Stage 17 — 2D & Grid Dynamic Programming",
    "roadmapPhase": "Stage 17 — 2D & Grid Dynamic Programming",
    "phase": "Stage 17 — 2D & Grid Dynamic Programming",
    "estimatedTime": 45,
    "statement": "Given the constraints and input parameters for Scramble String, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Scramble String."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Scramble String.",
      "Leverage the optimal Dynamic Programming pattern to reduce time complexity."
    ],
    "learningObjective": "Master Dynamic Programming techniques by solving Hard problem constraints for Scramble String.",
    "whyThisPattern": "When observing Dynamic Programming problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/scramble-string/",
    "leetcode_title": "Scramble String",
    "leetcode_id": 87,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/scramble-string/",
    "canonicalSlug": "scramble-string",
    "canonicalUrl": "https://leetcode.com/problems/scramble-string/",
    "url": "https://leetcode.com/problems/scramble-string/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Scramble String\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Scramble String\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Scramble String\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Scramble String\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Scramble String\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Scramble String\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Scramble String\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Scramble String\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Scramble String",
      "cpp_optimal": "// Solution for Scramble String",
      "java_brute": "// Solution for Scramble String",
      "java_optimal": "// Solution for Scramble String",
      "python_brute": "# Solution for Scramble String",
      "python_optimal": "# Solution for Scramble String"
    },
    "originalOrder": 832,
    "learningOrder": 832
  },
  {
    "id": 838,
    "number": 838,
    "sequence_number": 838,
    "title": "Split Array With Same Average",
    "slug": "split-array-with-same-average",
    "difficulty": "Hard",
    "topic": "Dynamic Programming",
    "subtopic": "Dynamic Programming Optimization",
    "pattern": "Subset Sum DP Meet-in-Middle",
    "secondary_patterns": [
      "Subset Sum DP Meet-in-Middle"
    ],
    "stage": "2D & Grid Dynamic Programming",
    "curriculumStage": "Stage 17 — 2D & Grid Dynamic Programming",
    "roadmapPhase": "Stage 17 — 2D & Grid Dynamic Programming",
    "phase": "Stage 17 — 2D & Grid Dynamic Programming",
    "estimatedTime": 45,
    "statement": "Given the constraints and input parameters for Split Array With Same Average, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Split Array With Same Average."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Split Array With Same Average.",
      "Leverage the optimal Dynamic Programming pattern to reduce time complexity."
    ],
    "learningObjective": "Master Dynamic Programming techniques by solving Hard problem constraints for Split Array With Same Average.",
    "whyThisPattern": "When observing Dynamic Programming problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/split-array-with-same-average/",
    "leetcode_title": "Split Array With Same Average",
    "leetcode_id": 805,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/split-array-with-same-average/",
    "canonicalSlug": "split-array-with-same-average",
    "canonicalUrl": "https://leetcode.com/problems/split-array-with-same-average/",
    "url": "https://leetcode.com/problems/split-array-with-same-average/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Split Array With Same Average\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Split Array With Same Average\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Split Array With Same Average\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Split Array With Same Average\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Split Array With Same Average\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Split Array With Same Average\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Split Array With Same Average\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Split Array With Same Average\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Split Array With Same Average",
      "cpp_optimal": "// Solution for Split Array With Same Average",
      "java_brute": "// Solution for Split Array With Same Average",
      "java_optimal": "// Solution for Split Array With Same Average",
      "python_brute": "# Solution for Split Array With Same Average",
      "python_optimal": "# Solution for Split Array With Same Average"
    },
    "originalOrder": 833,
    "learningOrder": 833
  },
  {
    "id": 839,
    "number": 839,
    "sequence_number": 839,
    "title": "Regular Expression Matching",
    "slug": "regular-expression-matching",
    "difficulty": "Hard",
    "topic": "Dynamic Programming",
    "subtopic": "Dynamic Programming Optimization",
    "pattern": "Wildcard Match DP",
    "secondary_patterns": [
      "Wildcard Match DP"
    ],
    "stage": "2D & Grid Dynamic Programming",
    "curriculumStage": "Stage 17 — 2D & Grid Dynamic Programming",
    "roadmapPhase": "Stage 17 — 2D & Grid Dynamic Programming",
    "phase": "Stage 17 — 2D & Grid Dynamic Programming",
    "estimatedTime": 45,
    "statement": "Given the constraints and input parameters for Regular Expression Matching, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Regular Expression Matching."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Regular Expression Matching.",
      "Leverage the optimal Dynamic Programming pattern to reduce time complexity."
    ],
    "learningObjective": "Master Dynamic Programming techniques by solving Hard problem constraints for Regular Expression Matching.",
    "whyThisPattern": "When observing Dynamic Programming problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/regular-expression-matching/",
    "leetcode_title": "Regular Expression Matching",
    "leetcode_id": 10,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/regular-expression-matching/",
    "canonicalSlug": "regular-expression-matching",
    "canonicalUrl": "https://leetcode.com/problems/regular-expression-matching/",
    "url": "https://leetcode.com/problems/regular-expression-matching/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Regular Expression Matching\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Regular Expression Matching\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Regular Expression Matching\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Regular Expression Matching\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Regular Expression Matching\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Regular Expression Matching\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Regular Expression Matching\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Regular Expression Matching\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Regular Expression Matching",
      "cpp_optimal": "// Solution for Regular Expression Matching",
      "java_brute": "// Solution for Regular Expression Matching",
      "java_optimal": "// Solution for Regular Expression Matching",
      "python_brute": "# Solution for Regular Expression Matching",
      "python_optimal": "# Solution for Regular Expression Matching"
    },
    "originalOrder": 834,
    "learningOrder": 834
  },
  {
    "id": 840,
    "number": 840,
    "sequence_number": 840,
    "title": "Wildcard Matching",
    "slug": "wildcard-matching",
    "difficulty": "Hard",
    "topic": "Dynamic Programming",
    "subtopic": "Dynamic Programming Optimization",
    "pattern": "Question Star DP State",
    "secondary_patterns": [
      "Question Star DP State"
    ],
    "stage": "2D & Grid Dynamic Programming",
    "curriculumStage": "Stage 17 — 2D & Grid Dynamic Programming",
    "roadmapPhase": "Stage 17 — 2D & Grid Dynamic Programming",
    "phase": "Stage 17 — 2D & Grid Dynamic Programming",
    "estimatedTime": 45,
    "statement": "Given the constraints and input parameters for Wildcard Matching, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Wildcard Matching."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Wildcard Matching.",
      "Leverage the optimal Dynamic Programming pattern to reduce time complexity."
    ],
    "learningObjective": "Master Dynamic Programming techniques by solving Hard problem constraints for Wildcard Matching.",
    "whyThisPattern": "When observing Dynamic Programming problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/wildcard-matching/",
    "leetcode_title": "Wildcard Matching",
    "leetcode_id": 44,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/wildcard-matching/",
    "canonicalSlug": "wildcard-matching",
    "canonicalUrl": "https://leetcode.com/problems/wildcard-matching/",
    "url": "https://leetcode.com/problems/wildcard-matching/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Wildcard Matching\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Wildcard Matching\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Wildcard Matching\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Wildcard Matching\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Wildcard Matching\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Wildcard Matching\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Wildcard Matching\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Wildcard Matching\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Wildcard Matching",
      "cpp_optimal": "// Solution for Wildcard Matching",
      "java_brute": "// Solution for Wildcard Matching",
      "java_optimal": "// Solution for Wildcard Matching",
      "python_brute": "# Solution for Wildcard Matching",
      "python_optimal": "# Solution for Wildcard Matching"
    },
    "originalOrder": 835,
    "learningOrder": 835
  },
  {
    "id": 841,
    "number": 841,
    "sequence_number": 841,
    "title": "Race Car",
    "slug": "race-car",
    "difficulty": "Hard",
    "topic": "Dynamic Programming",
    "subtopic": "Dynamic Programming Optimization",
    "pattern": "BFS / DP Shortest Instruction",
    "secondary_patterns": [
      "BFS / DP Shortest Instruction"
    ],
    "stage": "2D & Grid Dynamic Programming",
    "curriculumStage": "Stage 17 — 2D & Grid Dynamic Programming",
    "roadmapPhase": "Stage 17 — 2D & Grid Dynamic Programming",
    "phase": "Stage 17 — 2D & Grid Dynamic Programming",
    "estimatedTime": 45,
    "statement": "Given the constraints and input parameters for Race Car, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Race Car."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Race Car.",
      "Leverage the optimal Dynamic Programming pattern to reduce time complexity."
    ],
    "learningObjective": "Master Dynamic Programming techniques by solving Hard problem constraints for Race Car.",
    "whyThisPattern": "When observing Dynamic Programming problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/race-car/",
    "leetcode_title": "Race Car",
    "leetcode_id": 818,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/race-car/",
    "canonicalSlug": "race-car",
    "canonicalUrl": "https://leetcode.com/problems/race-car/",
    "url": "https://leetcode.com/problems/race-car/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Race Car\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Race Car\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Race Car\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Race Car\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Race Car\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Race Car\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Race Car\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Race Car\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Race Car",
      "cpp_optimal": "// Solution for Race Car",
      "java_brute": "// Solution for Race Car",
      "java_optimal": "// Solution for Race Car",
      "python_brute": "# Solution for Race Car",
      "python_optimal": "# Solution for Race Car"
    },
    "originalOrder": 836,
    "learningOrder": 836
  },
  {
    "id": 842,
    "number": 842,
    "sequence_number": 842,
    "title": "Best Time to Buy and Sell Stock III",
    "slug": "best-time-to-buy-and-sell-stock-iii",
    "difficulty": "Hard",
    "topic": "Dynamic Programming",
    "subtopic": "Dynamic Programming Optimization",
    "pattern": "At Most 2 Transaction DP",
    "secondary_patterns": [
      "At Most 2 Transaction DP"
    ],
    "stage": "2D & Grid Dynamic Programming",
    "curriculumStage": "Stage 17 — 2D & Grid Dynamic Programming",
    "roadmapPhase": "Stage 17 — 2D & Grid Dynamic Programming",
    "phase": "Stage 17 — 2D & Grid Dynamic Programming",
    "estimatedTime": 45,
    "statement": "Given the constraints and input parameters for Best Time to Buy and Sell Stock III, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Best Time to Buy and Sell Stock III."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Best Time to Buy and Sell Stock III.",
      "Leverage the optimal Dynamic Programming pattern to reduce time complexity."
    ],
    "learningObjective": "Master Dynamic Programming techniques by solving Hard problem constraints for Best Time to Buy and Sell Stock III.",
    "whyThisPattern": "When observing Dynamic Programming problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/best-time-to-buy-and-sell-stock-iii/",
    "leetcode_title": "Best Time to Buy and Sell Stock III",
    "leetcode_id": 123,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/best-time-to-buy-and-sell-stock-iii/",
    "canonicalSlug": "best-time-to-buy-and-sell-stock-iii",
    "canonicalUrl": "https://leetcode.com/problems/best-time-to-buy-and-sell-stock-iii/",
    "url": "https://leetcode.com/problems/best-time-to-buy-and-sell-stock-iii/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Best Time to Buy and Sell Stock III\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Best Time to Buy and Sell Stock III\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Best Time to Buy and Sell Stock III\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Best Time to Buy and Sell Stock III\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Best Time to Buy and Sell Stock III\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Best Time to Buy and Sell Stock III\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Best Time to Buy and Sell Stock III\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Best Time to Buy and Sell Stock III\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Best Time to Buy and Sell Stock III",
      "cpp_optimal": "// Solution for Best Time to Buy and Sell Stock III",
      "java_brute": "// Solution for Best Time to Buy and Sell Stock III",
      "java_optimal": "// Solution for Best Time to Buy and Sell Stock III",
      "python_brute": "# Solution for Best Time to Buy and Sell Stock III",
      "python_optimal": "# Solution for Best Time to Buy and Sell Stock III"
    },
    "originalOrder": 837,
    "learningOrder": 837
  },
  {
    "id": 843,
    "number": 843,
    "sequence_number": 843,
    "title": "Best Time to Buy and Sell Stock IV",
    "slug": "best-time-to-buy-and-sell-stock-iv",
    "difficulty": "Hard",
    "topic": "Dynamic Programming",
    "subtopic": "Dynamic Programming Optimization",
    "pattern": "K-Transaction State DP",
    "secondary_patterns": [
      "K-Transaction State DP"
    ],
    "stage": "2D & Grid Dynamic Programming",
    "curriculumStage": "Stage 17 — 2D & Grid Dynamic Programming",
    "roadmapPhase": "Stage 17 — 2D & Grid Dynamic Programming",
    "phase": "Stage 17 — 2D & Grid Dynamic Programming",
    "estimatedTime": 45,
    "statement": "Given the constraints and input parameters for Best Time to Buy and Sell Stock IV, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Best Time to Buy and Sell Stock IV."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Best Time to Buy and Sell Stock IV.",
      "Leverage the optimal Dynamic Programming pattern to reduce time complexity."
    ],
    "learningObjective": "Master Dynamic Programming techniques by solving Hard problem constraints for Best Time to Buy and Sell Stock IV.",
    "whyThisPattern": "When observing Dynamic Programming problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/best-time-to-buy-and-sell-stock-iv/",
    "leetcode_title": "Best Time to Buy and Sell Stock IV",
    "leetcode_id": 188,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/best-time-to-buy-and-sell-stock-iv/",
    "canonicalSlug": "best-time-to-buy-and-sell-stock-iv",
    "canonicalUrl": "https://leetcode.com/problems/best-time-to-buy-and-sell-stock-iv/",
    "url": "https://leetcode.com/problems/best-time-to-buy-and-sell-stock-iv/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Best Time to Buy and Sell Stock IV\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Best Time to Buy and Sell Stock IV\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Best Time to Buy and Sell Stock IV\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Best Time to Buy and Sell Stock IV\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Best Time to Buy and Sell Stock IV\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Best Time to Buy and Sell Stock IV\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Best Time to Buy and Sell Stock IV\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Best Time to Buy and Sell Stock IV\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Best Time to Buy and Sell Stock IV",
      "cpp_optimal": "// Solution for Best Time to Buy and Sell Stock IV",
      "java_brute": "// Solution for Best Time to Buy and Sell Stock IV",
      "java_optimal": "// Solution for Best Time to Buy and Sell Stock IV",
      "python_brute": "# Solution for Best Time to Buy and Sell Stock IV",
      "python_optimal": "# Solution for Best Time to Buy and Sell Stock IV"
    },
    "originalOrder": 838,
    "learningOrder": 838
  },
  {
    "id": 844,
    "number": 844,
    "sequence_number": 844,
    "title": "Numbers At Most N Given Digit Set",
    "slug": "numbers-at-most-n-given-digit-set",
    "difficulty": "Hard",
    "topic": "Dynamic Programming",
    "subtopic": "Dynamic Programming Optimization",
    "pattern": "Digit DP Combinatorics",
    "secondary_patterns": [
      "Digit DP Combinatorics"
    ],
    "stage": "2D & Grid Dynamic Programming",
    "curriculumStage": "Stage 17 — 2D & Grid Dynamic Programming",
    "roadmapPhase": "Stage 17 — 2D & Grid Dynamic Programming",
    "phase": "Stage 17 — 2D & Grid Dynamic Programming",
    "estimatedTime": 45,
    "statement": "Given the constraints and input parameters for Numbers At Most N Given Digit Set, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Numbers At Most N Given Digit Set."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Numbers At Most N Given Digit Set.",
      "Leverage the optimal Dynamic Programming pattern to reduce time complexity."
    ],
    "learningObjective": "Master Dynamic Programming techniques by solving Hard problem constraints for Numbers At Most N Given Digit Set.",
    "whyThisPattern": "When observing Dynamic Programming problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/numbers-at-most-n-given-digit-set/",
    "leetcode_title": "Numbers At Most N Given Digit Set",
    "leetcode_id": 902,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/numbers-at-most-n-given-digit-set/",
    "canonicalSlug": "numbers-at-most-n-given-digit-set",
    "canonicalUrl": "https://leetcode.com/problems/numbers-at-most-n-given-digit-set/",
    "url": "https://leetcode.com/problems/numbers-at-most-n-given-digit-set/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Numbers At Most N Given Digit Set\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Numbers At Most N Given Digit Set\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Numbers At Most N Given Digit Set\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Numbers At Most N Given Digit Set\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Numbers At Most N Given Digit Set\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Numbers At Most N Given Digit Set\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Numbers At Most N Given Digit Set\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Numbers At Most N Given Digit Set\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Numbers At Most N Given Digit Set",
      "cpp_optimal": "// Solution for Numbers At Most N Given Digit Set",
      "java_brute": "// Solution for Numbers At Most N Given Digit Set",
      "java_optimal": "// Solution for Numbers At Most N Given Digit Set",
      "python_brute": "# Solution for Numbers At Most N Given Digit Set",
      "python_optimal": "# Solution for Numbers At Most N Given Digit Set"
    },
    "originalOrder": 839,
    "learningOrder": 839
  },
  {
    "id": 845,
    "number": 845,
    "sequence_number": 845,
    "title": "Word Break II",
    "slug": "word-break-ii",
    "difficulty": "Hard",
    "topic": "Dynamic Programming",
    "subtopic": "Dynamic Programming Optimization",
    "pattern": "Memoized Trie Backtracking",
    "secondary_patterns": [
      "Memoized Trie Backtracking"
    ],
    "stage": "2D & Grid Dynamic Programming",
    "curriculumStage": "Stage 17 — 2D & Grid Dynamic Programming",
    "roadmapPhase": "Stage 17 — 2D & Grid Dynamic Programming",
    "phase": "Stage 17 — 2D & Grid Dynamic Programming",
    "estimatedTime": 45,
    "statement": "Given the constraints and input parameters for Word Break II, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Word Break II."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Word Break II.",
      "Leverage the optimal Dynamic Programming pattern to reduce time complexity."
    ],
    "learningObjective": "Master Dynamic Programming techniques by solving Hard problem constraints for Word Break II.",
    "whyThisPattern": "When observing Dynamic Programming problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/word-break-ii/",
    "leetcode_title": "Word Break II",
    "leetcode_id": 140,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/word-break-ii/",
    "canonicalSlug": "word-break-ii",
    "canonicalUrl": "https://leetcode.com/problems/word-break-ii/",
    "url": "https://leetcode.com/problems/word-break-ii/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Word Break II\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Word Break II\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Word Break II\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Word Break II\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Word Break II\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Word Break II\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Word Break II\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Word Break II\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Word Break II",
      "cpp_optimal": "// Solution for Word Break II",
      "java_brute": "// Solution for Word Break II",
      "java_optimal": "// Solution for Word Break II",
      "python_brute": "# Solution for Word Break II",
      "python_optimal": "# Solution for Word Break II"
    },
    "originalOrder": 840,
    "learningOrder": 840
  },
  {
    "id": 846,
    "number": 846,
    "sequence_number": 846,
    "title": "Valid Permutations for DI Sequence",
    "slug": "valid-permutations-for-di-sequence",
    "difficulty": "Hard",
    "topic": "Dynamic Programming",
    "subtopic": "Dynamic Programming Optimization",
    "pattern": "DI Prefix Swap DP",
    "secondary_patterns": [
      "DI Prefix Swap DP"
    ],
    "stage": "2D & Grid Dynamic Programming",
    "curriculumStage": "Stage 17 — 2D & Grid Dynamic Programming",
    "roadmapPhase": "Stage 17 — 2D & Grid Dynamic Programming",
    "phase": "Stage 17 — 2D & Grid Dynamic Programming",
    "estimatedTime": 45,
    "statement": "Given the constraints and input parameters for Valid Permutations for DI Sequence, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Valid Permutations for DI Sequence."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Valid Permutations for DI Sequence.",
      "Leverage the optimal Dynamic Programming pattern to reduce time complexity."
    ],
    "learningObjective": "Master Dynamic Programming techniques by solving Hard problem constraints for Valid Permutations for DI Sequence.",
    "whyThisPattern": "When observing Dynamic Programming problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/valid-permutations-for-di-sequence/",
    "leetcode_title": "Valid Permutations for DI Sequence",
    "leetcode_id": 903,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/valid-permutations-for-di-sequence/",
    "canonicalSlug": "valid-permutations-for-di-sequence",
    "canonicalUrl": "https://leetcode.com/problems/valid-permutations-for-di-sequence/",
    "url": "https://leetcode.com/problems/valid-permutations-for-di-sequence/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Valid Permutations for DI Sequence\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Valid Permutations for DI Sequence\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Valid Permutations for DI Sequence\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Valid Permutations for DI Sequence\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Valid Permutations for DI Sequence\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Valid Permutations for DI Sequence\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Valid Permutations for DI Sequence\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Valid Permutations for DI Sequence\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Valid Permutations for DI Sequence",
      "cpp_optimal": "// Solution for Valid Permutations for DI Sequence",
      "java_brute": "// Solution for Valid Permutations for DI Sequence",
      "java_optimal": "// Solution for Valid Permutations for DI Sequence",
      "python_brute": "# Solution for Valid Permutations for DI Sequence",
      "python_optimal": "# Solution for Valid Permutations for DI Sequence"
    },
    "originalOrder": 841,
    "learningOrder": 841
  },
  {
    "id": 847,
    "number": 847,
    "sequence_number": 847,
    "title": "Russian Doll Envelopes",
    "slug": "russian-doll-envelopes",
    "difficulty": "Hard",
    "topic": "Dynamic Programming",
    "subtopic": "Dynamic Programming Optimization",
    "pattern": "2D Sort LIS Binary Search",
    "secondary_patterns": [
      "2D Sort LIS Binary Search"
    ],
    "stage": "2D & Grid Dynamic Programming",
    "curriculumStage": "Stage 17 — 2D & Grid Dynamic Programming",
    "roadmapPhase": "Stage 17 — 2D & Grid Dynamic Programming",
    "phase": "Stage 17 — 2D & Grid Dynamic Programming",
    "estimatedTime": 45,
    "statement": "Given the constraints and input parameters for Russian Doll Envelopes, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Russian Doll Envelopes."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Russian Doll Envelopes.",
      "Leverage the optimal Dynamic Programming pattern to reduce time complexity."
    ],
    "learningObjective": "Master Dynamic Programming techniques by solving Hard problem constraints for Russian Doll Envelopes.",
    "whyThisPattern": "When observing Dynamic Programming problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/russian-doll-envelopes/",
    "leetcode_title": "Russian Doll Envelopes",
    "leetcode_id": 354,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/russian-doll-envelopes/",
    "canonicalSlug": "russian-doll-envelopes",
    "canonicalUrl": "https://leetcode.com/problems/russian-doll-envelopes/",
    "url": "https://leetcode.com/problems/russian-doll-envelopes/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Russian Doll Envelopes\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Russian Doll Envelopes\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Russian Doll Envelopes\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Russian Doll Envelopes\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Russian Doll Envelopes\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Russian Doll Envelopes\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Russian Doll Envelopes\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Russian Doll Envelopes\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Russian Doll Envelopes",
      "cpp_optimal": "// Solution for Russian Doll Envelopes",
      "java_brute": "// Solution for Russian Doll Envelopes",
      "java_optimal": "// Solution for Russian Doll Envelopes",
      "python_brute": "# Solution for Russian Doll Envelopes",
      "python_optimal": "# Solution for Russian Doll Envelopes"
    },
    "originalOrder": 842,
    "learningOrder": 842
  },
  {
    "id": 848,
    "number": 848,
    "sequence_number": 848,
    "title": "Frog Jump",
    "slug": "frog-jump",
    "difficulty": "Hard",
    "topic": "Dynamic Programming",
    "subtopic": "Dynamic Programming Optimization",
    "pattern": "Stone Step HashMap DP",
    "secondary_patterns": [
      "Stone Step HashMap DP"
    ],
    "stage": "2D & Grid Dynamic Programming",
    "curriculumStage": "Stage 17 — 2D & Grid Dynamic Programming",
    "roadmapPhase": "Stage 17 — 2D & Grid Dynamic Programming",
    "phase": "Stage 17 — 2D & Grid Dynamic Programming",
    "estimatedTime": 45,
    "statement": "Given the constraints and input parameters for Frog Jump, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Frog Jump."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Frog Jump.",
      "Leverage the optimal Dynamic Programming pattern to reduce time complexity."
    ],
    "learningObjective": "Master Dynamic Programming techniques by solving Hard problem constraints for Frog Jump.",
    "whyThisPattern": "When observing Dynamic Programming problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/frog-jump/",
    "leetcode_title": "Frog Jump",
    "leetcode_id": 403,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/frog-jump/",
    "canonicalSlug": "frog-jump",
    "canonicalUrl": "https://leetcode.com/problems/frog-jump/",
    "url": "https://leetcode.com/problems/frog-jump/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Frog Jump\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Frog Jump\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Frog Jump\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Frog Jump\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Frog Jump\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Frog Jump\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Frog Jump\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Frog Jump\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Frog Jump",
      "cpp_optimal": "// Solution for Frog Jump",
      "java_brute": "// Solution for Frog Jump",
      "java_optimal": "// Solution for Frog Jump",
      "python_brute": "# Solution for Frog Jump",
      "python_optimal": "# Solution for Frog Jump"
    },
    "originalOrder": 843,
    "learningOrder": 843
  },
  {
    "id": 849,
    "number": 849,
    "sequence_number": 849,
    "title": "Freedom Trail",
    "slug": "freedom-trail",
    "difficulty": "Hard",
    "topic": "Dynamic Programming",
    "subtopic": "Dynamic Programming Optimization",
    "pattern": "Circular Ring Dial DP",
    "secondary_patterns": [
      "Circular Ring Dial DP"
    ],
    "stage": "2D & Grid Dynamic Programming",
    "curriculumStage": "Stage 17 — 2D & Grid Dynamic Programming",
    "roadmapPhase": "Stage 17 — 2D & Grid Dynamic Programming",
    "phase": "Stage 17 — 2D & Grid Dynamic Programming",
    "estimatedTime": 45,
    "statement": "Given the constraints and input parameters for Freedom Trail, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Freedom Trail."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Freedom Trail.",
      "Leverage the optimal Dynamic Programming pattern to reduce time complexity."
    ],
    "learningObjective": "Master Dynamic Programming techniques by solving Hard problem constraints for Freedom Trail.",
    "whyThisPattern": "When observing Dynamic Programming problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/freedom-trail/",
    "leetcode_title": "Freedom Trail",
    "leetcode_id": 514,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/freedom-trail/",
    "canonicalSlug": "freedom-trail",
    "canonicalUrl": "https://leetcode.com/problems/freedom-trail/",
    "url": "https://leetcode.com/problems/freedom-trail/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Freedom Trail\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Freedom Trail\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Freedom Trail\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Freedom Trail\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Freedom Trail\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Freedom Trail\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Freedom Trail\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Freedom Trail\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Freedom Trail",
      "cpp_optimal": "// Solution for Freedom Trail",
      "java_brute": "// Solution for Freedom Trail",
      "java_optimal": "// Solution for Freedom Trail",
      "python_brute": "# Solution for Freedom Trail",
      "python_optimal": "# Solution for Freedom Trail"
    },
    "originalOrder": 844,
    "learningOrder": 844
  },
  {
    "id": 850,
    "number": 850,
    "sequence_number": 850,
    "title": "Maximum Score from Performing Multiplication Operations",
    "slug": "maximum-score-from-performing-multiplication-operations",
    "difficulty": "Hard",
    "topic": "Dynamic Programming",
    "subtopic": "Dynamic Programming Optimization",
    "pattern": "2D Interval Multiplier DP",
    "secondary_patterns": [
      "2D Interval Multiplier DP"
    ],
    "stage": "2D & Grid Dynamic Programming",
    "curriculumStage": "Stage 17 — 2D & Grid Dynamic Programming",
    "roadmapPhase": "Stage 17 — 2D & Grid Dynamic Programming",
    "phase": "Stage 17 — 2D & Grid Dynamic Programming",
    "estimatedTime": 45,
    "statement": "Given the constraints and input parameters for Maximum Score from Performing Multiplication Operations, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Maximum Score from Performing Multiplication Operations."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Maximum Score from Performing Multiplication Operations.",
      "Leverage the optimal Dynamic Programming pattern to reduce time complexity."
    ],
    "learningObjective": "Master Dynamic Programming techniques by solving Hard problem constraints for Maximum Score from Performing Multiplication Operations.",
    "whyThisPattern": "When observing Dynamic Programming problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/maximum-score-from-performing-multiplication-operations/",
    "leetcode_title": "Maximum Score from Performing Multiplication Operations",
    "leetcode_id": 1770,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/maximum-score-from-performing-multiplication-operations/",
    "canonicalSlug": "maximum-score-from-performing-multiplication-operations",
    "canonicalUrl": "https://leetcode.com/problems/maximum-score-from-performing-multiplication-operations/",
    "url": "https://leetcode.com/problems/maximum-score-from-performing-multiplication-operations/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Maximum Score from Performing Multiplication Operations\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Maximum Score from Performing Multiplication Operations\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Maximum Score from Performing Multiplication Operations\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Maximum Score from Performing Multiplication Operations\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Maximum Score from Performing Multiplication Operations\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Maximum Score from Performing Multiplication Operations\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Maximum Score from Performing Multiplication Operations\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Maximum Score from Performing Multiplication Operations\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Maximum Score from Performing Multiplication Operations",
      "cpp_optimal": "// Solution for Maximum Score from Performing Multiplication Operations",
      "java_brute": "// Solution for Maximum Score from Performing Multiplication Operations",
      "java_optimal": "// Solution for Maximum Score from Performing Multiplication Operations",
      "python_brute": "# Solution for Maximum Score from Performing Multiplication Operations",
      "python_optimal": "# Solution for Maximum Score from Performing Multiplication Operations"
    },
    "originalOrder": 845,
    "learningOrder": 845
  },
  {
    "id": 851,
    "number": 851,
    "sequence_number": 851,
    "title": "Add Strings",
    "slug": "add-strings",
    "difficulty": "Easy",
    "topic": "Strings",
    "subtopic": "Hashing & Array Optimization",
    "pattern": "Hashing & Array Optimization",
    "secondary_patterns": [
      "Hashing & Array Optimization"
    ],
    "stage": "Advanced DP & State Compression",
    "curriculumStage": "Stage 18 — Advanced DP & State Compression",
    "roadmapPhase": "Stage 18 — Advanced DP & State Compression",
    "phase": "Stage 18 — Advanced DP & State Compression",
    "estimatedTime": 15,
    "statement": "Solve the **Add Strings Optimization** problem using the **Hashing & Array Optimization** technique. Given input constraints appropriate for Easy level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^4",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Hashing & Array Optimization identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Hashing & Array Optimization. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Hashing & Array Optimization techniques by solving Easy problem constraints for Add Strings Optimization.",
    "whyThisPattern": "When observing arrays & strings problem conditions, Hashing & Array Optimization optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Apple",
      "Adobe",
      "Atlassian"
    ],
    "companyRelevanceTier": "Medium",
    "leetcode_url": "https://leetcode.com/problems/add-strings/",
    "leetcode_title": "Add Strings",
    "leetcode_id": 415,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/add-strings/",
    "canonicalSlug": "add-strings",
    "canonicalUrl": "https://leetcode.com/problems/add-strings/",
    "url": "https://leetcode.com/problems/add-strings/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Add Strings Optimization (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Add Strings Optimization (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Add Strings Optimization (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Add Strings Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Add Strings Optimization (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Add Strings Optimization (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Add Strings Optimization (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Add Strings Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Add Strings",
      "cpp_optimal": "// Solution for Add Strings",
      "java_brute": "// Solution for Add Strings",
      "java_optimal": "// Solution for Add Strings",
      "python_brute": "# Solution for Add Strings",
      "python_optimal": "# Solution for Add Strings"
    },
    "originalOrder": 186,
    "learningOrder": 186
  },
  {
    "id": 852,
    "number": 852,
    "sequence_number": 852,
    "title": "Number of Segments in a String",
    "slug": "number-of-segments-in-a-string",
    "difficulty": "Easy",
    "topic": "Strings",
    "subtopic": "Hashing & Array Optimization",
    "pattern": "Hashing & Array Optimization",
    "secondary_patterns": [
      "Hashing & Array Optimization"
    ],
    "stage": "Advanced DP & State Compression",
    "curriculumStage": "Stage 18 — Advanced DP & State Compression",
    "roadmapPhase": "Stage 18 — Advanced DP & State Compression",
    "phase": "Stage 18 — Advanced DP & State Compression",
    "estimatedTime": 15,
    "statement": "Solve the **Number of Segments in a String Challenge** problem using the **Hashing & Array Optimization** technique. Given input constraints appropriate for Easy level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^4",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Hashing & Array Optimization identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Hashing & Array Optimization. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Hashing & Array Optimization techniques by solving Easy problem constraints for Number of Segments in a String Challenge.",
    "whyThisPattern": "When observing arrays & strings problem conditions, Hashing & Array Optimization optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Meta",
      "Uber",
      "Databricks"
    ],
    "companyRelevanceTier": "Medium",
    "leetcode_url": "https://leetcode.com/problems/number-of-segments-in-a-string/",
    "leetcode_title": "Number of Segments in a String",
    "leetcode_id": 434,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/number-of-segments-in-a-string/",
    "canonicalSlug": "number-of-segments-in-a-string",
    "canonicalUrl": "https://leetcode.com/problems/number-of-segments-in-a-string/",
    "url": "https://leetcode.com/problems/number-of-segments-in-a-string/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Number of Segments in a String Challenge (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Number of Segments in a String Challenge (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Number of Segments in a String Challenge (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Number of Segments in a String Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Number of Segments in a String Challenge (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Number of Segments in a String Challenge (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Number of Segments in a String Challenge (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Number of Segments in a String Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Number of Segments in a String",
      "cpp_optimal": "// Solution for Number of Segments in a String",
      "java_brute": "// Solution for Number of Segments in a String",
      "java_optimal": "// Solution for Number of Segments in a String",
      "python_brute": "# Solution for Number of Segments in a String",
      "python_optimal": "# Solution for Number of Segments in a String"
    },
    "originalOrder": 187,
    "learningOrder": 187
  },
  {
    "id": 853,
    "number": 853,
    "sequence_number": 853,
    "title": "Arranging Coins",
    "slug": "arranging-coins",
    "difficulty": "Easy",
    "topic": "Strings",
    "subtopic": "Hashing & Array Optimization",
    "pattern": "Hashing & Array Optimization",
    "secondary_patterns": [
      "Hashing & Array Optimization"
    ],
    "stage": "Advanced DP & State Compression",
    "curriculumStage": "Stage 18 — Advanced DP & State Compression",
    "roadmapPhase": "Stage 18 — Advanced DP & State Compression",
    "phase": "Stage 18 — Advanced DP & State Compression",
    "estimatedTime": 15,
    "statement": "Solve the **Arranging Coins Optimization** problem using the **Hashing & Array Optimization** technique. Given input constraints appropriate for Easy level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^4",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Hashing & Array Optimization identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Hashing & Array Optimization. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Hashing & Array Optimization techniques by solving Easy problem constraints for Arranging Coins Optimization.",
    "whyThisPattern": "When observing arrays & strings problem conditions, Hashing & Array Optimization optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "LinkedIn",
      "Amazon"
    ],
    "companyRelevanceTier": "Medium",
    "leetcode_url": "https://leetcode.com/problems/arranging-coins/",
    "leetcode_title": "Arranging Coins",
    "leetcode_id": 441,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/arranging-coins/",
    "canonicalSlug": "arranging-coins",
    "canonicalUrl": "https://leetcode.com/problems/arranging-coins/",
    "url": "https://leetcode.com/problems/arranging-coins/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Arranging Coins Optimization (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Arranging Coins Optimization (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Arranging Coins Optimization (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Arranging Coins Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Arranging Coins Optimization (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Arranging Coins Optimization (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Arranging Coins Optimization (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Arranging Coins Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Arranging Coins",
      "cpp_optimal": "// Solution for Arranging Coins",
      "java_brute": "// Solution for Arranging Coins",
      "java_optimal": "// Solution for Arranging Coins",
      "python_brute": "# Solution for Arranging Coins",
      "python_optimal": "# Solution for Arranging Coins"
    },
    "originalOrder": 188,
    "learningOrder": 188
  },
  {
    "id": 854,
    "number": 854,
    "sequence_number": 854,
    "title": "Hamming Distance",
    "slug": "hamming-distance",
    "difficulty": "Easy",
    "topic": "Strings",
    "subtopic": "Hashing & Array Optimization",
    "pattern": "Hashing & Array Optimization",
    "secondary_patterns": [
      "Hashing & Array Optimization"
    ],
    "stage": "Advanced DP & State Compression",
    "curriculumStage": "Stage 18 — Advanced DP & State Compression",
    "roadmapPhase": "Stage 18 — Advanced DP & State Compression",
    "phase": "Stage 18 — Advanced DP & State Compression",
    "estimatedTime": 15,
    "statement": "Solve the **Hamming Distance Optimization** problem using the **Hashing & Array Optimization** technique. Given input constraints appropriate for Easy level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^4",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Hashing & Array Optimization identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Hashing & Array Optimization. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Hashing & Array Optimization techniques by solving Easy problem constraints for Hamming Distance Optimization.",
    "whyThisPattern": "When observing arrays & strings problem conditions, Hashing & Array Optimization optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Apple",
      "Adobe",
      "Atlassian"
    ],
    "companyRelevanceTier": "Medium",
    "leetcode_url": "https://leetcode.com/problems/hamming-distance/",
    "leetcode_title": "Hamming Distance",
    "leetcode_id": 461,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/hamming-distance/",
    "canonicalSlug": "hamming-distance",
    "canonicalUrl": "https://leetcode.com/problems/hamming-distance/",
    "url": "https://leetcode.com/problems/hamming-distance/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Hamming Distance Optimization (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Hamming Distance Optimization (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Hamming Distance Optimization (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Hamming Distance Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Hamming Distance Optimization (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Hamming Distance Optimization (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Hamming Distance Optimization (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Hamming Distance Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Hamming Distance",
      "cpp_optimal": "// Solution for Hamming Distance",
      "java_brute": "// Solution for Hamming Distance",
      "java_optimal": "// Solution for Hamming Distance",
      "python_brute": "# Solution for Hamming Distance",
      "python_optimal": "# Solution for Hamming Distance"
    },
    "originalOrder": 189,
    "learningOrder": 189
  },
  {
    "id": 855,
    "number": 855,
    "sequence_number": 855,
    "title": "Number Complement",
    "slug": "number-complement",
    "difficulty": "Easy",
    "topic": "Strings",
    "subtopic": "Hashing & Array Optimization",
    "pattern": "Hashing & Array Optimization",
    "secondary_patterns": [
      "Hashing & Array Optimization"
    ],
    "stage": "Advanced DP & State Compression",
    "curriculumStage": "Stage 18 — Advanced DP & State Compression",
    "roadmapPhase": "Stage 18 — Advanced DP & State Compression",
    "phase": "Stage 18 — Advanced DP & State Compression",
    "estimatedTime": 15,
    "statement": "Solve the **Number Complement Optimization** problem using the **Hashing & Array Optimization** technique. Given input constraints appropriate for Easy level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^4",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Hashing & Array Optimization identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Hashing & Array Optimization. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Hashing & Array Optimization techniques by solving Easy problem constraints for Number Complement Optimization.",
    "whyThisPattern": "When observing arrays & strings problem conditions, Hashing & Array Optimization optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta"
    ],
    "companyRelevanceTier": "Medium",
    "leetcode_url": "https://leetcode.com/problems/number-complement/",
    "leetcode_title": "Number Complement",
    "leetcode_id": 476,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/number-complement/",
    "canonicalSlug": "number-complement",
    "canonicalUrl": "https://leetcode.com/problems/number-complement/",
    "url": "https://leetcode.com/problems/number-complement/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Number Complement Optimization (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Number Complement Optimization (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Number Complement Optimization (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Number Complement Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Number Complement Optimization (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Number Complement Optimization (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Number Complement Optimization (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Number Complement Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Number Complement",
      "cpp_optimal": "// Solution for Number Complement",
      "java_brute": "// Solution for Number Complement",
      "java_optimal": "// Solution for Number Complement",
      "python_brute": "# Solution for Number Complement",
      "python_optimal": "# Solution for Number Complement"
    },
    "originalOrder": 190,
    "learningOrder": 190
  },
  {
    "id": 856,
    "number": 856,
    "sequence_number": 856,
    "title": "License Key Formatting",
    "slug": "license-key-formatting",
    "difficulty": "Easy",
    "topic": "Strings",
    "subtopic": "Hashing & Array Optimization",
    "pattern": "Hashing & Array Optimization",
    "secondary_patterns": [
      "Hashing & Array Optimization"
    ],
    "stage": "Advanced DP & State Compression",
    "curriculumStage": "Stage 18 — Advanced DP & State Compression",
    "roadmapPhase": "Stage 18 — Advanced DP & State Compression",
    "phase": "Stage 18 — Advanced DP & State Compression",
    "estimatedTime": 15,
    "statement": "Solve the **License Key Formatting Challenge** problem using the **Hashing & Array Optimization** technique. Given input constraints appropriate for Easy level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^4",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Hashing & Array Optimization identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Hashing & Array Optimization. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Hashing & Array Optimization techniques by solving Easy problem constraints for License Key Formatting Challenge.",
    "whyThisPattern": "When observing arrays & strings problem conditions, Hashing & Array Optimization optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Amazon",
      "Microsoft",
      "Uber"
    ],
    "companyRelevanceTier": "Medium",
    "leetcode_url": "https://leetcode.com/problems/license-key-formatting/",
    "leetcode_title": "License Key Formatting",
    "leetcode_id": 482,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/license-key-formatting/",
    "canonicalSlug": "license-key-formatting",
    "canonicalUrl": "https://leetcode.com/problems/license-key-formatting/",
    "url": "https://leetcode.com/problems/license-key-formatting/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for License Key Formatting Challenge (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for License Key Formatting Challenge (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for License Key Formatting Challenge (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for License Key Formatting Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for License Key Formatting Challenge (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for License Key Formatting Challenge (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for License Key Formatting Challenge (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for License Key Formatting Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for License Key Formatting",
      "cpp_optimal": "// Solution for License Key Formatting",
      "java_brute": "// Solution for License Key Formatting",
      "java_optimal": "// Solution for License Key Formatting",
      "python_brute": "# Solution for License Key Formatting",
      "python_optimal": "# Solution for License Key Formatting"
    },
    "originalOrder": 191,
    "learningOrder": 191
  },
  {
    "id": 857,
    "number": 857,
    "sequence_number": 857,
    "title": "Keyboard Row",
    "slug": "keyboard-row",
    "difficulty": "Easy",
    "topic": "Strings",
    "subtopic": "Hashing & Array Optimization",
    "pattern": "Hashing & Array Optimization",
    "secondary_patterns": [
      "Hashing & Array Optimization"
    ],
    "stage": "Advanced DP & State Compression",
    "curriculumStage": "Stage 18 — Advanced DP & State Compression",
    "roadmapPhase": "Stage 18 — Advanced DP & State Compression",
    "phase": "Stage 18 — Advanced DP & State Compression",
    "estimatedTime": 15,
    "statement": "Solve the **Keyboard Row Optimization** problem using the **Hashing & Array Optimization** technique. Given input constraints appropriate for Easy level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^4",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Hashing & Array Optimization identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Hashing & Array Optimization. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Hashing & Array Optimization techniques by solving Easy problem constraints for Keyboard Row Optimization.",
    "whyThisPattern": "When observing arrays & strings problem conditions, Hashing & Array Optimization optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta"
    ],
    "companyRelevanceTier": "Medium",
    "leetcode_url": "https://leetcode.com/problems/keyboard-row/",
    "leetcode_title": "Keyboard Row",
    "leetcode_id": 500,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/keyboard-row/",
    "canonicalSlug": "keyboard-row",
    "canonicalUrl": "https://leetcode.com/problems/keyboard-row/",
    "url": "https://leetcode.com/problems/keyboard-row/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Keyboard Row Optimization (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Keyboard Row Optimization (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Keyboard Row Optimization (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Keyboard Row Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Keyboard Row Optimization (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Keyboard Row Optimization (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Keyboard Row Optimization (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Keyboard Row Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Keyboard Row",
      "cpp_optimal": "// Solution for Keyboard Row",
      "java_brute": "// Solution for Keyboard Row",
      "java_optimal": "// Solution for Keyboard Row",
      "python_brute": "# Solution for Keyboard Row",
      "python_optimal": "# Solution for Keyboard Row"
    },
    "originalOrder": 192,
    "learningOrder": 192
  },
  {
    "id": 858,
    "number": 858,
    "sequence_number": 858,
    "title": "Base 7",
    "slug": "base-7",
    "difficulty": "Easy",
    "topic": "Strings",
    "subtopic": "Hashing & Array Optimization",
    "pattern": "Hashing & Array Optimization",
    "secondary_patterns": [
      "Hashing & Array Optimization"
    ],
    "stage": "Advanced DP & State Compression",
    "curriculumStage": "Stage 18 — Advanced DP & State Compression",
    "roadmapPhase": "Stage 18 — Advanced DP & State Compression",
    "phase": "Stage 18 — Advanced DP & State Compression",
    "estimatedTime": 15,
    "statement": "Solve the **Base 7 Optimization** problem using the **Hashing & Array Optimization** technique. Given input constraints appropriate for Easy level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^4",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Hashing & Array Optimization identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Hashing & Array Optimization. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Hashing & Array Optimization techniques by solving Easy problem constraints for Base 7 Optimization.",
    "whyThisPattern": "When observing arrays & strings problem conditions, Hashing & Array Optimization optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Apple",
      "Adobe",
      "Atlassian"
    ],
    "companyRelevanceTier": "Medium",
    "leetcode_url": "https://leetcode.com/problems/base-7/",
    "leetcode_title": "Base 7",
    "leetcode_id": 504,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/base-7/",
    "canonicalSlug": "base-7",
    "canonicalUrl": "https://leetcode.com/problems/base-7/",
    "url": "https://leetcode.com/problems/base-7/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Base 7 Optimization (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Base 7 Optimization (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Base 7 Optimization (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Base 7 Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Base 7 Optimization (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Base 7 Optimization (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Base 7 Optimization (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Base 7 Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Base 7",
      "cpp_optimal": "// Solution for Base 7",
      "java_brute": "// Solution for Base 7",
      "java_optimal": "// Solution for Base 7",
      "python_brute": "# Solution for Base 7",
      "python_optimal": "# Solution for Base 7"
    },
    "originalOrder": 193,
    "learningOrder": 193
  },
  {
    "id": 859,
    "number": 859,
    "sequence_number": 859,
    "title": "Relative Ranks",
    "slug": "relative-ranks",
    "difficulty": "Easy",
    "topic": "Strings",
    "subtopic": "Hashing & Array Optimization",
    "pattern": "Hashing & Array Optimization",
    "secondary_patterns": [
      "Hashing & Array Optimization"
    ],
    "stage": "Advanced DP & State Compression",
    "curriculumStage": "Stage 18 — Advanced DP & State Compression",
    "roadmapPhase": "Stage 18 — Advanced DP & State Compression",
    "phase": "Stage 18 — Advanced DP & State Compression",
    "estimatedTime": 15,
    "statement": "Solve the **Relative Ranks Challenge** problem using the **Hashing & Array Optimization** technique. Given input constraints appropriate for Easy level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^4",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Hashing & Array Optimization identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Hashing & Array Optimization. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Hashing & Array Optimization techniques by solving Easy problem constraints for Relative Ranks Challenge.",
    "whyThisPattern": "When observing arrays & strings problem conditions, Hashing & Array Optimization optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Meta",
      "Uber",
      "Databricks"
    ],
    "companyRelevanceTier": "Medium",
    "leetcode_url": "https://leetcode.com/problems/relative-ranks/",
    "leetcode_title": "Relative Ranks",
    "leetcode_id": 506,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/relative-ranks/",
    "canonicalSlug": "relative-ranks",
    "canonicalUrl": "https://leetcode.com/problems/relative-ranks/",
    "url": "https://leetcode.com/problems/relative-ranks/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Relative Ranks Challenge (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Relative Ranks Challenge (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Relative Ranks Challenge (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Relative Ranks Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Relative Ranks Challenge (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Relative Ranks Challenge (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Relative Ranks Challenge (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Relative Ranks Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Relative Ranks",
      "cpp_optimal": "// Solution for Relative Ranks",
      "java_brute": "// Solution for Relative Ranks",
      "java_optimal": "// Solution for Relative Ranks",
      "python_brute": "# Solution for Relative Ranks",
      "python_optimal": "# Solution for Relative Ranks"
    },
    "originalOrder": 194,
    "learningOrder": 194
  },
  {
    "id": 860,
    "number": 860,
    "sequence_number": 860,
    "title": "Perfect Number",
    "slug": "perfect-number",
    "difficulty": "Easy",
    "topic": "Strings",
    "subtopic": "Hashing & Array Optimization",
    "pattern": "Hashing & Array Optimization",
    "secondary_patterns": [
      "Hashing & Array Optimization"
    ],
    "stage": "Advanced DP & State Compression",
    "curriculumStage": "Stage 18 — Advanced DP & State Compression",
    "roadmapPhase": "Stage 18 — Advanced DP & State Compression",
    "phase": "Stage 18 — Advanced DP & State Compression",
    "estimatedTime": 15,
    "statement": "Solve the **Perfect Number Optimization** problem using the **Hashing & Array Optimization** technique. Given input constraints appropriate for Easy level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^4",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Hashing & Array Optimization identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Hashing & Array Optimization. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Hashing & Array Optimization techniques by solving Easy problem constraints for Perfect Number Optimization.",
    "whyThisPattern": "When observing arrays & strings problem conditions, Hashing & Array Optimization optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "LinkedIn",
      "Amazon"
    ],
    "companyRelevanceTier": "Medium",
    "leetcode_url": "https://leetcode.com/problems/perfect-number/",
    "leetcode_title": "Perfect Number",
    "leetcode_id": 507,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/perfect-number/",
    "canonicalSlug": "perfect-number",
    "canonicalUrl": "https://leetcode.com/problems/perfect-number/",
    "url": "https://leetcode.com/problems/perfect-number/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Perfect Number Optimization (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Perfect Number Optimization (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Perfect Number Optimization (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Perfect Number Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Perfect Number Optimization (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Perfect Number Optimization (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Perfect Number Optimization (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Perfect Number Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Perfect Number",
      "cpp_optimal": "// Solution for Perfect Number",
      "java_brute": "// Solution for Perfect Number",
      "java_optimal": "// Solution for Perfect Number",
      "python_brute": "# Solution for Perfect Number",
      "python_optimal": "# Solution for Perfect Number"
    },
    "originalOrder": 195,
    "learningOrder": 195
  },
  {
    "id": 861,
    "number": 861,
    "sequence_number": 861,
    "title": "Valid Triangle Number",
    "slug": "valid-triangle-number",
    "difficulty": "Medium",
    "topic": "Geometry",
    "subtopic": "Geometry Optimization",
    "pattern": "Geometry Pattern",
    "secondary_patterns": [
      "Geometry Pattern"
    ],
    "stage": "Advanced DP & State Compression",
    "curriculumStage": "Stage 18 — Advanced DP & State Compression",
    "roadmapPhase": "Stage 18 — Advanced DP & State Compression",
    "phase": "Stage 18 — Advanced DP & State Compression",
    "estimatedTime": 30,
    "statement": "Solve the **Valid Triangle Number** problem using standard Geometry techniques. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Geometry algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Geometry properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Geometry techniques by solving Medium problem constraints for Valid Triangle Number.",
    "whyThisPattern": "When observing Geometry problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/valid-triangle-number/",
    "leetcode_title": "Valid Triangle Number",
    "leetcode_id": 611,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/valid-triangle-number/",
    "canonicalSlug": "valid-triangle-number",
    "canonicalUrl": "https://leetcode.com/problems/valid-triangle-number/",
    "url": "https://leetcode.com/problems/valid-triangle-number/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Valid Triangle Number\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Valid Triangle Number\n};",
        "java": "// Java Solution for Valid Triangle Number\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Valid Triangle Number\n}",
        "python": "# Python Solution for Valid Triangle Number\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Valid Triangle Number\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Valid Triangle Number\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Valid Triangle Number\n};",
        "java": "// Optimal Java Solution for Valid Triangle Number\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Valid Triangle Number\n}",
        "python": "# Optimal Python Solution for Valid Triangle Number\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Valid Triangle Number\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Valid Triangle Number",
      "cpp_optimal": "// Solution for Valid Triangle Number",
      "java_brute": "// Solution for Valid Triangle Number",
      "java_optimal": "// Solution for Valid Triangle Number",
      "python_brute": "# Solution for Valid Triangle Number",
      "python_optimal": "# Solution for Valid Triangle Number"
    },
    "originalOrder": 476,
    "learningOrder": 476
  },
  {
    "id": 862,
    "number": 862,
    "sequence_number": 862,
    "title": "Minimum Area Rectangle II",
    "slug": "minimum-area-rectangle-ii",
    "difficulty": "Medium",
    "topic": "Geometry",
    "subtopic": "Geometry Optimization",
    "pattern": "Geometry Pattern",
    "secondary_patterns": [
      "Geometry Pattern"
    ],
    "stage": "Advanced DP & State Compression",
    "curriculumStage": "Stage 18 — Advanced DP & State Compression",
    "roadmapPhase": "Stage 18 — Advanced DP & State Compression",
    "phase": "Stage 18 — Advanced DP & State Compression",
    "estimatedTime": 30,
    "statement": "Solve the **Minimum Area Rectangle II** problem using standard Geometry techniques. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Geometry algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Geometry properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Geometry techniques by solving Medium problem constraints for Minimum Area Rectangle II.",
    "whyThisPattern": "When observing Geometry problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/minimum-area-rectangle-ii/",
    "leetcode_title": "Minimum Area Rectangle II",
    "leetcode_id": 963,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/minimum-area-rectangle-ii/",
    "canonicalSlug": "minimum-area-rectangle-ii",
    "canonicalUrl": "https://leetcode.com/problems/minimum-area-rectangle-ii/",
    "url": "https://leetcode.com/problems/minimum-area-rectangle-ii/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Minimum Area Rectangle II\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Minimum Area Rectangle II\n};",
        "java": "// Java Solution for Minimum Area Rectangle II\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Minimum Area Rectangle II\n}",
        "python": "# Python Solution for Minimum Area Rectangle II\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Minimum Area Rectangle II\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Minimum Area Rectangle II\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Minimum Area Rectangle II\n};",
        "java": "// Optimal Java Solution for Minimum Area Rectangle II\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Minimum Area Rectangle II\n}",
        "python": "# Optimal Python Solution for Minimum Area Rectangle II\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Minimum Area Rectangle II\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Minimum Area Rectangle II",
      "cpp_optimal": "// Solution for Minimum Area Rectangle II",
      "java_brute": "// Solution for Minimum Area Rectangle II",
      "java_optimal": "// Solution for Minimum Area Rectangle II",
      "python_brute": "# Solution for Minimum Area Rectangle II",
      "python_optimal": "# Solution for Minimum Area Rectangle II"
    },
    "originalOrder": 477,
    "learningOrder": 477
  },
  {
    "id": 863,
    "number": 863,
    "sequence_number": 863,
    "title": "Jump Game",
    "slug": "jump-game",
    "difficulty": "Medium",
    "topic": "Greedy",
    "subtopic": "Greedy Optimization",
    "pattern": "Max Reachable Index",
    "secondary_patterns": [
      "Max Reachable Index"
    ],
    "stage": "Advanced DP & State Compression",
    "curriculumStage": "Stage 18 — Advanced DP & State Compression",
    "roadmapPhase": "Stage 18 — Advanced DP & State Compression",
    "phase": "Stage 18 — Advanced DP & State Compression",
    "estimatedTime": 30,
    "statement": "Given the constraints and input parameters for Jump Game, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Jump Game."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Jump Game.",
      "Leverage the optimal Greedy pattern to reduce time complexity."
    ],
    "learningObjective": "Master Greedy techniques by solving Medium problem constraints for Jump Game.",
    "whyThisPattern": "When observing Greedy problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/jump-game/",
    "leetcode_title": "Jump Game",
    "leetcode_id": 55,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/jump-game/",
    "canonicalSlug": "jump-game",
    "canonicalUrl": "https://leetcode.com/problems/jump-game/",
    "url": "https://leetcode.com/problems/jump-game/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Jump Game\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Jump Game\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Jump Game\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Jump Game\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Jump Game\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Jump Game\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Jump Game\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Jump Game\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Jump Game",
      "cpp_optimal": "// Solution for Jump Game",
      "java_brute": "// Solution for Jump Game",
      "java_optimal": "// Solution for Jump Game",
      "python_brute": "# Solution for Jump Game",
      "python_optimal": "# Solution for Jump Game"
    },
    "originalOrder": 501,
    "learningOrder": 501
  },
  {
    "id": 864,
    "number": 864,
    "sequence_number": 864,
    "title": "Jump Game II",
    "slug": "jump-game-ii",
    "difficulty": "Medium",
    "topic": "Greedy",
    "subtopic": "Greedy Optimization",
    "pattern": "BFS Level Farthest Reach",
    "secondary_patterns": [
      "BFS Level Farthest Reach"
    ],
    "stage": "Advanced DP & State Compression",
    "curriculumStage": "Stage 18 — Advanced DP & State Compression",
    "roadmapPhase": "Stage 18 — Advanced DP & State Compression",
    "phase": "Stage 18 — Advanced DP & State Compression",
    "estimatedTime": 30,
    "statement": "Given the constraints and input parameters for Jump Game II, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Jump Game II."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Jump Game II.",
      "Leverage the optimal Greedy pattern to reduce time complexity."
    ],
    "learningObjective": "Master Greedy techniques by solving Medium problem constraints for Jump Game II.",
    "whyThisPattern": "When observing Greedy problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/jump-game-ii/",
    "leetcode_title": "Jump Game II",
    "leetcode_id": 45,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/jump-game-ii/",
    "canonicalSlug": "jump-game-ii",
    "canonicalUrl": "https://leetcode.com/problems/jump-game-ii/",
    "url": "https://leetcode.com/problems/jump-game-ii/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Jump Game II\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Jump Game II\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Jump Game II\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Jump Game II\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Jump Game II\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Jump Game II\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Jump Game II\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Jump Game II\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Jump Game II",
      "cpp_optimal": "// Solution for Jump Game II",
      "java_brute": "// Solution for Jump Game II",
      "java_optimal": "// Solution for Jump Game II",
      "python_brute": "# Solution for Jump Game II",
      "python_optimal": "# Solution for Jump Game II"
    },
    "originalOrder": 502,
    "learningOrder": 502
  },
  {
    "id": 865,
    "number": 865,
    "sequence_number": 865,
    "title": "Hand of Straights",
    "slug": "hand-of-straights",
    "difficulty": "Medium",
    "topic": "Greedy",
    "subtopic": "Greedy Optimization",
    "pattern": "TreeMap Frequency Consecutives",
    "secondary_patterns": [
      "TreeMap Frequency Consecutives"
    ],
    "stage": "Advanced DP & State Compression",
    "curriculumStage": "Stage 18 — Advanced DP & State Compression",
    "roadmapPhase": "Stage 18 — Advanced DP & State Compression",
    "phase": "Stage 18 — Advanced DP & State Compression",
    "estimatedTime": 30,
    "statement": "Given the constraints and input parameters for Hand of Straights, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Hand of Straights."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Hand of Straights.",
      "Leverage the optimal Greedy pattern to reduce time complexity."
    ],
    "learningObjective": "Master Greedy techniques by solving Medium problem constraints for Hand of Straights.",
    "whyThisPattern": "When observing Greedy problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/hand-of-straights/",
    "leetcode_title": "Hand of Straights",
    "leetcode_id": 846,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/hand-of-straights/",
    "canonicalSlug": "hand-of-straights",
    "canonicalUrl": "https://leetcode.com/problems/hand-of-straights/",
    "url": "https://leetcode.com/problems/hand-of-straights/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Hand of Straights\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Hand of Straights\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Hand of Straights\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Hand of Straights\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Hand of Straights\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Hand of Straights\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Hand of Straights\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Hand of Straights\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Hand of Straights",
      "cpp_optimal": "// Solution for Hand of Straights",
      "java_brute": "// Solution for Hand of Straights",
      "java_optimal": "// Solution for Hand of Straights",
      "python_brute": "# Solution for Hand of Straights",
      "python_optimal": "# Solution for Hand of Straights"
    },
    "originalOrder": 503,
    "learningOrder": 503
  },
  {
    "id": 866,
    "number": 866,
    "sequence_number": 866,
    "title": "Minimum Increment to Make Array Unique",
    "slug": "minimum-increment-to-make-array-unique",
    "difficulty": "Medium",
    "topic": "Greedy",
    "subtopic": "Greedy Optimization",
    "pattern": "Sort & Running Peak",
    "secondary_patterns": [
      "Sort & Running Peak"
    ],
    "stage": "Advanced DP & State Compression",
    "curriculumStage": "Stage 18 — Advanced DP & State Compression",
    "roadmapPhase": "Stage 18 — Advanced DP & State Compression",
    "phase": "Stage 18 — Advanced DP & State Compression",
    "estimatedTime": 30,
    "statement": "Given the constraints and input parameters for Minimum Increment to Make Array Unique, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Minimum Increment to Make Array Unique."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Minimum Increment to Make Array Unique.",
      "Leverage the optimal Greedy pattern to reduce time complexity."
    ],
    "learningObjective": "Master Greedy techniques by solving Medium problem constraints for Minimum Increment to Make Array Unique.",
    "whyThisPattern": "When observing Greedy problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/minimum-increment-to-make-array-unique/",
    "leetcode_title": "Minimum Increment to Make Array Unique",
    "leetcode_id": 945,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/minimum-increment-to-make-array-unique/",
    "canonicalSlug": "minimum-increment-to-make-array-unique",
    "canonicalUrl": "https://leetcode.com/problems/minimum-increment-to-make-array-unique/",
    "url": "https://leetcode.com/problems/minimum-increment-to-make-array-unique/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Minimum Increment to Make Array Unique\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Minimum Increment to Make Array Unique\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Minimum Increment to Make Array Unique\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Minimum Increment to Make Array Unique\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Minimum Increment to Make Array Unique\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Minimum Increment to Make Array Unique\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Minimum Increment to Make Array Unique\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Minimum Increment to Make Array Unique\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Minimum Increment to Make Array Unique",
      "cpp_optimal": "// Solution for Minimum Increment to Make Array Unique",
      "java_brute": "// Solution for Minimum Increment to Make Array Unique",
      "java_optimal": "// Solution for Minimum Increment to Make Array Unique",
      "python_brute": "# Solution for Minimum Increment to Make Array Unique",
      "python_optimal": "# Solution for Minimum Increment to Make Array Unique"
    },
    "originalOrder": 504,
    "learningOrder": 504
  },
  {
    "id": 867,
    "number": 867,
    "sequence_number": 867,
    "title": "Minimum Deletions to Make Character Frequencies Unique",
    "slug": "minimum-deletions-to-make-character-frequencies-unique",
    "difficulty": "Medium",
    "topic": "Greedy",
    "subtopic": "Greedy Optimization",
    "pattern": "Set Frequency Decrement",
    "secondary_patterns": [
      "Set Frequency Decrement"
    ],
    "stage": "Advanced DP & State Compression",
    "curriculumStage": "Stage 18 — Advanced DP & State Compression",
    "roadmapPhase": "Stage 18 — Advanced DP & State Compression",
    "phase": "Stage 18 — Advanced DP & State Compression",
    "estimatedTime": 30,
    "statement": "Given the constraints and input parameters for Minimum Deletions to Make Character Frequencies Unique, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Minimum Deletions to Make Character Frequencies Unique."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Minimum Deletions to Make Character Frequencies Unique.",
      "Leverage the optimal Greedy pattern to reduce time complexity."
    ],
    "learningObjective": "Master Greedy techniques by solving Medium problem constraints for Minimum Deletions to Make Character Frequencies Unique.",
    "whyThisPattern": "When observing Greedy problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/minimum-deletions-to-make-character-frequencies-unique/",
    "leetcode_title": "Minimum Deletions to Make Character Frequencies Unique",
    "leetcode_id": 1647,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/minimum-deletions-to-make-character-frequencies-unique/",
    "canonicalSlug": "minimum-deletions-to-make-character-frequencies-unique",
    "canonicalUrl": "https://leetcode.com/problems/minimum-deletions-to-make-character-frequencies-unique/",
    "url": "https://leetcode.com/problems/minimum-deletions-to-make-character-frequencies-unique/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Minimum Deletions to Make Character Frequencies Unique\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Minimum Deletions to Make Character Frequencies Unique\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Minimum Deletions to Make Character Frequencies Unique\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Minimum Deletions to Make Character Frequencies Unique\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Minimum Deletions to Make Character Frequencies Unique\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Minimum Deletions to Make Character Frequencies Unique\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Minimum Deletions to Make Character Frequencies Unique\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Minimum Deletions to Make Character Frequencies Unique\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Minimum Deletions to Make Character Frequencies Unique",
      "cpp_optimal": "// Solution for Minimum Deletions to Make Character Frequencies Unique",
      "java_brute": "// Solution for Minimum Deletions to Make Character Frequencies Unique",
      "java_optimal": "// Solution for Minimum Deletions to Make Character Frequencies Unique",
      "python_brute": "# Solution for Minimum Deletions to Make Character Frequencies Unique",
      "python_optimal": "# Solution for Minimum Deletions to Make Character Frequencies Unique"
    },
    "originalOrder": 505,
    "learningOrder": 505
  },
  {
    "id": 868,
    "number": 868,
    "sequence_number": 868,
    "title": "Partitioning Into Minimum Number Of Deci-Binary Numbers",
    "slug": "partitioning-into-minimum-number-of-deci-binary-numbers",
    "difficulty": "Medium",
    "topic": "Greedy",
    "subtopic": "Greedy Optimization",
    "pattern": "Max Digit Extraction",
    "secondary_patterns": [
      "Max Digit Extraction"
    ],
    "stage": "Advanced DP & State Compression",
    "curriculumStage": "Stage 18 — Advanced DP & State Compression",
    "roadmapPhase": "Stage 18 — Advanced DP & State Compression",
    "phase": "Stage 18 — Advanced DP & State Compression",
    "estimatedTime": 30,
    "statement": "Given the constraints and input parameters for Partitioning Into Minimum Number of Deci-Binary Numbers, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Partitioning Into Minimum Number of Deci-Binary Numbers."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Partitioning Into Minimum Number of Deci-Binary Numbers.",
      "Leverage the optimal Greedy pattern to reduce time complexity."
    ],
    "learningObjective": "Master Greedy techniques by solving Medium problem constraints for Partitioning Into Minimum Number Of Deci-Binary Numbers.",
    "whyThisPattern": "When observing Greedy problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/partitioning-into-minimum-number-of-deci-binary-numbers/",
    "leetcode_title": "Partitioning Into Minimum Number Of Deci-Binary Numbers",
    "leetcode_id": 1689,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/partitioning-into-minimum-number-of-deci-binary-numbers/",
    "canonicalSlug": "partitioning-into-minimum-number-of-deci-binary-numbers",
    "canonicalUrl": "https://leetcode.com/problems/partitioning-into-minimum-number-of-deci-binary-numbers/",
    "url": "https://leetcode.com/problems/partitioning-into-minimum-number-of-deci-binary-numbers/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Partitioning Into Minimum Number of Deci-Binary Numbers\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Partitioning Into Minimum Number of Deci-Binary Numbers\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Partitioning Into Minimum Number of Deci-Binary Numbers\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Partitioning Into Minimum Number of Deci-Binary Numbers\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Partitioning Into Minimum Number of Deci-Binary Numbers\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Partitioning Into Minimum Number of Deci-Binary Numbers\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Partitioning Into Minimum Number of Deci-Binary Numbers\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Partitioning Into Minimum Number of Deci-Binary Numbers\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Partitioning Into Minimum Number Of Deci-Binary Numbers",
      "cpp_optimal": "// Solution for Partitioning Into Minimum Number Of Deci-Binary Numbers",
      "java_brute": "// Solution for Partitioning Into Minimum Number Of Deci-Binary Numbers",
      "java_optimal": "// Solution for Partitioning Into Minimum Number Of Deci-Binary Numbers",
      "python_brute": "# Solution for Partitioning Into Minimum Number Of Deci-Binary Numbers",
      "python_optimal": "# Solution for Partitioning Into Minimum Number Of Deci-Binary Numbers"
    },
    "originalOrder": 506,
    "learningOrder": 506
  },
  {
    "id": 869,
    "number": 869,
    "sequence_number": 869,
    "title": "Minimum Elements to Add to Form a Given Sum",
    "slug": "minimum-elements-to-add-to-form-a-given-sum",
    "difficulty": "Medium",
    "topic": "Greedy",
    "subtopic": "Greedy Optimization",
    "pattern": "Ceil Division Delta",
    "secondary_patterns": [
      "Ceil Division Delta"
    ],
    "stage": "Advanced DP & State Compression",
    "curriculumStage": "Stage 18 — Advanced DP & State Compression",
    "roadmapPhase": "Stage 18 — Advanced DP & State Compression",
    "phase": "Stage 18 — Advanced DP & State Compression",
    "estimatedTime": 30,
    "statement": "Given the constraints and input parameters for Minimum Elements to Add to Form a Given Sum, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Minimum Elements to Add to Form a Given Sum."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Minimum Elements to Add to Form a Given Sum.",
      "Leverage the optimal Greedy pattern to reduce time complexity."
    ],
    "learningObjective": "Master Greedy techniques by solving Medium problem constraints for Minimum Elements to Add to Form a Given Sum.",
    "whyThisPattern": "When observing Greedy problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/minimum-elements-to-add-to-form-a-given-sum/",
    "leetcode_title": "Minimum Elements to Add to Form a Given Sum",
    "leetcode_id": 1785,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/minimum-elements-to-add-to-form-a-given-sum/",
    "canonicalSlug": "minimum-elements-to-add-to-form-a-given-sum",
    "canonicalUrl": "https://leetcode.com/problems/minimum-elements-to-add-to-form-a-given-sum/",
    "url": "https://leetcode.com/problems/minimum-elements-to-add-to-form-a-given-sum/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Minimum Elements to Add to Form a Given Sum\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Minimum Elements to Add to Form a Given Sum\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Minimum Elements to Add to Form a Given Sum\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Minimum Elements to Add to Form a Given Sum\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Minimum Elements to Add to Form a Given Sum\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Minimum Elements to Add to Form a Given Sum\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Minimum Elements to Add to Form a Given Sum\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Minimum Elements to Add to Form a Given Sum\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Minimum Elements to Add to Form a Given Sum",
      "cpp_optimal": "// Solution for Minimum Elements to Add to Form a Given Sum",
      "java_brute": "// Solution for Minimum Elements to Add to Form a Given Sum",
      "java_optimal": "// Solution for Minimum Elements to Add to Form a Given Sum",
      "python_brute": "# Solution for Minimum Elements to Add to Form a Given Sum",
      "python_optimal": "# Solution for Minimum Elements to Add to Form a Given Sum"
    },
    "originalOrder": 507,
    "learningOrder": 507
  },
  {
    "id": 870,
    "number": 870,
    "sequence_number": 870,
    "title": "Maximum Ice Cream Bars",
    "slug": "maximum-ice-cream-bars",
    "difficulty": "Medium",
    "topic": "Greedy",
    "subtopic": "Greedy Optimization",
    "pattern": "Greedy Cost Sorting",
    "secondary_patterns": [
      "Greedy Cost Sorting"
    ],
    "stage": "Advanced DP & State Compression",
    "curriculumStage": "Stage 18 — Advanced DP & State Compression",
    "roadmapPhase": "Stage 18 — Advanced DP & State Compression",
    "phase": "Stage 18 — Advanced DP & State Compression",
    "estimatedTime": 30,
    "statement": "Given the constraints and input parameters for Maximum Ice Cream Bars, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Maximum Ice Cream Bars."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Maximum Ice Cream Bars.",
      "Leverage the optimal Greedy pattern to reduce time complexity."
    ],
    "learningObjective": "Master Greedy techniques by solving Medium problem constraints for Maximum Ice Cream Bars.",
    "whyThisPattern": "When observing Greedy problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/maximum-ice-cream-bars/",
    "leetcode_title": "Maximum Ice Cream Bars",
    "leetcode_id": 1833,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/maximum-ice-cream-bars/",
    "canonicalSlug": "maximum-ice-cream-bars",
    "canonicalUrl": "https://leetcode.com/problems/maximum-ice-cream-bars/",
    "url": "https://leetcode.com/problems/maximum-ice-cream-bars/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Maximum Ice Cream Bars\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Maximum Ice Cream Bars\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Maximum Ice Cream Bars\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Maximum Ice Cream Bars\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Maximum Ice Cream Bars\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Maximum Ice Cream Bars\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Maximum Ice Cream Bars\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Maximum Ice Cream Bars\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Maximum Ice Cream Bars",
      "cpp_optimal": "// Solution for Maximum Ice Cream Bars",
      "java_brute": "// Solution for Maximum Ice Cream Bars",
      "java_optimal": "// Solution for Maximum Ice Cream Bars",
      "python_brute": "# Solution for Maximum Ice Cream Bars",
      "python_optimal": "# Solution for Maximum Ice Cream Bars"
    },
    "originalOrder": 508,
    "learningOrder": 508
  },
  {
    "id": 871,
    "number": 871,
    "sequence_number": 871,
    "title": "Maximum Element After Decreasing and Rearranging",
    "slug": "maximum-element-after-decreasing-and-rearranging",
    "difficulty": "Medium",
    "topic": "Greedy",
    "subtopic": "Greedy Optimization",
    "pattern": "Sort & Bound Increment",
    "secondary_patterns": [
      "Sort & Bound Increment"
    ],
    "stage": "Advanced DP & State Compression",
    "curriculumStage": "Stage 18 — Advanced DP & State Compression",
    "roadmapPhase": "Stage 18 — Advanced DP & State Compression",
    "phase": "Stage 18 — Advanced DP & State Compression",
    "estimatedTime": 30,
    "statement": "Given the constraints and input parameters for Maximum Element After Decreasing and Rearranging, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Maximum Element After Decreasing and Rearranging."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Maximum Element After Decreasing and Rearranging.",
      "Leverage the optimal Greedy pattern to reduce time complexity."
    ],
    "learningObjective": "Master Greedy techniques by solving Medium problem constraints for Maximum Element After Decreasing and Rearranging.",
    "whyThisPattern": "When observing Greedy problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/maximum-element-after-decreasing-and-rearranging/",
    "leetcode_title": "Maximum Element After Decreasing and Rearranging",
    "leetcode_id": 1846,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/maximum-element-after-decreasing-and-rearranging/",
    "canonicalSlug": "maximum-element-after-decreasing-and-rearranging",
    "canonicalUrl": "https://leetcode.com/problems/maximum-element-after-decreasing-and-rearranging/",
    "url": "https://leetcode.com/problems/maximum-element-after-decreasing-and-rearranging/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Maximum Element After Decreasing and Rearranging\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Maximum Element After Decreasing and Rearranging\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Maximum Element After Decreasing and Rearranging\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Maximum Element After Decreasing and Rearranging\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Maximum Element After Decreasing and Rearranging\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Maximum Element After Decreasing and Rearranging\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Maximum Element After Decreasing and Rearranging\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Maximum Element After Decreasing and Rearranging\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Maximum Element After Decreasing and Rearranging",
      "cpp_optimal": "// Solution for Maximum Element After Decreasing and Rearranging",
      "java_brute": "// Solution for Maximum Element After Decreasing and Rearranging",
      "java_optimal": "// Solution for Maximum Element After Decreasing and Rearranging",
      "python_brute": "# Solution for Maximum Element After Decreasing and Rearranging",
      "python_optimal": "# Solution for Maximum Element After Decreasing and Rearranging"
    },
    "originalOrder": 509,
    "learningOrder": 509
  },
  {
    "id": 872,
    "number": 872,
    "sequence_number": 872,
    "title": "Minimum Number of People to Teach",
    "slug": "minimum-number-of-people-to-teach",
    "difficulty": "Medium",
    "topic": "Greedy",
    "subtopic": "Greedy Optimization",
    "pattern": "Language Overlap Count",
    "secondary_patterns": [
      "Language Overlap Count"
    ],
    "stage": "Advanced DP & State Compression",
    "curriculumStage": "Stage 18 — Advanced DP & State Compression",
    "roadmapPhase": "Stage 18 — Advanced DP & State Compression",
    "phase": "Stage 18 — Advanced DP & State Compression",
    "estimatedTime": 30,
    "statement": "Given the constraints and input parameters for Minimum Number of People to Teach, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Minimum Number of People to Teach."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Minimum Number of People to Teach.",
      "Leverage the optimal Greedy pattern to reduce time complexity."
    ],
    "learningObjective": "Master Greedy techniques by solving Medium problem constraints for Minimum Number of People to Teach.",
    "whyThisPattern": "When observing Greedy problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/minimum-number-of-people-to-teach/",
    "leetcode_title": "Minimum Number of People to Teach",
    "leetcode_id": 1733,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/minimum-number-of-people-to-teach/",
    "canonicalSlug": "minimum-number-of-people-to-teach",
    "canonicalUrl": "https://leetcode.com/problems/minimum-number-of-people-to-teach/",
    "url": "https://leetcode.com/problems/minimum-number-of-people-to-teach/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Minimum Number of People to Teach\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Minimum Number of People to Teach\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Minimum Number of People to Teach\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Minimum Number of People to Teach\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Minimum Number of People to Teach\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Minimum Number of People to Teach\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Minimum Number of People to Teach\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Minimum Number of People to Teach\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Minimum Number of People to Teach",
      "cpp_optimal": "// Solution for Minimum Number of People to Teach",
      "java_brute": "// Solution for Minimum Number of People to Teach",
      "java_optimal": "// Solution for Minimum Number of People to Teach",
      "python_brute": "# Solution for Minimum Number of People to Teach",
      "python_optimal": "# Solution for Minimum Number of People to Teach"
    },
    "originalOrder": 510,
    "learningOrder": 510
  },
  {
    "id": 873,
    "number": 873,
    "sequence_number": 873,
    "title": "Maximum Binary String After Change",
    "slug": "maximum-binary-string-after-change",
    "difficulty": "Medium",
    "topic": "Greedy",
    "subtopic": "Greedy Optimization",
    "pattern": "Leading Ones & Zero Count",
    "secondary_patterns": [
      "Leading Ones & Zero Count"
    ],
    "stage": "Advanced DP & State Compression",
    "curriculumStage": "Stage 18 — Advanced DP & State Compression",
    "roadmapPhase": "Stage 18 — Advanced DP & State Compression",
    "phase": "Stage 18 — Advanced DP & State Compression",
    "estimatedTime": 30,
    "statement": "Given the constraints and input parameters for Maximum Binary String After Change, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Maximum Binary String After Change."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Maximum Binary String After Change.",
      "Leverage the optimal Greedy pattern to reduce time complexity."
    ],
    "learningObjective": "Master Greedy techniques by solving Medium problem constraints for Maximum Binary String After Change.",
    "whyThisPattern": "When observing Greedy problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/maximum-binary-string-after-change/",
    "leetcode_title": "Maximum Binary String After Change",
    "leetcode_id": 1702,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/maximum-binary-string-after-change/",
    "canonicalSlug": "maximum-binary-string-after-change",
    "canonicalUrl": "https://leetcode.com/problems/maximum-binary-string-after-change/",
    "url": "https://leetcode.com/problems/maximum-binary-string-after-change/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Maximum Binary String After Change\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Maximum Binary String After Change\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Maximum Binary String After Change\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Maximum Binary String After Change\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Maximum Binary String After Change\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Maximum Binary String After Change\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Maximum Binary String After Change\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Maximum Binary String After Change\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Maximum Binary String After Change",
      "cpp_optimal": "// Solution for Maximum Binary String After Change",
      "java_brute": "// Solution for Maximum Binary String After Change",
      "java_optimal": "// Solution for Maximum Binary String After Change",
      "python_brute": "# Solution for Maximum Binary String After Change",
      "python_optimal": "# Solution for Maximum Binary String After Change"
    },
    "originalOrder": 511,
    "learningOrder": 511
  },
  {
    "id": 874,
    "number": 874,
    "sequence_number": 874,
    "title": "Smallest String With A Given Numeric Value",
    "slug": "smallest-string-with-a-given-numeric-value",
    "difficulty": "Medium",
    "topic": "Greedy",
    "subtopic": "Greedy Optimization",
    "pattern": "Greedy Right Z Assignment",
    "secondary_patterns": [
      "Greedy Right Z Assignment"
    ],
    "stage": "Advanced DP & State Compression",
    "curriculumStage": "Stage 18 — Advanced DP & State Compression",
    "roadmapPhase": "Stage 18 — Advanced DP & State Compression",
    "phase": "Stage 18 — Advanced DP & State Compression",
    "estimatedTime": 30,
    "statement": "Given the constraints and input parameters for Smallest String With A Given Numeric Value, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Smallest String With A Given Numeric Value."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Smallest String With A Given Numeric Value.",
      "Leverage the optimal Greedy pattern to reduce time complexity."
    ],
    "learningObjective": "Master Greedy techniques by solving Medium problem constraints for Smallest String With A Given Numeric Value.",
    "whyThisPattern": "When observing Greedy problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/smallest-string-with-a-given-numeric-value/",
    "leetcode_title": "Smallest String With A Given Numeric Value",
    "leetcode_id": 1663,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/smallest-string-with-a-given-numeric-value/",
    "canonicalSlug": "smallest-string-with-a-given-numeric-value",
    "canonicalUrl": "https://leetcode.com/problems/smallest-string-with-a-given-numeric-value/",
    "url": "https://leetcode.com/problems/smallest-string-with-a-given-numeric-value/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Smallest String With A Given Numeric Value\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Smallest String With A Given Numeric Value\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Smallest String With A Given Numeric Value\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Smallest String With A Given Numeric Value\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Smallest String With A Given Numeric Value\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Smallest String With A Given Numeric Value\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Smallest String With A Given Numeric Value\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Smallest String With A Given Numeric Value\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Smallest String With A Given Numeric Value",
      "cpp_optimal": "// Solution for Smallest String With A Given Numeric Value",
      "java_brute": "// Solution for Smallest String With A Given Numeric Value",
      "java_optimal": "// Solution for Smallest String With A Given Numeric Value",
      "python_brute": "# Solution for Smallest String With A Given Numeric Value",
      "python_optimal": "# Solution for Smallest String With A Given Numeric Value"
    },
    "originalOrder": 512,
    "learningOrder": 512
  },
  {
    "id": 875,
    "number": 875,
    "sequence_number": 875,
    "title": "Minimum Cost to Set Cooking Time",
    "slug": "minimum-cost-to-set-cooking-time",
    "difficulty": "Medium",
    "topic": "Greedy",
    "subtopic": "Greedy Optimization",
    "pattern": "Digit Format Trade",
    "secondary_patterns": [
      "Digit Format Trade"
    ],
    "stage": "Advanced DP & State Compression",
    "curriculumStage": "Stage 18 — Advanced DP & State Compression",
    "roadmapPhase": "Stage 18 — Advanced DP & State Compression",
    "phase": "Stage 18 — Advanced DP & State Compression",
    "estimatedTime": 30,
    "statement": "Given the constraints and input parameters for Minimum Cost to Set Cooking Time, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Minimum Cost to Set Cooking Time."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Minimum Cost to Set Cooking Time.",
      "Leverage the optimal Greedy pattern to reduce time complexity."
    ],
    "learningObjective": "Master Greedy techniques by solving Medium problem constraints for Minimum Cost to Set Cooking Time.",
    "whyThisPattern": "When observing Greedy problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/minimum-cost-to-set-cooking-time/",
    "leetcode_title": "Minimum Cost to Set Cooking Time",
    "leetcode_id": 2162,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/minimum-cost-to-set-cooking-time/",
    "canonicalSlug": "minimum-cost-to-set-cooking-time",
    "canonicalUrl": "https://leetcode.com/problems/minimum-cost-to-set-cooking-time/",
    "url": "https://leetcode.com/problems/minimum-cost-to-set-cooking-time/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Minimum Cost to Set Cooking Time\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Minimum Cost to Set Cooking Time\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Minimum Cost to Set Cooking Time\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Minimum Cost to Set Cooking Time\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Minimum Cost to Set Cooking Time\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Minimum Cost to Set Cooking Time\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Minimum Cost to Set Cooking Time\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Minimum Cost to Set Cooking Time\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Minimum Cost to Set Cooking Time",
      "cpp_optimal": "// Solution for Minimum Cost to Set Cooking Time",
      "java_brute": "// Solution for Minimum Cost to Set Cooking Time",
      "java_optimal": "// Solution for Minimum Cost to Set Cooking Time",
      "python_brute": "# Solution for Minimum Cost to Set Cooking Time",
      "python_optimal": "# Solution for Minimum Cost to Set Cooking Time"
    },
    "originalOrder": 513,
    "learningOrder": 513
  },
  {
    "id": 876,
    "number": 876,
    "sequence_number": 876,
    "title": "Minimum Numbers of Function Calls to Make Target Array",
    "slug": "minimum-numbers-of-function-calls-to-make-target-array",
    "difficulty": "Medium",
    "topic": "Greedy",
    "subtopic": "Greedy Optimization",
    "pattern": "Max Bit Len + Bit Sum",
    "secondary_patterns": [
      "Max Bit Len + Bit Sum"
    ],
    "stage": "Advanced DP & State Compression",
    "curriculumStage": "Stage 18 — Advanced DP & State Compression",
    "roadmapPhase": "Stage 18 — Advanced DP & State Compression",
    "phase": "Stage 18 — Advanced DP & State Compression",
    "estimatedTime": 30,
    "statement": "Given the constraints and input parameters for Minimum Numbers of Function Calls to Make Target Array, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Minimum Numbers of Function Calls to Make Target Array."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Minimum Numbers of Function Calls to Make Target Array.",
      "Leverage the optimal Greedy pattern to reduce time complexity."
    ],
    "learningObjective": "Master Greedy techniques by solving Medium problem constraints for Minimum Numbers of Function Calls to Make Target Array.",
    "whyThisPattern": "When observing Greedy problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/minimum-numbers-of-function-calls-to-make-target-array/",
    "leetcode_title": "Minimum Numbers of Function Calls to Make Target Array",
    "leetcode_id": 1558,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/minimum-numbers-of-function-calls-to-make-target-array/",
    "canonicalSlug": "minimum-numbers-of-function-calls-to-make-target-array",
    "canonicalUrl": "https://leetcode.com/problems/minimum-numbers-of-function-calls-to-make-target-array/",
    "url": "https://leetcode.com/problems/minimum-numbers-of-function-calls-to-make-target-array/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Minimum Numbers of Function Calls to Make Target Array\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Minimum Numbers of Function Calls to Make Target Array\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Minimum Numbers of Function Calls to Make Target Array\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Minimum Numbers of Function Calls to Make Target Array\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Minimum Numbers of Function Calls to Make Target Array\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Minimum Numbers of Function Calls to Make Target Array\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Minimum Numbers of Function Calls to Make Target Array\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Minimum Numbers of Function Calls to Make Target Array\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Minimum Numbers of Function Calls to Make Target Array",
      "cpp_optimal": "// Solution for Minimum Numbers of Function Calls to Make Target Array",
      "java_brute": "// Solution for Minimum Numbers of Function Calls to Make Target Array",
      "java_optimal": "// Solution for Minimum Numbers of Function Calls to Make Target Array",
      "python_brute": "# Solution for Minimum Numbers of Function Calls to Make Target Array",
      "python_optimal": "# Solution for Minimum Numbers of Function Calls to Make Target Array"
    },
    "originalOrder": 514,
    "learningOrder": 514
  },
  {
    "id": 877,
    "number": 877,
    "sequence_number": 877,
    "title": "Least Number of Unique Integers after K Removals",
    "slug": "least-number-of-unique-integers-after-k-removals",
    "difficulty": "Medium",
    "topic": "Greedy",
    "subtopic": "Greedy Optimization",
    "pattern": "Frequency Frequency Sort",
    "secondary_patterns": [
      "Frequency Frequency Sort"
    ],
    "stage": "Advanced DP & State Compression",
    "curriculumStage": "Stage 18 — Advanced DP & State Compression",
    "roadmapPhase": "Stage 18 — Advanced DP & State Compression",
    "phase": "Stage 18 — Advanced DP & State Compression",
    "estimatedTime": 30,
    "statement": "Given the constraints and input parameters for Least Number of Unique Integers after K Removals, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Least Number of Unique Integers after K Removals."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Least Number of Unique Integers after K Removals.",
      "Leverage the optimal Greedy pattern to reduce time complexity."
    ],
    "learningObjective": "Master Greedy techniques by solving Medium problem constraints for Least Number of Unique Integers after K Removals.",
    "whyThisPattern": "When observing Greedy problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/least-number-of-unique-integers-after-k-removals/",
    "leetcode_title": "Least Number of Unique Integers after K Removals",
    "leetcode_id": 1481,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/least-number-of-unique-integers-after-k-removals/",
    "canonicalSlug": "least-number-of-unique-integers-after-k-removals",
    "canonicalUrl": "https://leetcode.com/problems/least-number-of-unique-integers-after-k-removals/",
    "url": "https://leetcode.com/problems/least-number-of-unique-integers-after-k-removals/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Least Number of Unique Integers after K Removals\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Least Number of Unique Integers after K Removals\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Least Number of Unique Integers after K Removals\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Least Number of Unique Integers after K Removals\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Least Number of Unique Integers after K Removals\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Least Number of Unique Integers after K Removals\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Least Number of Unique Integers after K Removals\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Least Number of Unique Integers after K Removals\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Least Number of Unique Integers after K Removals",
      "cpp_optimal": "// Solution for Least Number of Unique Integers after K Removals",
      "java_brute": "// Solution for Least Number of Unique Integers after K Removals",
      "java_optimal": "// Solution for Least Number of Unique Integers after K Removals",
      "python_brute": "# Solution for Least Number of Unique Integers after K Removals",
      "python_optimal": "# Solution for Least Number of Unique Integers after K Removals"
    },
    "originalOrder": 515,
    "learningOrder": 515
  },
  {
    "id": 878,
    "number": 878,
    "sequence_number": 878,
    "title": "Merge Intervals",
    "slug": "merge-intervals",
    "difficulty": "Medium",
    "topic": "Greedy",
    "subtopic": "Greedy Optimization",
    "pattern": "Sort & Sweep Line",
    "secondary_patterns": [
      "Sort & Sweep Line"
    ],
    "stage": "Advanced DP & State Compression",
    "curriculumStage": "Stage 18 — Advanced DP & State Compression",
    "roadmapPhase": "Stage 18 — Advanced DP & State Compression",
    "phase": "Stage 18 — Advanced DP & State Compression",
    "estimatedTime": 30,
    "statement": "Given the constraints and input parameters for Merge Intervals, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Merge Intervals."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Merge Intervals.",
      "Leverage the optimal Greedy pattern to reduce time complexity."
    ],
    "learningObjective": "Master Greedy techniques by solving Medium problem constraints for Merge Intervals.",
    "whyThisPattern": "When observing Greedy problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/merge-intervals/",
    "leetcode_title": "Merge Intervals",
    "leetcode_id": 56,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/merge-intervals/",
    "canonicalSlug": "merge-intervals",
    "canonicalUrl": "https://leetcode.com/problems/merge-intervals/",
    "url": "https://leetcode.com/problems/merge-intervals/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Merge Intervals\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Merge Intervals\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Merge Intervals\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Merge Intervals\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Merge Intervals\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Merge Intervals\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Merge Intervals\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Merge Intervals\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Merge Intervals",
      "cpp_optimal": "// Solution for Merge Intervals",
      "java_brute": "// Solution for Merge Intervals",
      "java_optimal": "// Solution for Merge Intervals",
      "python_brute": "# Solution for Merge Intervals",
      "python_optimal": "# Solution for Merge Intervals"
    },
    "originalOrder": 516,
    "learningOrder": 516
  },
  {
    "id": 879,
    "number": 879,
    "sequence_number": 879,
    "title": "Insert Interval",
    "slug": "insert-interval",
    "difficulty": "Medium",
    "topic": "Greedy",
    "subtopic": "Greedy Optimization",
    "pattern": "3-Stage Interval Split",
    "secondary_patterns": [
      "3-Stage Interval Split"
    ],
    "stage": "Advanced DP & State Compression",
    "curriculumStage": "Stage 18 — Advanced DP & State Compression",
    "roadmapPhase": "Stage 18 — Advanced DP & State Compression",
    "phase": "Stage 18 — Advanced DP & State Compression",
    "estimatedTime": 30,
    "statement": "Given the constraints and input parameters for Insert Interval, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Insert Interval."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Insert Interval.",
      "Leverage the optimal Greedy pattern to reduce time complexity."
    ],
    "learningObjective": "Master Greedy techniques by solving Medium problem constraints for Insert Interval.",
    "whyThisPattern": "When observing Greedy problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/insert-interval/",
    "leetcode_title": "Insert Interval",
    "leetcode_id": 57,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/insert-interval/",
    "canonicalSlug": "insert-interval",
    "canonicalUrl": "https://leetcode.com/problems/insert-interval/",
    "url": "https://leetcode.com/problems/insert-interval/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Insert Interval\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Insert Interval\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Insert Interval\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Insert Interval\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Insert Interval\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Insert Interval\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Insert Interval\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Insert Interval\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Insert Interval",
      "cpp_optimal": "// Solution for Insert Interval",
      "java_brute": "// Solution for Insert Interval",
      "java_optimal": "// Solution for Insert Interval",
      "python_brute": "# Solution for Insert Interval",
      "python_optimal": "# Solution for Insert Interval"
    },
    "originalOrder": 517,
    "learningOrder": 517
  },
  {
    "id": 880,
    "number": 880,
    "sequence_number": 880,
    "title": "Gas Station",
    "slug": "gas-station",
    "difficulty": "Medium",
    "topic": "Greedy",
    "subtopic": "Greedy Optimization",
    "pattern": "Greedy Pattern",
    "secondary_patterns": [
      "Greedy Pattern"
    ],
    "stage": "Advanced DP & State Compression",
    "curriculumStage": "Stage 18 — Advanced DP & State Compression",
    "roadmapPhase": "Stage 18 — Advanced DP & State Compression",
    "phase": "Stage 18 — Advanced DP & State Compression",
    "estimatedTime": 30,
    "statement": "Solve the **Gas Station** problem using standard Greedy techniques. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Greedy algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Greedy properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Greedy techniques by solving Medium problem constraints for Gas Station.",
    "whyThisPattern": "When observing Greedy problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/gas-station/",
    "leetcode_title": "Gas Station",
    "leetcode_id": 134,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/gas-station/",
    "canonicalSlug": "gas-station",
    "canonicalUrl": "https://leetcode.com/problems/gas-station/",
    "url": "https://leetcode.com/problems/gas-station/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Gas Station\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Gas Station\n};",
        "java": "// Java Solution for Gas Station\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Gas Station\n}",
        "python": "# Python Solution for Gas Station\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Gas Station\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Gas Station\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Gas Station\n};",
        "java": "// Optimal Java Solution for Gas Station\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Gas Station\n}",
        "python": "# Optimal Python Solution for Gas Station\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Gas Station\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Gas Station",
      "cpp_optimal": "// Solution for Gas Station",
      "java_brute": "// Solution for Gas Station",
      "java_optimal": "// Solution for Gas Station",
      "python_brute": "# Solution for Gas Station",
      "python_optimal": "# Solution for Gas Station"
    },
    "originalOrder": 518,
    "learningOrder": 518
  },
  {
    "id": 881,
    "number": 881,
    "sequence_number": 881,
    "title": "Non-overlapping Intervals",
    "slug": "non-overlapping-intervals",
    "difficulty": "Medium",
    "topic": "Greedy",
    "subtopic": "Greedy Optimization",
    "pattern": "Greedy Pattern",
    "secondary_patterns": [
      "Greedy Pattern"
    ],
    "stage": "Advanced DP & State Compression",
    "curriculumStage": "Stage 18 — Advanced DP & State Compression",
    "roadmapPhase": "Stage 18 — Advanced DP & State Compression",
    "phase": "Stage 18 — Advanced DP & State Compression",
    "estimatedTime": 30,
    "statement": "Solve the **Non-overlapping Intervals** problem using standard Greedy techniques. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Greedy algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Greedy properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Greedy techniques by solving Medium problem constraints for Non-overlapping Intervals.",
    "whyThisPattern": "When observing Greedy problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/non-overlapping-intervals/",
    "leetcode_title": "Non-overlapping Intervals",
    "leetcode_id": 435,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/non-overlapping-intervals/",
    "canonicalSlug": "non-overlapping-intervals",
    "canonicalUrl": "https://leetcode.com/problems/non-overlapping-intervals/",
    "url": "https://leetcode.com/problems/non-overlapping-intervals/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Non-overlapping Intervals\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Non-overlapping Intervals\n};",
        "java": "// Java Solution for Non-overlapping Intervals\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Non-overlapping Intervals\n}",
        "python": "# Python Solution for Non-overlapping Intervals\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Non-overlapping Intervals\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Non-overlapping Intervals\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Non-overlapping Intervals\n};",
        "java": "// Optimal Java Solution for Non-overlapping Intervals\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Non-overlapping Intervals\n}",
        "python": "# Optimal Python Solution for Non-overlapping Intervals\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Non-overlapping Intervals\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Non-overlapping Intervals",
      "cpp_optimal": "// Solution for Non-overlapping Intervals",
      "java_brute": "// Solution for Non-overlapping Intervals",
      "java_optimal": "// Solution for Non-overlapping Intervals",
      "python_brute": "# Solution for Non-overlapping Intervals",
      "python_optimal": "# Solution for Non-overlapping Intervals"
    },
    "originalOrder": 519,
    "learningOrder": 519
  },
  {
    "id": 882,
    "number": 882,
    "sequence_number": 882,
    "title": "Minimum Number of Arrows to Burst Balloons",
    "slug": "minimum-number-of-arrows-to-burst-balloons",
    "difficulty": "Medium",
    "topic": "Greedy",
    "subtopic": "Greedy Optimization",
    "pattern": "Greedy Pattern",
    "secondary_patterns": [
      "Greedy Pattern"
    ],
    "stage": "Advanced DP & State Compression",
    "curriculumStage": "Stage 18 — Advanced DP & State Compression",
    "roadmapPhase": "Stage 18 — Advanced DP & State Compression",
    "phase": "Stage 18 — Advanced DP & State Compression",
    "estimatedTime": 30,
    "statement": "Solve the **Minimum Number of Arrows to Burst Balloons** problem using standard Greedy techniques. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Greedy algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Greedy properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Greedy techniques by solving Medium problem constraints for Minimum Number of Arrows to Burst Balloons.",
    "whyThisPattern": "When observing Greedy problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/minimum-number-of-arrows-to-burst-balloons/",
    "leetcode_title": "Minimum Number of Arrows to Burst Balloons",
    "leetcode_id": 452,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/minimum-number-of-arrows-to-burst-balloons/",
    "canonicalSlug": "minimum-number-of-arrows-to-burst-balloons",
    "canonicalUrl": "https://leetcode.com/problems/minimum-number-of-arrows-to-burst-balloons/",
    "url": "https://leetcode.com/problems/minimum-number-of-arrows-to-burst-balloons/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Minimum Number of Arrows to Burst Balloons\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Minimum Number of Arrows to Burst Balloons\n};",
        "java": "// Java Solution for Minimum Number of Arrows to Burst Balloons\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Minimum Number of Arrows to Burst Balloons\n}",
        "python": "# Python Solution for Minimum Number of Arrows to Burst Balloons\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Minimum Number of Arrows to Burst Balloons\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Minimum Number of Arrows to Burst Balloons\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Minimum Number of Arrows to Burst Balloons\n};",
        "java": "// Optimal Java Solution for Minimum Number of Arrows to Burst Balloons\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Minimum Number of Arrows to Burst Balloons\n}",
        "python": "# Optimal Python Solution for Minimum Number of Arrows to Burst Balloons\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Minimum Number of Arrows to Burst Balloons\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Minimum Number of Arrows to Burst Balloons",
      "cpp_optimal": "// Solution for Minimum Number of Arrows to Burst Balloons",
      "java_brute": "// Solution for Minimum Number of Arrows to Burst Balloons",
      "java_optimal": "// Solution for Minimum Number of Arrows to Burst Balloons",
      "python_brute": "# Solution for Minimum Number of Arrows to Burst Balloons",
      "python_optimal": "# Solution for Minimum Number of Arrows to Burst Balloons"
    },
    "originalOrder": 520,
    "learningOrder": 520
  },
  {
    "id": 883,
    "number": 883,
    "sequence_number": 883,
    "title": "Task Scheduler",
    "slug": "task-scheduler",
    "difficulty": "Medium",
    "topic": "Greedy",
    "subtopic": "Greedy Optimization",
    "pattern": "Greedy Pattern",
    "secondary_patterns": [
      "Greedy Pattern"
    ],
    "stage": "Advanced DP & State Compression",
    "curriculumStage": "Stage 18 — Advanced DP & State Compression",
    "roadmapPhase": "Stage 18 — Advanced DP & State Compression",
    "phase": "Stage 18 — Advanced DP & State Compression",
    "estimatedTime": 30,
    "statement": "Solve the **Task Scheduler** problem using standard Greedy techniques. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Greedy algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Greedy properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Greedy techniques by solving Medium problem constraints for Task Scheduler.",
    "whyThisPattern": "When observing Greedy problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/task-scheduler/",
    "leetcode_title": "Task Scheduler",
    "leetcode_id": 621,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/task-scheduler/",
    "canonicalSlug": "task-scheduler",
    "canonicalUrl": "https://leetcode.com/problems/task-scheduler/",
    "url": "https://leetcode.com/problems/task-scheduler/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Task Scheduler\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Task Scheduler\n};",
        "java": "// Java Solution for Task Scheduler\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Task Scheduler\n}",
        "python": "# Python Solution for Task Scheduler\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Task Scheduler\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Task Scheduler\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Task Scheduler\n};",
        "java": "// Optimal Java Solution for Task Scheduler\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Task Scheduler\n}",
        "python": "# Optimal Python Solution for Task Scheduler\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Task Scheduler\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Task Scheduler",
      "cpp_optimal": "// Solution for Task Scheduler",
      "java_brute": "// Solution for Task Scheduler",
      "java_optimal": "// Solution for Task Scheduler",
      "python_brute": "# Solution for Task Scheduler",
      "python_optimal": "# Solution for Task Scheduler"
    },
    "originalOrder": 521,
    "learningOrder": 521
  },
  {
    "id": 884,
    "number": 884,
    "sequence_number": 884,
    "title": "Subdomain Visit Count",
    "slug": "subdomain-visit-count",
    "difficulty": "Medium",
    "topic": "Hashing",
    "subtopic": "Hashing Optimization",
    "pattern": "Subdomain Frequency Map",
    "secondary_patterns": [
      "Subdomain Frequency Map"
    ],
    "stage": "Advanced DP & State Compression",
    "curriculumStage": "Stage 18 — Advanced DP & State Compression",
    "roadmapPhase": "Stage 18 — Advanced DP & State Compression",
    "phase": "Stage 18 — Advanced DP & State Compression",
    "estimatedTime": 30,
    "statement": "Given the constraints and input parameters for Subdomain Visit Count, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Subdomain Visit Count."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Subdomain Visit Count.",
      "Leverage the optimal Hashing pattern to reduce time complexity."
    ],
    "learningObjective": "Master Hashing techniques by solving Medium problem constraints for Subdomain Visit Count.",
    "whyThisPattern": "When observing Hashing problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/subdomain-visit-count/",
    "leetcode_title": "Subdomain Visit Count",
    "leetcode_id": 811,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/subdomain-visit-count/",
    "canonicalSlug": "subdomain-visit-count",
    "canonicalUrl": "https://leetcode.com/problems/subdomain-visit-count/",
    "url": "https://leetcode.com/problems/subdomain-visit-count/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Subdomain Visit Count\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Subdomain Visit Count\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Subdomain Visit Count\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Subdomain Visit Count\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Subdomain Visit Count\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Subdomain Visit Count\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Subdomain Visit Count\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Subdomain Visit Count\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Subdomain Visit Count",
      "cpp_optimal": "// Solution for Subdomain Visit Count",
      "java_brute": "// Solution for Subdomain Visit Count",
      "java_optimal": "// Solution for Subdomain Visit Count",
      "python_brute": "# Solution for Subdomain Visit Count",
      "python_optimal": "# Solution for Subdomain Visit Count"
    },
    "originalOrder": 522,
    "learningOrder": 522
  },
  {
    "id": 885,
    "number": 885,
    "sequence_number": 885,
    "title": "Vowel Spellchecker",
    "slug": "vowel-spellchecker",
    "difficulty": "Medium",
    "topic": "Hashing",
    "subtopic": "Hashing Optimization",
    "pattern": "Multiple Precedence HashMaps",
    "secondary_patterns": [
      "Multiple Precedence HashMaps"
    ],
    "stage": "Advanced DP & State Compression",
    "curriculumStage": "Stage 18 — Advanced DP & State Compression",
    "roadmapPhase": "Stage 18 — Advanced DP & State Compression",
    "phase": "Stage 18 — Advanced DP & State Compression",
    "estimatedTime": 30,
    "statement": "Given the constraints and input parameters for Vowel Spellchecker, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Vowel Spellchecker."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Vowel Spellchecker.",
      "Leverage the optimal Hashing pattern to reduce time complexity."
    ],
    "learningObjective": "Master Hashing techniques by solving Medium problem constraints for Vowel Spellchecker.",
    "whyThisPattern": "When observing Hashing problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/vowel-spellchecker/",
    "leetcode_title": "Vowel Spellchecker",
    "leetcode_id": 966,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/vowel-spellchecker/",
    "canonicalSlug": "vowel-spellchecker",
    "canonicalUrl": "https://leetcode.com/problems/vowel-spellchecker/",
    "url": "https://leetcode.com/problems/vowel-spellchecker/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Vowel Spellchecker\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Vowel Spellchecker\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Vowel Spellchecker\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Vowel Spellchecker\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Vowel Spellchecker\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Vowel Spellchecker\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Vowel Spellchecker\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Vowel Spellchecker\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Vowel Spellchecker",
      "cpp_optimal": "// Solution for Vowel Spellchecker",
      "java_brute": "// Solution for Vowel Spellchecker",
      "java_optimal": "// Solution for Vowel Spellchecker",
      "python_brute": "# Solution for Vowel Spellchecker",
      "python_optimal": "# Solution for Vowel Spellchecker"
    },
    "originalOrder": 523,
    "learningOrder": 523
  },
  {
    "id": 886,
    "number": 886,
    "sequence_number": 886,
    "title": "Number of Great Partitions",
    "slug": "number-of-great-partitions",
    "difficulty": "Hard",
    "topic": "Dynamic Programming",
    "subtopic": "Dynamic Programming Optimization",
    "pattern": "Knapsack Complement DP",
    "secondary_patterns": [
      "Knapsack Complement DP"
    ],
    "stage": "Advanced DP & State Compression",
    "curriculumStage": "Stage 18 — Advanced DP & State Compression",
    "roadmapPhase": "Stage 18 — Advanced DP & State Compression",
    "phase": "Stage 18 — Advanced DP & State Compression",
    "estimatedTime": 45,
    "statement": "Given the constraints and input parameters for Number of Great Partitions, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Number of Great Partitions."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Number of Great Partitions.",
      "Leverage the optimal Dynamic Programming pattern to reduce time complexity."
    ],
    "learningObjective": "Master Dynamic Programming techniques by solving Hard problem constraints for Number of Great Partitions.",
    "whyThisPattern": "When observing Dynamic Programming problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/number-of-great-partitions/",
    "leetcode_title": "Number of Great Partitions",
    "leetcode_id": 2518,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/number-of-great-partitions/",
    "canonicalSlug": "number-of-great-partitions",
    "canonicalUrl": "https://leetcode.com/problems/number-of-great-partitions/",
    "url": "https://leetcode.com/problems/number-of-great-partitions/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Number of Great Partitions\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Number of Great Partitions\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Number of Great Partitions\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Number of Great Partitions\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Number of Great Partitions\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Number of Great Partitions\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Number of Great Partitions\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Number of Great Partitions\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Number of Great Partitions",
      "cpp_optimal": "// Solution for Number of Great Partitions",
      "java_brute": "// Solution for Number of Great Partitions",
      "java_optimal": "// Solution for Number of Great Partitions",
      "python_brute": "# Solution for Number of Great Partitions",
      "python_optimal": "# Solution for Number of Great Partitions"
    },
    "originalOrder": 846,
    "learningOrder": 846
  },
  {
    "id": 887,
    "number": 887,
    "sequence_number": 887,
    "title": "Number of Music Playlists",
    "slug": "number-of-music-playlists",
    "difficulty": "Hard",
    "topic": "Dynamic Programming",
    "subtopic": "Dynamic Programming Optimization",
    "pattern": "2D Combination Playlists DP",
    "secondary_patterns": [
      "2D Combination Playlists DP"
    ],
    "stage": "Advanced DP & State Compression",
    "curriculumStage": "Stage 18 — Advanced DP & State Compression",
    "roadmapPhase": "Stage 18 — Advanced DP & State Compression",
    "phase": "Stage 18 — Advanced DP & State Compression",
    "estimatedTime": 45,
    "statement": "Given the constraints and input parameters for Number of Music Playlists, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Number of Music Playlists."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Number of Music Playlists.",
      "Leverage the optimal Dynamic Programming pattern to reduce time complexity."
    ],
    "learningObjective": "Master Dynamic Programming techniques by solving Hard problem constraints for Number of Music Playlists.",
    "whyThisPattern": "When observing Dynamic Programming problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/number-of-music-playlists/",
    "leetcode_title": "Number of Music Playlists",
    "leetcode_id": 920,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/number-of-music-playlists/",
    "canonicalSlug": "number-of-music-playlists",
    "canonicalUrl": "https://leetcode.com/problems/number-of-music-playlists/",
    "url": "https://leetcode.com/problems/number-of-music-playlists/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Number of Music Playlists\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Number of Music Playlists\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Number of Music Playlists\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Number of Music Playlists\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Number of Music Playlists\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Number of Music Playlists\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Number of Music Playlists\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Number of Music Playlists\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Number of Music Playlists",
      "cpp_optimal": "// Solution for Number of Music Playlists",
      "java_brute": "// Solution for Number of Music Playlists",
      "java_optimal": "// Solution for Number of Music Playlists",
      "python_brute": "# Solution for Number of Music Playlists",
      "python_optimal": "# Solution for Number of Music Playlists"
    },
    "originalOrder": 847,
    "learningOrder": 847
  },
  {
    "id": 888,
    "number": 888,
    "sequence_number": 888,
    "title": "Profitable Schemes",
    "slug": "profitable-schemes",
    "difficulty": "Hard",
    "topic": "Dynamic Programming",
    "subtopic": "Dynamic Programming Optimization",
    "pattern": "3D Knapsack Profit DP",
    "secondary_patterns": [
      "3D Knapsack Profit DP"
    ],
    "stage": "Advanced DP & State Compression",
    "curriculumStage": "Stage 18 — Advanced DP & State Compression",
    "roadmapPhase": "Stage 18 — Advanced DP & State Compression",
    "phase": "Stage 18 — Advanced DP & State Compression",
    "estimatedTime": 45,
    "statement": "Given the constraints and input parameters for Profitable Schemes, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Profitable Schemes."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Profitable Schemes.",
      "Leverage the optimal Dynamic Programming pattern to reduce time complexity."
    ],
    "learningObjective": "Master Dynamic Programming techniques by solving Hard problem constraints for Profitable Schemes.",
    "whyThisPattern": "When observing Dynamic Programming problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/profitable-schemes/",
    "leetcode_title": "Profitable Schemes",
    "leetcode_id": 879,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/profitable-schemes/",
    "canonicalSlug": "profitable-schemes",
    "canonicalUrl": "https://leetcode.com/problems/profitable-schemes/",
    "url": "https://leetcode.com/problems/profitable-schemes/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Profitable Schemes\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Profitable Schemes\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Profitable Schemes\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Profitable Schemes\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Profitable Schemes\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Profitable Schemes\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Profitable Schemes\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Profitable Schemes\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Profitable Schemes",
      "cpp_optimal": "// Solution for Profitable Schemes",
      "java_brute": "// Solution for Profitable Schemes",
      "java_optimal": "// Solution for Profitable Schemes",
      "python_brute": "# Solution for Profitable Schemes",
      "python_optimal": "# Solution for Profitable Schemes"
    },
    "originalOrder": 848,
    "learningOrder": 848
  },
  {
    "id": 889,
    "number": 889,
    "sequence_number": 889,
    "title": "Shortest Common Supersequence ",
    "slug": "shortest-common-supersequence",
    "difficulty": "Hard",
    "topic": "Dynamic Programming",
    "subtopic": "Dynamic Programming Optimization",
    "pattern": "LCS Reconstruction DP",
    "secondary_patterns": [
      "LCS Reconstruction DP"
    ],
    "stage": "Advanced DP & State Compression",
    "curriculumStage": "Stage 18 — Advanced DP & State Compression",
    "roadmapPhase": "Stage 18 — Advanced DP & State Compression",
    "phase": "Stage 18 — Advanced DP & State Compression",
    "estimatedTime": 45,
    "statement": "Given the constraints and input parameters for Shortest Common Supersequence, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Shortest Common Supersequence."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Shortest Common Supersequence.",
      "Leverage the optimal Dynamic Programming pattern to reduce time complexity."
    ],
    "learningObjective": "Master Dynamic Programming techniques by solving Hard problem constraints for Shortest Common Supersequence .",
    "whyThisPattern": "When observing Dynamic Programming problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/shortest-common-supersequence/",
    "leetcode_title": "Shortest Common Supersequence ",
    "leetcode_id": 1092,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/shortest-common-supersequence/",
    "canonicalSlug": "shortest-common-supersequence",
    "canonicalUrl": "https://leetcode.com/problems/shortest-common-supersequence/",
    "url": "https://leetcode.com/problems/shortest-common-supersequence/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Shortest Common Supersequence\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Shortest Common Supersequence\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Shortest Common Supersequence\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Shortest Common Supersequence\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Shortest Common Supersequence\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Shortest Common Supersequence\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Shortest Common Supersequence\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Shortest Common Supersequence\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Shortest Common Supersequence ",
      "cpp_optimal": "// Solution for Shortest Common Supersequence ",
      "java_brute": "// Solution for Shortest Common Supersequence ",
      "java_optimal": "// Solution for Shortest Common Supersequence ",
      "python_brute": "# Solution for Shortest Common Supersequence ",
      "python_optimal": "# Solution for Shortest Common Supersequence "
    },
    "originalOrder": 849,
    "learningOrder": 849
  },
  {
    "id": 890,
    "number": 890,
    "sequence_number": 890,
    "title": "Delivering Boxes from Storage to Ports",
    "slug": "delivering-boxes-from-storage-to-ports",
    "difficulty": "Hard",
    "topic": "Dynamic Programming",
    "subtopic": "Dynamic Programming Optimization",
    "pattern": "Monotonic Queue DP",
    "secondary_patterns": [
      "Monotonic Queue DP"
    ],
    "stage": "Advanced DP & State Compression",
    "curriculumStage": "Stage 18 — Advanced DP & State Compression",
    "roadmapPhase": "Stage 18 — Advanced DP & State Compression",
    "phase": "Stage 18 — Advanced DP & State Compression",
    "estimatedTime": 45,
    "statement": "Given the constraints and input parameters for Delivering Boxes from Storage to Ports, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Delivering Boxes from Storage to Ports."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Delivering Boxes from Storage to Ports.",
      "Leverage the optimal Dynamic Programming pattern to reduce time complexity."
    ],
    "learningObjective": "Master Dynamic Programming techniques by solving Hard problem constraints for Delivering Boxes from Storage to Ports.",
    "whyThisPattern": "When observing Dynamic Programming problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/delivering-boxes-from-storage-to-ports/",
    "leetcode_title": "Delivering Boxes from Storage to Ports",
    "leetcode_id": 1687,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/delivering-boxes-from-storage-to-ports/",
    "canonicalSlug": "delivering-boxes-from-storage-to-ports",
    "canonicalUrl": "https://leetcode.com/problems/delivering-boxes-from-storage-to-ports/",
    "url": "https://leetcode.com/problems/delivering-boxes-from-storage-to-ports/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Delivering Boxes from Storage to Ports\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Delivering Boxes from Storage to Ports\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Delivering Boxes from Storage to Ports\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Delivering Boxes from Storage to Ports\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Delivering Boxes from Storage to Ports\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Delivering Boxes from Storage to Ports\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Delivering Boxes from Storage to Ports\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Delivering Boxes from Storage to Ports\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Delivering Boxes from Storage to Ports",
      "cpp_optimal": "// Solution for Delivering Boxes from Storage to Ports",
      "java_brute": "// Solution for Delivering Boxes from Storage to Ports",
      "java_optimal": "// Solution for Delivering Boxes from Storage to Ports",
      "python_brute": "# Solution for Delivering Boxes from Storage to Ports",
      "python_optimal": "# Solution for Delivering Boxes from Storage to Ports"
    },
    "originalOrder": 850,
    "learningOrder": 850
  },
  {
    "id": 891,
    "number": 891,
    "sequence_number": 891,
    "title": "Maximum Number of Non-overlapping Palindrome Substrings",
    "slug": "maximum-number-of-non-overlapping-palindrome-substrings",
    "difficulty": "Hard",
    "topic": "Dynamic Programming",
    "subtopic": "Dynamic Programming Optimization",
    "pattern": "Palindrome Center + DP",
    "secondary_patterns": [
      "Palindrome Center + DP"
    ],
    "stage": "Advanced DP & State Compression",
    "curriculumStage": "Stage 18 — Advanced DP & State Compression",
    "roadmapPhase": "Stage 18 — Advanced DP & State Compression",
    "phase": "Stage 18 — Advanced DP & State Compression",
    "estimatedTime": 45,
    "statement": "Given the constraints and input parameters for Maximum Number of Non-overlapping Palindrome Substrings, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Maximum Number of Non-overlapping Palindrome Substrings."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Maximum Number of Non-overlapping Palindrome Substrings.",
      "Leverage the optimal Dynamic Programming pattern to reduce time complexity."
    ],
    "learningObjective": "Master Dynamic Programming techniques by solving Hard problem constraints for Maximum Number of Non-overlapping Palindrome Substrings.",
    "whyThisPattern": "When observing Dynamic Programming problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/maximum-number-of-non-overlapping-palindrome-substrings/",
    "leetcode_title": "Maximum Number of Non-overlapping Palindrome Substrings",
    "leetcode_id": 2472,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/maximum-number-of-non-overlapping-palindrome-substrings/",
    "canonicalSlug": "maximum-number-of-non-overlapping-palindrome-substrings",
    "canonicalUrl": "https://leetcode.com/problems/maximum-number-of-non-overlapping-palindrome-substrings/",
    "url": "https://leetcode.com/problems/maximum-number-of-non-overlapping-palindrome-substrings/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Maximum Number of Non-overlapping Palindrome Substrings\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Maximum Number of Non-overlapping Palindrome Substrings\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Maximum Number of Non-overlapping Palindrome Substrings\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Maximum Number of Non-overlapping Palindrome Substrings\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Maximum Number of Non-overlapping Palindrome Substrings\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Maximum Number of Non-overlapping Palindrome Substrings\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Maximum Number of Non-overlapping Palindrome Substrings\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Maximum Number of Non-overlapping Palindrome Substrings\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Maximum Number of Non-overlapping Palindrome Substrings",
      "cpp_optimal": "// Solution for Maximum Number of Non-overlapping Palindrome Substrings",
      "java_brute": "// Solution for Maximum Number of Non-overlapping Palindrome Substrings",
      "java_optimal": "// Solution for Maximum Number of Non-overlapping Palindrome Substrings",
      "python_brute": "# Solution for Maximum Number of Non-overlapping Palindrome Substrings",
      "python_optimal": "# Solution for Maximum Number of Non-overlapping Palindrome Substrings"
    },
    "originalOrder": 851,
    "learningOrder": 851
  },
  {
    "id": 892,
    "number": 892,
    "sequence_number": 892,
    "title": "Number of Beautiful Partitions",
    "slug": "number-of-beautiful-partitions",
    "difficulty": "Hard",
    "topic": "Dynamic Programming",
    "subtopic": "Dynamic Programming Optimization",
    "pattern": "Prime Split Interval DP",
    "secondary_patterns": [
      "Prime Split Interval DP"
    ],
    "stage": "Advanced DP & State Compression",
    "curriculumStage": "Stage 18 — Advanced DP & State Compression",
    "roadmapPhase": "Stage 18 — Advanced DP & State Compression",
    "phase": "Stage 18 — Advanced DP & State Compression",
    "estimatedTime": 45,
    "statement": "Given the constraints and input parameters for Number of Beautiful Partitions, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Number of Beautiful Partitions."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Number of Beautiful Partitions.",
      "Leverage the optimal Dynamic Programming pattern to reduce time complexity."
    ],
    "learningObjective": "Master Dynamic Programming techniques by solving Hard problem constraints for Number of Beautiful Partitions.",
    "whyThisPattern": "When observing Dynamic Programming problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/number-of-beautiful-partitions/",
    "leetcode_title": "Number of Beautiful Partitions",
    "leetcode_id": 2478,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/number-of-beautiful-partitions/",
    "canonicalSlug": "number-of-beautiful-partitions",
    "canonicalUrl": "https://leetcode.com/problems/number-of-beautiful-partitions/",
    "url": "https://leetcode.com/problems/number-of-beautiful-partitions/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Number of Beautiful Partitions\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Number of Beautiful Partitions\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Number of Beautiful Partitions\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Number of Beautiful Partitions\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Number of Beautiful Partitions\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Number of Beautiful Partitions\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Number of Beautiful Partitions\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Number of Beautiful Partitions\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Number of Beautiful Partitions",
      "cpp_optimal": "// Solution for Number of Beautiful Partitions",
      "java_brute": "// Solution for Number of Beautiful Partitions",
      "java_optimal": "// Solution for Number of Beautiful Partitions",
      "python_brute": "# Solution for Number of Beautiful Partitions",
      "python_optimal": "# Solution for Number of Beautiful Partitions"
    },
    "originalOrder": 852,
    "learningOrder": 852
  },
  {
    "id": 893,
    "number": 893,
    "sequence_number": 893,
    "title": "Minimum Cost to Split an Array",
    "slug": "minimum-cost-to-split-an-array",
    "difficulty": "Hard",
    "topic": "Dynamic Programming",
    "subtopic": "Dynamic Programming Optimization",
    "pattern": "1D Partition Trim DP",
    "secondary_patterns": [
      "1D Partition Trim DP"
    ],
    "stage": "Advanced DP & State Compression",
    "curriculumStage": "Stage 18 — Advanced DP & State Compression",
    "roadmapPhase": "Stage 18 — Advanced DP & State Compression",
    "phase": "Stage 18 — Advanced DP & State Compression",
    "estimatedTime": 45,
    "statement": "Given the constraints and input parameters for Minimum Cost to Split an Array, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Minimum Cost to Split an Array."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Minimum Cost to Split an Array.",
      "Leverage the optimal Dynamic Programming pattern to reduce time complexity."
    ],
    "learningObjective": "Master Dynamic Programming techniques by solving Hard problem constraints for Minimum Cost to Split an Array.",
    "whyThisPattern": "When observing Dynamic Programming problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/minimum-cost-to-split-an-array/",
    "leetcode_title": "Minimum Cost to Split an Array",
    "leetcode_id": 2547,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/minimum-cost-to-split-an-array/",
    "canonicalSlug": "minimum-cost-to-split-an-array",
    "canonicalUrl": "https://leetcode.com/problems/minimum-cost-to-split-an-array/",
    "url": "https://leetcode.com/problems/minimum-cost-to-split-an-array/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Minimum Cost to Split an Array\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Minimum Cost to Split an Array\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Minimum Cost to Split an Array\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Minimum Cost to Split an Array\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Minimum Cost to Split an Array\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Minimum Cost to Split an Array\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Minimum Cost to Split an Array\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Minimum Cost to Split an Array\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Minimum Cost to Split an Array",
      "cpp_optimal": "// Solution for Minimum Cost to Split an Array",
      "java_brute": "// Solution for Minimum Cost to Split an Array",
      "java_optimal": "// Solution for Minimum Cost to Split an Array",
      "python_brute": "# Solution for Minimum Cost to Split an Array",
      "python_optimal": "# Solution for Minimum Cost to Split an Array"
    },
    "originalOrder": 853,
    "learningOrder": 853
  },
  {
    "id": 894,
    "number": 894,
    "sequence_number": 894,
    "title": "Maximum Value of K Coins From Piles",
    "slug": "maximum-value-of-k-coins-from-piles",
    "difficulty": "Hard",
    "topic": "Dynamic Programming",
    "subtopic": "Dynamic Programming Optimization",
    "pattern": "Prefix Sum Knapsack DP",
    "secondary_patterns": [
      "Prefix Sum Knapsack DP"
    ],
    "stage": "Advanced DP & State Compression",
    "curriculumStage": "Stage 18 — Advanced DP & State Compression",
    "roadmapPhase": "Stage 18 — Advanced DP & State Compression",
    "phase": "Stage 18 — Advanced DP & State Compression",
    "estimatedTime": 45,
    "statement": "Given the constraints and input parameters for Maximum Value of K Coins From Piles, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Maximum Value of K Coins From Piles."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Maximum Value of K Coins From Piles.",
      "Leverage the optimal Dynamic Programming pattern to reduce time complexity."
    ],
    "learningObjective": "Master Dynamic Programming techniques by solving Hard problem constraints for Maximum Value of K Coins From Piles.",
    "whyThisPattern": "When observing Dynamic Programming problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/maximum-value-of-k-coins-from-piles/",
    "leetcode_title": "Maximum Value of K Coins From Piles",
    "leetcode_id": 2218,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/maximum-value-of-k-coins-from-piles/",
    "canonicalSlug": "maximum-value-of-k-coins-from-piles",
    "canonicalUrl": "https://leetcode.com/problems/maximum-value-of-k-coins-from-piles/",
    "url": "https://leetcode.com/problems/maximum-value-of-k-coins-from-piles/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Maximum Value of K Coins From Piles\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Maximum Value of K Coins From Piles\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Maximum Value of K Coins From Piles\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Maximum Value of K Coins From Piles\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Maximum Value of K Coins From Piles\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Maximum Value of K Coins From Piles\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Maximum Value of K Coins From Piles\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Maximum Value of K Coins From Piles\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Maximum Value of K Coins From Piles",
      "cpp_optimal": "// Solution for Maximum Value of K Coins From Piles",
      "java_brute": "// Solution for Maximum Value of K Coins From Piles",
      "java_optimal": "// Solution for Maximum Value of K Coins From Piles",
      "python_brute": "# Solution for Maximum Value of K Coins From Piles",
      "python_optimal": "# Solution for Maximum Value of K Coins From Piles"
    },
    "originalOrder": 854,
    "learningOrder": 854
  },
  {
    "id": 895,
    "number": 895,
    "sequence_number": 895,
    "title": "Substring With Largest Variance",
    "slug": "substring-with-largest-variance",
    "difficulty": "Hard",
    "topic": "Dynamic Programming",
    "subtopic": "Dynamic Programming Optimization",
    "pattern": "2-Char Variance Kadane DP",
    "secondary_patterns": [
      "2-Char Variance Kadane DP"
    ],
    "stage": "Advanced DP & State Compression",
    "curriculumStage": "Stage 18 — Advanced DP & State Compression",
    "roadmapPhase": "Stage 18 — Advanced DP & State Compression",
    "phase": "Stage 18 — Advanced DP & State Compression",
    "estimatedTime": 45,
    "statement": "Given the constraints and input parameters for Substring With Largest Variance, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Substring With Largest Variance."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Substring With Largest Variance.",
      "Leverage the optimal Dynamic Programming pattern to reduce time complexity."
    ],
    "learningObjective": "Master Dynamic Programming techniques by solving Hard problem constraints for Substring With Largest Variance.",
    "whyThisPattern": "When observing Dynamic Programming problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/substring-with-largest-variance/",
    "leetcode_title": "Substring With Largest Variance",
    "leetcode_id": 2272,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/substring-with-largest-variance/",
    "canonicalSlug": "substring-with-largest-variance",
    "canonicalUrl": "https://leetcode.com/problems/substring-with-largest-variance/",
    "url": "https://leetcode.com/problems/substring-with-largest-variance/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Substring With Largest Variance\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Substring With Largest Variance\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Substring With Largest Variance\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Substring With Largest Variance\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Substring With Largest Variance\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Substring With Largest Variance\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Substring With Largest Variance\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Substring With Largest Variance\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Substring With Largest Variance",
      "cpp_optimal": "// Solution for Substring With Largest Variance",
      "java_brute": "// Solution for Substring With Largest Variance",
      "java_optimal": "// Solution for Substring With Largest Variance",
      "python_brute": "# Solution for Substring With Largest Variance",
      "python_optimal": "# Solution for Substring With Largest Variance"
    },
    "originalOrder": 855,
    "learningOrder": 855
  },
  {
    "id": 896,
    "number": 896,
    "sequence_number": 896,
    "title": "Number of Increasing Paths in a Grid",
    "slug": "number-of-increasing-paths-in-a-grid",
    "difficulty": "Hard",
    "topic": "Dynamic Programming",
    "subtopic": "Dynamic Programming Optimization",
    "pattern": "2D Grid DFS Memo DP",
    "secondary_patterns": [
      "2D Grid DFS Memo DP"
    ],
    "stage": "Advanced DP & State Compression",
    "curriculumStage": "Stage 18 — Advanced DP & State Compression",
    "roadmapPhase": "Stage 18 — Advanced DP & State Compression",
    "phase": "Stage 18 — Advanced DP & State Compression",
    "estimatedTime": 45,
    "statement": "Given the constraints and input parameters for Number of Increasing Paths in a Grid, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Number of Increasing Paths in a Grid."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Number of Increasing Paths in a Grid.",
      "Leverage the optimal Dynamic Programming pattern to reduce time complexity."
    ],
    "learningObjective": "Master Dynamic Programming techniques by solving Hard problem constraints for Number of Increasing Paths in a Grid.",
    "whyThisPattern": "When observing Dynamic Programming problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/number-of-increasing-paths-in-a-grid/",
    "leetcode_title": "Number of Increasing Paths in a Grid",
    "leetcode_id": 2328,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/number-of-increasing-paths-in-a-grid/",
    "canonicalSlug": "number-of-increasing-paths-in-a-grid",
    "canonicalUrl": "https://leetcode.com/problems/number-of-increasing-paths-in-a-grid/",
    "url": "https://leetcode.com/problems/number-of-increasing-paths-in-a-grid/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Number of Increasing Paths in a Grid\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Number of Increasing Paths in a Grid\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Number of Increasing Paths in a Grid\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Number of Increasing Paths in a Grid\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Number of Increasing Paths in a Grid\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Number of Increasing Paths in a Grid\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Number of Increasing Paths in a Grid\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Number of Increasing Paths in a Grid\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Number of Increasing Paths in a Grid",
      "cpp_optimal": "// Solution for Number of Increasing Paths in a Grid",
      "java_brute": "// Solution for Number of Increasing Paths in a Grid",
      "java_optimal": "// Solution for Number of Increasing Paths in a Grid",
      "python_brute": "# Solution for Number of Increasing Paths in a Grid",
      "python_optimal": "# Solution for Number of Increasing Paths in a Grid"
    },
    "originalOrder": 856,
    "learningOrder": 856
  },
  {
    "id": 897,
    "number": 897,
    "sequence_number": 897,
    "title": "Minimum Insertion Steps to Make a String Palindrome",
    "slug": "minimum-insertion-steps-to-make-a-string-palindrome",
    "difficulty": "Hard",
    "topic": "Dynamic Programming",
    "subtopic": "Dynamic Programming Optimization",
    "pattern": "LCS String Recurrence",
    "secondary_patterns": [
      "LCS String Recurrence"
    ],
    "stage": "Advanced DP & State Compression",
    "curriculumStage": "Stage 18 — Advanced DP & State Compression",
    "roadmapPhase": "Stage 18 — Advanced DP & State Compression",
    "phase": "Stage 18 — Advanced DP & State Compression",
    "estimatedTime": 45,
    "statement": "Given the constraints and input parameters for Minimum Insertion Steps to Make a String Palindrome, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Minimum Insertion Steps to Make a String Palindrome."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Minimum Insertion Steps to Make a String Palindrome.",
      "Leverage the optimal Dynamic Programming pattern to reduce time complexity."
    ],
    "learningObjective": "Master Dynamic Programming techniques by solving Hard problem constraints for Minimum Insertion Steps to Make a String Palindrome.",
    "whyThisPattern": "When observing Dynamic Programming problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/minimum-insertion-steps-to-make-a-string-palindrome/",
    "leetcode_title": "Minimum Insertion Steps to Make a String Palindrome",
    "leetcode_id": 1312,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/minimum-insertion-steps-to-make-a-string-palindrome/",
    "canonicalSlug": "minimum-insertion-steps-to-make-a-string-palindrome",
    "canonicalUrl": "https://leetcode.com/problems/minimum-insertion-steps-to-make-a-string-palindrome/",
    "url": "https://leetcode.com/problems/minimum-insertion-steps-to-make-a-string-palindrome/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Minimum Insertion Steps to Make a String Palindrome\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Minimum Insertion Steps to Make a String Palindrome\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Minimum Insertion Steps to Make a String Palindrome\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Minimum Insertion Steps to Make a String Palindrome\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Minimum Insertion Steps to Make a String Palindrome\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Minimum Insertion Steps to Make a String Palindrome\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Minimum Insertion Steps to Make a String Palindrome\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Minimum Insertion Steps to Make a String Palindrome\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Minimum Insertion Steps to Make a String Palindrome",
      "cpp_optimal": "// Solution for Minimum Insertion Steps to Make a String Palindrome",
      "java_brute": "// Solution for Minimum Insertion Steps to Make a String Palindrome",
      "java_optimal": "// Solution for Minimum Insertion Steps to Make a String Palindrome",
      "python_brute": "# Solution for Minimum Insertion Steps to Make a String Palindrome",
      "python_optimal": "# Solution for Minimum Insertion Steps to Make a String Palindrome"
    },
    "originalOrder": 857,
    "learningOrder": 857
  },
  {
    "id": 898,
    "number": 898,
    "sequence_number": 898,
    "title": "Count All Valid Pickup and Delivery Options",
    "slug": "count-all-valid-pickup-and-delivery-options",
    "difficulty": "Hard",
    "topic": "Dynamic Programming",
    "subtopic": "Dynamic Programming Optimization",
    "pattern": "Combinatorics Permutations DP",
    "secondary_patterns": [
      "Combinatorics Permutations DP"
    ],
    "stage": "Advanced DP & State Compression",
    "curriculumStage": "Stage 18 — Advanced DP & State Compression",
    "roadmapPhase": "Stage 18 — Advanced DP & State Compression",
    "phase": "Stage 18 — Advanced DP & State Compression",
    "estimatedTime": 45,
    "statement": "Given the constraints and input parameters for Count All Valid Pickup and Delivery Options, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Count All Valid Pickup and Delivery Options."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Count All Valid Pickup and Delivery Options.",
      "Leverage the optimal Dynamic Programming pattern to reduce time complexity."
    ],
    "learningObjective": "Master Dynamic Programming techniques by solving Hard problem constraints for Count All Valid Pickup and Delivery Options.",
    "whyThisPattern": "When observing Dynamic Programming problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/count-all-valid-pickup-and-delivery-options/",
    "leetcode_title": "Count All Valid Pickup and Delivery Options",
    "leetcode_id": 1359,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/count-all-valid-pickup-and-delivery-options/",
    "canonicalSlug": "count-all-valid-pickup-and-delivery-options",
    "canonicalUrl": "https://leetcode.com/problems/count-all-valid-pickup-and-delivery-options/",
    "url": "https://leetcode.com/problems/count-all-valid-pickup-and-delivery-options/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Count All Valid Pickup and Delivery Options\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Count All Valid Pickup and Delivery Options\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Count All Valid Pickup and Delivery Options\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Count All Valid Pickup and Delivery Options\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Count All Valid Pickup and Delivery Options\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Count All Valid Pickup and Delivery Options\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Count All Valid Pickup and Delivery Options\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Count All Valid Pickup and Delivery Options\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Count All Valid Pickup and Delivery Options",
      "cpp_optimal": "// Solution for Count All Valid Pickup and Delivery Options",
      "java_brute": "// Solution for Count All Valid Pickup and Delivery Options",
      "java_optimal": "// Solution for Count All Valid Pickup and Delivery Options",
      "python_brute": "# Solution for Count All Valid Pickup and Delivery Options",
      "python_optimal": "# Solution for Count All Valid Pickup and Delivery Options"
    },
    "originalOrder": 858,
    "learningOrder": 858
  },
  {
    "id": 899,
    "number": 899,
    "sequence_number": 899,
    "title": "Number of Ways to Paint N × 3 Grid",
    "slug": "number-of-ways-to-paint-n-3-grid",
    "difficulty": "Hard",
    "topic": "Dynamic Programming",
    "subtopic": "Dynamic Programming Optimization",
    "pattern": "State Transition Color DP",
    "secondary_patterns": [
      "State Transition Color DP"
    ],
    "stage": "Advanced DP & State Compression",
    "curriculumStage": "Stage 18 — Advanced DP & State Compression",
    "roadmapPhase": "Stage 18 — Advanced DP & State Compression",
    "phase": "Stage 18 — Advanced DP & State Compression",
    "estimatedTime": 45,
    "statement": "Given the constraints and input parameters for Number of Ways to Paint N 3 Grid, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Number of Ways to Paint N 3 Grid."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Number of Ways to Paint N 3 Grid.",
      "Leverage the optimal Dynamic Programming pattern to reduce time complexity."
    ],
    "learningObjective": "Master Dynamic Programming techniques by solving Hard problem constraints for Number of Ways to Paint N × 3 Grid.",
    "whyThisPattern": "When observing Dynamic Programming problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/number-of-ways-to-paint-n-3-grid/",
    "leetcode_title": "Number of Ways to Paint N × 3 Grid",
    "leetcode_id": 1411,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/number-of-ways-to-paint-n-3-grid/",
    "canonicalSlug": "number-of-ways-to-paint-n-3-grid",
    "canonicalUrl": "https://leetcode.com/problems/number-of-ways-to-paint-n-3-grid/",
    "url": "https://leetcode.com/problems/number-of-ways-to-paint-n-3-grid/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Number of Ways to Paint N 3 Grid\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Number of Ways to Paint N 3 Grid\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Number of Ways to Paint N 3 Grid\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Number of Ways to Paint N 3 Grid\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Number of Ways to Paint N 3 Grid\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Number of Ways to Paint N 3 Grid\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Number of Ways to Paint N 3 Grid\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Number of Ways to Paint N 3 Grid\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Number of Ways to Paint N × 3 Grid",
      "cpp_optimal": "// Solution for Number of Ways to Paint N × 3 Grid",
      "java_brute": "// Solution for Number of Ways to Paint N × 3 Grid",
      "java_optimal": "// Solution for Number of Ways to Paint N × 3 Grid",
      "python_brute": "# Solution for Number of Ways to Paint N × 3 Grid",
      "python_optimal": "# Solution for Number of Ways to Paint N × 3 Grid"
    },
    "originalOrder": 859,
    "learningOrder": 859
  },
  {
    "id": 900,
    "number": 900,
    "sequence_number": 900,
    "title": "Restore The Array",
    "slug": "restore-the-array",
    "difficulty": "Hard",
    "topic": "Dynamic Programming",
    "subtopic": "Dynamic Programming Optimization",
    "pattern": "1D String Parsing DP",
    "secondary_patterns": [
      "1D String Parsing DP"
    ],
    "stage": "Advanced DP & State Compression",
    "curriculumStage": "Stage 18 — Advanced DP & State Compression",
    "roadmapPhase": "Stage 18 — Advanced DP & State Compression",
    "phase": "Stage 18 — Advanced DP & State Compression",
    "estimatedTime": 45,
    "statement": "Given the constraints and input parameters for Restore The Array, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Restore The Array."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Restore The Array.",
      "Leverage the optimal Dynamic Programming pattern to reduce time complexity."
    ],
    "learningObjective": "Master Dynamic Programming techniques by solving Hard problem constraints for Restore The Array.",
    "whyThisPattern": "When observing Dynamic Programming problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/restore-the-array/",
    "leetcode_title": "Restore The Array",
    "leetcode_id": 1416,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/restore-the-array/",
    "canonicalSlug": "restore-the-array",
    "canonicalUrl": "https://leetcode.com/problems/restore-the-array/",
    "url": "https://leetcode.com/problems/restore-the-array/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Restore The Array\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Restore The Array\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Restore The Array\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Restore The Array\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Restore The Array\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Restore The Array\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Restore The Array\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Restore The Array\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Restore The Array",
      "cpp_optimal": "// Solution for Restore The Array",
      "java_brute": "// Solution for Restore The Array",
      "java_optimal": "// Solution for Restore The Array",
      "python_brute": "# Solution for Restore The Array",
      "python_optimal": "# Solution for Restore The Array"
    },
    "originalOrder": 860,
    "learningOrder": 860
  },
  {
    "id": 901,
    "number": 901,
    "sequence_number": 901,
    "title": "Fibonacci Number",
    "slug": "fibonacci-number",
    "difficulty": "Easy",
    "topic": "Strings",
    "subtopic": "Hashing & Array Optimization",
    "pattern": "Hashing & Array Optimization",
    "secondary_patterns": [
      "Hashing & Array Optimization"
    ],
    "stage": "Bit Manipulation, Math & Geometry",
    "curriculumStage": "Stage 19 — Bit Manipulation, Math & Geometry",
    "roadmapPhase": "Stage 19 — Bit Manipulation, Math & Geometry",
    "phase": "Stage 19 — Bit Manipulation, Math & Geometry",
    "estimatedTime": 15,
    "statement": "Solve the **Fibonacci Number Optimization** problem using the **Hashing & Array Optimization** technique. Given input constraints appropriate for Easy level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^4",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Hashing & Array Optimization identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Hashing & Array Optimization. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Hashing & Array Optimization techniques by solving Easy problem constraints for Fibonacci Number Optimization.",
    "whyThisPattern": "When observing arrays & strings problem conditions, Hashing & Array Optimization optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta"
    ],
    "companyRelevanceTier": "Medium",
    "leetcode_url": "https://leetcode.com/problems/fibonacci-number/",
    "leetcode_title": "Fibonacci Number",
    "leetcode_id": 509,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/fibonacci-number/",
    "canonicalSlug": "fibonacci-number",
    "canonicalUrl": "https://leetcode.com/problems/fibonacci-number/",
    "url": "https://leetcode.com/problems/fibonacci-number/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Fibonacci Number Optimization (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Fibonacci Number Optimization (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Fibonacci Number Optimization (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Fibonacci Number Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Fibonacci Number Optimization (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Fibonacci Number Optimization (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Fibonacci Number Optimization (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Fibonacci Number Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Fibonacci Number",
      "cpp_optimal": "// Solution for Fibonacci Number",
      "java_brute": "// Solution for Fibonacci Number",
      "java_optimal": "// Solution for Fibonacci Number",
      "python_brute": "# Solution for Fibonacci Number",
      "python_optimal": "# Solution for Fibonacci Number"
    },
    "originalOrder": 196,
    "learningOrder": 196
  },
  {
    "id": 902,
    "number": 902,
    "sequence_number": 902,
    "title": "Game Play Analysis I",
    "slug": "game-play-analysis-i",
    "difficulty": "Easy",
    "topic": "Strings",
    "subtopic": "Hashing & Array Optimization",
    "pattern": "Hashing & Array Optimization",
    "secondary_patterns": [
      "Hashing & Array Optimization"
    ],
    "stage": "Bit Manipulation, Math & Geometry",
    "curriculumStage": "Stage 19 — Bit Manipulation, Math & Geometry",
    "roadmapPhase": "Stage 19 — Bit Manipulation, Math & Geometry",
    "phase": "Stage 19 — Bit Manipulation, Math & Geometry",
    "estimatedTime": 15,
    "statement": "Solve the **Game Play Analysis I Optimization** problem using the **Hashing & Array Optimization** technique. Given input constraints appropriate for Easy level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^4",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Hashing & Array Optimization identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Hashing & Array Optimization. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Hashing & Array Optimization techniques by solving Easy problem constraints for Game Play Analysis I Optimization.",
    "whyThisPattern": "When observing arrays & strings problem conditions, Hashing & Array Optimization optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Meta",
      "Apple",
      "Netflix"
    ],
    "companyRelevanceTier": "Medium",
    "leetcode_url": "https://leetcode.com/problems/game-play-analysis-i/",
    "leetcode_title": "Game Play Analysis I",
    "leetcode_id": 511,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/game-play-analysis-i/",
    "canonicalSlug": "game-play-analysis-i",
    "canonicalUrl": "https://leetcode.com/problems/game-play-analysis-i/",
    "url": "https://leetcode.com/problems/game-play-analysis-i/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Game Play Analysis I Optimization (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Game Play Analysis I Optimization (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Game Play Analysis I Optimization (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Game Play Analysis I Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Game Play Analysis I Optimization (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Game Play Analysis I Optimization (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Game Play Analysis I Optimization (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Game Play Analysis I Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Game Play Analysis I",
      "cpp_optimal": "// Solution for Game Play Analysis I",
      "java_brute": "// Solution for Game Play Analysis I",
      "java_optimal": "// Solution for Game Play Analysis I",
      "python_brute": "# Solution for Game Play Analysis I",
      "python_optimal": "# Solution for Game Play Analysis I"
    },
    "originalOrder": 197,
    "learningOrder": 197
  },
  {
    "id": 903,
    "number": 903,
    "sequence_number": 903,
    "title": "Detect Capital",
    "slug": "detect-capital",
    "difficulty": "Easy",
    "topic": "Strings",
    "subtopic": "Hashing & Array Optimization",
    "pattern": "Hashing & Array Optimization",
    "secondary_patterns": [
      "Hashing & Array Optimization"
    ],
    "stage": "Bit Manipulation, Math & Geometry",
    "curriculumStage": "Stage 19 — Bit Manipulation, Math & Geometry",
    "roadmapPhase": "Stage 19 — Bit Manipulation, Math & Geometry",
    "phase": "Stage 19 — Bit Manipulation, Math & Geometry",
    "estimatedTime": 15,
    "statement": "Solve the **Detect Capital Challenge** problem using the **Hashing & Array Optimization** technique. Given input constraints appropriate for Easy level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^4",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Hashing & Array Optimization identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Hashing & Array Optimization. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Hashing & Array Optimization techniques by solving Easy problem constraints for Detect Capital Challenge.",
    "whyThisPattern": "When observing arrays & strings problem conditions, Hashing & Array Optimization optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Microsoft",
      "Bloomberg"
    ],
    "companyRelevanceTier": "Medium",
    "leetcode_url": "https://leetcode.com/problems/detect-capital/",
    "leetcode_title": "Detect Capital",
    "leetcode_id": 520,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/detect-capital/",
    "canonicalSlug": "detect-capital",
    "canonicalUrl": "https://leetcode.com/problems/detect-capital/",
    "url": "https://leetcode.com/problems/detect-capital/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Detect Capital Challenge (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Detect Capital Challenge (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Detect Capital Challenge (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Detect Capital Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Detect Capital Challenge (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Detect Capital Challenge (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Detect Capital Challenge (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Detect Capital Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Detect Capital",
      "cpp_optimal": "// Solution for Detect Capital",
      "java_brute": "// Solution for Detect Capital",
      "java_optimal": "// Solution for Detect Capital",
      "python_brute": "# Solution for Detect Capital",
      "python_optimal": "# Solution for Detect Capital"
    },
    "originalOrder": 198,
    "learningOrder": 198
  },
  {
    "id": 904,
    "number": 904,
    "sequence_number": 904,
    "title": "Reverse String II",
    "slug": "reverse-string-ii",
    "difficulty": "Easy",
    "topic": "Strings",
    "subtopic": "Hashing & Array Optimization",
    "pattern": "Hashing & Array Optimization",
    "secondary_patterns": [
      "Hashing & Array Optimization"
    ],
    "stage": "Bit Manipulation, Math & Geometry",
    "curriculumStage": "Stage 19 — Bit Manipulation, Math & Geometry",
    "roadmapPhase": "Stage 19 — Bit Manipulation, Math & Geometry",
    "phase": "Stage 19 — Bit Manipulation, Math & Geometry",
    "estimatedTime": 15,
    "statement": "Solve the **Reverse String II Optimization** problem using the **Hashing & Array Optimization** technique. Given input constraints appropriate for Easy level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^4",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Hashing & Array Optimization identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Hashing & Array Optimization. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Hashing & Array Optimization techniques by solving Easy problem constraints for Reverse String II Optimization.",
    "whyThisPattern": "When observing arrays & strings problem conditions, Hashing & Array Optimization optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta"
    ],
    "companyRelevanceTier": "Medium",
    "leetcode_url": "https://leetcode.com/problems/reverse-string-ii/",
    "leetcode_title": "Reverse String II",
    "leetcode_id": 541,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/reverse-string-ii/",
    "canonicalSlug": "reverse-string-ii",
    "canonicalUrl": "https://leetcode.com/problems/reverse-string-ii/",
    "url": "https://leetcode.com/problems/reverse-string-ii/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Reverse String II Optimization (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Reverse String II Optimization (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Reverse String II Optimization (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Reverse String II Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Reverse String II Optimization (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Reverse String II Optimization (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Reverse String II Optimization (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Reverse String II Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Reverse String II",
      "cpp_optimal": "// Solution for Reverse String II",
      "java_brute": "// Solution for Reverse String II",
      "java_optimal": "// Solution for Reverse String II",
      "python_brute": "# Solution for Reverse String II",
      "python_optimal": "# Solution for Reverse String II"
    },
    "originalOrder": 199,
    "learningOrder": 199
  },
  {
    "id": 905,
    "number": 905,
    "sequence_number": 905,
    "title": "Student Attendance Record I",
    "slug": "student-attendance-record-i",
    "difficulty": "Easy",
    "topic": "Strings",
    "subtopic": "Hashing & Array Optimization",
    "pattern": "Hashing & Array Optimization",
    "secondary_patterns": [
      "Hashing & Array Optimization"
    ],
    "stage": "Bit Manipulation, Math & Geometry",
    "curriculumStage": "Stage 19 — Bit Manipulation, Math & Geometry",
    "roadmapPhase": "Stage 19 — Bit Manipulation, Math & Geometry",
    "phase": "Stage 19 — Bit Manipulation, Math & Geometry",
    "estimatedTime": 15,
    "statement": "Solve the **Student Attendance Record I Optimization** problem using the **Hashing & Array Optimization** technique. Given input constraints appropriate for Easy level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^4",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Hashing & Array Optimization identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Hashing & Array Optimization. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Hashing & Array Optimization techniques by solving Easy problem constraints for Student Attendance Record I Optimization.",
    "whyThisPattern": "When observing arrays & strings problem conditions, Hashing & Array Optimization optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Meta",
      "Apple",
      "Netflix"
    ],
    "companyRelevanceTier": "Medium",
    "leetcode_url": "https://leetcode.com/problems/student-attendance-record-i/",
    "leetcode_title": "Student Attendance Record I",
    "leetcode_id": 551,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/student-attendance-record-i/",
    "canonicalSlug": "student-attendance-record-i",
    "canonicalUrl": "https://leetcode.com/problems/student-attendance-record-i/",
    "url": "https://leetcode.com/problems/student-attendance-record-i/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Student Attendance Record I Optimization (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Student Attendance Record I Optimization (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Student Attendance Record I Optimization (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Student Attendance Record I Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Student Attendance Record I Optimization (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Student Attendance Record I Optimization (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Student Attendance Record I Optimization (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Student Attendance Record I Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Student Attendance Record I",
      "cpp_optimal": "// Solution for Student Attendance Record I",
      "java_brute": "// Solution for Student Attendance Record I",
      "java_optimal": "// Solution for Student Attendance Record I",
      "python_brute": "# Solution for Student Attendance Record I",
      "python_optimal": "# Solution for Student Attendance Record I"
    },
    "originalOrder": 200,
    "learningOrder": 200
  },
  {
    "id": 906,
    "number": 906,
    "sequence_number": 906,
    "title": "Reverse Words in a String III",
    "slug": "reverse-words-in-a-string-iii",
    "difficulty": "Easy",
    "topic": "Strings",
    "subtopic": "Hashing & Array Optimization",
    "pattern": "Hashing & Array Optimization",
    "secondary_patterns": [
      "Hashing & Array Optimization"
    ],
    "stage": "Bit Manipulation, Math & Geometry",
    "curriculumStage": "Stage 19 — Bit Manipulation, Math & Geometry",
    "roadmapPhase": "Stage 19 — Bit Manipulation, Math & Geometry",
    "phase": "Stage 19 — Bit Manipulation, Math & Geometry",
    "estimatedTime": 15,
    "statement": "Solve the **Reverse Words in a String III Optimization** problem using the **Hashing & Array Optimization** technique. Given input constraints appropriate for Easy level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^4",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Hashing & Array Optimization identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Hashing & Array Optimization. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Hashing & Array Optimization techniques by solving Easy problem constraints for Reverse Words in a String III Optimization.",
    "whyThisPattern": "When observing arrays & strings problem conditions, Hashing & Array Optimization optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Apple",
      "Adobe",
      "Atlassian"
    ],
    "companyRelevanceTier": "Medium",
    "leetcode_url": "https://leetcode.com/problems/reverse-words-in-a-string-iii/",
    "leetcode_title": "Reverse Words in a String III",
    "leetcode_id": 557,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/reverse-words-in-a-string-iii/",
    "canonicalSlug": "reverse-words-in-a-string-iii",
    "canonicalUrl": "https://leetcode.com/problems/reverse-words-in-a-string-iii/",
    "url": "https://leetcode.com/problems/reverse-words-in-a-string-iii/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Reverse Words in a String III Optimization (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Reverse Words in a String III Optimization (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Reverse Words in a String III Optimization (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Reverse Words in a String III Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Reverse Words in a String III Optimization (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Reverse Words in a String III Optimization (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Reverse Words in a String III Optimization (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Reverse Words in a String III Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Reverse Words in a String III",
      "cpp_optimal": "// Solution for Reverse Words in a String III",
      "java_brute": "// Solution for Reverse Words in a String III",
      "java_optimal": "// Solution for Reverse Words in a String III",
      "python_brute": "# Solution for Reverse Words in a String III",
      "python_optimal": "# Solution for Reverse Words in a String III"
    },
    "originalOrder": 201,
    "learningOrder": 201
  },
  {
    "id": 907,
    "number": 907,
    "sequence_number": 907,
    "title": "Distribute Candies",
    "slug": "distribute-candies",
    "difficulty": "Easy",
    "topic": "Strings",
    "subtopic": "Hashing & Array Optimization",
    "pattern": "Hashing & Array Optimization",
    "secondary_patterns": [
      "Hashing & Array Optimization"
    ],
    "stage": "Bit Manipulation, Math & Geometry",
    "curriculumStage": "Stage 19 — Bit Manipulation, Math & Geometry",
    "roadmapPhase": "Stage 19 — Bit Manipulation, Math & Geometry",
    "phase": "Stage 19 — Bit Manipulation, Math & Geometry",
    "estimatedTime": 15,
    "statement": "Solve the **Distribute Candies Optimization** problem using the **Hashing & Array Optimization** technique. Given input constraints appropriate for Easy level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^4",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Hashing & Array Optimization identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Hashing & Array Optimization. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Hashing & Array Optimization techniques by solving Easy problem constraints for Distribute Candies Optimization.",
    "whyThisPattern": "When observing arrays & strings problem conditions, Hashing & Array Optimization optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Meta",
      "Apple",
      "Netflix"
    ],
    "companyRelevanceTier": "Medium",
    "leetcode_url": "https://leetcode.com/problems/distribute-candies/",
    "leetcode_title": "Distribute Candies",
    "leetcode_id": 575,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/distribute-candies/",
    "canonicalSlug": "distribute-candies",
    "canonicalUrl": "https://leetcode.com/problems/distribute-candies/",
    "url": "https://leetcode.com/problems/distribute-candies/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Distribute Candies Optimization (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Distribute Candies Optimization (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Distribute Candies Optimization (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Distribute Candies Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Distribute Candies Optimization (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Distribute Candies Optimization (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Distribute Candies Optimization (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Distribute Candies Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Distribute Candies",
      "cpp_optimal": "// Solution for Distribute Candies",
      "java_brute": "// Solution for Distribute Candies",
      "java_optimal": "// Solution for Distribute Candies",
      "python_brute": "# Solution for Distribute Candies",
      "python_optimal": "# Solution for Distribute Candies"
    },
    "originalOrder": 202,
    "learningOrder": 202
  },
  {
    "id": 908,
    "number": 908,
    "sequence_number": 908,
    "title": "Find Words That Can Be Formed by Characters",
    "slug": "find-words-that-can-be-formed-by-characters",
    "difficulty": "Easy",
    "topic": "Strings",
    "subtopic": "Strings Optimization",
    "pattern": "Frequency Map Subset",
    "secondary_patterns": [
      "Frequency Map Subset"
    ],
    "stage": "Bit Manipulation, Math & Geometry",
    "curriculumStage": "Stage 19 — Bit Manipulation, Math & Geometry",
    "roadmapPhase": "Stage 19 — Bit Manipulation, Math & Geometry",
    "phase": "Stage 19 — Bit Manipulation, Math & Geometry",
    "estimatedTime": 15,
    "statement": "Given the constraints and input parameters for Find Words That Can Be Formed by Characters, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Find Words That Can Be Formed by Characters."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Find Words That Can Be Formed by Characters.",
      "Leverage the optimal Strings pattern to reduce time complexity."
    ],
    "learningObjective": "Master Strings techniques by solving Easy problem constraints for Find Words That Can Be Formed by Characters.",
    "whyThisPattern": "When observing Strings problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/find-words-that-can-be-formed-by-characters/",
    "leetcode_title": "Find Words That Can Be Formed by Characters",
    "leetcode_id": 1160,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/find-words-that-can-be-formed-by-characters/",
    "canonicalSlug": "find-words-that-can-be-formed-by-characters",
    "canonicalUrl": "https://leetcode.com/problems/find-words-that-can-be-formed-by-characters/",
    "url": "https://leetcode.com/problems/find-words-that-can-be-formed-by-characters/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Find Words That Can Be Formed by Characters\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Find Words That Can Be Formed by Characters\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Find Words That Can Be Formed by Characters\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Find Words That Can Be Formed by Characters\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Find Words That Can Be Formed by Characters\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Find Words That Can Be Formed by Characters\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Find Words That Can Be Formed by Characters\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Find Words That Can Be Formed by Characters\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Find Words That Can Be Formed by Characters",
      "cpp_optimal": "// Solution for Find Words That Can Be Formed by Characters",
      "java_brute": "// Solution for Find Words That Can Be Formed by Characters",
      "java_optimal": "// Solution for Find Words That Can Be Formed by Characters",
      "python_brute": "# Solution for Find Words That Can Be Formed by Characters",
      "python_optimal": "# Solution for Find Words That Can Be Formed by Characters"
    },
    "originalOrder": 203,
    "learningOrder": 203
  },
  {
    "id": 909,
    "number": 909,
    "sequence_number": 909,
    "title": "Defanging an IP Address",
    "slug": "defanging-an-ip-address",
    "difficulty": "Easy",
    "topic": "Strings",
    "subtopic": "Strings Optimization",
    "pattern": "Substring Replace",
    "secondary_patterns": [
      "Substring Replace"
    ],
    "stage": "Bit Manipulation, Math & Geometry",
    "curriculumStage": "Stage 19 — Bit Manipulation, Math & Geometry",
    "roadmapPhase": "Stage 19 — Bit Manipulation, Math & Geometry",
    "phase": "Stage 19 — Bit Manipulation, Math & Geometry",
    "estimatedTime": 15,
    "statement": "Given the constraints and input parameters for Defanging an IP Address, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Defanging an IP Address."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Defanging an IP Address.",
      "Leverage the optimal Strings pattern to reduce time complexity."
    ],
    "learningObjective": "Master Strings techniques by solving Easy problem constraints for Defanging an IP Address.",
    "whyThisPattern": "When observing Strings problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/defanging-an-ip-address/",
    "leetcode_title": "Defanging an IP Address",
    "leetcode_id": 1108,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/defanging-an-ip-address/",
    "canonicalSlug": "defanging-an-ip-address",
    "canonicalUrl": "https://leetcode.com/problems/defanging-an-ip-address/",
    "url": "https://leetcode.com/problems/defanging-an-ip-address/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Defanging an IP Address\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Defanging an IP Address\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Defanging an IP Address\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Defanging an IP Address\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Defanging an IP Address\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Defanging an IP Address\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Defanging an IP Address\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Defanging an IP Address\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Defanging an IP Address",
      "cpp_optimal": "// Solution for Defanging an IP Address",
      "java_brute": "// Solution for Defanging an IP Address",
      "java_optimal": "// Solution for Defanging an IP Address",
      "python_brute": "# Solution for Defanging an IP Address",
      "python_optimal": "# Solution for Defanging an IP Address"
    },
    "originalOrder": 204,
    "learningOrder": 204
  },
  {
    "id": 910,
    "number": 910,
    "sequence_number": 910,
    "title": "Most Common Word",
    "slug": "most-common-word",
    "difficulty": "Easy",
    "topic": "Strings",
    "subtopic": "Strings Optimization",
    "pattern": "Clean Word Frequency",
    "secondary_patterns": [
      "Clean Word Frequency"
    ],
    "stage": "Bit Manipulation, Math & Geometry",
    "curriculumStage": "Stage 19 — Bit Manipulation, Math & Geometry",
    "roadmapPhase": "Stage 19 — Bit Manipulation, Math & Geometry",
    "phase": "Stage 19 — Bit Manipulation, Math & Geometry",
    "estimatedTime": 15,
    "statement": "Given the constraints and input parameters for Most Common Word, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Most Common Word."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Most Common Word.",
      "Leverage the optimal Strings pattern to reduce time complexity."
    ],
    "learningObjective": "Master Strings techniques by solving Easy problem constraints for Most Common Word.",
    "whyThisPattern": "When observing Strings problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/most-common-word/",
    "leetcode_title": "Most Common Word",
    "leetcode_id": 819,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/most-common-word/",
    "canonicalSlug": "most-common-word",
    "canonicalUrl": "https://leetcode.com/problems/most-common-word/",
    "url": "https://leetcode.com/problems/most-common-word/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Most Common Word\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Most Common Word\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Most Common Word\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Most Common Word\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Most Common Word\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Most Common Word\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Most Common Word\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Most Common Word\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Most Common Word",
      "cpp_optimal": "// Solution for Most Common Word",
      "java_brute": "// Solution for Most Common Word",
      "java_optimal": "// Solution for Most Common Word",
      "python_brute": "# Solution for Most Common Word",
      "python_optimal": "# Solution for Most Common Word"
    },
    "originalOrder": 205,
    "learningOrder": 205
  },
  {
    "id": 911,
    "number": 911,
    "sequence_number": 911,
    "title": "Count Primes",
    "slug": "count-primes",
    "difficulty": "Medium",
    "topic": "Math",
    "subtopic": "Math Optimization",
    "pattern": "Math Pattern",
    "secondary_patterns": [
      "Math Pattern"
    ],
    "stage": "Bit Manipulation, Math & Geometry",
    "curriculumStage": "Stage 19 — Bit Manipulation, Math & Geometry",
    "roadmapPhase": "Stage 19 — Bit Manipulation, Math & Geometry",
    "phase": "Stage 19 — Bit Manipulation, Math & Geometry",
    "estimatedTime": 30,
    "statement": "Solve the **Count Primes** problem using standard Math techniques. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Math algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Math properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Math techniques by solving Medium problem constraints for Count Primes.",
    "whyThisPattern": "When observing Math problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/count-primes/",
    "leetcode_title": "Count Primes",
    "leetcode_id": 204,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/count-primes/",
    "canonicalSlug": "count-primes",
    "canonicalUrl": "https://leetcode.com/problems/count-primes/",
    "url": "https://leetcode.com/problems/count-primes/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Count Primes\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Count Primes\n};",
        "java": "// Java Solution for Count Primes\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Count Primes\n}",
        "python": "# Python Solution for Count Primes\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Count Primes\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Count Primes\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Count Primes\n};",
        "java": "// Optimal Java Solution for Count Primes\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Count Primes\n}",
        "python": "# Optimal Python Solution for Count Primes\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Count Primes\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Count Primes",
      "cpp_optimal": "// Solution for Count Primes",
      "java_brute": "// Solution for Count Primes",
      "java_optimal": "// Solution for Count Primes",
      "python_brute": "# Solution for Count Primes",
      "python_optimal": "# Solution for Count Primes"
    },
    "originalOrder": 567,
    "learningOrder": 567
  },
  {
    "id": 912,
    "number": 912,
    "sequence_number": 912,
    "title": "Fraction Addition and Subtraction",
    "slug": "fraction-addition-and-subtraction",
    "difficulty": "Medium",
    "topic": "Math",
    "subtopic": "Math Optimization",
    "pattern": "Math Pattern",
    "secondary_patterns": [
      "Math Pattern"
    ],
    "stage": "Bit Manipulation, Math & Geometry",
    "curriculumStage": "Stage 19 — Bit Manipulation, Math & Geometry",
    "roadmapPhase": "Stage 19 — Bit Manipulation, Math & Geometry",
    "phase": "Stage 19 — Bit Manipulation, Math & Geometry",
    "estimatedTime": 30,
    "statement": "Solve the **Fraction Addition and Subtraction** problem using standard Math techniques. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Math algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Math properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Math techniques by solving Medium problem constraints for Fraction Addition and Subtraction.",
    "whyThisPattern": "When observing Math problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/fraction-addition-and-subtraction/",
    "leetcode_title": "Fraction Addition and Subtraction",
    "leetcode_id": 592,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/fraction-addition-and-subtraction/",
    "canonicalSlug": "fraction-addition-and-subtraction",
    "canonicalUrl": "https://leetcode.com/problems/fraction-addition-and-subtraction/",
    "url": "https://leetcode.com/problems/fraction-addition-and-subtraction/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Fraction Addition and Subtraction\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Fraction Addition and Subtraction\n};",
        "java": "// Java Solution for Fraction Addition and Subtraction\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Fraction Addition and Subtraction\n}",
        "python": "# Python Solution for Fraction Addition and Subtraction\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Fraction Addition and Subtraction\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Fraction Addition and Subtraction\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Fraction Addition and Subtraction\n};",
        "java": "// Optimal Java Solution for Fraction Addition and Subtraction\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Fraction Addition and Subtraction\n}",
        "python": "# Optimal Python Solution for Fraction Addition and Subtraction\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Fraction Addition and Subtraction\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Fraction Addition and Subtraction",
      "cpp_optimal": "// Solution for Fraction Addition and Subtraction",
      "java_brute": "// Solution for Fraction Addition and Subtraction",
      "java_optimal": "// Solution for Fraction Addition and Subtraction",
      "python_brute": "# Solution for Fraction Addition and Subtraction",
      "python_optimal": "# Solution for Fraction Addition and Subtraction"
    },
    "originalOrder": 568,
    "learningOrder": 568
  },
  {
    "id": 913,
    "number": 913,
    "sequence_number": 913,
    "title": "Groups of Special-Equivalent Strings",
    "slug": "groups-of-special-equivalent-strings",
    "difficulty": "Medium",
    "topic": "Hashing",
    "subtopic": "Hashing Optimization",
    "pattern": "Odd-Even Character Signature",
    "secondary_patterns": [
      "Odd-Even Character Signature"
    ],
    "stage": "Bit Manipulation, Math & Geometry",
    "curriculumStage": "Stage 19 — Bit Manipulation, Math & Geometry",
    "roadmapPhase": "Stage 19 — Bit Manipulation, Math & Geometry",
    "phase": "Stage 19 — Bit Manipulation, Math & Geometry",
    "estimatedTime": 30,
    "statement": "Given the constraints and input parameters for Groups of Special-Equivalent Strings, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Groups of Special-Equivalent Strings."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Groups of Special-Equivalent Strings.",
      "Leverage the optimal Hashing pattern to reduce time complexity."
    ],
    "learningObjective": "Master Hashing techniques by solving Medium problem constraints for Groups of Special-Equivalent Strings.",
    "whyThisPattern": "When observing Hashing problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/groups-of-special-equivalent-strings/",
    "leetcode_title": "Groups of Special-Equivalent Strings",
    "leetcode_id": 893,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/groups-of-special-equivalent-strings/",
    "canonicalSlug": "groups-of-special-equivalent-strings",
    "canonicalUrl": "https://leetcode.com/problems/groups-of-special-equivalent-strings/",
    "url": "https://leetcode.com/problems/groups-of-special-equivalent-strings/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Groups of Special-Equivalent Strings\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Groups of Special-Equivalent Strings\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Groups of Special-Equivalent Strings\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Groups of Special-Equivalent Strings\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Groups of Special-Equivalent Strings\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Groups of Special-Equivalent Strings\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Groups of Special-Equivalent Strings\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Groups of Special-Equivalent Strings\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Groups of Special-Equivalent Strings",
      "cpp_optimal": "// Solution for Groups of Special-Equivalent Strings",
      "java_brute": "// Solution for Groups of Special-Equivalent Strings",
      "java_optimal": "// Solution for Groups of Special-Equivalent Strings",
      "python_brute": "# Solution for Groups of Special-Equivalent Strings",
      "python_optimal": "# Solution for Groups of Special-Equivalent Strings"
    },
    "originalOrder": 524,
    "learningOrder": 524
  },
  {
    "id": 914,
    "number": 914,
    "sequence_number": 914,
    "title": "Minimum Area Rectangle",
    "slug": "minimum-area-rectangle",
    "difficulty": "Medium",
    "topic": "Hashing",
    "subtopic": "Hashing Optimization",
    "pattern": "Diagonal Point Set Lookup",
    "secondary_patterns": [
      "Diagonal Point Set Lookup"
    ],
    "stage": "Bit Manipulation, Math & Geometry",
    "curriculumStage": "Stage 19 — Bit Manipulation, Math & Geometry",
    "roadmapPhase": "Stage 19 — Bit Manipulation, Math & Geometry",
    "phase": "Stage 19 — Bit Manipulation, Math & Geometry",
    "estimatedTime": 30,
    "statement": "Given the constraints and input parameters for Minimum Area Rectangle, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Minimum Area Rectangle."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Minimum Area Rectangle.",
      "Leverage the optimal Hashing pattern to reduce time complexity."
    ],
    "learningObjective": "Master Hashing techniques by solving Medium problem constraints for Minimum Area Rectangle.",
    "whyThisPattern": "When observing Hashing problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/minimum-area-rectangle/",
    "leetcode_title": "Minimum Area Rectangle",
    "leetcode_id": 939,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/minimum-area-rectangle/",
    "canonicalSlug": "minimum-area-rectangle",
    "canonicalUrl": "https://leetcode.com/problems/minimum-area-rectangle/",
    "url": "https://leetcode.com/problems/minimum-area-rectangle/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Minimum Area Rectangle\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Minimum Area Rectangle\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Minimum Area Rectangle\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Minimum Area Rectangle\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Minimum Area Rectangle\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Minimum Area Rectangle\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Minimum Area Rectangle\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Minimum Area Rectangle\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Minimum Area Rectangle",
      "cpp_optimal": "// Solution for Minimum Area Rectangle",
      "java_brute": "// Solution for Minimum Area Rectangle",
      "java_optimal": "// Solution for Minimum Area Rectangle",
      "python_brute": "# Solution for Minimum Area Rectangle",
      "python_optimal": "# Solution for Minimum Area Rectangle"
    },
    "originalOrder": 525,
    "learningOrder": 525
  },
  {
    "id": 915,
    "number": 915,
    "sequence_number": 915,
    "title": "Display Table of Food Orders in a Restaurant",
    "slug": "display-table-of-food-orders-in-a-restaurant",
    "difficulty": "Medium",
    "topic": "Hashing",
    "subtopic": "Hashing Optimization",
    "pattern": "Nested TreeMap Hash",
    "secondary_patterns": [
      "Nested TreeMap Hash"
    ],
    "stage": "Bit Manipulation, Math & Geometry",
    "curriculumStage": "Stage 19 — Bit Manipulation, Math & Geometry",
    "roadmapPhase": "Stage 19 — Bit Manipulation, Math & Geometry",
    "phase": "Stage 19 — Bit Manipulation, Math & Geometry",
    "estimatedTime": 30,
    "statement": "Given the constraints and input parameters for Display Table of Food Orders in a Restaurant, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Display Table of Food Orders in a Restaurant."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Display Table of Food Orders in a Restaurant.",
      "Leverage the optimal Hashing pattern to reduce time complexity."
    ],
    "learningObjective": "Master Hashing techniques by solving Medium problem constraints for Display Table of Food Orders in a Restaurant.",
    "whyThisPattern": "When observing Hashing problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/display-table-of-food-orders-in-a-restaurant/",
    "leetcode_title": "Display Table of Food Orders in a Restaurant",
    "leetcode_id": 1418,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/display-table-of-food-orders-in-a-restaurant/",
    "canonicalSlug": "display-table-of-food-orders-in-a-restaurant",
    "canonicalUrl": "https://leetcode.com/problems/display-table-of-food-orders-in-a-restaurant/",
    "url": "https://leetcode.com/problems/display-table-of-food-orders-in-a-restaurant/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Display Table of Food Orders in a Restaurant\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Display Table of Food Orders in a Restaurant\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Display Table of Food Orders in a Restaurant\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Display Table of Food Orders in a Restaurant\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Display Table of Food Orders in a Restaurant\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Display Table of Food Orders in a Restaurant\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Display Table of Food Orders in a Restaurant\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Display Table of Food Orders in a Restaurant\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Display Table of Food Orders in a Restaurant",
      "cpp_optimal": "// Solution for Display Table of Food Orders in a Restaurant",
      "java_brute": "// Solution for Display Table of Food Orders in a Restaurant",
      "java_optimal": "// Solution for Display Table of Food Orders in a Restaurant",
      "python_brute": "# Solution for Display Table of Food Orders in a Restaurant",
      "python_optimal": "# Solution for Display Table of Food Orders in a Restaurant"
    },
    "originalOrder": 526,
    "learningOrder": 526
  },
  {
    "id": 916,
    "number": 916,
    "sequence_number": 916,
    "title": "Minimum Number of Steps to Make Two Strings Anagram",
    "slug": "minimum-number-of-steps-to-make-two-strings-anagram",
    "difficulty": "Medium",
    "topic": "Hashing",
    "subtopic": "Hashing Optimization",
    "pattern": "Frequency Delta Sum",
    "secondary_patterns": [
      "Frequency Delta Sum"
    ],
    "stage": "Bit Manipulation, Math & Geometry",
    "curriculumStage": "Stage 19 — Bit Manipulation, Math & Geometry",
    "roadmapPhase": "Stage 19 — Bit Manipulation, Math & Geometry",
    "phase": "Stage 19 — Bit Manipulation, Math & Geometry",
    "estimatedTime": 30,
    "statement": "Given the constraints and input parameters for Minimum Number of Steps to Make Two Strings Anagram, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Minimum Number of Steps to Make Two Strings Anagram."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Minimum Number of Steps to Make Two Strings Anagram.",
      "Leverage the optimal Hashing pattern to reduce time complexity."
    ],
    "learningObjective": "Master Hashing techniques by solving Medium problem constraints for Minimum Number of Steps to Make Two Strings Anagram.",
    "whyThisPattern": "When observing Hashing problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/minimum-number-of-steps-to-make-two-strings-anagram/",
    "leetcode_title": "Minimum Number of Steps to Make Two Strings Anagram",
    "leetcode_id": 1347,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/minimum-number-of-steps-to-make-two-strings-anagram/",
    "canonicalSlug": "minimum-number-of-steps-to-make-two-strings-anagram",
    "canonicalUrl": "https://leetcode.com/problems/minimum-number-of-steps-to-make-two-strings-anagram/",
    "url": "https://leetcode.com/problems/minimum-number-of-steps-to-make-two-strings-anagram/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Minimum Number of Steps to Make Two Strings Anagram\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Minimum Number of Steps to Make Two Strings Anagram\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Minimum Number of Steps to Make Two Strings Anagram\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Minimum Number of Steps to Make Two Strings Anagram\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Minimum Number of Steps to Make Two Strings Anagram\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Minimum Number of Steps to Make Two Strings Anagram\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Minimum Number of Steps to Make Two Strings Anagram\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Minimum Number of Steps to Make Two Strings Anagram\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Minimum Number of Steps to Make Two Strings Anagram",
      "cpp_optimal": "// Solution for Minimum Number of Steps to Make Two Strings Anagram",
      "java_brute": "// Solution for Minimum Number of Steps to Make Two Strings Anagram",
      "java_optimal": "// Solution for Minimum Number of Steps to Make Two Strings Anagram",
      "python_brute": "# Solution for Minimum Number of Steps to Make Two Strings Anagram",
      "python_optimal": "# Solution for Minimum Number of Steps to Make Two Strings Anagram"
    },
    "originalOrder": 527,
    "learningOrder": 527
  },
  {
    "id": 917,
    "number": 917,
    "sequence_number": 917,
    "title": "Tuple with Same Product",
    "slug": "tuple-with-same-product",
    "difficulty": "Medium",
    "topic": "Hashing",
    "subtopic": "Hashing Optimization",
    "pattern": "Product Pair Frequency",
    "secondary_patterns": [
      "Product Pair Frequency"
    ],
    "stage": "Bit Manipulation, Math & Geometry",
    "curriculumStage": "Stage 19 — Bit Manipulation, Math & Geometry",
    "roadmapPhase": "Stage 19 — Bit Manipulation, Math & Geometry",
    "phase": "Stage 19 — Bit Manipulation, Math & Geometry",
    "estimatedTime": 30,
    "statement": "Given the constraints and input parameters for Tuple with Same Product, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Tuple with Same Product."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Tuple with Same Product.",
      "Leverage the optimal Hashing pattern to reduce time complexity."
    ],
    "learningObjective": "Master Hashing techniques by solving Medium problem constraints for Tuple with Same Product.",
    "whyThisPattern": "When observing Hashing problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/tuple-with-same-product/",
    "leetcode_title": "Tuple with Same Product",
    "leetcode_id": 1726,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/tuple-with-same-product/",
    "canonicalSlug": "tuple-with-same-product",
    "canonicalUrl": "https://leetcode.com/problems/tuple-with-same-product/",
    "url": "https://leetcode.com/problems/tuple-with-same-product/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Tuple with Same Product\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Tuple with Same Product\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Tuple with Same Product\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Tuple with Same Product\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Tuple with Same Product\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Tuple with Same Product\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Tuple with Same Product\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Tuple with Same Product\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Tuple with Same Product",
      "cpp_optimal": "// Solution for Tuple with Same Product",
      "java_brute": "// Solution for Tuple with Same Product",
      "java_optimal": "// Solution for Tuple with Same Product",
      "python_brute": "# Solution for Tuple with Same Product",
      "python_optimal": "# Solution for Tuple with Same Product"
    },
    "originalOrder": 528,
    "learningOrder": 528
  },
  {
    "id": 918,
    "number": 918,
    "sequence_number": 918,
    "title": "Evaluate the Bracket Pairs of a String",
    "slug": "evaluate-the-bracket-pairs-of-a-string",
    "difficulty": "Medium",
    "topic": "Hashing",
    "subtopic": "Hashing Optimization",
    "pattern": "Key Map Replacement",
    "secondary_patterns": [
      "Key Map Replacement"
    ],
    "stage": "Bit Manipulation, Math & Geometry",
    "curriculumStage": "Stage 19 — Bit Manipulation, Math & Geometry",
    "roadmapPhase": "Stage 19 — Bit Manipulation, Math & Geometry",
    "phase": "Stage 19 — Bit Manipulation, Math & Geometry",
    "estimatedTime": 30,
    "statement": "Given the constraints and input parameters for Evaluate the Bracket Pairs of a String, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Evaluate the Bracket Pairs of a String."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Evaluate the Bracket Pairs of a String.",
      "Leverage the optimal Hashing pattern to reduce time complexity."
    ],
    "learningObjective": "Master Hashing techniques by solving Medium problem constraints for Evaluate the Bracket Pairs of a String.",
    "whyThisPattern": "When observing Hashing problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/evaluate-the-bracket-pairs-of-a-string/",
    "leetcode_title": "Evaluate the Bracket Pairs of a String",
    "leetcode_id": 1807,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/evaluate-the-bracket-pairs-of-a-string/",
    "canonicalSlug": "evaluate-the-bracket-pairs-of-a-string",
    "canonicalUrl": "https://leetcode.com/problems/evaluate-the-bracket-pairs-of-a-string/",
    "url": "https://leetcode.com/problems/evaluate-the-bracket-pairs-of-a-string/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Evaluate the Bracket Pairs of a String\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Evaluate the Bracket Pairs of a String\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Evaluate the Bracket Pairs of a String\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Evaluate the Bracket Pairs of a String\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Evaluate the Bracket Pairs of a String\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Evaluate the Bracket Pairs of a String\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Evaluate the Bracket Pairs of a String\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Evaluate the Bracket Pairs of a String\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Evaluate the Bracket Pairs of a String",
      "cpp_optimal": "// Solution for Evaluate the Bracket Pairs of a String",
      "java_brute": "// Solution for Evaluate the Bracket Pairs of a String",
      "java_optimal": "// Solution for Evaluate the Bracket Pairs of a String",
      "python_brute": "# Solution for Evaluate the Bracket Pairs of a String",
      "python_optimal": "# Solution for Evaluate the Bracket Pairs of a String"
    },
    "originalOrder": 529,
    "learningOrder": 529
  },
  {
    "id": 919,
    "number": 919,
    "sequence_number": 919,
    "title": "Finding the Users Active Minutes",
    "slug": "finding-the-users-active-minutes",
    "difficulty": "Medium",
    "topic": "Hashing",
    "subtopic": "Hashing Optimization",
    "pattern": "Set Map Minute Counter",
    "secondary_patterns": [
      "Set Map Minute Counter"
    ],
    "stage": "Bit Manipulation, Math & Geometry",
    "curriculumStage": "Stage 19 — Bit Manipulation, Math & Geometry",
    "roadmapPhase": "Stage 19 — Bit Manipulation, Math & Geometry",
    "phase": "Stage 19 — Bit Manipulation, Math & Geometry",
    "estimatedTime": 30,
    "statement": "Given the constraints and input parameters for Finding the Users Active Minutes, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Finding the Users Active Minutes."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Finding the Users Active Minutes.",
      "Leverage the optimal Hashing pattern to reduce time complexity."
    ],
    "learningObjective": "Master Hashing techniques by solving Medium problem constraints for Finding the Users Active Minutes.",
    "whyThisPattern": "When observing Hashing problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/finding-the-users-active-minutes/",
    "leetcode_title": "Finding the Users Active Minutes",
    "leetcode_id": 1817,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/finding-the-users-active-minutes/",
    "canonicalSlug": "finding-the-users-active-minutes",
    "canonicalUrl": "https://leetcode.com/problems/finding-the-users-active-minutes/",
    "url": "https://leetcode.com/problems/finding-the-users-active-minutes/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Finding the Users Active Minutes\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Finding the Users Active Minutes\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Finding the Users Active Minutes\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Finding the Users Active Minutes\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Finding the Users Active Minutes\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Finding the Users Active Minutes\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Finding the Users Active Minutes\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Finding the Users Active Minutes\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Finding the Users Active Minutes",
      "cpp_optimal": "// Solution for Finding the Users Active Minutes",
      "java_brute": "// Solution for Finding the Users Active Minutes",
      "java_optimal": "// Solution for Finding the Users Active Minutes",
      "python_brute": "# Solution for Finding the Users Active Minutes",
      "python_optimal": "# Solution for Finding the Users Active Minutes"
    },
    "originalOrder": 530,
    "learningOrder": 530
  },
  {
    "id": 920,
    "number": 920,
    "sequence_number": 920,
    "title": "Determine if Two Strings Are Close",
    "slug": "determine-if-two-strings-are-close",
    "difficulty": "Medium",
    "topic": "Hashing",
    "subtopic": "Hashing Optimization",
    "pattern": "Set & Frequency Sort Match",
    "secondary_patterns": [
      "Set & Frequency Sort Match"
    ],
    "stage": "Bit Manipulation, Math & Geometry",
    "curriculumStage": "Stage 19 — Bit Manipulation, Math & Geometry",
    "roadmapPhase": "Stage 19 — Bit Manipulation, Math & Geometry",
    "phase": "Stage 19 — Bit Manipulation, Math & Geometry",
    "estimatedTime": 30,
    "statement": "Given the constraints and input parameters for Determine if Two Strings Are Close, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Determine if Two Strings Are Close."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Determine if Two Strings Are Close.",
      "Leverage the optimal Hashing pattern to reduce time complexity."
    ],
    "learningObjective": "Master Hashing techniques by solving Medium problem constraints for Determine if Two Strings Are Close.",
    "whyThisPattern": "When observing Hashing problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/determine-if-two-strings-are-close/",
    "leetcode_title": "Determine if Two Strings Are Close",
    "leetcode_id": 1657,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/determine-if-two-strings-are-close/",
    "canonicalSlug": "determine-if-two-strings-are-close",
    "canonicalUrl": "https://leetcode.com/problems/determine-if-two-strings-are-close/",
    "url": "https://leetcode.com/problems/determine-if-two-strings-are-close/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Determine if Two Strings Are Close\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Determine if Two Strings Are Close\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Determine if Two Strings Are Close\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Determine if Two Strings Are Close\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Determine if Two Strings Are Close\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Determine if Two Strings Are Close\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Determine if Two Strings Are Close\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Determine if Two Strings Are Close\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Determine if Two Strings Are Close",
      "cpp_optimal": "// Solution for Determine if Two Strings Are Close",
      "java_brute": "// Solution for Determine if Two Strings Are Close",
      "java_optimal": "// Solution for Determine if Two Strings Are Close",
      "python_brute": "# Solution for Determine if Two Strings Are Close",
      "python_optimal": "# Solution for Determine if Two Strings Are Close"
    },
    "originalOrder": 531,
    "learningOrder": 531
  },
  {
    "id": 921,
    "number": 921,
    "sequence_number": 921,
    "title": "Number of Ways Where Square of Number Is Equal to Product of Two Numbers",
    "slug": "number-of-ways-where-square-of-number-is-equal-to-product-of-two-numbers",
    "difficulty": "Medium",
    "topic": "Hashing",
    "subtopic": "Hashing Optimization",
    "pattern": "Product Frequency Hash",
    "secondary_patterns": [
      "Product Frequency Hash"
    ],
    "stage": "Bit Manipulation, Math & Geometry",
    "curriculumStage": "Stage 19 — Bit Manipulation, Math & Geometry",
    "roadmapPhase": "Stage 19 — Bit Manipulation, Math & Geometry",
    "phase": "Stage 19 — Bit Manipulation, Math & Geometry",
    "estimatedTime": 30,
    "statement": "Given the constraints and input parameters for Number of Ways Where Square of Number Is Equal to Product of Two Numbers, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Number of Ways Where Square of Number Is Equal to Product of Two Numbers."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Number of Ways Where Square of Number Is Equal to Product of Two Numbers.",
      "Leverage the optimal Hashing pattern to reduce time complexity."
    ],
    "learningObjective": "Master Hashing techniques by solving Medium problem constraints for Number of Ways Where Square of Number Is Equal to Product of Two Numbers.",
    "whyThisPattern": "When observing Hashing problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/number-of-ways-where-square-of-number-is-equal-to-product-of-two-numbers/",
    "leetcode_title": "Number of Ways Where Square of Number Is Equal to Product of Two Numbers",
    "leetcode_id": 1577,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/number-of-ways-where-square-of-number-is-equal-to-product-of-two-numbers/",
    "canonicalSlug": "number-of-ways-where-square-of-number-is-equal-to-product-of-two-numbers",
    "canonicalUrl": "https://leetcode.com/problems/number-of-ways-where-square-of-number-is-equal-to-product-of-two-numbers/",
    "url": "https://leetcode.com/problems/number-of-ways-where-square-of-number-is-equal-to-product-of-two-numbers/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Number of Ways Where Square of Number Is Equal to Product of Two Numbers\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Number of Ways Where Square of Number Is Equal to Product of Two Numbers\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Number of Ways Where Square of Number Is Equal to Product of Two Numbers\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Number of Ways Where Square of Number Is Equal to Product of Two Numbers\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Number of Ways Where Square of Number Is Equal to Product of Two Numbers\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Number of Ways Where Square of Number Is Equal to Product of Two Numbers\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Number of Ways Where Square of Number Is Equal to Product of Two Numbers\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Number of Ways Where Square of Number Is Equal to Product of Two Numbers\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Number of Ways Where Square of Number Is Equal to Product of Two Numbers",
      "cpp_optimal": "// Solution for Number of Ways Where Square of Number Is Equal to Product of Two Numbers",
      "java_brute": "// Solution for Number of Ways Where Square of Number Is Equal to Product of Two Numbers",
      "java_optimal": "// Solution for Number of Ways Where Square of Number Is Equal to Product of Two Numbers",
      "python_brute": "# Solution for Number of Ways Where Square of Number Is Equal to Product of Two Numbers",
      "python_optimal": "# Solution for Number of Ways Where Square of Number Is Equal to Product of Two Numbers"
    },
    "originalOrder": 532,
    "learningOrder": 532
  },
  {
    "id": 922,
    "number": 922,
    "sequence_number": 922,
    "title": "Group Anagrams",
    "slug": "group-anagrams",
    "difficulty": "Medium",
    "topic": "Hashing",
    "subtopic": "Hashing & Array Optimization",
    "pattern": "Hashing & Array Optimization",
    "secondary_patterns": [
      "Hashing & Array Optimization"
    ],
    "stage": "Bit Manipulation, Math & Geometry",
    "curriculumStage": "Stage 19 — Bit Manipulation, Math & Geometry",
    "roadmapPhase": "Stage 19 — Bit Manipulation, Math & Geometry",
    "phase": "Stage 19 — Bit Manipulation, Math & Geometry",
    "estimatedTime": 30,
    "statement": "Solve the **Group Anagrams Challenge** problem using the **Hashing & Array Optimization** technique. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Hashing & Array Optimization identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Hashing & Array Optimization. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Hashing & Array Optimization techniques by solving Medium problem constraints for Group Anagrams Challenge.",
    "whyThisPattern": "When observing arrays & strings problem conditions, Hashing & Array Optimization optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Microsoft",
      "Bloomberg",
      "Adobe"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/group-anagrams/",
    "leetcode_title": "Group Anagrams",
    "leetcode_id": 49,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/group-anagrams/",
    "canonicalSlug": "group-anagrams",
    "canonicalUrl": "https://leetcode.com/problems/group-anagrams/",
    "url": "https://leetcode.com/problems/group-anagrams/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Group Anagrams Challenge (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Group Anagrams Challenge (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Group Anagrams Challenge (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Group Anagrams Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Group Anagrams Challenge (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Group Anagrams Challenge (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Group Anagrams Challenge (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Group Anagrams Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Group Anagrams",
      "cpp_optimal": "// Solution for Group Anagrams",
      "java_brute": "// Solution for Group Anagrams",
      "java_optimal": "// Solution for Group Anagrams",
      "python_brute": "# Solution for Group Anagrams",
      "python_optimal": "# Solution for Group Anagrams"
    },
    "originalOrder": 533,
    "learningOrder": 533
  },
  {
    "id": 923,
    "number": 923,
    "sequence_number": 923,
    "title": "Making File Names Unique",
    "slug": "making-file-names-unique",
    "difficulty": "Medium",
    "topic": "Hashing",
    "subtopic": "Hashing Optimization",
    "pattern": "Folder Name Counter",
    "secondary_patterns": [
      "Folder Name Counter"
    ],
    "stage": "Bit Manipulation, Math & Geometry",
    "curriculumStage": "Stage 19 — Bit Manipulation, Math & Geometry",
    "roadmapPhase": "Stage 19 — Bit Manipulation, Math & Geometry",
    "phase": "Stage 19 — Bit Manipulation, Math & Geometry",
    "estimatedTime": 30,
    "statement": "Given the constraints and input parameters for Making File Names Unique, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Making File Names Unique."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Making File Names Unique.",
      "Leverage the optimal Hashing pattern to reduce time complexity."
    ],
    "learningObjective": "Master Hashing techniques by solving Medium problem constraints for Making File Names Unique.",
    "whyThisPattern": "When observing Hashing problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/making-file-names-unique/",
    "leetcode_title": "Making File Names Unique",
    "leetcode_id": 1487,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/making-file-names-unique/",
    "canonicalSlug": "making-file-names-unique",
    "canonicalUrl": "https://leetcode.com/problems/making-file-names-unique/",
    "url": "https://leetcode.com/problems/making-file-names-unique/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Making File Names Unique\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Making File Names Unique\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Making File Names Unique\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Making File Names Unique\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Making File Names Unique\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Making File Names Unique\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Making File Names Unique\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Making File Names Unique\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Making File Names Unique",
      "cpp_optimal": "// Solution for Making File Names Unique",
      "java_brute": "// Solution for Making File Names Unique",
      "java_optimal": "// Solution for Making File Names Unique",
      "python_brute": "# Solution for Making File Names Unique",
      "python_optimal": "# Solution for Making File Names Unique"
    },
    "originalOrder": 534,
    "learningOrder": 534
  },
  {
    "id": 924,
    "number": 924,
    "sequence_number": 924,
    "title": "Word Frequency",
    "slug": "word-frequency",
    "difficulty": "Medium",
    "topic": "Hashing",
    "subtopic": "Hashing & Array Optimization",
    "pattern": "Hashing & Array Optimization",
    "secondary_patterns": [
      "Hashing & Array Optimization"
    ],
    "stage": "Bit Manipulation, Math & Geometry",
    "curriculumStage": "Stage 19 — Bit Manipulation, Math & Geometry",
    "roadmapPhase": "Stage 19 — Bit Manipulation, Math & Geometry",
    "phase": "Stage 19 — Bit Manipulation, Math & Geometry",
    "estimatedTime": 30,
    "statement": "Solve the **Word Frequency Optimization** problem using the **Hashing & Array Optimization** technique. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Hashing & Array Optimization identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Hashing & Array Optimization. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Hashing & Array Optimization techniques by solving Medium problem constraints for Word Frequency Optimization.",
    "whyThisPattern": "When observing arrays & strings problem conditions, Hashing & Array Optimization optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Apple",
      "Adobe",
      "Atlassian"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/word-frequency/",
    "leetcode_title": "Word Frequency",
    "leetcode_id": 192,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/word-frequency/",
    "canonicalSlug": "word-frequency",
    "canonicalUrl": "https://leetcode.com/problems/word-frequency/",
    "url": "https://leetcode.com/problems/word-frequency/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Word Frequency Optimization (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Word Frequency Optimization (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Word Frequency Optimization (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Word Frequency Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Word Frequency Optimization (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Word Frequency Optimization (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Word Frequency Optimization (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Word Frequency Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Word Frequency",
      "cpp_optimal": "// Solution for Word Frequency",
      "java_brute": "// Solution for Word Frequency",
      "java_optimal": "// Solution for Word Frequency",
      "python_brute": "# Solution for Word Frequency",
      "python_optimal": "# Solution for Word Frequency"
    },
    "originalOrder": 535,
    "learningOrder": 535
  },
  {
    "id": 925,
    "number": 925,
    "sequence_number": 925,
    "title": "Check If a String Contains All Binary Codes of Size K",
    "slug": "check-if-a-string-contains-all-binary-codes-of-size-k",
    "difficulty": "Medium",
    "topic": "Hashing",
    "subtopic": "Hashing Optimization",
    "pattern": "Rolling Bitmask Set",
    "secondary_patterns": [
      "Rolling Bitmask Set"
    ],
    "stage": "Bit Manipulation, Math & Geometry",
    "curriculumStage": "Stage 19 — Bit Manipulation, Math & Geometry",
    "roadmapPhase": "Stage 19 — Bit Manipulation, Math & Geometry",
    "phase": "Stage 19 — Bit Manipulation, Math & Geometry",
    "estimatedTime": 30,
    "statement": "Given the constraints and input parameters for Check If a String Contains All Binary Codes of Size K, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Check If a String Contains All Binary Codes of Size K."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Check If a String Contains All Binary Codes of Size K.",
      "Leverage the optimal Hashing pattern to reduce time complexity."
    ],
    "learningObjective": "Master Hashing techniques by solving Medium problem constraints for Check If a String Contains All Binary Codes of Size K.",
    "whyThisPattern": "When observing Hashing problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/check-if-a-string-contains-all-binary-codes-of-size-k/",
    "leetcode_title": "Check If a String Contains All Binary Codes of Size K",
    "leetcode_id": 1461,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/check-if-a-string-contains-all-binary-codes-of-size-k/",
    "canonicalSlug": "check-if-a-string-contains-all-binary-codes-of-size-k",
    "canonicalUrl": "https://leetcode.com/problems/check-if-a-string-contains-all-binary-codes-of-size-k/",
    "url": "https://leetcode.com/problems/check-if-a-string-contains-all-binary-codes-of-size-k/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Check If a String Contains All Binary Codes of Size K\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Check If a String Contains All Binary Codes of Size K\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Check If a String Contains All Binary Codes of Size K\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Check If a String Contains All Binary Codes of Size K\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Check If a String Contains All Binary Codes of Size K\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Check If a String Contains All Binary Codes of Size K\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Check If a String Contains All Binary Codes of Size K\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Check If a String Contains All Binary Codes of Size K\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Check If a String Contains All Binary Codes of Size K",
      "cpp_optimal": "// Solution for Check If a String Contains All Binary Codes of Size K",
      "java_brute": "// Solution for Check If a String Contains All Binary Codes of Size K",
      "java_optimal": "// Solution for Check If a String Contains All Binary Codes of Size K",
      "python_brute": "# Solution for Check If a String Contains All Binary Codes of Size K",
      "python_optimal": "# Solution for Check If a String Contains All Binary Codes of Size K"
    },
    "originalOrder": 536,
    "learningOrder": 536
  },
  {
    "id": 926,
    "number": 926,
    "sequence_number": 926,
    "title": "Sort Characters By Frequency",
    "slug": "sort-characters-by-frequency",
    "difficulty": "Medium",
    "topic": "Hashing",
    "subtopic": "Hashing & Array Optimization",
    "pattern": "Hashing & Array Optimization",
    "secondary_patterns": [
      "Hashing & Array Optimization"
    ],
    "stage": "Bit Manipulation, Math & Geometry",
    "curriculumStage": "Stage 19 — Bit Manipulation, Math & Geometry",
    "roadmapPhase": "Stage 19 — Bit Manipulation, Math & Geometry",
    "phase": "Stage 19 — Bit Manipulation, Math & Geometry",
    "estimatedTime": 30,
    "statement": "Solve the **Sort Characters By Frequency Optimization** problem using the **Hashing & Array Optimization** technique. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Hashing & Array Optimization identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Hashing & Array Optimization. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Hashing & Array Optimization techniques by solving Medium problem constraints for Sort Characters By Frequency Optimization.",
    "whyThisPattern": "When observing arrays & strings problem conditions, Hashing & Array Optimization optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Apple",
      "Adobe",
      "Atlassian"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/sort-characters-by-frequency/",
    "leetcode_title": "Sort Characters By Frequency",
    "leetcode_id": 451,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/sort-characters-by-frequency/",
    "canonicalSlug": "sort-characters-by-frequency",
    "canonicalUrl": "https://leetcode.com/problems/sort-characters-by-frequency/",
    "url": "https://leetcode.com/problems/sort-characters-by-frequency/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Sort Characters By Frequency Optimization (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Sort Characters By Frequency Optimization (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Sort Characters By Frequency Optimization (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Sort Characters By Frequency Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Sort Characters By Frequency Optimization (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Sort Characters By Frequency Optimization (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Sort Characters By Frequency Optimization (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Sort Characters By Frequency Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Sort Characters By Frequency",
      "cpp_optimal": "// Solution for Sort Characters By Frequency",
      "java_brute": "// Solution for Sort Characters By Frequency",
      "java_optimal": "// Solution for Sort Characters By Frequency",
      "python_brute": "# Solution for Sort Characters By Frequency",
      "python_optimal": "# Solution for Sort Characters By Frequency"
    },
    "originalOrder": 537,
    "learningOrder": 537
  },
  {
    "id": 927,
    "number": 927,
    "sequence_number": 927,
    "title": "Max Increase to Keep City Skyline",
    "slug": "max-increase-to-keep-city-skyline",
    "difficulty": "Medium",
    "topic": "Segment Tree",
    "subtopic": "Segment Tree Optimization",
    "pattern": "Row & Column Max Vectors",
    "secondary_patterns": [
      "Row & Column Max Vectors"
    ],
    "stage": "Bit Manipulation, Math & Geometry",
    "curriculumStage": "Stage 19 — Bit Manipulation, Math & Geometry",
    "roadmapPhase": "Stage 19 — Bit Manipulation, Math & Geometry",
    "phase": "Stage 19 — Bit Manipulation, Math & Geometry",
    "estimatedTime": 30,
    "statement": "Given the constraints and input parameters for Max Increase to Keep City Skyline, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Max Increase to Keep City Skyline."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Max Increase to Keep City Skyline.",
      "Leverage the optimal Arrays pattern to reduce time complexity."
    ],
    "learningObjective": "Master Segment Tree techniques by solving Medium problem constraints for Max Increase to Keep City Skyline.",
    "whyThisPattern": "When observing Segment Tree problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/max-increase-to-keep-city-skyline/",
    "leetcode_title": "Max Increase to Keep City Skyline",
    "leetcode_id": 807,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/max-increase-to-keep-city-skyline/",
    "canonicalSlug": "max-increase-to-keep-city-skyline",
    "canonicalUrl": "https://leetcode.com/problems/max-increase-to-keep-city-skyline/",
    "url": "https://leetcode.com/problems/max-increase-to-keep-city-skyline/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Max Increase to Keep City Skyline\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Max Increase to Keep City Skyline\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Max Increase to Keep City Skyline\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Max Increase to Keep City Skyline\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Max Increase to Keep City Skyline\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Max Increase to Keep City Skyline\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Max Increase to Keep City Skyline\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Max Increase to Keep City Skyline\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Max Increase to Keep City Skyline",
      "cpp_optimal": "// Solution for Max Increase to Keep City Skyline",
      "java_brute": "// Solution for Max Increase to Keep City Skyline",
      "java_optimal": "// Solution for Max Increase to Keep City Skyline",
      "python_brute": "# Solution for Max Increase to Keep City Skyline",
      "python_optimal": "# Solution for Max Increase to Keep City Skyline"
    },
    "originalOrder": 579,
    "learningOrder": 579
  },
  {
    "id": 928,
    "number": 928,
    "sequence_number": 928,
    "title": "Range Frequency Queries",
    "slug": "range-frequency-queries",
    "difficulty": "Medium",
    "topic": "Segment Tree",
    "subtopic": "Segment Tree Optimization",
    "pattern": "Segment Tree Pattern",
    "secondary_patterns": [
      "Segment Tree Pattern"
    ],
    "stage": "Bit Manipulation, Math & Geometry",
    "curriculumStage": "Stage 19 — Bit Manipulation, Math & Geometry",
    "roadmapPhase": "Stage 19 — Bit Manipulation, Math & Geometry",
    "phase": "Stage 19 — Bit Manipulation, Math & Geometry",
    "estimatedTime": 30,
    "statement": "Solve the **Range Frequency Queries** problem using standard Segment Tree techniques. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Segment Tree algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Segment Tree properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Segment Tree techniques by solving Medium problem constraints for Range Frequency Queries.",
    "whyThisPattern": "When observing Segment Tree problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/range-frequency-queries/",
    "leetcode_title": "Range Frequency Queries",
    "leetcode_id": 2080,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/range-frequency-queries/",
    "canonicalSlug": "range-frequency-queries",
    "canonicalUrl": "https://leetcode.com/problems/range-frequency-queries/",
    "url": "https://leetcode.com/problems/range-frequency-queries/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Range Frequency Queries\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Range Frequency Queries\n};",
        "java": "// Java Solution for Range Frequency Queries\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Range Frequency Queries\n}",
        "python": "# Python Solution for Range Frequency Queries\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Range Frequency Queries\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Range Frequency Queries\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Range Frequency Queries\n};",
        "java": "// Optimal Java Solution for Range Frequency Queries\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Range Frequency Queries\n}",
        "python": "# Optimal Python Solution for Range Frequency Queries\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Range Frequency Queries\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Range Frequency Queries",
      "cpp_optimal": "// Solution for Range Frequency Queries",
      "java_brute": "// Solution for Range Frequency Queries",
      "java_optimal": "// Solution for Range Frequency Queries",
      "python_brute": "# Solution for Range Frequency Queries",
      "python_optimal": "# Solution for Range Frequency Queries"
    },
    "originalOrder": 580,
    "learningOrder": 580
  },
  {
    "id": 929,
    "number": 929,
    "sequence_number": 929,
    "title": "Decode String",
    "slug": "decode-string",
    "difficulty": "Medium",
    "topic": "Stack",
    "subtopic": "Stack Optimization",
    "pattern": "Nested Bracket Multiplier Stack",
    "secondary_patterns": [
      "Nested Bracket Multiplier Stack"
    ],
    "stage": "Bit Manipulation, Math & Geometry",
    "curriculumStage": "Stage 19 — Bit Manipulation, Math & Geometry",
    "roadmapPhase": "Stage 19 — Bit Manipulation, Math & Geometry",
    "phase": "Stage 19 — Bit Manipulation, Math & Geometry",
    "estimatedTime": 30,
    "statement": "Given the constraints and input parameters for Decode String, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Decode String."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Decode String.",
      "Leverage the optimal Stack pattern to reduce time complexity."
    ],
    "learningObjective": "Master Stack techniques by solving Medium problem constraints for Decode String.",
    "whyThisPattern": "When observing Stack problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/decode-string/",
    "leetcode_title": "Decode String",
    "leetcode_id": 394,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/decode-string/",
    "canonicalSlug": "decode-string",
    "canonicalUrl": "https://leetcode.com/problems/decode-string/",
    "url": "https://leetcode.com/problems/decode-string/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Decode String\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Decode String\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Decode String\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Decode String\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Decode String\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Decode String\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Decode String\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Decode String\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Decode String",
      "cpp_optimal": "// Solution for Decode String",
      "java_brute": "// Solution for Decode String",
      "java_optimal": "// Solution for Decode String",
      "python_brute": "# Solution for Decode String",
      "python_optimal": "# Solution for Decode String"
    },
    "originalOrder": 621,
    "learningOrder": 621
  },
  {
    "id": 930,
    "number": 930,
    "sequence_number": 930,
    "title": "Build an Array With Stack Operations",
    "slug": "build-an-array-with-stack-operations",
    "difficulty": "Medium",
    "topic": "Stack",
    "subtopic": "Stack Optimization",
    "pattern": "Push Pop Stream Simulation",
    "secondary_patterns": [
      "Push Pop Stream Simulation"
    ],
    "stage": "Bit Manipulation, Math & Geometry",
    "curriculumStage": "Stage 19 — Bit Manipulation, Math & Geometry",
    "roadmapPhase": "Stage 19 — Bit Manipulation, Math & Geometry",
    "phase": "Stage 19 — Bit Manipulation, Math & Geometry",
    "estimatedTime": 30,
    "statement": "Given the constraints and input parameters for Build an Array With Stack Operations, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Build an Array With Stack Operations."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Build an Array With Stack Operations.",
      "Leverage the optimal Stack pattern to reduce time complexity."
    ],
    "learningObjective": "Master Stack techniques by solving Medium problem constraints for Build an Array With Stack Operations.",
    "whyThisPattern": "When observing Stack problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/build-an-array-with-stack-operations/",
    "leetcode_title": "Build an Array With Stack Operations",
    "leetcode_id": 1441,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/build-an-array-with-stack-operations/",
    "canonicalSlug": "build-an-array-with-stack-operations",
    "canonicalUrl": "https://leetcode.com/problems/build-an-array-with-stack-operations/",
    "url": "https://leetcode.com/problems/build-an-array-with-stack-operations/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Build an Array With Stack Operations\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Build an Array With Stack Operations\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Build an Array With Stack Operations\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Build an Array With Stack Operations\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Build an Array With Stack Operations\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Build an Array With Stack Operations\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Build an Array With Stack Operations\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Build an Array With Stack Operations\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Build an Array With Stack Operations",
      "cpp_optimal": "// Solution for Build an Array With Stack Operations",
      "java_brute": "// Solution for Build an Array With Stack Operations",
      "java_optimal": "// Solution for Build an Array With Stack Operations",
      "python_brute": "# Solution for Build an Array With Stack Operations",
      "python_optimal": "# Solution for Build an Array With Stack Operations"
    },
    "originalOrder": 622,
    "learningOrder": 622
  },
  {
    "id": 931,
    "number": 931,
    "sequence_number": 931,
    "title": "Reverse Substrings Between Each Pair of Parentheses",
    "slug": "reverse-substrings-between-each-pair-of-parentheses",
    "difficulty": "Medium",
    "topic": "Stack",
    "subtopic": "Stack Optimization",
    "pattern": "Stack Jump Manipulation",
    "secondary_patterns": [
      "Stack Jump Manipulation"
    ],
    "stage": "Bit Manipulation, Math & Geometry",
    "curriculumStage": "Stage 19 — Bit Manipulation, Math & Geometry",
    "roadmapPhase": "Stage 19 — Bit Manipulation, Math & Geometry",
    "phase": "Stage 19 — Bit Manipulation, Math & Geometry",
    "estimatedTime": 30,
    "statement": "Given the constraints and input parameters for Reverse Substrings Between Each Pair of Parentheses, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Reverse Substrings Between Each Pair of Parentheses."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Reverse Substrings Between Each Pair of Parentheses.",
      "Leverage the optimal Stack pattern to reduce time complexity."
    ],
    "learningObjective": "Master Stack techniques by solving Medium problem constraints for Reverse Substrings Between Each Pair of Parentheses.",
    "whyThisPattern": "When observing Stack problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/reverse-substrings-between-each-pair-of-parentheses/",
    "leetcode_title": "Reverse Substrings Between Each Pair of Parentheses",
    "leetcode_id": 1190,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/reverse-substrings-between-each-pair-of-parentheses/",
    "canonicalSlug": "reverse-substrings-between-each-pair-of-parentheses",
    "canonicalUrl": "https://leetcode.com/problems/reverse-substrings-between-each-pair-of-parentheses/",
    "url": "https://leetcode.com/problems/reverse-substrings-between-each-pair-of-parentheses/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Reverse Substrings Between Each Pair of Parentheses\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Reverse Substrings Between Each Pair of Parentheses\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Reverse Substrings Between Each Pair of Parentheses\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Reverse Substrings Between Each Pair of Parentheses\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Reverse Substrings Between Each Pair of Parentheses\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Reverse Substrings Between Each Pair of Parentheses\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Reverse Substrings Between Each Pair of Parentheses\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Reverse Substrings Between Each Pair of Parentheses\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Reverse Substrings Between Each Pair of Parentheses",
      "cpp_optimal": "// Solution for Reverse Substrings Between Each Pair of Parentheses",
      "java_brute": "// Solution for Reverse Substrings Between Each Pair of Parentheses",
      "java_optimal": "// Solution for Reverse Substrings Between Each Pair of Parentheses",
      "python_brute": "# Solution for Reverse Substrings Between Each Pair of Parentheses",
      "python_optimal": "# Solution for Reverse Substrings Between Each Pair of Parentheses"
    },
    "originalOrder": 623,
    "learningOrder": 623
  },
  {
    "id": 932,
    "number": 932,
    "sequence_number": 932,
    "title": "Smallest Subtree with all the Deepest Nodes",
    "slug": "smallest-subtree-with-all-the-deepest-nodes",
    "difficulty": "Medium",
    "topic": "Trees",
    "subtopic": "Pointer Manipulation",
    "pattern": "Pointer Manipulation",
    "secondary_patterns": [
      "Pointer Manipulation"
    ],
    "stage": "Bit Manipulation, Math & Geometry",
    "curriculumStage": "Stage 19 — Bit Manipulation, Math & Geometry",
    "roadmapPhase": "Stage 19 — Bit Manipulation, Math & Geometry",
    "phase": "Stage 19 — Bit Manipulation, Math & Geometry",
    "estimatedTime": 30,
    "statement": "Solve the **Smallest Subtree with all the Deepest Nodes Challenge** problem using the **Pointer Manipulation** technique. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Pointer Manipulation identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Pointer Manipulation. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Pointer Manipulation techniques by solving Medium problem constraints for Smallest Subtree with all the Deepest Nodes Challenge.",
    "whyThisPattern": "When observing binary trees problem conditions, Pointer Manipulation optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Microsoft",
      "Bloomberg"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/smallest-subtree-with-all-the-deepest-nodes/",
    "leetcode_title": "Smallest Subtree with all the Deepest Nodes",
    "leetcode_id": 865,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/smallest-subtree-with-all-the-deepest-nodes/",
    "canonicalSlug": "smallest-subtree-with-all-the-deepest-nodes",
    "canonicalUrl": "https://leetcode.com/problems/smallest-subtree-with-all-the-deepest-nodes/",
    "url": "https://leetcode.com/problems/smallest-subtree-with-all-the-deepest-nodes/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Smallest Subtree with all the Deepest Nodes Challenge (Pointer Manipulation)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Smallest Subtree with all the Deepest Nodes Challenge (Pointer Manipulation)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Smallest Subtree with all the Deepest Nodes Challenge (Pointer Manipulation)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Smallest Subtree with all the Deepest Nodes Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Smallest Subtree with all the Deepest Nodes Challenge (Pointer Manipulation)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Smallest Subtree with all the Deepest Nodes Challenge (Pointer Manipulation)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Smallest Subtree with all the Deepest Nodes Challenge (Pointer Manipulation)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Smallest Subtree with all the Deepest Nodes Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Smallest Subtree with all the Deepest Nodes",
      "cpp_optimal": "// Solution for Smallest Subtree with all the Deepest Nodes",
      "java_brute": "// Solution for Smallest Subtree with all the Deepest Nodes",
      "java_optimal": "// Solution for Smallest Subtree with all the Deepest Nodes",
      "python_brute": "# Solution for Smallest Subtree with all the Deepest Nodes",
      "python_optimal": "# Solution for Smallest Subtree with all the Deepest Nodes"
    },
    "originalOrder": 649,
    "learningOrder": 649
  },
  {
    "id": 933,
    "number": 933,
    "sequence_number": 933,
    "title": "Construct Binary Tree from Preorder and Postorder Traversal",
    "slug": "construct-binary-tree-from-preorder-and-postorder-traversal",
    "difficulty": "Medium",
    "topic": "Trees",
    "subtopic": "Tree Traversal & Recursion",
    "pattern": "Tree Traversal & Recursion",
    "secondary_patterns": [
      "Tree Traversal & Recursion"
    ],
    "stage": "Bit Manipulation, Math & Geometry",
    "curriculumStage": "Stage 19 — Bit Manipulation, Math & Geometry",
    "roadmapPhase": "Stage 19 — Bit Manipulation, Math & Geometry",
    "phase": "Stage 19 — Bit Manipulation, Math & Geometry",
    "estimatedTime": 30,
    "statement": "Solve the **Construct Binary Tree from Preorder and Postorder Traversal Challenge** problem using the **Tree Traversal & Recursion** technique. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Tree Traversal & Recursion identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Tree Traversal & Recursion. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Tree Traversal & Recursion techniques by solving Medium problem constraints for Construct Binary Tree from Preorder and Postorder Traversal Challenge.",
    "whyThisPattern": "When observing binary trees problem conditions, Tree Traversal & Recursion optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Meta",
      "Uber",
      "Databricks"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/construct-binary-tree-from-preorder-and-postorder-traversal/",
    "leetcode_title": "Construct Binary Tree from Preorder and Postorder Traversal",
    "leetcode_id": 889,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/construct-binary-tree-from-preorder-and-postorder-traversal/",
    "canonicalSlug": "construct-binary-tree-from-preorder-and-postorder-traversal",
    "canonicalUrl": "https://leetcode.com/problems/construct-binary-tree-from-preorder-and-postorder-traversal/",
    "url": "https://leetcode.com/problems/construct-binary-tree-from-preorder-and-postorder-traversal/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Construct Binary Tree from Preorder and Postorder Traversal Challenge (Tree Traversal & Recursion)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Construct Binary Tree from Preorder and Postorder Traversal Challenge (Tree Traversal & Recursion)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Construct Binary Tree from Preorder and Postorder Traversal Challenge (Tree Traversal & Recursion)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Construct Binary Tree from Preorder and Postorder Traversal Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Construct Binary Tree from Preorder and Postorder Traversal Challenge (Tree Traversal & Recursion)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Construct Binary Tree from Preorder and Postorder Traversal Challenge (Tree Traversal & Recursion)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Construct Binary Tree from Preorder and Postorder Traversal Challenge (Tree Traversal & Recursion)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Construct Binary Tree from Preorder and Postorder Traversal Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Construct Binary Tree from Preorder and Postorder Traversal",
      "cpp_optimal": "// Solution for Construct Binary Tree from Preorder and Postorder Traversal",
      "java_brute": "// Solution for Construct Binary Tree from Preorder and Postorder Traversal",
      "java_optimal": "// Solution for Construct Binary Tree from Preorder and Postorder Traversal",
      "python_brute": "# Solution for Construct Binary Tree from Preorder and Postorder Traversal",
      "python_optimal": "# Solution for Construct Binary Tree from Preorder and Postorder Traversal"
    },
    "originalOrder": 650,
    "learningOrder": 650
  },
  {
    "id": 934,
    "number": 934,
    "sequence_number": 934,
    "title": "All Possible Full Binary Trees",
    "slug": "all-possible-full-binary-trees",
    "difficulty": "Medium",
    "topic": "Trees",
    "subtopic": "Tree Traversal & Recursion",
    "pattern": "Tree Traversal & Recursion",
    "secondary_patterns": [
      "Tree Traversal & Recursion"
    ],
    "stage": "Bit Manipulation, Math & Geometry",
    "curriculumStage": "Stage 19 — Bit Manipulation, Math & Geometry",
    "roadmapPhase": "Stage 19 — Bit Manipulation, Math & Geometry",
    "phase": "Stage 19 — Bit Manipulation, Math & Geometry",
    "estimatedTime": 30,
    "statement": "Solve the **All Possible Full Binary Trees Optimization** problem using the **Tree Traversal & Recursion** technique. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Tree Traversal & Recursion identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Tree Traversal & Recursion. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Tree Traversal & Recursion techniques by solving Medium problem constraints for All Possible Full Binary Trees Optimization.",
    "whyThisPattern": "When observing binary trees problem conditions, Tree Traversal & Recursion optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Meta",
      "Apple",
      "Netflix"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/all-possible-full-binary-trees/",
    "leetcode_title": "All Possible Full Binary Trees",
    "leetcode_id": 894,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/all-possible-full-binary-trees/",
    "canonicalSlug": "all-possible-full-binary-trees",
    "canonicalUrl": "https://leetcode.com/problems/all-possible-full-binary-trees/",
    "url": "https://leetcode.com/problems/all-possible-full-binary-trees/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for All Possible Full Binary Trees Optimization (Tree Traversal & Recursion)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for All Possible Full Binary Trees Optimization (Tree Traversal & Recursion)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for All Possible Full Binary Trees Optimization (Tree Traversal & Recursion)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for All Possible Full Binary Trees Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for All Possible Full Binary Trees Optimization (Tree Traversal & Recursion)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for All Possible Full Binary Trees Optimization (Tree Traversal & Recursion)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for All Possible Full Binary Trees Optimization (Tree Traversal & Recursion)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for All Possible Full Binary Trees Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for All Possible Full Binary Trees",
      "cpp_optimal": "// Solution for All Possible Full Binary Trees",
      "java_brute": "// Solution for All Possible Full Binary Trees",
      "java_optimal": "// Solution for All Possible Full Binary Trees",
      "python_brute": "# Solution for All Possible Full Binary Trees",
      "python_optimal": "# Solution for All Possible Full Binary Trees"
    },
    "originalOrder": 651,
    "learningOrder": 651
  },
  {
    "id": 935,
    "number": 935,
    "sequence_number": 935,
    "title": "Complete Binary Tree Inserter",
    "slug": "complete-binary-tree-inserter",
    "difficulty": "Medium",
    "topic": "Trees",
    "subtopic": "Tree Traversal & Recursion",
    "pattern": "Tree Traversal & Recursion",
    "secondary_patterns": [
      "Tree Traversal & Recursion"
    ],
    "stage": "Bit Manipulation, Math & Geometry",
    "curriculumStage": "Stage 19 — Bit Manipulation, Math & Geometry",
    "roadmapPhase": "Stage 19 — Bit Manipulation, Math & Geometry",
    "phase": "Stage 19 — Bit Manipulation, Math & Geometry",
    "estimatedTime": 30,
    "statement": "Solve the **Complete Binary Tree Inserter Challenge** problem using the **Tree Traversal & Recursion** technique. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Tree Traversal & Recursion identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Tree Traversal & Recursion. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Tree Traversal & Recursion techniques by solving Medium problem constraints for Complete Binary Tree Inserter Challenge.",
    "whyThisPattern": "When observing binary trees problem conditions, Tree Traversal & Recursion optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Meta",
      "Uber",
      "Databricks"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/complete-binary-tree-inserter/",
    "leetcode_title": "Complete Binary Tree Inserter",
    "leetcode_id": 919,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/complete-binary-tree-inserter/",
    "canonicalSlug": "complete-binary-tree-inserter",
    "canonicalUrl": "https://leetcode.com/problems/complete-binary-tree-inserter/",
    "url": "https://leetcode.com/problems/complete-binary-tree-inserter/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Complete Binary Tree Inserter Challenge (Tree Traversal & Recursion)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Complete Binary Tree Inserter Challenge (Tree Traversal & Recursion)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Complete Binary Tree Inserter Challenge (Tree Traversal & Recursion)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Complete Binary Tree Inserter Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Complete Binary Tree Inserter Challenge (Tree Traversal & Recursion)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Complete Binary Tree Inserter Challenge (Tree Traversal & Recursion)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Complete Binary Tree Inserter Challenge (Tree Traversal & Recursion)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Complete Binary Tree Inserter Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Complete Binary Tree Inserter",
      "cpp_optimal": "// Solution for Complete Binary Tree Inserter",
      "java_brute": "// Solution for Complete Binary Tree Inserter",
      "java_optimal": "// Solution for Complete Binary Tree Inserter",
      "python_brute": "# Solution for Complete Binary Tree Inserter",
      "python_optimal": "# Solution for Complete Binary Tree Inserter"
    },
    "originalOrder": 652,
    "learningOrder": 652
  },
  {
    "id": 936,
    "number": 936,
    "sequence_number": 936,
    "title": "Erect the Fence",
    "slug": "erect-the-fence",
    "difficulty": "Hard",
    "topic": "Geometry",
    "subtopic": "Geometry Optimization",
    "pattern": "Monotone Chain Convex Hull",
    "secondary_patterns": [
      "Monotone Chain Convex Hull"
    ],
    "stage": "Bit Manipulation, Math & Geometry",
    "curriculumStage": "Stage 19 — Bit Manipulation, Math & Geometry",
    "roadmapPhase": "Stage 19 — Bit Manipulation, Math & Geometry",
    "phase": "Stage 19 — Bit Manipulation, Math & Geometry",
    "estimatedTime": 45,
    "statement": "Given the constraints and input parameters for Erect the Fence, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Erect the Fence."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Erect the Fence.",
      "Leverage the optimal Geometry pattern to reduce time complexity."
    ],
    "learningObjective": "Master Geometry techniques by solving Hard problem constraints for Erect the Fence.",
    "whyThisPattern": "When observing Geometry problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/erect-the-fence/",
    "leetcode_title": "Erect the Fence",
    "leetcode_id": 587,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/erect-the-fence/",
    "canonicalSlug": "erect-the-fence",
    "canonicalUrl": "https://leetcode.com/problems/erect-the-fence/",
    "url": "https://leetcode.com/problems/erect-the-fence/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Erect the Fence\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Erect the Fence\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Erect the Fence\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Erect the Fence\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Erect the Fence\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Erect the Fence\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Erect the Fence\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Erect the Fence\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Erect the Fence",
      "cpp_optimal": "// Solution for Erect the Fence",
      "java_brute": "// Solution for Erect the Fence",
      "java_optimal": "// Solution for Erect the Fence",
      "python_brute": "# Solution for Erect the Fence",
      "python_optimal": "# Solution for Erect the Fence"
    },
    "originalOrder": 866,
    "learningOrder": 866
  },
  {
    "id": 937,
    "number": 937,
    "sequence_number": 937,
    "title": "Best Position for a Service Centre",
    "slug": "best-position-for-a-service-centre",
    "difficulty": "Hard",
    "topic": "Geometry",
    "subtopic": "Geometry Optimization",
    "pattern": "Weiszfeld Algorithm / Gradient Descent",
    "secondary_patterns": [
      "Weiszfeld Algorithm / Gradient Descent"
    ],
    "stage": "Bit Manipulation, Math & Geometry",
    "curriculumStage": "Stage 19 — Bit Manipulation, Math & Geometry",
    "roadmapPhase": "Stage 19 — Bit Manipulation, Math & Geometry",
    "phase": "Stage 19 — Bit Manipulation, Math & Geometry",
    "estimatedTime": 45,
    "statement": "Given the constraints and input parameters for Best Position for a Service Centre, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Best Position for a Service Centre."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Best Position for a Service Centre.",
      "Leverage the optimal Geometry pattern to reduce time complexity."
    ],
    "learningObjective": "Master Geometry techniques by solving Hard problem constraints for Best Position for a Service Centre.",
    "whyThisPattern": "When observing Geometry problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/best-position-for-a-service-centre/",
    "leetcode_title": "Best Position for a Service Centre",
    "leetcode_id": 1515,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/best-position-for-a-service-centre/",
    "canonicalSlug": "best-position-for-a-service-centre",
    "canonicalUrl": "https://leetcode.com/problems/best-position-for-a-service-centre/",
    "url": "https://leetcode.com/problems/best-position-for-a-service-centre/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Best Position for a Service Centre\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Best Position for a Service Centre\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Best Position for a Service Centre\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Best Position for a Service Centre\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Best Position for a Service Centre\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Best Position for a Service Centre\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Best Position for a Service Centre\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Best Position for a Service Centre\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Best Position for a Service Centre",
      "cpp_optimal": "// Solution for Best Position for a Service Centre",
      "java_brute": "// Solution for Best Position for a Service Centre",
      "java_optimal": "// Solution for Best Position for a Service Centre",
      "python_brute": "# Solution for Best Position for a Service Centre",
      "python_optimal": "# Solution for Best Position for a Service Centre"
    },
    "originalOrder": 867,
    "learningOrder": 867
  },
  {
    "id": 938,
    "number": 938,
    "sequence_number": 938,
    "title": "Perfect Rectangle",
    "slug": "perfect-rectangle",
    "difficulty": "Hard",
    "topic": "Geometry",
    "subtopic": "Geometry Optimization",
    "pattern": "Geometry Pattern",
    "secondary_patterns": [
      "Geometry Pattern"
    ],
    "stage": "Bit Manipulation, Math & Geometry",
    "curriculumStage": "Stage 19 — Bit Manipulation, Math & Geometry",
    "roadmapPhase": "Stage 19 — Bit Manipulation, Math & Geometry",
    "phase": "Stage 19 — Bit Manipulation, Math & Geometry",
    "estimatedTime": 45,
    "statement": "Solve the **Perfect Rectangle** problem using standard Geometry techniques. Given input constraints appropriate for Hard level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Geometry algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Geometry properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Geometry techniques by solving Hard problem constraints for Perfect Rectangle.",
    "whyThisPattern": "When observing Geometry problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/perfect-rectangle/",
    "leetcode_title": "Perfect Rectangle",
    "leetcode_id": 391,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/perfect-rectangle/",
    "canonicalSlug": "perfect-rectangle",
    "canonicalUrl": "https://leetcode.com/problems/perfect-rectangle/",
    "url": "https://leetcode.com/problems/perfect-rectangle/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Perfect Rectangle\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Perfect Rectangle\n};",
        "java": "// Java Solution for Perfect Rectangle\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Perfect Rectangle\n}",
        "python": "# Python Solution for Perfect Rectangle\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Perfect Rectangle\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Perfect Rectangle\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Perfect Rectangle\n};",
        "java": "// Optimal Java Solution for Perfect Rectangle\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Perfect Rectangle\n}",
        "python": "# Optimal Python Solution for Perfect Rectangle\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Perfect Rectangle\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Perfect Rectangle",
      "cpp_optimal": "// Solution for Perfect Rectangle",
      "java_brute": "// Solution for Perfect Rectangle",
      "java_optimal": "// Solution for Perfect Rectangle",
      "python_brute": "# Solution for Perfect Rectangle",
      "python_optimal": "# Solution for Perfect Rectangle"
    },
    "originalOrder": 868,
    "learningOrder": 868
  },
  {
    "id": 939,
    "number": 939,
    "sequence_number": 939,
    "title": "Online Majority Element In Subarray",
    "slug": "online-majority-element-in-subarray",
    "difficulty": "Hard",
    "topic": "Geometry",
    "subtopic": "Geometry Optimization",
    "pattern": "Geometry Pattern",
    "secondary_patterns": [
      "Geometry Pattern"
    ],
    "stage": "Bit Manipulation, Math & Geometry",
    "curriculumStage": "Stage 19 — Bit Manipulation, Math & Geometry",
    "roadmapPhase": "Stage 19 — Bit Manipulation, Math & Geometry",
    "phase": "Stage 19 — Bit Manipulation, Math & Geometry",
    "estimatedTime": 45,
    "statement": "Solve the **Online Majority Element In Subarray** problem using standard Geometry techniques. Given input constraints appropriate for Hard level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Geometry algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Geometry properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Geometry techniques by solving Hard problem constraints for Online Majority Element In Subarray.",
    "whyThisPattern": "When observing Geometry problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/online-majority-element-in-subarray/",
    "leetcode_title": "Online Majority Element In Subarray",
    "leetcode_id": 1157,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/online-majority-element-in-subarray/",
    "canonicalSlug": "online-majority-element-in-subarray",
    "canonicalUrl": "https://leetcode.com/problems/online-majority-element-in-subarray/",
    "url": "https://leetcode.com/problems/online-majority-element-in-subarray/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Online Majority Element In Subarray\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Online Majority Element In Subarray\n};",
        "java": "// Java Solution for Online Majority Element In Subarray\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Online Majority Element In Subarray\n}",
        "python": "# Python Solution for Online Majority Element In Subarray\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Online Majority Element In Subarray\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Online Majority Element In Subarray\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Online Majority Element In Subarray\n};",
        "java": "// Optimal Java Solution for Online Majority Element In Subarray\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Online Majority Element In Subarray\n}",
        "python": "# Optimal Python Solution for Online Majority Element In Subarray\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Online Majority Element In Subarray\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Online Majority Element In Subarray",
      "cpp_optimal": "// Solution for Online Majority Element In Subarray",
      "java_brute": "// Solution for Online Majority Element In Subarray",
      "java_optimal": "// Solution for Online Majority Element In Subarray",
      "python_brute": "# Solution for Online Majority Element In Subarray",
      "python_optimal": "# Solution for Online Majority Element In Subarray"
    },
    "originalOrder": 869,
    "learningOrder": 869
  },
  {
    "id": 940,
    "number": 940,
    "sequence_number": 940,
    "title": "Tiling a Rectangle with the Fewest Squares",
    "slug": "tiling-a-rectangle-with-the-fewest-squares",
    "difficulty": "Hard",
    "topic": "Geometry",
    "subtopic": "Geometry Optimization",
    "pattern": "Geometry Pattern",
    "secondary_patterns": [
      "Geometry Pattern"
    ],
    "stage": "Bit Manipulation, Math & Geometry",
    "curriculumStage": "Stage 19 — Bit Manipulation, Math & Geometry",
    "roadmapPhase": "Stage 19 — Bit Manipulation, Math & Geometry",
    "phase": "Stage 19 — Bit Manipulation, Math & Geometry",
    "estimatedTime": 45,
    "statement": "Solve the **Tiling a Rectangle with the Fewest Squares** problem using standard Geometry techniques. Given input constraints appropriate for Hard level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Geometry algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Geometry properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Geometry techniques by solving Hard problem constraints for Tiling a Rectangle with the Fewest Squares.",
    "whyThisPattern": "When observing Geometry problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/tiling-a-rectangle-with-the-fewest-squares/",
    "leetcode_title": "Tiling a Rectangle with the Fewest Squares",
    "leetcode_id": 1240,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/tiling-a-rectangle-with-the-fewest-squares/",
    "canonicalSlug": "tiling-a-rectangle-with-the-fewest-squares",
    "canonicalUrl": "https://leetcode.com/problems/tiling-a-rectangle-with-the-fewest-squares/",
    "url": "https://leetcode.com/problems/tiling-a-rectangle-with-the-fewest-squares/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Tiling a Rectangle with the Fewest Squares\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Tiling a Rectangle with the Fewest Squares\n};",
        "java": "// Java Solution for Tiling a Rectangle with the Fewest Squares\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Tiling a Rectangle with the Fewest Squares\n}",
        "python": "# Python Solution for Tiling a Rectangle with the Fewest Squares\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Tiling a Rectangle with the Fewest Squares\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Tiling a Rectangle with the Fewest Squares\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Tiling a Rectangle with the Fewest Squares\n};",
        "java": "// Optimal Java Solution for Tiling a Rectangle with the Fewest Squares\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Tiling a Rectangle with the Fewest Squares\n}",
        "python": "# Optimal Python Solution for Tiling a Rectangle with the Fewest Squares\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Tiling a Rectangle with the Fewest Squares\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Tiling a Rectangle with the Fewest Squares",
      "cpp_optimal": "// Solution for Tiling a Rectangle with the Fewest Squares",
      "java_brute": "// Solution for Tiling a Rectangle with the Fewest Squares",
      "java_optimal": "// Solution for Tiling a Rectangle with the Fewest Squares",
      "python_brute": "# Solution for Tiling a Rectangle with the Fewest Squares",
      "python_optimal": "# Solution for Tiling a Rectangle with the Fewest Squares"
    },
    "originalOrder": 870,
    "learningOrder": 870
  },
  {
    "id": 941,
    "number": 941,
    "sequence_number": 941,
    "title": "Super Palindromes",
    "slug": "super-palindromes",
    "difficulty": "Hard",
    "topic": "Math",
    "subtopic": "Math Optimization",
    "pattern": "Palindrome Square Search",
    "secondary_patterns": [
      "Palindrome Square Search"
    ],
    "stage": "Bit Manipulation, Math & Geometry",
    "curriculumStage": "Stage 19 — Bit Manipulation, Math & Geometry",
    "roadmapPhase": "Stage 19 — Bit Manipulation, Math & Geometry",
    "phase": "Stage 19 — Bit Manipulation, Math & Geometry",
    "estimatedTime": 45,
    "statement": "Given the constraints and input parameters for Super Palindromes, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Super Palindromes."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Super Palindromes.",
      "Leverage the optimal Math pattern to reduce time complexity."
    ],
    "learningObjective": "Master Math techniques by solving Hard problem constraints for Super Palindromes.",
    "whyThisPattern": "When observing Math problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/super-palindromes/",
    "leetcode_title": "Super Palindromes",
    "leetcode_id": 906,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/super-palindromes/",
    "canonicalSlug": "super-palindromes",
    "canonicalUrl": "https://leetcode.com/problems/super-palindromes/",
    "url": "https://leetcode.com/problems/super-palindromes/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Super Palindromes\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Super Palindromes\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Super Palindromes\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Super Palindromes\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Super Palindromes\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Super Palindromes\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Super Palindromes\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Super Palindromes\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Super Palindromes",
      "cpp_optimal": "// Solution for Super Palindromes",
      "java_brute": "// Solution for Super Palindromes",
      "java_optimal": "// Solution for Super Palindromes",
      "python_brute": "# Solution for Super Palindromes",
      "python_optimal": "# Solution for Super Palindromes"
    },
    "originalOrder": 917,
    "learningOrder": 917
  },
  {
    "id": 942,
    "number": 942,
    "sequence_number": 942,
    "title": "Reaching Points",
    "slug": "reaching-points",
    "difficulty": "Hard",
    "topic": "Math",
    "subtopic": "Math Optimization",
    "pattern": "Modulo Backward Reduction",
    "secondary_patterns": [
      "Modulo Backward Reduction"
    ],
    "stage": "Bit Manipulation, Math & Geometry",
    "curriculumStage": "Stage 19 — Bit Manipulation, Math & Geometry",
    "roadmapPhase": "Stage 19 — Bit Manipulation, Math & Geometry",
    "phase": "Stage 19 — Bit Manipulation, Math & Geometry",
    "estimatedTime": 45,
    "statement": "Given the constraints and input parameters for Reaching Points, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Reaching Points."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Reaching Points.",
      "Leverage the optimal Math pattern to reduce time complexity."
    ],
    "learningObjective": "Master Math techniques by solving Hard problem constraints for Reaching Points.",
    "whyThisPattern": "When observing Math problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/reaching-points/",
    "leetcode_title": "Reaching Points",
    "leetcode_id": 780,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/reaching-points/",
    "canonicalSlug": "reaching-points",
    "canonicalUrl": "https://leetcode.com/problems/reaching-points/",
    "url": "https://leetcode.com/problems/reaching-points/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Reaching Points\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Reaching Points\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Reaching Points\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Reaching Points\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Reaching Points\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Reaching Points\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Reaching Points\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Reaching Points\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Reaching Points",
      "cpp_optimal": "// Solution for Reaching Points",
      "java_brute": "// Solution for Reaching Points",
      "java_optimal": "// Solution for Reaching Points",
      "python_brute": "# Solution for Reaching Points",
      "python_optimal": "# Solution for Reaching Points"
    },
    "originalOrder": 918,
    "learningOrder": 918
  },
  {
    "id": 943,
    "number": 943,
    "sequence_number": 943,
    "title": "Equal Rational Numbers",
    "slug": "equal-rational-numbers",
    "difficulty": "Hard",
    "topic": "Math",
    "subtopic": "Math Optimization",
    "pattern": "Fraction Parsing Equality",
    "secondary_patterns": [
      "Fraction Parsing Equality"
    ],
    "stage": "Bit Manipulation, Math & Geometry",
    "curriculumStage": "Stage 19 — Bit Manipulation, Math & Geometry",
    "roadmapPhase": "Stage 19 — Bit Manipulation, Math & Geometry",
    "phase": "Stage 19 — Bit Manipulation, Math & Geometry",
    "estimatedTime": 45,
    "statement": "Given the constraints and input parameters for Equal Rational Numbers, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Equal Rational Numbers."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Equal Rational Numbers.",
      "Leverage the optimal Math pattern to reduce time complexity."
    ],
    "learningObjective": "Master Math techniques by solving Hard problem constraints for Equal Rational Numbers.",
    "whyThisPattern": "When observing Math problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/equal-rational-numbers/",
    "leetcode_title": "Equal Rational Numbers",
    "leetcode_id": 972,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/equal-rational-numbers/",
    "canonicalSlug": "equal-rational-numbers",
    "canonicalUrl": "https://leetcode.com/problems/equal-rational-numbers/",
    "url": "https://leetcode.com/problems/equal-rational-numbers/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Equal Rational Numbers\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Equal Rational Numbers\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Equal Rational Numbers\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Equal Rational Numbers\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Equal Rational Numbers\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Equal Rational Numbers\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Equal Rational Numbers\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Equal Rational Numbers\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Equal Rational Numbers",
      "cpp_optimal": "// Solution for Equal Rational Numbers",
      "java_brute": "// Solution for Equal Rational Numbers",
      "java_optimal": "// Solution for Equal Rational Numbers",
      "python_brute": "# Solution for Equal Rational Numbers",
      "python_optimal": "# Solution for Equal Rational Numbers"
    },
    "originalOrder": 919,
    "learningOrder": 919
  },
  {
    "id": 944,
    "number": 944,
    "sequence_number": 944,
    "title": "Number of Digit One",
    "slug": "number-of-digit-one",
    "difficulty": "Hard",
    "topic": "Math",
    "subtopic": "Math Optimization",
    "pattern": "Digit Position Count Formula",
    "secondary_patterns": [
      "Digit Position Count Formula"
    ],
    "stage": "Bit Manipulation, Math & Geometry",
    "curriculumStage": "Stage 19 — Bit Manipulation, Math & Geometry",
    "roadmapPhase": "Stage 19 — Bit Manipulation, Math & Geometry",
    "phase": "Stage 19 — Bit Manipulation, Math & Geometry",
    "estimatedTime": 45,
    "statement": "Given the constraints and input parameters for Number of Digit One, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Number of Digit One."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Number of Digit One.",
      "Leverage the optimal Math pattern to reduce time complexity."
    ],
    "learningObjective": "Master Math techniques by solving Hard problem constraints for Number of Digit One.",
    "whyThisPattern": "When observing Math problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/number-of-digit-one/",
    "leetcode_title": "Number of Digit One",
    "leetcode_id": 233,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/number-of-digit-one/",
    "canonicalSlug": "number-of-digit-one",
    "canonicalUrl": "https://leetcode.com/problems/number-of-digit-one/",
    "url": "https://leetcode.com/problems/number-of-digit-one/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Number of Digit One\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Number of Digit One\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Number of Digit One\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Number of Digit One\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Number of Digit One\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Number of Digit One\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Number of Digit One\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Number of Digit One\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Number of Digit One",
      "cpp_optimal": "// Solution for Number of Digit One",
      "java_brute": "// Solution for Number of Digit One",
      "java_optimal": "// Solution for Number of Digit One",
      "python_brute": "# Solution for Number of Digit One",
      "python_optimal": "# Solution for Number of Digit One"
    },
    "originalOrder": 920,
    "learningOrder": 920
  },
  {
    "id": 945,
    "number": 945,
    "sequence_number": 945,
    "title": "Self Crossing",
    "slug": "self-crossing",
    "difficulty": "Hard",
    "topic": "Math",
    "subtopic": "Math Optimization",
    "pattern": "Segment Intersection Conditions",
    "secondary_patterns": [
      "Segment Intersection Conditions"
    ],
    "stage": "Bit Manipulation, Math & Geometry",
    "curriculumStage": "Stage 19 — Bit Manipulation, Math & Geometry",
    "roadmapPhase": "Stage 19 — Bit Manipulation, Math & Geometry",
    "phase": "Stage 19 — Bit Manipulation, Math & Geometry",
    "estimatedTime": 45,
    "statement": "Given the constraints and input parameters for Self Crossing, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Self Crossing."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Self Crossing.",
      "Leverage the optimal Math pattern to reduce time complexity."
    ],
    "learningObjective": "Master Math techniques by solving Hard problem constraints for Self Crossing.",
    "whyThisPattern": "When observing Math problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/self-crossing/",
    "leetcode_title": "Self Crossing",
    "leetcode_id": 335,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/self-crossing/",
    "canonicalSlug": "self-crossing",
    "canonicalUrl": "https://leetcode.com/problems/self-crossing/",
    "url": "https://leetcode.com/problems/self-crossing/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Self Crossing\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Self Crossing\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Self Crossing\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Self Crossing\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Self Crossing\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Self Crossing\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Self Crossing\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Self Crossing\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Self Crossing",
      "cpp_optimal": "// Solution for Self Crossing",
      "java_brute": "// Solution for Self Crossing",
      "java_optimal": "// Solution for Self Crossing",
      "python_brute": "# Solution for Self Crossing",
      "python_optimal": "# Solution for Self Crossing"
    },
    "originalOrder": 921,
    "learningOrder": 921
  },
  {
    "id": 946,
    "number": 946,
    "sequence_number": 946,
    "title": "Count Array Pairs Divisible by K",
    "slug": "count-array-pairs-divisible-by-k",
    "difficulty": "Hard",
    "topic": "Math",
    "subtopic": "Math Optimization",
    "pattern": "GCD Map Frequency Pairs",
    "secondary_patterns": [
      "GCD Map Frequency Pairs"
    ],
    "stage": "Bit Manipulation, Math & Geometry",
    "curriculumStage": "Stage 19 — Bit Manipulation, Math & Geometry",
    "roadmapPhase": "Stage 19 — Bit Manipulation, Math & Geometry",
    "phase": "Stage 19 — Bit Manipulation, Math & Geometry",
    "estimatedTime": 45,
    "statement": "Given the constraints and input parameters for Count Array Pairs Divisible by K, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Count Array Pairs Divisible by K."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Count Array Pairs Divisible by K.",
      "Leverage the optimal Math pattern to reduce time complexity."
    ],
    "learningObjective": "Master Math techniques by solving Hard problem constraints for Count Array Pairs Divisible by K.",
    "whyThisPattern": "When observing Math problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/count-array-pairs-divisible-by-k/",
    "leetcode_title": "Count Array Pairs Divisible by K",
    "leetcode_id": 2183,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/count-array-pairs-divisible-by-k/",
    "canonicalSlug": "count-array-pairs-divisible-by-k",
    "canonicalUrl": "https://leetcode.com/problems/count-array-pairs-divisible-by-k/",
    "url": "https://leetcode.com/problems/count-array-pairs-divisible-by-k/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Count Array Pairs Divisible by K\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Count Array Pairs Divisible by K\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Count Array Pairs Divisible by K\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Count Array Pairs Divisible by K\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Count Array Pairs Divisible by K\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Count Array Pairs Divisible by K\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Count Array Pairs Divisible by K\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Count Array Pairs Divisible by K\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Count Array Pairs Divisible by K",
      "cpp_optimal": "// Solution for Count Array Pairs Divisible by K",
      "java_brute": "// Solution for Count Array Pairs Divisible by K",
      "java_optimal": "// Solution for Count Array Pairs Divisible by K",
      "python_brute": "# Solution for Count Array Pairs Divisible by K",
      "python_optimal": "# Solution for Count Array Pairs Divisible by K"
    },
    "originalOrder": 922,
    "learningOrder": 922
  },
  {
    "id": 947,
    "number": 947,
    "sequence_number": 947,
    "title": "Preimage Size of Factorial Zeroes Function",
    "slug": "preimage-size-of-factorial-zeroes-function",
    "difficulty": "Hard",
    "topic": "Math",
    "subtopic": "Math Optimization",
    "pattern": "Math Pattern",
    "secondary_patterns": [
      "Math Pattern"
    ],
    "stage": "Bit Manipulation, Math & Geometry",
    "curriculumStage": "Stage 19 — Bit Manipulation, Math & Geometry",
    "roadmapPhase": "Stage 19 — Bit Manipulation, Math & Geometry",
    "phase": "Stage 19 — Bit Manipulation, Math & Geometry",
    "estimatedTime": 45,
    "statement": "Solve the **Preimage Size of Factorial Zeroes Function** problem using standard Math techniques. Given input constraints appropriate for Hard level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Math algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Math properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Math techniques by solving Hard problem constraints for Preimage Size of Factorial Zeroes Function.",
    "whyThisPattern": "When observing Math problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/preimage-size-of-factorial-zeroes-function/",
    "leetcode_title": "Preimage Size of Factorial Zeroes Function",
    "leetcode_id": 793,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/preimage-size-of-factorial-zeroes-function/",
    "canonicalSlug": "preimage-size-of-factorial-zeroes-function",
    "canonicalUrl": "https://leetcode.com/problems/preimage-size-of-factorial-zeroes-function/",
    "url": "https://leetcode.com/problems/preimage-size-of-factorial-zeroes-function/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Preimage Size of Factorial Zeroes Function\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Preimage Size of Factorial Zeroes Function\n};",
        "java": "// Java Solution for Preimage Size of Factorial Zeroes Function\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Preimage Size of Factorial Zeroes Function\n}",
        "python": "# Python Solution for Preimage Size of Factorial Zeroes Function\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Preimage Size of Factorial Zeroes Function\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Preimage Size of Factorial Zeroes Function\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Preimage Size of Factorial Zeroes Function\n};",
        "java": "// Optimal Java Solution for Preimage Size of Factorial Zeroes Function\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Preimage Size of Factorial Zeroes Function\n}",
        "python": "# Optimal Python Solution for Preimage Size of Factorial Zeroes Function\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Preimage Size of Factorial Zeroes Function\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Preimage Size of Factorial Zeroes Function",
      "cpp_optimal": "// Solution for Preimage Size of Factorial Zeroes Function",
      "java_brute": "// Solution for Preimage Size of Factorial Zeroes Function",
      "java_optimal": "// Solution for Preimage Size of Factorial Zeroes Function",
      "python_brute": "# Solution for Preimage Size of Factorial Zeroes Function",
      "python_optimal": "# Solution for Preimage Size of Factorial Zeroes Function"
    },
    "originalOrder": 923,
    "learningOrder": 923
  },
  {
    "id": 948,
    "number": 948,
    "sequence_number": 948,
    "title": "Max Dot Product of Two Subsequences",
    "slug": "max-dot-product-of-two-subsequences",
    "difficulty": "Hard",
    "topic": "Dynamic Programming",
    "subtopic": "Dynamic Programming Optimization",
    "pattern": "2D Subsequence Dot Product DP",
    "secondary_patterns": [
      "2D Subsequence Dot Product DP"
    ],
    "stage": "Bit Manipulation, Math & Geometry",
    "curriculumStage": "Stage 19 — Bit Manipulation, Math & Geometry",
    "roadmapPhase": "Stage 19 — Bit Manipulation, Math & Geometry",
    "phase": "Stage 19 — Bit Manipulation, Math & Geometry",
    "estimatedTime": 45,
    "statement": "Given the constraints and input parameters for Max Dot Product of Two Subsequences, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Max Dot Product of Two Subsequences."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Max Dot Product of Two Subsequences.",
      "Leverage the optimal Dynamic Programming pattern to reduce time complexity."
    ],
    "learningObjective": "Master Dynamic Programming techniques by solving Hard problem constraints for Max Dot Product of Two Subsequences.",
    "whyThisPattern": "When observing Dynamic Programming problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/max-dot-product-of-two-subsequences/",
    "leetcode_title": "Max Dot Product of Two Subsequences",
    "leetcode_id": 1458,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/max-dot-product-of-two-subsequences/",
    "canonicalSlug": "max-dot-product-of-two-subsequences",
    "canonicalUrl": "https://leetcode.com/problems/max-dot-product-of-two-subsequences/",
    "url": "https://leetcode.com/problems/max-dot-product-of-two-subsequences/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Max Dot Product of Two Subsequences\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Max Dot Product of Two Subsequences\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Max Dot Product of Two Subsequences\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Max Dot Product of Two Subsequences\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Max Dot Product of Two Subsequences\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Max Dot Product of Two Subsequences\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Max Dot Product of Two Subsequences\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Max Dot Product of Two Subsequences\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Max Dot Product of Two Subsequences",
      "cpp_optimal": "// Solution for Max Dot Product of Two Subsequences",
      "java_brute": "// Solution for Max Dot Product of Two Subsequences",
      "java_optimal": "// Solution for Max Dot Product of Two Subsequences",
      "python_brute": "# Solution for Max Dot Product of Two Subsequences",
      "python_optimal": "# Solution for Max Dot Product of Two Subsequences"
    },
    "originalOrder": 861,
    "learningOrder": 861
  },
  {
    "id": 949,
    "number": 949,
    "sequence_number": 949,
    "title": "Minimum Cost to Connect Two Groups of Points",
    "slug": "minimum-cost-to-connect-two-groups-of-points",
    "difficulty": "Hard",
    "topic": "Dynamic Programming",
    "subtopic": "Dynamic Programming Optimization",
    "pattern": "Bipartite Bitmask DP",
    "secondary_patterns": [
      "Bipartite Bitmask DP"
    ],
    "stage": "Bit Manipulation, Math & Geometry",
    "curriculumStage": "Stage 19 — Bit Manipulation, Math & Geometry",
    "roadmapPhase": "Stage 19 — Bit Manipulation, Math & Geometry",
    "phase": "Stage 19 — Bit Manipulation, Math & Geometry",
    "estimatedTime": 45,
    "statement": "Given the constraints and input parameters for Minimum Cost to Connect Two Groups of Points, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Minimum Cost to Connect Two Groups of Points."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Minimum Cost to Connect Two Groups of Points.",
      "Leverage the optimal Dynamic Programming pattern to reduce time complexity."
    ],
    "learningObjective": "Master Dynamic Programming techniques by solving Hard problem constraints for Minimum Cost to Connect Two Groups of Points.",
    "whyThisPattern": "When observing Dynamic Programming problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/minimum-cost-to-connect-two-groups-of-points/",
    "leetcode_title": "Minimum Cost to Connect Two Groups of Points",
    "leetcode_id": 1595,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/minimum-cost-to-connect-two-groups-of-points/",
    "canonicalSlug": "minimum-cost-to-connect-two-groups-of-points",
    "canonicalUrl": "https://leetcode.com/problems/minimum-cost-to-connect-two-groups-of-points/",
    "url": "https://leetcode.com/problems/minimum-cost-to-connect-two-groups-of-points/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Minimum Cost to Connect Two Groups of Points\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Minimum Cost to Connect Two Groups of Points\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Minimum Cost to Connect Two Groups of Points\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Minimum Cost to Connect Two Groups of Points\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Minimum Cost to Connect Two Groups of Points\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Minimum Cost to Connect Two Groups of Points\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Minimum Cost to Connect Two Groups of Points\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Minimum Cost to Connect Two Groups of Points\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Minimum Cost to Connect Two Groups of Points",
      "cpp_optimal": "// Solution for Minimum Cost to Connect Two Groups of Points",
      "java_brute": "// Solution for Minimum Cost to Connect Two Groups of Points",
      "java_optimal": "// Solution for Minimum Cost to Connect Two Groups of Points",
      "python_brute": "# Solution for Minimum Cost to Connect Two Groups of Points",
      "python_optimal": "# Solution for Minimum Cost to Connect Two Groups of Points"
    },
    "originalOrder": 862,
    "learningOrder": 862
  },
  {
    "id": 950,
    "number": 950,
    "sequence_number": 950,
    "title": "Number of Ways to Form a Target String Given a Dictionary",
    "slug": "number-of-ways-to-form-a-target-string-given-a-dictionary",
    "difficulty": "Hard",
    "topic": "Dynamic Programming",
    "subtopic": "Dynamic Programming Optimization",
    "pattern": "2D Frequency Vector Target DP",
    "secondary_patterns": [
      "2D Frequency Vector Target DP"
    ],
    "stage": "Bit Manipulation, Math & Geometry",
    "curriculumStage": "Stage 19 — Bit Manipulation, Math & Geometry",
    "roadmapPhase": "Stage 19 — Bit Manipulation, Math & Geometry",
    "phase": "Stage 19 — Bit Manipulation, Math & Geometry",
    "estimatedTime": 45,
    "statement": "Given the constraints and input parameters for Number of Ways to Form a Target String Given a Dictionary, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Number of Ways to Form a Target String Given a Dictionary."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Number of Ways to Form a Target String Given a Dictionary.",
      "Leverage the optimal Dynamic Programming pattern to reduce time complexity."
    ],
    "learningObjective": "Master Dynamic Programming techniques by solving Hard problem constraints for Number of Ways to Form a Target String Given a Dictionary.",
    "whyThisPattern": "When observing Dynamic Programming problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/number-of-ways-to-form-a-target-string-given-a-dictionary/",
    "leetcode_title": "Number of Ways to Form a Target String Given a Dictionary",
    "leetcode_id": 1639,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/number-of-ways-to-form-a-target-string-given-a-dictionary/",
    "canonicalSlug": "number-of-ways-to-form-a-target-string-given-a-dictionary",
    "canonicalUrl": "https://leetcode.com/problems/number-of-ways-to-form-a-target-string-given-a-dictionary/",
    "url": "https://leetcode.com/problems/number-of-ways-to-form-a-target-string-given-a-dictionary/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Number of Ways to Form a Target String Given a Dictionary\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Number of Ways to Form a Target String Given a Dictionary\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Number of Ways to Form a Target String Given a Dictionary\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Number of Ways to Form a Target String Given a Dictionary\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Number of Ways to Form a Target String Given a Dictionary\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Number of Ways to Form a Target String Given a Dictionary\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Number of Ways to Form a Target String Given a Dictionary\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Number of Ways to Form a Target String Given a Dictionary\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Number of Ways to Form a Target String Given a Dictionary",
      "cpp_optimal": "// Solution for Number of Ways to Form a Target String Given a Dictionary",
      "java_brute": "// Solution for Number of Ways to Form a Target String Given a Dictionary",
      "java_optimal": "// Solution for Number of Ways to Form a Target String Given a Dictionary",
      "python_brute": "# Solution for Number of Ways to Form a Target String Given a Dictionary",
      "python_optimal": "# Solution for Number of Ways to Form a Target String Given a Dictionary"
    },
    "originalOrder": 863,
    "learningOrder": 863
  },
  {
    "id": 951,
    "number": 951,
    "sequence_number": 951,
    "title": "Goat Latin",
    "slug": "goat-latin",
    "difficulty": "Easy",
    "topic": "Strings",
    "subtopic": "Strings Optimization",
    "pattern": "Vowel/Consonant String Transform",
    "secondary_patterns": [
      "Vowel/Consonant String Transform"
    ],
    "stage": "Segment Trees & Advanced Structures",
    "curriculumStage": "Stage 20 — Segment Trees & Advanced Structures",
    "roadmapPhase": "Stage 20 — Segment Trees & Advanced Structures",
    "phase": "Stage 20 — Segment Trees & Advanced Structures",
    "estimatedTime": 15,
    "statement": "Given the constraints and input parameters for Goat Latin, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Goat Latin."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Goat Latin.",
      "Leverage the optimal Strings pattern to reduce time complexity."
    ],
    "learningObjective": "Master Strings techniques by solving Easy problem constraints for Goat Latin.",
    "whyThisPattern": "When observing Strings problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/goat-latin/",
    "leetcode_title": "Goat Latin",
    "leetcode_id": 824,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/goat-latin/",
    "canonicalSlug": "goat-latin",
    "canonicalUrl": "https://leetcode.com/problems/goat-latin/",
    "url": "https://leetcode.com/problems/goat-latin/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Goat Latin\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Goat Latin\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Goat Latin\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Goat Latin\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Goat Latin\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Goat Latin\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Goat Latin\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Goat Latin\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Goat Latin",
      "cpp_optimal": "// Solution for Goat Latin",
      "java_brute": "// Solution for Goat Latin",
      "java_optimal": "// Solution for Goat Latin",
      "python_brute": "# Solution for Goat Latin",
      "python_optimal": "# Solution for Goat Latin"
    },
    "originalOrder": 206,
    "learningOrder": 206
  },
  {
    "id": 952,
    "number": 952,
    "sequence_number": 952,
    "title": "Find Common Characters",
    "slug": "find-common-characters",
    "difficulty": "Easy",
    "topic": "Strings",
    "subtopic": "Strings Optimization",
    "pattern": "Frequency Min Intersect",
    "secondary_patterns": [
      "Frequency Min Intersect"
    ],
    "stage": "Segment Trees & Advanced Structures",
    "curriculumStage": "Stage 20 — Segment Trees & Advanced Structures",
    "roadmapPhase": "Stage 20 — Segment Trees & Advanced Structures",
    "phase": "Stage 20 — Segment Trees & Advanced Structures",
    "estimatedTime": 15,
    "statement": "Given the constraints and input parameters for Find Common Characters, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Find Common Characters."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Find Common Characters.",
      "Leverage the optimal Strings pattern to reduce time complexity."
    ],
    "learningObjective": "Master Strings techniques by solving Easy problem constraints for Find Common Characters.",
    "whyThisPattern": "When observing Strings problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/find-common-characters/",
    "leetcode_title": "Find Common Characters",
    "leetcode_id": 1002,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/find-common-characters/",
    "canonicalSlug": "find-common-characters",
    "canonicalUrl": "https://leetcode.com/problems/find-common-characters/",
    "url": "https://leetcode.com/problems/find-common-characters/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Find Common Characters\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Find Common Characters\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Find Common Characters\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Find Common Characters\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Find Common Characters\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Find Common Characters\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Find Common Characters\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Find Common Characters\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Find Common Characters",
      "cpp_optimal": "// Solution for Find Common Characters",
      "java_brute": "// Solution for Find Common Characters",
      "java_optimal": "// Solution for Find Common Characters",
      "python_brute": "# Solution for Find Common Characters",
      "python_optimal": "# Solution for Find Common Characters"
    },
    "originalOrder": 207,
    "learningOrder": 207
  },
  {
    "id": 953,
    "number": 953,
    "sequence_number": 953,
    "title": "Greatest Common Divisor of Strings",
    "slug": "greatest-common-divisor-of-strings",
    "difficulty": "Easy",
    "topic": "Strings",
    "subtopic": "Strings Optimization",
    "pattern": "GCD String Length Check",
    "secondary_patterns": [
      "GCD String Length Check"
    ],
    "stage": "Segment Trees & Advanced Structures",
    "curriculumStage": "Stage 20 — Segment Trees & Advanced Structures",
    "roadmapPhase": "Stage 20 — Segment Trees & Advanced Structures",
    "phase": "Stage 20 — Segment Trees & Advanced Structures",
    "estimatedTime": 15,
    "statement": "Given the constraints and input parameters for Greatest Common Divisor of Strings, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Greatest Common Divisor of Strings."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Greatest Common Divisor of Strings.",
      "Leverage the optimal Strings pattern to reduce time complexity."
    ],
    "learningObjective": "Master Strings techniques by solving Easy problem constraints for Greatest Common Divisor of Strings.",
    "whyThisPattern": "When observing Strings problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/greatest-common-divisor-of-strings/",
    "leetcode_title": "Greatest Common Divisor of Strings",
    "leetcode_id": 1071,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/greatest-common-divisor-of-strings/",
    "canonicalSlug": "greatest-common-divisor-of-strings",
    "canonicalUrl": "https://leetcode.com/problems/greatest-common-divisor-of-strings/",
    "url": "https://leetcode.com/problems/greatest-common-divisor-of-strings/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Greatest Common Divisor of Strings\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Greatest Common Divisor of Strings\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Greatest Common Divisor of Strings\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Greatest Common Divisor of Strings\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Greatest Common Divisor of Strings\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Greatest Common Divisor of Strings\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Greatest Common Divisor of Strings\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Greatest Common Divisor of Strings\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Greatest Common Divisor of Strings",
      "cpp_optimal": "// Solution for Greatest Common Divisor of Strings",
      "java_brute": "// Solution for Greatest Common Divisor of Strings",
      "java_optimal": "// Solution for Greatest Common Divisor of Strings",
      "python_brute": "# Solution for Greatest Common Divisor of Strings",
      "python_optimal": "# Solution for Greatest Common Divisor of Strings"
    },
    "originalOrder": 208,
    "learningOrder": 208
  },
  {
    "id": 954,
    "number": 954,
    "sequence_number": 954,
    "title": "Split a String in Balanced Strings",
    "slug": "split-a-string-in-balanced-strings",
    "difficulty": "Easy",
    "topic": "Strings",
    "subtopic": "Strings Optimization",
    "pattern": "Greedy Counter",
    "secondary_patterns": [
      "Greedy Counter"
    ],
    "stage": "Segment Trees & Advanced Structures",
    "curriculumStage": "Stage 20 — Segment Trees & Advanced Structures",
    "roadmapPhase": "Stage 20 — Segment Trees & Advanced Structures",
    "phase": "Stage 20 — Segment Trees & Advanced Structures",
    "estimatedTime": 15,
    "statement": "Given the constraints and input parameters for Split a String in Balanced Strings, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Split a String in Balanced Strings."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Split a String in Balanced Strings.",
      "Leverage the optimal Strings pattern to reduce time complexity."
    ],
    "learningObjective": "Master Strings techniques by solving Easy problem constraints for Split a String in Balanced Strings.",
    "whyThisPattern": "When observing Strings problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/split-a-string-in-balanced-strings/",
    "leetcode_title": "Split a String in Balanced Strings",
    "leetcode_id": 1221,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/split-a-string-in-balanced-strings/",
    "canonicalSlug": "split-a-string-in-balanced-strings",
    "canonicalUrl": "https://leetcode.com/problems/split-a-string-in-balanced-strings/",
    "url": "https://leetcode.com/problems/split-a-string-in-balanced-strings/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Split a String in Balanced Strings\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Split a String in Balanced Strings\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Split a String in Balanced Strings\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Split a String in Balanced Strings\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Split a String in Balanced Strings\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Split a String in Balanced Strings\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Split a String in Balanced Strings\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Split a String in Balanced Strings\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Split a String in Balanced Strings",
      "cpp_optimal": "// Solution for Split a String in Balanced Strings",
      "java_brute": "// Solution for Split a String in Balanced Strings",
      "java_optimal": "// Solution for Split a String in Balanced Strings",
      "python_brute": "# Solution for Split a String in Balanced Strings",
      "python_optimal": "# Solution for Split a String in Balanced Strings"
    },
    "originalOrder": 209,
    "learningOrder": 209
  },
  {
    "id": 955,
    "number": 955,
    "sequence_number": 955,
    "title": "Reformat The String",
    "slug": "reformat-the-string",
    "difficulty": "Easy",
    "topic": "Strings",
    "subtopic": "Strings Optimization",
    "pattern": "Alpha-Digit Interleave",
    "secondary_patterns": [
      "Alpha-Digit Interleave"
    ],
    "stage": "Segment Trees & Advanced Structures",
    "curriculumStage": "Stage 20 — Segment Trees & Advanced Structures",
    "roadmapPhase": "Stage 20 — Segment Trees & Advanced Structures",
    "phase": "Stage 20 — Segment Trees & Advanced Structures",
    "estimatedTime": 15,
    "statement": "Given the constraints and input parameters for Reformat The String, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Reformat The String."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Reformat The String.",
      "Leverage the optimal Strings pattern to reduce time complexity."
    ],
    "learningObjective": "Master Strings techniques by solving Easy problem constraints for Reformat The String.",
    "whyThisPattern": "When observing Strings problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/reformat-the-string/",
    "leetcode_title": "Reformat The String",
    "leetcode_id": 1417,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/reformat-the-string/",
    "canonicalSlug": "reformat-the-string",
    "canonicalUrl": "https://leetcode.com/problems/reformat-the-string/",
    "url": "https://leetcode.com/problems/reformat-the-string/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Reformat The String\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Reformat The String\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Reformat The String\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Reformat The String\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Reformat The String\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Reformat The String\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Reformat The String\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Reformat The String\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Reformat The String",
      "cpp_optimal": "// Solution for Reformat The String",
      "java_brute": "// Solution for Reformat The String",
      "java_optimal": "// Solution for Reformat The String",
      "python_brute": "# Solution for Reformat The String",
      "python_optimal": "# Solution for Reformat The String"
    },
    "originalOrder": 210,
    "learningOrder": 210
  },
  {
    "id": 956,
    "number": 956,
    "sequence_number": 956,
    "title": "Consecutive Characters",
    "slug": "consecutive-characters",
    "difficulty": "Easy",
    "topic": "Strings",
    "subtopic": "Strings Optimization",
    "pattern": "Max Streak Counter",
    "secondary_patterns": [
      "Max Streak Counter"
    ],
    "stage": "Segment Trees & Advanced Structures",
    "curriculumStage": "Stage 20 — Segment Trees & Advanced Structures",
    "roadmapPhase": "Stage 20 — Segment Trees & Advanced Structures",
    "phase": "Stage 20 — Segment Trees & Advanced Structures",
    "estimatedTime": 15,
    "statement": "Given the constraints and input parameters for Consecutive Characters, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Consecutive Characters."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Consecutive Characters.",
      "Leverage the optimal Strings pattern to reduce time complexity."
    ],
    "learningObjective": "Master Strings techniques by solving Easy problem constraints for Consecutive Characters.",
    "whyThisPattern": "When observing Strings problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/consecutive-characters/",
    "leetcode_title": "Consecutive Characters",
    "leetcode_id": 1446,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/consecutive-characters/",
    "canonicalSlug": "consecutive-characters",
    "canonicalUrl": "https://leetcode.com/problems/consecutive-characters/",
    "url": "https://leetcode.com/problems/consecutive-characters/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Consecutive Characters\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Consecutive Characters\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Consecutive Characters\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Consecutive Characters\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Consecutive Characters\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Consecutive Characters\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Consecutive Characters\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Consecutive Characters\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Consecutive Characters",
      "cpp_optimal": "// Solution for Consecutive Characters",
      "java_brute": "// Solution for Consecutive Characters",
      "java_optimal": "// Solution for Consecutive Characters",
      "python_brute": "# Solution for Consecutive Characters",
      "python_optimal": "# Solution for Consecutive Characters"
    },
    "originalOrder": 211,
    "learningOrder": 211
  },
  {
    "id": 957,
    "number": 957,
    "sequence_number": 957,
    "title": "Shuffle String",
    "slug": "shuffle-string",
    "difficulty": "Easy",
    "topic": "Strings",
    "subtopic": "Strings Optimization",
    "pattern": "Index Placement Swap",
    "secondary_patterns": [
      "Index Placement Swap"
    ],
    "stage": "Segment Trees & Advanced Structures",
    "curriculumStage": "Stage 20 — Segment Trees & Advanced Structures",
    "roadmapPhase": "Stage 20 — Segment Trees & Advanced Structures",
    "phase": "Stage 20 — Segment Trees & Advanced Structures",
    "estimatedTime": 15,
    "statement": "Given the constraints and input parameters for Shuffle String, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Shuffle String."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Shuffle String.",
      "Leverage the optimal Strings pattern to reduce time complexity."
    ],
    "learningObjective": "Master Strings techniques by solving Easy problem constraints for Shuffle String.",
    "whyThisPattern": "When observing Strings problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/shuffle-string/",
    "leetcode_title": "Shuffle String",
    "leetcode_id": 1528,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/shuffle-string/",
    "canonicalSlug": "shuffle-string",
    "canonicalUrl": "https://leetcode.com/problems/shuffle-string/",
    "url": "https://leetcode.com/problems/shuffle-string/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Shuffle String\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Shuffle String\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Shuffle String\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Shuffle String\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Shuffle String\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Shuffle String\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Shuffle String\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Shuffle String\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Shuffle String",
      "cpp_optimal": "// Solution for Shuffle String",
      "java_brute": "// Solution for Shuffle String",
      "java_optimal": "// Solution for Shuffle String",
      "python_brute": "# Solution for Shuffle String",
      "python_optimal": "# Solution for Shuffle String"
    },
    "originalOrder": 212,
    "learningOrder": 212
  },
  {
    "id": 958,
    "number": 958,
    "sequence_number": 958,
    "title": "Reformat Date",
    "slug": "reformat-date",
    "difficulty": "Easy",
    "topic": "Strings",
    "subtopic": "Strings Optimization",
    "pattern": "Date Parsing",
    "secondary_patterns": [
      "Date Parsing"
    ],
    "stage": "Segment Trees & Advanced Structures",
    "curriculumStage": "Stage 20 — Segment Trees & Advanced Structures",
    "roadmapPhase": "Stage 20 — Segment Trees & Advanced Structures",
    "phase": "Stage 20 — Segment Trees & Advanced Structures",
    "estimatedTime": 15,
    "statement": "Given the constraints and input parameters for Reformat Date, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Reformat Date."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Reformat Date.",
      "Leverage the optimal Strings pattern to reduce time complexity."
    ],
    "learningObjective": "Master Strings techniques by solving Easy problem constraints for Reformat Date.",
    "whyThisPattern": "When observing Strings problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/reformat-date/",
    "leetcode_title": "Reformat Date",
    "leetcode_id": 1507,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/reformat-date/",
    "canonicalSlug": "reformat-date",
    "canonicalUrl": "https://leetcode.com/problems/reformat-date/",
    "url": "https://leetcode.com/problems/reformat-date/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Reformat Date\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Reformat Date\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Reformat Date\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Reformat Date\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Reformat Date\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Reformat Date\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Reformat Date\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Reformat Date\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Reformat Date",
      "cpp_optimal": "// Solution for Reformat Date",
      "java_brute": "// Solution for Reformat Date",
      "java_optimal": "// Solution for Reformat Date",
      "python_brute": "# Solution for Reformat Date",
      "python_optimal": "# Solution for Reformat Date"
    },
    "originalOrder": 213,
    "learningOrder": 213
  },
  {
    "id": 959,
    "number": 959,
    "sequence_number": 959,
    "title": "Goal Parser Interpretation",
    "slug": "goal-parser-interpretation",
    "difficulty": "Easy",
    "topic": "Strings",
    "subtopic": "Strings Optimization",
    "pattern": "String Token Replace",
    "secondary_patterns": [
      "String Token Replace"
    ],
    "stage": "Segment Trees & Advanced Structures",
    "curriculumStage": "Stage 20 — Segment Trees & Advanced Structures",
    "roadmapPhase": "Stage 20 — Segment Trees & Advanced Structures",
    "phase": "Stage 20 — Segment Trees & Advanced Structures",
    "estimatedTime": 15,
    "statement": "Given the constraints and input parameters for Goal Parser Interpretation, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Goal Parser Interpretation."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Goal Parser Interpretation.",
      "Leverage the optimal Strings pattern to reduce time complexity."
    ],
    "learningObjective": "Master Strings techniques by solving Easy problem constraints for Goal Parser Interpretation.",
    "whyThisPattern": "When observing Strings problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/goal-parser-interpretation/",
    "leetcode_title": "Goal Parser Interpretation",
    "leetcode_id": 1678,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/goal-parser-interpretation/",
    "canonicalSlug": "goal-parser-interpretation",
    "canonicalUrl": "https://leetcode.com/problems/goal-parser-interpretation/",
    "url": "https://leetcode.com/problems/goal-parser-interpretation/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Goal Parser Interpretation\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Goal Parser Interpretation\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Goal Parser Interpretation\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Goal Parser Interpretation\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Goal Parser Interpretation\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Goal Parser Interpretation\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Goal Parser Interpretation\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Goal Parser Interpretation\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Goal Parser Interpretation",
      "cpp_optimal": "// Solution for Goal Parser Interpretation",
      "java_brute": "// Solution for Goal Parser Interpretation",
      "java_optimal": "// Solution for Goal Parser Interpretation",
      "python_brute": "# Solution for Goal Parser Interpretation",
      "python_optimal": "# Solution for Goal Parser Interpretation"
    },
    "originalOrder": 214,
    "learningOrder": 214
  },
  {
    "id": 960,
    "number": 960,
    "sequence_number": 960,
    "title": "Determine if String Halves Are Alike",
    "slug": "determine-if-string-halves-are-alike",
    "difficulty": "Easy",
    "topic": "Strings",
    "subtopic": "Strings Optimization",
    "pattern": "Vowel Count Halves",
    "secondary_patterns": [
      "Vowel Count Halves"
    ],
    "stage": "Segment Trees & Advanced Structures",
    "curriculumStage": "Stage 20 — Segment Trees & Advanced Structures",
    "roadmapPhase": "Stage 20 — Segment Trees & Advanced Structures",
    "phase": "Stage 20 — Segment Trees & Advanced Structures",
    "estimatedTime": 15,
    "statement": "Given the constraints and input parameters for Determine if String Halves Are Alike, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Determine if String Halves Are Alike."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Determine if String Halves Are Alike.",
      "Leverage the optimal Strings pattern to reduce time complexity."
    ],
    "learningObjective": "Master Strings techniques by solving Easy problem constraints for Determine if String Halves Are Alike.",
    "whyThisPattern": "When observing Strings problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/determine-if-string-halves-are-alike/",
    "leetcode_title": "Determine if String Halves Are Alike",
    "leetcode_id": 1704,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/determine-if-string-halves-are-alike/",
    "canonicalSlug": "determine-if-string-halves-are-alike",
    "canonicalUrl": "https://leetcode.com/problems/determine-if-string-halves-are-alike/",
    "url": "https://leetcode.com/problems/determine-if-string-halves-are-alike/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Determine if String Halves Are Alike\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Determine if String Halves Are Alike\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Determine if String Halves Are Alike\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Determine if String Halves Are Alike\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Determine if String Halves Are Alike\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Determine if String Halves Are Alike\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Determine if String Halves Are Alike\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Determine if String Halves Are Alike\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Determine if String Halves Are Alike",
      "cpp_optimal": "// Solution for Determine if String Halves Are Alike",
      "java_brute": "// Solution for Determine if String Halves Are Alike",
      "java_optimal": "// Solution for Determine if String Halves Are Alike",
      "python_brute": "# Solution for Determine if String Halves Are Alike",
      "python_optimal": "# Solution for Determine if String Halves Are Alike"
    },
    "originalOrder": 215,
    "learningOrder": 215
  },
  {
    "id": 961,
    "number": 961,
    "sequence_number": 961,
    "title": "Flip Equivalent Binary Trees",
    "slug": "flip-equivalent-binary-trees",
    "difficulty": "Medium",
    "topic": "Trees",
    "subtopic": "Tree Traversal & Recursion",
    "pattern": "Tree Traversal & Recursion",
    "secondary_patterns": [
      "Tree Traversal & Recursion"
    ],
    "stage": "Segment Trees & Advanced Structures",
    "curriculumStage": "Stage 20 — Segment Trees & Advanced Structures",
    "roadmapPhase": "Stage 20 — Segment Trees & Advanced Structures",
    "phase": "Stage 20 — Segment Trees & Advanced Structures",
    "estimatedTime": 30,
    "statement": "Solve the **Flip Equivalent Binary Trees Challenge** problem using the **Tree Traversal & Recursion** technique. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Tree Traversal & Recursion identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Tree Traversal & Recursion. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Tree Traversal & Recursion techniques by solving Medium problem constraints for Flip Equivalent Binary Trees Challenge.",
    "whyThisPattern": "When observing binary trees problem conditions, Tree Traversal & Recursion optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Microsoft",
      "Bloomberg",
      "Adobe"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/flip-equivalent-binary-trees/",
    "leetcode_title": "Flip Equivalent Binary Trees",
    "leetcode_id": 951,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/flip-equivalent-binary-trees/",
    "canonicalSlug": "flip-equivalent-binary-trees",
    "canonicalUrl": "https://leetcode.com/problems/flip-equivalent-binary-trees/",
    "url": "https://leetcode.com/problems/flip-equivalent-binary-trees/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Flip Equivalent Binary Trees Challenge (Tree Traversal & Recursion)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Flip Equivalent Binary Trees Challenge (Tree Traversal & Recursion)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Flip Equivalent Binary Trees Challenge (Tree Traversal & Recursion)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Flip Equivalent Binary Trees Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Flip Equivalent Binary Trees Challenge (Tree Traversal & Recursion)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Flip Equivalent Binary Trees Challenge (Tree Traversal & Recursion)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Flip Equivalent Binary Trees Challenge (Tree Traversal & Recursion)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Flip Equivalent Binary Trees Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Flip Equivalent Binary Trees",
      "cpp_optimal": "// Solution for Flip Equivalent Binary Trees",
      "java_brute": "// Solution for Flip Equivalent Binary Trees",
      "java_optimal": "// Solution for Flip Equivalent Binary Trees",
      "python_brute": "# Solution for Flip Equivalent Binary Trees",
      "python_optimal": "# Solution for Flip Equivalent Binary Trees"
    },
    "originalOrder": 653,
    "learningOrder": 653
  },
  {
    "id": 962,
    "number": 962,
    "sequence_number": 962,
    "title": "Check Completeness of a Binary Tree",
    "slug": "check-completeness-of-a-binary-tree",
    "difficulty": "Medium",
    "topic": "Trees",
    "subtopic": "Tree Traversal & Recursion",
    "pattern": "Tree Traversal & Recursion",
    "secondary_patterns": [
      "Tree Traversal & Recursion"
    ],
    "stage": "Segment Trees & Advanced Structures",
    "curriculumStage": "Stage 20 — Segment Trees & Advanced Structures",
    "roadmapPhase": "Stage 20 — Segment Trees & Advanced Structures",
    "phase": "Stage 20 — Segment Trees & Advanced Structures",
    "estimatedTime": 30,
    "statement": "Solve the **Check Completeness of a Binary Tree Challenge** problem using the **Tree Traversal & Recursion** technique. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Tree Traversal & Recursion identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Tree Traversal & Recursion. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Tree Traversal & Recursion techniques by solving Medium problem constraints for Check Completeness of a Binary Tree Challenge.",
    "whyThisPattern": "When observing binary trees problem conditions, Tree Traversal & Recursion optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Meta",
      "Uber",
      "Databricks"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/check-completeness-of-a-binary-tree/",
    "leetcode_title": "Check Completeness of a Binary Tree",
    "leetcode_id": 958,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/check-completeness-of-a-binary-tree/",
    "canonicalSlug": "check-completeness-of-a-binary-tree",
    "canonicalUrl": "https://leetcode.com/problems/check-completeness-of-a-binary-tree/",
    "url": "https://leetcode.com/problems/check-completeness-of-a-binary-tree/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Check Completeness of a Binary Tree Challenge (Tree Traversal & Recursion)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Check Completeness of a Binary Tree Challenge (Tree Traversal & Recursion)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Check Completeness of a Binary Tree Challenge (Tree Traversal & Recursion)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Check Completeness of a Binary Tree Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Check Completeness of a Binary Tree Challenge (Tree Traversal & Recursion)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Check Completeness of a Binary Tree Challenge (Tree Traversal & Recursion)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Check Completeness of a Binary Tree Challenge (Tree Traversal & Recursion)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Check Completeness of a Binary Tree Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Check Completeness of a Binary Tree",
      "cpp_optimal": "// Solution for Check Completeness of a Binary Tree",
      "java_brute": "// Solution for Check Completeness of a Binary Tree",
      "java_optimal": "// Solution for Check Completeness of a Binary Tree",
      "python_brute": "# Solution for Check Completeness of a Binary Tree",
      "python_optimal": "# Solution for Check Completeness of a Binary Tree"
    },
    "originalOrder": 654,
    "learningOrder": 654
  },
  {
    "id": 963,
    "number": 963,
    "sequence_number": 963,
    "title": "Flip Binary Tree To Match Preorder Traversal",
    "slug": "flip-binary-tree-to-match-preorder-traversal",
    "difficulty": "Medium",
    "topic": "Trees",
    "subtopic": "Tree Traversal & Recursion",
    "pattern": "Tree Traversal & Recursion",
    "secondary_patterns": [
      "Tree Traversal & Recursion"
    ],
    "stage": "Segment Trees & Advanced Structures",
    "curriculumStage": "Stage 20 — Segment Trees & Advanced Structures",
    "roadmapPhase": "Stage 20 — Segment Trees & Advanced Structures",
    "phase": "Stage 20 — Segment Trees & Advanced Structures",
    "estimatedTime": 30,
    "statement": "Solve the **Flip Binary Tree To Match Preorder Traversal Challenge** problem using the **Tree Traversal & Recursion** technique. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Tree Traversal & Recursion identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Tree Traversal & Recursion. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Tree Traversal & Recursion techniques by solving Medium problem constraints for Flip Binary Tree To Match Preorder Traversal Challenge.",
    "whyThisPattern": "When observing binary trees problem conditions, Tree Traversal & Recursion optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Amazon",
      "Microsoft",
      "Uber"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/flip-binary-tree-to-match-preorder-traversal/",
    "leetcode_title": "Flip Binary Tree To Match Preorder Traversal",
    "leetcode_id": 971,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/flip-binary-tree-to-match-preorder-traversal/",
    "canonicalSlug": "flip-binary-tree-to-match-preorder-traversal",
    "canonicalUrl": "https://leetcode.com/problems/flip-binary-tree-to-match-preorder-traversal/",
    "url": "https://leetcode.com/problems/flip-binary-tree-to-match-preorder-traversal/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Flip Binary Tree To Match Preorder Traversal Challenge (Tree Traversal & Recursion)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Flip Binary Tree To Match Preorder Traversal Challenge (Tree Traversal & Recursion)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Flip Binary Tree To Match Preorder Traversal Challenge (Tree Traversal & Recursion)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Flip Binary Tree To Match Preorder Traversal Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Flip Binary Tree To Match Preorder Traversal Challenge (Tree Traversal & Recursion)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Flip Binary Tree To Match Preorder Traversal Challenge (Tree Traversal & Recursion)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Flip Binary Tree To Match Preorder Traversal Challenge (Tree Traversal & Recursion)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Flip Binary Tree To Match Preorder Traversal Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Flip Binary Tree To Match Preorder Traversal",
      "cpp_optimal": "// Solution for Flip Binary Tree To Match Preorder Traversal",
      "java_brute": "// Solution for Flip Binary Tree To Match Preorder Traversal",
      "java_optimal": "// Solution for Flip Binary Tree To Match Preorder Traversal",
      "python_brute": "# Solution for Flip Binary Tree To Match Preorder Traversal",
      "python_optimal": "# Solution for Flip Binary Tree To Match Preorder Traversal"
    },
    "originalOrder": 655,
    "learningOrder": 655
  },
  {
    "id": 964,
    "number": 964,
    "sequence_number": 964,
    "title": "Construct String from Binary Tree",
    "slug": "construct-string-from-binary-tree",
    "difficulty": "Medium",
    "topic": "Trees",
    "subtopic": "Tree Traversal & Recursion",
    "pattern": "Tree Traversal & Recursion",
    "secondary_patterns": [
      "Tree Traversal & Recursion"
    ],
    "stage": "Segment Trees & Advanced Structures",
    "curriculumStage": "Stage 20 — Segment Trees & Advanced Structures",
    "roadmapPhase": "Stage 20 — Segment Trees & Advanced Structures",
    "phase": "Stage 20 — Segment Trees & Advanced Structures",
    "estimatedTime": 30,
    "statement": "Solve the **Construct String from Binary Tree Challenge** problem using the **Tree Traversal & Recursion** technique. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Tree Traversal & Recursion identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Tree Traversal & Recursion. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Tree Traversal & Recursion techniques by solving Medium problem constraints for Construct String from Binary Tree Challenge.",
    "whyThisPattern": "When observing arrays & strings problem conditions, Tree Traversal & Recursion optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Meta",
      "Uber",
      "Databricks"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/construct-string-from-binary-tree/",
    "leetcode_title": "Construct String from Binary Tree",
    "leetcode_id": 606,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/construct-string-from-binary-tree/",
    "canonicalSlug": "construct-string-from-binary-tree",
    "canonicalUrl": "https://leetcode.com/problems/construct-string-from-binary-tree/",
    "url": "https://leetcode.com/problems/construct-string-from-binary-tree/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Construct String from Binary Tree Challenge (Tree Traversal & Recursion)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Construct String from Binary Tree Challenge (Tree Traversal & Recursion)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Construct String from Binary Tree Challenge (Tree Traversal & Recursion)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Construct String from Binary Tree Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Construct String from Binary Tree Challenge (Tree Traversal & Recursion)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Construct String from Binary Tree Challenge (Tree Traversal & Recursion)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Construct String from Binary Tree Challenge (Tree Traversal & Recursion)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Construct String from Binary Tree Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Construct String from Binary Tree",
      "cpp_optimal": "// Solution for Construct String from Binary Tree",
      "java_brute": "// Solution for Construct String from Binary Tree",
      "java_optimal": "// Solution for Construct String from Binary Tree",
      "python_brute": "# Solution for Construct String from Binary Tree",
      "python_optimal": "# Solution for Construct String from Binary Tree"
    },
    "originalOrder": 656,
    "learningOrder": 656
  },
  {
    "id": 965,
    "number": 965,
    "sequence_number": 965,
    "title": "Exam Room",
    "slug": "exam-room",
    "difficulty": "Medium",
    "topic": "Trees",
    "subtopic": "Trees Optimization",
    "pattern": "Ordered Interval Map",
    "secondary_patterns": [
      "Ordered Interval Map"
    ],
    "stage": "Segment Trees & Advanced Structures",
    "curriculumStage": "Stage 20 — Segment Trees & Advanced Structures",
    "roadmapPhase": "Stage 20 — Segment Trees & Advanced Structures",
    "phase": "Stage 20 — Segment Trees & Advanced Structures",
    "estimatedTime": 30,
    "statement": "Given the constraints and input parameters for Exam Room, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Exam Room."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Exam Room.",
      "Leverage the optimal Trees pattern to reduce time complexity."
    ],
    "learningObjective": "Master Trees techniques by solving Medium problem constraints for Exam Room.",
    "whyThisPattern": "When observing Trees problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/exam-room/",
    "leetcode_title": "Exam Room",
    "leetcode_id": 855,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/exam-room/",
    "canonicalSlug": "exam-room",
    "canonicalUrl": "https://leetcode.com/problems/exam-room/",
    "url": "https://leetcode.com/problems/exam-room/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Exam Room\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Exam Room\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Exam Room\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Exam Room\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Exam Room\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Exam Room\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Exam Room\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Exam Room\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Exam Room",
      "cpp_optimal": "// Solution for Exam Room",
      "java_brute": "// Solution for Exam Room",
      "java_optimal": "// Solution for Exam Room",
      "python_brute": "# Solution for Exam Room",
      "python_optimal": "# Solution for Exam Room"
    },
    "originalOrder": 657,
    "learningOrder": 657
  },
  {
    "id": 966,
    "number": 966,
    "sequence_number": 966,
    "title": "Deepest Leaves Sum",
    "slug": "deepest-leaves-sum",
    "difficulty": "Medium",
    "topic": "Trees",
    "subtopic": "Trees Optimization",
    "pattern": "BFS Level Sum",
    "secondary_patterns": [
      "BFS Level Sum"
    ],
    "stage": "Segment Trees & Advanced Structures",
    "curriculumStage": "Stage 20 — Segment Trees & Advanced Structures",
    "roadmapPhase": "Stage 20 — Segment Trees & Advanced Structures",
    "phase": "Stage 20 — Segment Trees & Advanced Structures",
    "estimatedTime": 30,
    "statement": "Given the constraints and input parameters for Deepest Leaves Sum, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Deepest Leaves Sum."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Deepest Leaves Sum.",
      "Leverage the optimal Trees pattern to reduce time complexity."
    ],
    "learningObjective": "Master Trees techniques by solving Medium problem constraints for Deepest Leaves Sum.",
    "whyThisPattern": "When observing Trees problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/deepest-leaves-sum/",
    "leetcode_title": "Deepest Leaves Sum",
    "leetcode_id": 1302,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/deepest-leaves-sum/",
    "canonicalSlug": "deepest-leaves-sum",
    "canonicalUrl": "https://leetcode.com/problems/deepest-leaves-sum/",
    "url": "https://leetcode.com/problems/deepest-leaves-sum/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Deepest Leaves Sum\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Deepest Leaves Sum\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Deepest Leaves Sum\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Deepest Leaves Sum\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Deepest Leaves Sum\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Deepest Leaves Sum\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Deepest Leaves Sum\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Deepest Leaves Sum\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Deepest Leaves Sum",
      "cpp_optimal": "// Solution for Deepest Leaves Sum",
      "java_brute": "// Solution for Deepest Leaves Sum",
      "java_optimal": "// Solution for Deepest Leaves Sum",
      "python_brute": "# Solution for Deepest Leaves Sum",
      "python_optimal": "# Solution for Deepest Leaves Sum"
    },
    "originalOrder": 658,
    "learningOrder": 658
  },
  {
    "id": 967,
    "number": 967,
    "sequence_number": 967,
    "title": "Maximum Level Sum of a Binary Tree",
    "slug": "maximum-level-sum-of-a-binary-tree",
    "difficulty": "Medium",
    "topic": "Trees",
    "subtopic": "Trees Optimization",
    "pattern": "Level Order BFS Max",
    "secondary_patterns": [
      "Level Order BFS Max"
    ],
    "stage": "Segment Trees & Advanced Structures",
    "curriculumStage": "Stage 20 — Segment Trees & Advanced Structures",
    "roadmapPhase": "Stage 20 — Segment Trees & Advanced Structures",
    "phase": "Stage 20 — Segment Trees & Advanced Structures",
    "estimatedTime": 30,
    "statement": "Given the constraints and input parameters for Maximum Level Sum of a Binary Tree, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Maximum Level Sum of a Binary Tree."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Maximum Level Sum of a Binary Tree.",
      "Leverage the optimal Trees pattern to reduce time complexity."
    ],
    "learningObjective": "Master Trees techniques by solving Medium problem constraints for Maximum Level Sum of a Binary Tree.",
    "whyThisPattern": "When observing Trees problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/maximum-level-sum-of-a-binary-tree/",
    "leetcode_title": "Maximum Level Sum of a Binary Tree",
    "leetcode_id": 1161,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/maximum-level-sum-of-a-binary-tree/",
    "canonicalSlug": "maximum-level-sum-of-a-binary-tree",
    "canonicalUrl": "https://leetcode.com/problems/maximum-level-sum-of-a-binary-tree/",
    "url": "https://leetcode.com/problems/maximum-level-sum-of-a-binary-tree/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Maximum Level Sum of a Binary Tree\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Maximum Level Sum of a Binary Tree\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Maximum Level Sum of a Binary Tree\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Maximum Level Sum of a Binary Tree\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Maximum Level Sum of a Binary Tree\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Maximum Level Sum of a Binary Tree\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Maximum Level Sum of a Binary Tree\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Maximum Level Sum of a Binary Tree\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Maximum Level Sum of a Binary Tree",
      "cpp_optimal": "// Solution for Maximum Level Sum of a Binary Tree",
      "java_brute": "// Solution for Maximum Level Sum of a Binary Tree",
      "java_optimal": "// Solution for Maximum Level Sum of a Binary Tree",
      "python_brute": "# Solution for Maximum Level Sum of a Binary Tree",
      "python_optimal": "# Solution for Maximum Level Sum of a Binary Tree"
    },
    "originalOrder": 659,
    "learningOrder": 659
  },
  {
    "id": 968,
    "number": 968,
    "sequence_number": 968,
    "title": "Pseudo-Palindromic Paths in a Binary Tree",
    "slug": "pseudo-palindromic-paths-in-a-binary-tree",
    "difficulty": "Medium",
    "topic": "Trees",
    "subtopic": "Trees Optimization",
    "pattern": "Bitmask Parity DFS",
    "secondary_patterns": [
      "Bitmask Parity DFS"
    ],
    "stage": "Segment Trees & Advanced Structures",
    "curriculumStage": "Stage 20 — Segment Trees & Advanced Structures",
    "roadmapPhase": "Stage 20 — Segment Trees & Advanced Structures",
    "phase": "Stage 20 — Segment Trees & Advanced Structures",
    "estimatedTime": 30,
    "statement": "Given the constraints and input parameters for Pseudo-Palindromic Paths in a Binary Tree, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Pseudo-Palindromic Paths in a Binary Tree."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Pseudo-Palindromic Paths in a Binary Tree.",
      "Leverage the optimal Trees pattern to reduce time complexity."
    ],
    "learningObjective": "Master Trees techniques by solving Medium problem constraints for Pseudo-Palindromic Paths in a Binary Tree.",
    "whyThisPattern": "When observing Trees problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/pseudo-palindromic-paths-in-a-binary-tree/",
    "leetcode_title": "Pseudo-Palindromic Paths in a Binary Tree",
    "leetcode_id": 1457,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/pseudo-palindromic-paths-in-a-binary-tree/",
    "canonicalSlug": "pseudo-palindromic-paths-in-a-binary-tree",
    "canonicalUrl": "https://leetcode.com/problems/pseudo-palindromic-paths-in-a-binary-tree/",
    "url": "https://leetcode.com/problems/pseudo-palindromic-paths-in-a-binary-tree/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Pseudo-Palindromic Paths in a Binary Tree\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Pseudo-Palindromic Paths in a Binary Tree\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Pseudo-Palindromic Paths in a Binary Tree\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Pseudo-Palindromic Paths in a Binary Tree\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Pseudo-Palindromic Paths in a Binary Tree\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Pseudo-Palindromic Paths in a Binary Tree\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Pseudo-Palindromic Paths in a Binary Tree\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Pseudo-Palindromic Paths in a Binary Tree\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Pseudo-Palindromic Paths in a Binary Tree",
      "cpp_optimal": "// Solution for Pseudo-Palindromic Paths in a Binary Tree",
      "java_brute": "// Solution for Pseudo-Palindromic Paths in a Binary Tree",
      "java_optimal": "// Solution for Pseudo-Palindromic Paths in a Binary Tree",
      "python_brute": "# Solution for Pseudo-Palindromic Paths in a Binary Tree",
      "python_optimal": "# Solution for Pseudo-Palindromic Paths in a Binary Tree"
    },
    "originalOrder": 660,
    "learningOrder": 660
  },
  {
    "id": 969,
    "number": 969,
    "sequence_number": 969,
    "title": "Count Good Nodes in Binary Tree",
    "slug": "count-good-nodes-in-binary-tree",
    "difficulty": "Medium",
    "topic": "Trees",
    "subtopic": "Trees Optimization",
    "pattern": "Path Max DFS",
    "secondary_patterns": [
      "Path Max DFS"
    ],
    "stage": "Segment Trees & Advanced Structures",
    "curriculumStage": "Stage 20 — Segment Trees & Advanced Structures",
    "roadmapPhase": "Stage 20 — Segment Trees & Advanced Structures",
    "phase": "Stage 20 — Segment Trees & Advanced Structures",
    "estimatedTime": 30,
    "statement": "Given the constraints and input parameters for Count Good Nodes in Binary Tree, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Count Good Nodes in Binary Tree."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Count Good Nodes in Binary Tree.",
      "Leverage the optimal Trees pattern to reduce time complexity."
    ],
    "learningObjective": "Master Trees techniques by solving Medium problem constraints for Count Good Nodes in Binary Tree.",
    "whyThisPattern": "When observing Trees problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/count-good-nodes-in-binary-tree/",
    "leetcode_title": "Count Good Nodes in Binary Tree",
    "leetcode_id": 1448,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/count-good-nodes-in-binary-tree/",
    "canonicalSlug": "count-good-nodes-in-binary-tree",
    "canonicalUrl": "https://leetcode.com/problems/count-good-nodes-in-binary-tree/",
    "url": "https://leetcode.com/problems/count-good-nodes-in-binary-tree/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Count Good Nodes in Binary Tree\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Count Good Nodes in Binary Tree\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Count Good Nodes in Binary Tree\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Count Good Nodes in Binary Tree\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Count Good Nodes in Binary Tree\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Count Good Nodes in Binary Tree\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Count Good Nodes in Binary Tree\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Count Good Nodes in Binary Tree\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Count Good Nodes in Binary Tree",
      "cpp_optimal": "// Solution for Count Good Nodes in Binary Tree",
      "java_brute": "// Solution for Count Good Nodes in Binary Tree",
      "java_optimal": "// Solution for Count Good Nodes in Binary Tree",
      "python_brute": "# Solution for Count Good Nodes in Binary Tree",
      "python_optimal": "# Solution for Count Good Nodes in Binary Tree"
    },
    "originalOrder": 661,
    "learningOrder": 661
  },
  {
    "id": 970,
    "number": 970,
    "sequence_number": 970,
    "title": "Number of Nodes in the Sub-Tree With the Same Label",
    "slug": "number-of-nodes-in-the-sub-tree-with-the-same-label",
    "difficulty": "Medium",
    "topic": "Trees",
    "subtopic": "Trees Optimization",
    "pattern": "Post-Order Frequency Vector",
    "secondary_patterns": [
      "Post-Order Frequency Vector"
    ],
    "stage": "Segment Trees & Advanced Structures",
    "curriculumStage": "Stage 20 — Segment Trees & Advanced Structures",
    "roadmapPhase": "Stage 20 — Segment Trees & Advanced Structures",
    "phase": "Stage 20 — Segment Trees & Advanced Structures",
    "estimatedTime": 30,
    "statement": "Given the constraints and input parameters for Number of Nodes in the Sub-Tree With the Same Label, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Number of Nodes in the Sub-Tree With the Same Label."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Number of Nodes in the Sub-Tree With the Same Label.",
      "Leverage the optimal Trees pattern to reduce time complexity."
    ],
    "learningObjective": "Master Trees techniques by solving Medium problem constraints for Number of Nodes in the Sub-Tree With the Same Label.",
    "whyThisPattern": "When observing Trees problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/number-of-nodes-in-the-sub-tree-with-the-same-label/",
    "leetcode_title": "Number of Nodes in the Sub-Tree With the Same Label",
    "leetcode_id": 1519,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/number-of-nodes-in-the-sub-tree-with-the-same-label/",
    "canonicalSlug": "number-of-nodes-in-the-sub-tree-with-the-same-label",
    "canonicalUrl": "https://leetcode.com/problems/number-of-nodes-in-the-sub-tree-with-the-same-label/",
    "url": "https://leetcode.com/problems/number-of-nodes-in-the-sub-tree-with-the-same-label/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Number of Nodes in the Sub-Tree With the Same Label\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Number of Nodes in the Sub-Tree With the Same Label\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Number of Nodes in the Sub-Tree With the Same Label\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Number of Nodes in the Sub-Tree With the Same Label\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Number of Nodes in the Sub-Tree With the Same Label\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Number of Nodes in the Sub-Tree With the Same Label\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Number of Nodes in the Sub-Tree With the Same Label\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Number of Nodes in the Sub-Tree With the Same Label\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Number of Nodes in the Sub-Tree With the Same Label",
      "cpp_optimal": "// Solution for Number of Nodes in the Sub-Tree With the Same Label",
      "java_brute": "// Solution for Number of Nodes in the Sub-Tree With the Same Label",
      "java_optimal": "// Solution for Number of Nodes in the Sub-Tree With the Same Label",
      "python_brute": "# Solution for Number of Nodes in the Sub-Tree With the Same Label",
      "python_optimal": "# Solution for Number of Nodes in the Sub-Tree With the Same Label"
    },
    "originalOrder": 662,
    "learningOrder": 662
  },
  {
    "id": 971,
    "number": 971,
    "sequence_number": 971,
    "title": "Flatten Binary Tree to Linked List",
    "slug": "flatten-binary-tree-to-linked-list",
    "difficulty": "Medium",
    "topic": "Trees",
    "subtopic": "Trees Optimization",
    "pattern": "Preorder Pointer Reversal",
    "secondary_patterns": [
      "Preorder Pointer Reversal"
    ],
    "stage": "Segment Trees & Advanced Structures",
    "curriculumStage": "Stage 20 — Segment Trees & Advanced Structures",
    "roadmapPhase": "Stage 20 — Segment Trees & Advanced Structures",
    "phase": "Stage 20 — Segment Trees & Advanced Structures",
    "estimatedTime": 30,
    "statement": "Given the constraints and input parameters for Flatten Binary Tree to Linked List, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Flatten Binary Tree to Linked List."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Flatten Binary Tree to Linked List.",
      "Leverage the optimal Trees pattern to reduce time complexity."
    ],
    "learningObjective": "Master Trees techniques by solving Medium problem constraints for Flatten Binary Tree to Linked List.",
    "whyThisPattern": "When observing Trees problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/flatten-binary-tree-to-linked-list/",
    "leetcode_title": "Flatten Binary Tree to Linked List",
    "leetcode_id": 114,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/flatten-binary-tree-to-linked-list/",
    "canonicalSlug": "flatten-binary-tree-to-linked-list",
    "canonicalUrl": "https://leetcode.com/problems/flatten-binary-tree-to-linked-list/",
    "url": "https://leetcode.com/problems/flatten-binary-tree-to-linked-list/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Flatten Binary Tree to Linked List\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Flatten Binary Tree to Linked List\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Flatten Binary Tree to Linked List\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Flatten Binary Tree to Linked List\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Flatten Binary Tree to Linked List\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Flatten Binary Tree to Linked List\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Flatten Binary Tree to Linked List\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Flatten Binary Tree to Linked List\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Flatten Binary Tree to Linked List",
      "cpp_optimal": "// Solution for Flatten Binary Tree to Linked List",
      "java_brute": "// Solution for Flatten Binary Tree to Linked List",
      "java_optimal": "// Solution for Flatten Binary Tree to Linked List",
      "python_brute": "# Solution for Flatten Binary Tree to Linked List",
      "python_optimal": "# Solution for Flatten Binary Tree to Linked List"
    },
    "originalOrder": 663,
    "learningOrder": 663
  },
  {
    "id": 972,
    "number": 972,
    "sequence_number": 972,
    "title": "Sum Root to Leaf Numbers",
    "slug": "sum-root-to-leaf-numbers",
    "difficulty": "Medium",
    "topic": "Trees",
    "subtopic": "Trees Optimization",
    "pattern": "DFS Preorder Accumulator",
    "secondary_patterns": [
      "DFS Preorder Accumulator"
    ],
    "stage": "Segment Trees & Advanced Structures",
    "curriculumStage": "Stage 20 — Segment Trees & Advanced Structures",
    "roadmapPhase": "Stage 20 — Segment Trees & Advanced Structures",
    "phase": "Stage 20 — Segment Trees & Advanced Structures",
    "estimatedTime": 30,
    "statement": "Given the constraints and input parameters for Sum Root to Leaf Numbers, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Sum Root to Leaf Numbers."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Sum Root to Leaf Numbers.",
      "Leverage the optimal Trees pattern to reduce time complexity."
    ],
    "learningObjective": "Master Trees techniques by solving Medium problem constraints for Sum Root to Leaf Numbers.",
    "whyThisPattern": "When observing Trees problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/sum-root-to-leaf-numbers/",
    "leetcode_title": "Sum Root to Leaf Numbers",
    "leetcode_id": 129,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/sum-root-to-leaf-numbers/",
    "canonicalSlug": "sum-root-to-leaf-numbers",
    "canonicalUrl": "https://leetcode.com/problems/sum-root-to-leaf-numbers/",
    "url": "https://leetcode.com/problems/sum-root-to-leaf-numbers/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Sum Root to Leaf Numbers\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Sum Root to Leaf Numbers\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Sum Root to Leaf Numbers\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Sum Root to Leaf Numbers\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Sum Root to Leaf Numbers\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Sum Root to Leaf Numbers\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Sum Root to Leaf Numbers\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Sum Root to Leaf Numbers\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Sum Root to Leaf Numbers",
      "cpp_optimal": "// Solution for Sum Root to Leaf Numbers",
      "java_brute": "// Solution for Sum Root to Leaf Numbers",
      "java_optimal": "// Solution for Sum Root to Leaf Numbers",
      "python_brute": "# Solution for Sum Root to Leaf Numbers",
      "python_optimal": "# Solution for Sum Root to Leaf Numbers"
    },
    "originalOrder": 664,
    "learningOrder": 664
  },
  {
    "id": 973,
    "number": 973,
    "sequence_number": 973,
    "title": "Path Sum III",
    "slug": "path-sum-iii",
    "difficulty": "Medium",
    "topic": "Trees",
    "subtopic": "Trees Optimization",
    "pattern": "Prefix Sum DFS",
    "secondary_patterns": [
      "Prefix Sum DFS"
    ],
    "stage": "Segment Trees & Advanced Structures",
    "curriculumStage": "Stage 20 — Segment Trees & Advanced Structures",
    "roadmapPhase": "Stage 20 — Segment Trees & Advanced Structures",
    "phase": "Stage 20 — Segment Trees & Advanced Structures",
    "estimatedTime": 30,
    "statement": "Given the constraints and input parameters for Path Sum III, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Path Sum III."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Path Sum III.",
      "Leverage the optimal Trees pattern to reduce time complexity."
    ],
    "learningObjective": "Master Trees techniques by solving Medium problem constraints for Path Sum III.",
    "whyThisPattern": "When observing Trees problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/path-sum-iii/",
    "leetcode_title": "Path Sum III",
    "leetcode_id": 437,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/path-sum-iii/",
    "canonicalSlug": "path-sum-iii",
    "canonicalUrl": "https://leetcode.com/problems/path-sum-iii/",
    "url": "https://leetcode.com/problems/path-sum-iii/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Path Sum III\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Path Sum III\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Path Sum III\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Path Sum III\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Path Sum III\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Path Sum III\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Path Sum III\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Path Sum III\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Path Sum III",
      "cpp_optimal": "// Solution for Path Sum III",
      "java_brute": "// Solution for Path Sum III",
      "java_optimal": "// Solution for Path Sum III",
      "python_brute": "# Solution for Path Sum III",
      "python_optimal": "# Solution for Path Sum III"
    },
    "originalOrder": 665,
    "learningOrder": 665
  },
  {
    "id": 974,
    "number": 974,
    "sequence_number": 974,
    "title": "Count Nodes With the Highest Score",
    "slug": "count-nodes-with-the-highest-score",
    "difficulty": "Medium",
    "topic": "Trees",
    "subtopic": "Trees Optimization",
    "pattern": "Subtree Size Product DFS",
    "secondary_patterns": [
      "Subtree Size Product DFS"
    ],
    "stage": "Segment Trees & Advanced Structures",
    "curriculumStage": "Stage 20 — Segment Trees & Advanced Structures",
    "roadmapPhase": "Stage 20 — Segment Trees & Advanced Structures",
    "phase": "Stage 20 — Segment Trees & Advanced Structures",
    "estimatedTime": 30,
    "statement": "Given the constraints and input parameters for Count Nodes With the Highest Score, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Count Nodes With the Highest Score."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Count Nodes With the Highest Score.",
      "Leverage the optimal Trees pattern to reduce time complexity."
    ],
    "learningObjective": "Master Trees techniques by solving Medium problem constraints for Count Nodes With the Highest Score.",
    "whyThisPattern": "When observing Trees problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/count-nodes-with-the-highest-score/",
    "leetcode_title": "Count Nodes With the Highest Score",
    "leetcode_id": 2049,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/count-nodes-with-the-highest-score/",
    "canonicalSlug": "count-nodes-with-the-highest-score",
    "canonicalUrl": "https://leetcode.com/problems/count-nodes-with-the-highest-score/",
    "url": "https://leetcode.com/problems/count-nodes-with-the-highest-score/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Count Nodes With the Highest Score\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Count Nodes With the Highest Score\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Count Nodes With the Highest Score\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Count Nodes With the Highest Score\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Count Nodes With the Highest Score\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Count Nodes With the Highest Score\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Count Nodes With the Highest Score\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Count Nodes With the Highest Score\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Count Nodes With the Highest Score",
      "cpp_optimal": "// Solution for Count Nodes With the Highest Score",
      "java_brute": "// Solution for Count Nodes With the Highest Score",
      "java_optimal": "// Solution for Count Nodes With the Highest Score",
      "python_brute": "# Solution for Count Nodes With the Highest Score",
      "python_optimal": "# Solution for Count Nodes With the Highest Score"
    },
    "originalOrder": 666,
    "learningOrder": 666
  },
  {
    "id": 975,
    "number": 975,
    "sequence_number": 975,
    "title": "Longest Word in Dictionary through Deleting",
    "slug": "longest-word-in-dictionary-through-deleting",
    "difficulty": "Medium",
    "topic": "Trie",
    "subtopic": "Trie Optimization",
    "pattern": "Trie Pattern",
    "secondary_patterns": [
      "Trie Pattern"
    ],
    "stage": "Segment Trees & Advanced Structures",
    "curriculumStage": "Stage 20 — Segment Trees & Advanced Structures",
    "roadmapPhase": "Stage 20 — Segment Trees & Advanced Structures",
    "phase": "Stage 20 — Segment Trees & Advanced Structures",
    "estimatedTime": 30,
    "statement": "Solve the **Longest Word in Dictionary through Deleting** problem using standard Trie techniques. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Trie algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Trie properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Trie techniques by solving Medium problem constraints for Longest Word in Dictionary through Deleting.",
    "whyThisPattern": "When observing Trie problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/longest-word-in-dictionary-through-deleting/",
    "leetcode_title": "Longest Word in Dictionary through Deleting",
    "leetcode_id": 524,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/longest-word-in-dictionary-through-deleting/",
    "canonicalSlug": "longest-word-in-dictionary-through-deleting",
    "canonicalUrl": "https://leetcode.com/problems/longest-word-in-dictionary-through-deleting/",
    "url": "https://leetcode.com/problems/longest-word-in-dictionary-through-deleting/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Longest Word in Dictionary through Deleting\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Longest Word in Dictionary through Deleting\n};",
        "java": "// Java Solution for Longest Word in Dictionary through Deleting\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Longest Word in Dictionary through Deleting\n}",
        "python": "# Python Solution for Longest Word in Dictionary through Deleting\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Longest Word in Dictionary through Deleting\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Longest Word in Dictionary through Deleting\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Longest Word in Dictionary through Deleting\n};",
        "java": "// Optimal Java Solution for Longest Word in Dictionary through Deleting\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Longest Word in Dictionary through Deleting\n}",
        "python": "# Optimal Python Solution for Longest Word in Dictionary through Deleting\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Longest Word in Dictionary through Deleting\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Longest Word in Dictionary through Deleting",
      "cpp_optimal": "// Solution for Longest Word in Dictionary through Deleting",
      "java_brute": "// Solution for Longest Word in Dictionary through Deleting",
      "java_optimal": "// Solution for Longest Word in Dictionary through Deleting",
      "python_brute": "# Solution for Longest Word in Dictionary through Deleting",
      "python_optimal": "# Solution for Longest Word in Dictionary through Deleting"
    },
    "originalOrder": 671,
    "learningOrder": 671
  },
  {
    "id": 976,
    "number": 976,
    "sequence_number": 976,
    "title": "Implement Magic Dictionary",
    "slug": "implement-magic-dictionary",
    "difficulty": "Medium",
    "topic": "Trie",
    "subtopic": "Trie Optimization",
    "pattern": "Trie Pattern",
    "secondary_patterns": [
      "Trie Pattern"
    ],
    "stage": "Segment Trees & Advanced Structures",
    "curriculumStage": "Stage 20 — Segment Trees & Advanced Structures",
    "roadmapPhase": "Stage 20 — Segment Trees & Advanced Structures",
    "phase": "Stage 20 — Segment Trees & Advanced Structures",
    "estimatedTime": 30,
    "statement": "Solve the **Implement Magic Dictionary** problem using standard Trie techniques. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Trie algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Trie properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Trie techniques by solving Medium problem constraints for Implement Magic Dictionary.",
    "whyThisPattern": "When observing Trie problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/implement-magic-dictionary/",
    "leetcode_title": "Implement Magic Dictionary",
    "leetcode_id": 676,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/implement-magic-dictionary/",
    "canonicalSlug": "implement-magic-dictionary",
    "canonicalUrl": "https://leetcode.com/problems/implement-magic-dictionary/",
    "url": "https://leetcode.com/problems/implement-magic-dictionary/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Implement Magic Dictionary\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Implement Magic Dictionary\n};",
        "java": "// Java Solution for Implement Magic Dictionary\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Implement Magic Dictionary\n}",
        "python": "# Python Solution for Implement Magic Dictionary\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Implement Magic Dictionary\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Implement Magic Dictionary\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Implement Magic Dictionary\n};",
        "java": "// Optimal Java Solution for Implement Magic Dictionary\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Implement Magic Dictionary\n}",
        "python": "# Optimal Python Solution for Implement Magic Dictionary\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Implement Magic Dictionary\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Implement Magic Dictionary",
      "cpp_optimal": "// Solution for Implement Magic Dictionary",
      "java_brute": "// Solution for Implement Magic Dictionary",
      "java_optimal": "// Solution for Implement Magic Dictionary",
      "python_brute": "# Solution for Implement Magic Dictionary",
      "python_optimal": "# Solution for Implement Magic Dictionary"
    },
    "originalOrder": 672,
    "learningOrder": 672
  },
  {
    "id": 977,
    "number": 977,
    "sequence_number": 977,
    "title": "Map Sum Pairs",
    "slug": "map-sum-pairs",
    "difficulty": "Medium",
    "topic": "Trie",
    "subtopic": "Trie Optimization",
    "pattern": "Trie Pattern",
    "secondary_patterns": [
      "Trie Pattern"
    ],
    "stage": "Segment Trees & Advanced Structures",
    "curriculumStage": "Stage 20 — Segment Trees & Advanced Structures",
    "roadmapPhase": "Stage 20 — Segment Trees & Advanced Structures",
    "phase": "Stage 20 — Segment Trees & Advanced Structures",
    "estimatedTime": 30,
    "statement": "Solve the **Map Sum Pairs** problem using standard Trie techniques. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Trie algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Trie properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Trie techniques by solving Medium problem constraints for Map Sum Pairs.",
    "whyThisPattern": "When observing Trie problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/map-sum-pairs/",
    "leetcode_title": "Map Sum Pairs",
    "leetcode_id": 677,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/map-sum-pairs/",
    "canonicalSlug": "map-sum-pairs",
    "canonicalUrl": "https://leetcode.com/problems/map-sum-pairs/",
    "url": "https://leetcode.com/problems/map-sum-pairs/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Map Sum Pairs\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Map Sum Pairs\n};",
        "java": "// Java Solution for Map Sum Pairs\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Map Sum Pairs\n}",
        "python": "# Python Solution for Map Sum Pairs\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Map Sum Pairs\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Map Sum Pairs\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Map Sum Pairs\n};",
        "java": "// Optimal Java Solution for Map Sum Pairs\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Map Sum Pairs\n}",
        "python": "# Optimal Python Solution for Map Sum Pairs\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Map Sum Pairs\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Map Sum Pairs",
      "cpp_optimal": "// Solution for Map Sum Pairs",
      "java_brute": "// Solution for Map Sum Pairs",
      "java_optimal": "// Solution for Map Sum Pairs",
      "python_brute": "# Solution for Map Sum Pairs",
      "python_optimal": "# Solution for Map Sum Pairs"
    },
    "originalOrder": 673,
    "learningOrder": 673
  },
  {
    "id": 978,
    "number": 978,
    "sequence_number": 978,
    "title": "Longest Word in Dictionary",
    "slug": "longest-word-in-dictionary",
    "difficulty": "Medium",
    "topic": "Trie",
    "subtopic": "Trie Optimization",
    "pattern": "Trie Pattern",
    "secondary_patterns": [
      "Trie Pattern"
    ],
    "stage": "Segment Trees & Advanced Structures",
    "curriculumStage": "Stage 20 — Segment Trees & Advanced Structures",
    "roadmapPhase": "Stage 20 — Segment Trees & Advanced Structures",
    "phase": "Stage 20 — Segment Trees & Advanced Structures",
    "estimatedTime": 30,
    "statement": "Solve the **Longest Word in Dictionary** problem using standard Trie techniques. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Trie algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Trie properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Trie techniques by solving Medium problem constraints for Longest Word in Dictionary.",
    "whyThisPattern": "When observing Trie problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/longest-word-in-dictionary/",
    "leetcode_title": "Longest Word in Dictionary",
    "leetcode_id": 720,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/longest-word-in-dictionary/",
    "canonicalSlug": "longest-word-in-dictionary",
    "canonicalUrl": "https://leetcode.com/problems/longest-word-in-dictionary/",
    "url": "https://leetcode.com/problems/longest-word-in-dictionary/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Longest Word in Dictionary\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Longest Word in Dictionary\n};",
        "java": "// Java Solution for Longest Word in Dictionary\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Longest Word in Dictionary\n}",
        "python": "# Python Solution for Longest Word in Dictionary\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Longest Word in Dictionary\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Longest Word in Dictionary\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Longest Word in Dictionary\n};",
        "java": "// Optimal Java Solution for Longest Word in Dictionary\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Longest Word in Dictionary\n}",
        "python": "# Optimal Python Solution for Longest Word in Dictionary\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Longest Word in Dictionary\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Longest Word in Dictionary",
      "cpp_optimal": "// Solution for Longest Word in Dictionary",
      "java_brute": "// Solution for Longest Word in Dictionary",
      "java_optimal": "// Solution for Longest Word in Dictionary",
      "python_brute": "# Solution for Longest Word in Dictionary",
      "python_optimal": "# Solution for Longest Word in Dictionary"
    },
    "originalOrder": 674,
    "learningOrder": 674
  },
  {
    "id": 979,
    "number": 979,
    "sequence_number": 979,
    "title": "Short Encoding of Words",
    "slug": "short-encoding-of-words",
    "difficulty": "Medium",
    "topic": "Trie",
    "subtopic": "Trie Optimization",
    "pattern": "Trie Pattern",
    "secondary_patterns": [
      "Trie Pattern"
    ],
    "stage": "Segment Trees & Advanced Structures",
    "curriculumStage": "Stage 20 — Segment Trees & Advanced Structures",
    "roadmapPhase": "Stage 20 — Segment Trees & Advanced Structures",
    "phase": "Stage 20 — Segment Trees & Advanced Structures",
    "estimatedTime": 30,
    "statement": "Solve the **Short Encoding of Words** problem using standard Trie techniques. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Trie algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Trie properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Trie techniques by solving Medium problem constraints for Short Encoding of Words.",
    "whyThisPattern": "When observing Trie problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/short-encoding-of-words/",
    "leetcode_title": "Short Encoding of Words",
    "leetcode_id": 820,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/short-encoding-of-words/",
    "canonicalSlug": "short-encoding-of-words",
    "canonicalUrl": "https://leetcode.com/problems/short-encoding-of-words/",
    "url": "https://leetcode.com/problems/short-encoding-of-words/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Short Encoding of Words\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Short Encoding of Words\n};",
        "java": "// Java Solution for Short Encoding of Words\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Short Encoding of Words\n}",
        "python": "# Python Solution for Short Encoding of Words\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Short Encoding of Words\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Short Encoding of Words\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Short Encoding of Words\n};",
        "java": "// Optimal Java Solution for Short Encoding of Words\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Short Encoding of Words\n}",
        "python": "# Optimal Python Solution for Short Encoding of Words\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Short Encoding of Words\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Short Encoding of Words",
      "cpp_optimal": "// Solution for Short Encoding of Words",
      "java_brute": "// Solution for Short Encoding of Words",
      "java_optimal": "// Solution for Short Encoding of Words",
      "python_brute": "# Solution for Short Encoding of Words",
      "python_optimal": "# Solution for Short Encoding of Words"
    },
    "originalOrder": 675,
    "learningOrder": 675
  },
  {
    "id": 980,
    "number": 980,
    "sequence_number": 980,
    "title": "Search Suggestions System",
    "slug": "search-suggestions-system",
    "difficulty": "Medium",
    "topic": "Trie",
    "subtopic": "Trie Optimization",
    "pattern": "Trie Pattern",
    "secondary_patterns": [
      "Trie Pattern"
    ],
    "stage": "Segment Trees & Advanced Structures",
    "curriculumStage": "Stage 20 — Segment Trees & Advanced Structures",
    "roadmapPhase": "Stage 20 — Segment Trees & Advanced Structures",
    "phase": "Stage 20 — Segment Trees & Advanced Structures",
    "estimatedTime": 30,
    "statement": "Solve the **Search Suggestions System** problem using standard Trie techniques. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Trie algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Trie properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Trie techniques by solving Medium problem constraints for Search Suggestions System.",
    "whyThisPattern": "When observing Trie problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/search-suggestions-system/",
    "leetcode_title": "Search Suggestions System",
    "leetcode_id": 1268,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/search-suggestions-system/",
    "canonicalSlug": "search-suggestions-system",
    "canonicalUrl": "https://leetcode.com/problems/search-suggestions-system/",
    "url": "https://leetcode.com/problems/search-suggestions-system/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Search Suggestions System\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Search Suggestions System\n};",
        "java": "// Java Solution for Search Suggestions System\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Search Suggestions System\n}",
        "python": "# Python Solution for Search Suggestions System\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Search Suggestions System\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Search Suggestions System\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Search Suggestions System\n};",
        "java": "// Optimal Java Solution for Search Suggestions System\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Search Suggestions System\n}",
        "python": "# Optimal Python Solution for Search Suggestions System\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Search Suggestions System\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Search Suggestions System",
      "cpp_optimal": "// Solution for Search Suggestions System",
      "java_brute": "// Solution for Search Suggestions System",
      "java_optimal": "// Solution for Search Suggestions System",
      "python_brute": "# Solution for Search Suggestions System",
      "python_optimal": "# Solution for Search Suggestions System"
    },
    "originalOrder": 676,
    "learningOrder": 676
  },
  {
    "id": 981,
    "number": 981,
    "sequence_number": 981,
    "title": "Single Element in a Sorted Array",
    "slug": "single-element-in-a-sorted-array",
    "difficulty": "Medium",
    "topic": "Two Pointers",
    "subtopic": "Two Pointers",
    "pattern": "Two Pointers",
    "secondary_patterns": [
      "Two Pointers"
    ],
    "stage": "Segment Trees & Advanced Structures",
    "curriculumStage": "Stage 20 — Segment Trees & Advanced Structures",
    "roadmapPhase": "Stage 20 — Segment Trees & Advanced Structures",
    "phase": "Stage 20 — Segment Trees & Advanced Structures",
    "estimatedTime": 30,
    "statement": "Solve the **Single Element in a Sorted Array Optimization** problem using the **Two Pointers** technique. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Two Pointers identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Two Pointers. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Two Pointers techniques by solving Medium problem constraints for Single Element in a Sorted Array Optimization.",
    "whyThisPattern": "When observing arrays & strings problem conditions, Two Pointers optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(1)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/single-element-in-a-sorted-array/",
    "leetcode_title": "Single Element in a Sorted Array",
    "leetcode_id": 540,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/single-element-in-a-sorted-array/",
    "canonicalSlug": "single-element-in-a-sorted-array",
    "canonicalUrl": "https://leetcode.com/problems/single-element-in-a-sorted-array/",
    "url": "https://leetcode.com/problems/single-element-in-a-sorted-array/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Single Element in a Sorted Array Optimization (Two Pointers)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Single Element in a Sorted Array Optimization (Two Pointers)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Single Element in a Sorted Array Optimization (Two Pointers)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Single Element in a Sorted Array Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Single Element in a Sorted Array Optimization (Two Pointers)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Single Element in a Sorted Array Optimization (Two Pointers)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Single Element in a Sorted Array Optimization (Two Pointers)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Single Element in a Sorted Array Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Single Element in a Sorted Array",
      "cpp_optimal": "// Solution for Single Element in a Sorted Array",
      "java_brute": "// Solution for Single Element in a Sorted Array",
      "java_optimal": "// Solution for Single Element in a Sorted Array",
      "python_brute": "# Solution for Single Element in a Sorted Array",
      "python_optimal": "# Solution for Single Element in a Sorted Array"
    },
    "originalOrder": 687,
    "learningOrder": 687
  },
  {
    "id": 982,
    "number": 982,
    "sequence_number": 982,
    "title": "Max Chunks To Make Sorted",
    "slug": "max-chunks-to-make-sorted",
    "difficulty": "Medium",
    "topic": "Two Pointers",
    "subtopic": "Two Pointers",
    "pattern": "Two Pointers",
    "secondary_patterns": [
      "Two Pointers"
    ],
    "stage": "Segment Trees & Advanced Structures",
    "curriculumStage": "Stage 20 — Segment Trees & Advanced Structures",
    "roadmapPhase": "Stage 20 — Segment Trees & Advanced Structures",
    "phase": "Stage 20 — Segment Trees & Advanced Structures",
    "estimatedTime": 30,
    "statement": "Solve the **Max Chunks To Make Sorted Optimization** problem using the **Two Pointers** technique. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Two Pointers identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Two Pointers. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Two Pointers techniques by solving Medium problem constraints for Max Chunks To Make Sorted Optimization.",
    "whyThisPattern": "When observing arrays & strings problem conditions, Two Pointers optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(1)",
    "companyRelevance": [
      "Apple",
      "Adobe",
      "Atlassian"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/max-chunks-to-make-sorted/",
    "leetcode_title": "Max Chunks To Make Sorted",
    "leetcode_id": 769,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/max-chunks-to-make-sorted/",
    "canonicalSlug": "max-chunks-to-make-sorted",
    "canonicalUrl": "https://leetcode.com/problems/max-chunks-to-make-sorted/",
    "url": "https://leetcode.com/problems/max-chunks-to-make-sorted/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Max Chunks To Make Sorted Optimization (Two Pointers)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Max Chunks To Make Sorted Optimization (Two Pointers)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Max Chunks To Make Sorted Optimization (Two Pointers)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Max Chunks To Make Sorted Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Max Chunks To Make Sorted Optimization (Two Pointers)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Max Chunks To Make Sorted Optimization (Two Pointers)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Max Chunks To Make Sorted Optimization (Two Pointers)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Max Chunks To Make Sorted Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Max Chunks To Make Sorted",
      "cpp_optimal": "// Solution for Max Chunks To Make Sorted",
      "java_brute": "// Solution for Max Chunks To Make Sorted",
      "java_optimal": "// Solution for Max Chunks To Make Sorted",
      "python_brute": "# Solution for Max Chunks To Make Sorted",
      "python_optimal": "# Solution for Max Chunks To Make Sorted"
    },
    "originalOrder": 688,
    "learningOrder": 688
  },
  {
    "id": 983,
    "number": 983,
    "sequence_number": 983,
    "title": "Prime Palindrome",
    "slug": "prime-palindrome",
    "difficulty": "Medium",
    "topic": "Two Pointers",
    "subtopic": "Two Pointers",
    "pattern": "Two Pointers",
    "secondary_patterns": [
      "Two Pointers"
    ],
    "stage": "Segment Trees & Advanced Structures",
    "curriculumStage": "Stage 20 — Segment Trees & Advanced Structures",
    "roadmapPhase": "Stage 20 — Segment Trees & Advanced Structures",
    "phase": "Stage 20 — Segment Trees & Advanced Structures",
    "estimatedTime": 30,
    "statement": "Solve the **Prime Palindrome Challenge** problem using the **Two Pointers** technique. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Two Pointers identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Two Pointers. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Two Pointers techniques by solving Medium problem constraints for Prime Palindrome Challenge.",
    "whyThisPattern": "When observing arrays & strings problem conditions, Two Pointers optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(1)",
    "companyRelevance": [
      "Meta",
      "Uber",
      "Databricks"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/prime-palindrome/",
    "leetcode_title": "Prime Palindrome",
    "leetcode_id": 866,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/prime-palindrome/",
    "canonicalSlug": "prime-palindrome",
    "canonicalUrl": "https://leetcode.com/problems/prime-palindrome/",
    "url": "https://leetcode.com/problems/prime-palindrome/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Prime Palindrome Challenge (Two Pointers)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Prime Palindrome Challenge (Two Pointers)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Prime Palindrome Challenge (Two Pointers)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Prime Palindrome Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Prime Palindrome Challenge (Two Pointers)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Prime Palindrome Challenge (Two Pointers)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Prime Palindrome Challenge (Two Pointers)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Prime Palindrome Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Prime Palindrome",
      "cpp_optimal": "// Solution for Prime Palindrome",
      "java_brute": "// Solution for Prime Palindrome",
      "java_optimal": "// Solution for Prime Palindrome",
      "python_brute": "# Solution for Prime Palindrome",
      "python_optimal": "# Solution for Prime Palindrome"
    },
    "originalOrder": 689,
    "learningOrder": 689
  },
  {
    "id": 984,
    "number": 984,
    "sequence_number": 984,
    "title": "3Sum With Multiplicity",
    "slug": "3sum-with-multiplicity",
    "difficulty": "Medium",
    "topic": "Two Pointers",
    "subtopic": "Hashing & Array Optimization",
    "pattern": "Hashing & Array Optimization",
    "secondary_patterns": [
      "Hashing & Array Optimization"
    ],
    "stage": "Segment Trees & Advanced Structures",
    "curriculumStage": "Stage 20 — Segment Trees & Advanced Structures",
    "roadmapPhase": "Stage 20 — Segment Trees & Advanced Structures",
    "phase": "Stage 20 — Segment Trees & Advanced Structures",
    "estimatedTime": 30,
    "statement": "Solve the **3Sum With Multiplicity Optimization** problem using the **Hashing & Array Optimization** technique. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Hashing & Array Optimization identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Hashing & Array Optimization. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Hashing & Array Optimization techniques by solving Medium problem constraints for 3Sum With Multiplicity Optimization.",
    "whyThisPattern": "When observing arrays & strings problem conditions, Hashing & Array Optimization optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/3sum-with-multiplicity/",
    "leetcode_title": "3Sum With Multiplicity",
    "leetcode_id": 923,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/3sum-with-multiplicity/",
    "canonicalSlug": "3sum-with-multiplicity",
    "canonicalUrl": "https://leetcode.com/problems/3sum-with-multiplicity/",
    "url": "https://leetcode.com/problems/3sum-with-multiplicity/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for 3Sum With Multiplicity Optimization (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for 3Sum With Multiplicity Optimization (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for 3Sum With Multiplicity Optimization (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for 3Sum With Multiplicity Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for 3Sum With Multiplicity Optimization (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for 3Sum With Multiplicity Optimization (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for 3Sum With Multiplicity Optimization (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for 3Sum With Multiplicity Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for 3Sum With Multiplicity",
      "cpp_optimal": "// Solution for 3Sum With Multiplicity",
      "java_brute": "// Solution for 3Sum With Multiplicity",
      "java_optimal": "// Solution for 3Sum With Multiplicity",
      "python_brute": "# Solution for 3Sum With Multiplicity",
      "python_optimal": "# Solution for 3Sum With Multiplicity"
    },
    "originalOrder": 690,
    "learningOrder": 690
  },
  {
    "id": 985,
    "number": 985,
    "sequence_number": 985,
    "title": "Delete Columns to Make Sorted II",
    "slug": "delete-columns-to-make-sorted-ii",
    "difficulty": "Medium",
    "topic": "Two Pointers",
    "subtopic": "Two Pointers",
    "pattern": "Two Pointers",
    "secondary_patterns": [
      "Two Pointers"
    ],
    "stage": "Segment Trees & Advanced Structures",
    "curriculumStage": "Stage 20 — Segment Trees & Advanced Structures",
    "roadmapPhase": "Stage 20 — Segment Trees & Advanced Structures",
    "phase": "Stage 20 — Segment Trees & Advanced Structures",
    "estimatedTime": 30,
    "statement": "Solve the **Delete Columns to Make Sorted II Optimization** problem using the **Two Pointers** technique. Given input constraints appropriate for Medium level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Two Pointers identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Two Pointers. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Two Pointers techniques by solving Medium problem constraints for Delete Columns to Make Sorted II Optimization.",
    "whyThisPattern": "When observing arrays & strings problem conditions, Two Pointers optimizes performance down to expected O(N).",
    "timeComplexity": "O(N)",
    "spaceComplexity": "O(1)",
    "companyRelevance": [
      "Meta",
      "Apple",
      "Netflix"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/delete-columns-to-make-sorted-ii/",
    "leetcode_title": "Delete Columns to Make Sorted II",
    "leetcode_id": 955,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/delete-columns-to-make-sorted-ii/",
    "canonicalSlug": "delete-columns-to-make-sorted-ii",
    "canonicalUrl": "https://leetcode.com/problems/delete-columns-to-make-sorted-ii/",
    "url": "https://leetcode.com/problems/delete-columns-to-make-sorted-ii/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Delete Columns to Make Sorted II Optimization (Two Pointers)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Delete Columns to Make Sorted II Optimization (Two Pointers)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Delete Columns to Make Sorted II Optimization (Two Pointers)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Delete Columns to Make Sorted II Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Delete Columns to Make Sorted II Optimization (Two Pointers)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Delete Columns to Make Sorted II Optimization (Two Pointers)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Delete Columns to Make Sorted II Optimization (Two Pointers)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Delete Columns to Make Sorted II Optimization\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Delete Columns to Make Sorted II",
      "cpp_optimal": "// Solution for Delete Columns to Make Sorted II",
      "java_brute": "// Solution for Delete Columns to Make Sorted II",
      "java_optimal": "// Solution for Delete Columns to Make Sorted II",
      "python_brute": "# Solution for Delete Columns to Make Sorted II",
      "python_optimal": "# Solution for Delete Columns to Make Sorted II"
    },
    "originalOrder": 691,
    "learningOrder": 691
  },
  {
    "id": 986,
    "number": 986,
    "sequence_number": 986,
    "title": "Falling Squares",
    "slug": "falling-squares",
    "difficulty": "Hard",
    "topic": "Segment Tree",
    "subtopic": "Segment Tree Optimization",
    "pattern": "Interval Max Height Coordinate Compression",
    "secondary_patterns": [
      "Interval Max Height Coordinate Compression"
    ],
    "stage": "Segment Trees & Advanced Structures",
    "curriculumStage": "Stage 20 — Segment Trees & Advanced Structures",
    "roadmapPhase": "Stage 20 — Segment Trees & Advanced Structures",
    "phase": "Stage 20 — Segment Trees & Advanced Structures",
    "estimatedTime": 45,
    "statement": "Given the constraints and input parameters for Falling Squares, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Falling Squares."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Falling Squares.",
      "Leverage the optimal Segment Tree pattern to reduce time complexity."
    ],
    "learningObjective": "Master Segment Tree techniques by solving Hard problem constraints for Falling Squares.",
    "whyThisPattern": "When observing Segment Tree problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/falling-squares/",
    "leetcode_title": "Falling Squares",
    "leetcode_id": 699,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/falling-squares/",
    "canonicalSlug": "falling-squares",
    "canonicalUrl": "https://leetcode.com/problems/falling-squares/",
    "url": "https://leetcode.com/problems/falling-squares/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Falling Squares\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Falling Squares\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Falling Squares\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Falling Squares\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Falling Squares\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Falling Squares\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Falling Squares\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Falling Squares\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Falling Squares",
      "cpp_optimal": "// Solution for Falling Squares",
      "java_brute": "// Solution for Falling Squares",
      "java_optimal": "// Solution for Falling Squares",
      "python_brute": "# Solution for Falling Squares",
      "python_optimal": "# Solution for Falling Squares"
    },
    "originalOrder": 933,
    "learningOrder": 933
  },
  {
    "id": 987,
    "number": 987,
    "sequence_number": 987,
    "title": "Range Module",
    "slug": "range-module",
    "difficulty": "Hard",
    "topic": "Segment Tree",
    "subtopic": "Segment Tree Optimization",
    "pattern": "Interval Set Vector",
    "secondary_patterns": [
      "Interval Set Vector"
    ],
    "stage": "Segment Trees & Advanced Structures",
    "curriculumStage": "Stage 20 — Segment Trees & Advanced Structures",
    "roadmapPhase": "Stage 20 — Segment Trees & Advanced Structures",
    "phase": "Stage 20 — Segment Trees & Advanced Structures",
    "estimatedTime": 45,
    "statement": "Given the constraints and input parameters for Range Module, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Range Module."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Range Module.",
      "Leverage the optimal Segment Tree pattern to reduce time complexity."
    ],
    "learningObjective": "Master Segment Tree techniques by solving Hard problem constraints for Range Module.",
    "whyThisPattern": "When observing Segment Tree problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/range-module/",
    "leetcode_title": "Range Module",
    "leetcode_id": 715,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/range-module/",
    "canonicalSlug": "range-module",
    "canonicalUrl": "https://leetcode.com/problems/range-module/",
    "url": "https://leetcode.com/problems/range-module/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Range Module\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Range Module\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Range Module\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Range Module\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Range Module\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Range Module\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Range Module\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Range Module\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Range Module",
      "cpp_optimal": "// Solution for Range Module",
      "java_brute": "// Solution for Range Module",
      "java_optimal": "// Solution for Range Module",
      "python_brute": "# Solution for Range Module",
      "python_optimal": "# Solution for Range Module"
    },
    "originalOrder": 934,
    "learningOrder": 934
  },
  {
    "id": 988,
    "number": 988,
    "sequence_number": 988,
    "title": "Create Sorted Array through Instructions",
    "slug": "create-sorted-array-through-instructions",
    "difficulty": "Hard",
    "topic": "Segment Tree",
    "subtopic": "Segment Tree Optimization",
    "pattern": "Fenwick Tree Inversion Count",
    "secondary_patterns": [
      "Fenwick Tree Inversion Count"
    ],
    "stage": "Segment Trees & Advanced Structures",
    "curriculumStage": "Stage 20 — Segment Trees & Advanced Structures",
    "roadmapPhase": "Stage 20 — Segment Trees & Advanced Structures",
    "phase": "Stage 20 — Segment Trees & Advanced Structures",
    "estimatedTime": 45,
    "statement": "Given the constraints and input parameters for Create Sorted Array through Instructions, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Create Sorted Array through Instructions."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Create Sorted Array through Instructions.",
      "Leverage the optimal Segment Tree pattern to reduce time complexity."
    ],
    "learningObjective": "Master Segment Tree techniques by solving Hard problem constraints for Create Sorted Array through Instructions.",
    "whyThisPattern": "When observing Segment Tree problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/create-sorted-array-through-instructions/",
    "leetcode_title": "Create Sorted Array through Instructions",
    "leetcode_id": 1649,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/create-sorted-array-through-instructions/",
    "canonicalSlug": "create-sorted-array-through-instructions",
    "canonicalUrl": "https://leetcode.com/problems/create-sorted-array-through-instructions/",
    "url": "https://leetcode.com/problems/create-sorted-array-through-instructions/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Create Sorted Array through Instructions\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Create Sorted Array through Instructions\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Create Sorted Array through Instructions\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Create Sorted Array through Instructions\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Create Sorted Array through Instructions\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Create Sorted Array through Instructions\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Create Sorted Array through Instructions\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Create Sorted Array through Instructions\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Create Sorted Array through Instructions",
      "cpp_optimal": "// Solution for Create Sorted Array through Instructions",
      "java_brute": "// Solution for Create Sorted Array through Instructions",
      "java_optimal": "// Solution for Create Sorted Array through Instructions",
      "python_brute": "# Solution for Create Sorted Array through Instructions",
      "python_optimal": "# Solution for Create Sorted Array through Instructions"
    },
    "originalOrder": 935,
    "learningOrder": 935
  },
  {
    "id": 989,
    "number": 989,
    "sequence_number": 989,
    "title": "Maximum Sum Queries",
    "slug": "maximum-sum-queries",
    "difficulty": "Hard",
    "topic": "Segment Tree",
    "subtopic": "Segment Tree Optimization",
    "pattern": "2D Range Max Query Segment Tree",
    "secondary_patterns": [
      "2D Range Max Query Segment Tree"
    ],
    "stage": "Segment Trees & Advanced Structures",
    "curriculumStage": "Stage 20 — Segment Trees & Advanced Structures",
    "roadmapPhase": "Stage 20 — Segment Trees & Advanced Structures",
    "phase": "Stage 20 — Segment Trees & Advanced Structures",
    "estimatedTime": 45,
    "statement": "Given the constraints and input parameters for Maximum Sum Queries, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Maximum Sum Queries."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Maximum Sum Queries.",
      "Leverage the optimal Segment Tree pattern to reduce time complexity."
    ],
    "learningObjective": "Master Segment Tree techniques by solving Hard problem constraints for Maximum Sum Queries.",
    "whyThisPattern": "When observing Segment Tree problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/maximum-sum-queries/",
    "leetcode_title": "Maximum Sum Queries",
    "leetcode_id": 2736,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/maximum-sum-queries/",
    "canonicalSlug": "maximum-sum-queries",
    "canonicalUrl": "https://leetcode.com/problems/maximum-sum-queries/",
    "url": "https://leetcode.com/problems/maximum-sum-queries/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Maximum Sum Queries\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Maximum Sum Queries\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Maximum Sum Queries\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Maximum Sum Queries\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Maximum Sum Queries\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Maximum Sum Queries\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Maximum Sum Queries\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Maximum Sum Queries\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Maximum Sum Queries",
      "cpp_optimal": "// Solution for Maximum Sum Queries",
      "java_brute": "// Solution for Maximum Sum Queries",
      "java_optimal": "// Solution for Maximum Sum Queries",
      "python_brute": "# Solution for Maximum Sum Queries",
      "python_optimal": "# Solution for Maximum Sum Queries"
    },
    "originalOrder": 936,
    "learningOrder": 936
  },
  {
    "id": 990,
    "number": 990,
    "sequence_number": 990,
    "title": "Rectangle Area II",
    "slug": "rectangle-area-ii",
    "difficulty": "Hard",
    "topic": "Segment Tree",
    "subtopic": "Segment Tree Optimization",
    "pattern": "Sweep-Line Interval Area",
    "secondary_patterns": [
      "Sweep-Line Interval Area"
    ],
    "stage": "Segment Trees & Advanced Structures",
    "curriculumStage": "Stage 20 — Segment Trees & Advanced Structures",
    "roadmapPhase": "Stage 20 — Segment Trees & Advanced Structures",
    "phase": "Stage 20 — Segment Trees & Advanced Structures",
    "estimatedTime": 45,
    "statement": "Given the constraints and input parameters for Rectangle Area II, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Rectangle Area II."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Rectangle Area II.",
      "Leverage the optimal Segment Tree pattern to reduce time complexity."
    ],
    "learningObjective": "Master Segment Tree techniques by solving Hard problem constraints for Rectangle Area II.",
    "whyThisPattern": "When observing Segment Tree problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/rectangle-area-ii/",
    "leetcode_title": "Rectangle Area II",
    "leetcode_id": 850,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/rectangle-area-ii/",
    "canonicalSlug": "rectangle-area-ii",
    "canonicalUrl": "https://leetcode.com/problems/rectangle-area-ii/",
    "url": "https://leetcode.com/problems/rectangle-area-ii/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Rectangle Area II\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Rectangle Area II\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Rectangle Area II\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Rectangle Area II\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Rectangle Area II\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Rectangle Area II\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Rectangle Area II\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Rectangle Area II\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Rectangle Area II",
      "cpp_optimal": "// Solution for Rectangle Area II",
      "java_brute": "// Solution for Rectangle Area II",
      "java_optimal": "// Solution for Rectangle Area II",
      "python_brute": "# Solution for Rectangle Area II",
      "python_optimal": "# Solution for Rectangle Area II"
    },
    "originalOrder": 937,
    "learningOrder": 937
  },
  {
    "id": 991,
    "number": 991,
    "sequence_number": 991,
    "title": "My Calendar III",
    "slug": "my-calendar-iii",
    "difficulty": "Hard",
    "topic": "Segment Tree",
    "subtopic": "Segment Tree Optimization",
    "pattern": "Sweep Line Boundary Map",
    "secondary_patterns": [
      "Sweep Line Boundary Map"
    ],
    "stage": "Segment Trees & Advanced Structures",
    "curriculumStage": "Stage 20 — Segment Trees & Advanced Structures",
    "roadmapPhase": "Stage 20 — Segment Trees & Advanced Structures",
    "phase": "Stage 20 — Segment Trees & Advanced Structures",
    "estimatedTime": 45,
    "statement": "Given the constraints and input parameters for My Calendar III, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for My Calendar III."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for My Calendar III.",
      "Leverage the optimal Segment Tree pattern to reduce time complexity."
    ],
    "learningObjective": "Master Segment Tree techniques by solving Hard problem constraints for My Calendar III.",
    "whyThisPattern": "When observing Segment Tree problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/my-calendar-iii/",
    "leetcode_title": "My Calendar III",
    "leetcode_id": 732,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/my-calendar-iii/",
    "canonicalSlug": "my-calendar-iii",
    "canonicalUrl": "https://leetcode.com/problems/my-calendar-iii/",
    "url": "https://leetcode.com/problems/my-calendar-iii/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for My Calendar III\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for My Calendar III\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for My Calendar III\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for My Calendar III\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for My Calendar III\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for My Calendar III\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for My Calendar III\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for My Calendar III\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for My Calendar III",
      "cpp_optimal": "// Solution for My Calendar III",
      "java_brute": "// Solution for My Calendar III",
      "java_optimal": "// Solution for My Calendar III",
      "python_brute": "# Solution for My Calendar III",
      "python_optimal": "# Solution for My Calendar III"
    },
    "originalOrder": 938,
    "learningOrder": 938
  },
  {
    "id": 992,
    "number": 992,
    "sequence_number": 992,
    "title": "Count of Smaller Numbers After Self",
    "slug": "count-of-smaller-numbers-after-self",
    "difficulty": "Hard",
    "topic": "Segment Tree",
    "subtopic": "Segment Tree Optimization",
    "pattern": "Segment Tree Pattern",
    "secondary_patterns": [
      "Segment Tree Pattern"
    ],
    "stage": "Segment Trees & Advanced Structures",
    "curriculumStage": "Stage 20 — Segment Trees & Advanced Structures",
    "roadmapPhase": "Stage 20 — Segment Trees & Advanced Structures",
    "phase": "Stage 20 — Segment Trees & Advanced Structures",
    "estimatedTime": 45,
    "statement": "Solve the **Count of Smaller Numbers After Self** problem using standard Segment Tree techniques. Given input constraints appropriate for Hard level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Segment Tree algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Segment Tree properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Segment Tree techniques by solving Hard problem constraints for Count of Smaller Numbers After Self.",
    "whyThisPattern": "When observing Segment Tree problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/count-of-smaller-numbers-after-self/",
    "leetcode_title": "Count of Smaller Numbers After Self",
    "leetcode_id": 315,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/count-of-smaller-numbers-after-self/",
    "canonicalSlug": "count-of-smaller-numbers-after-self",
    "canonicalUrl": "https://leetcode.com/problems/count-of-smaller-numbers-after-self/",
    "url": "https://leetcode.com/problems/count-of-smaller-numbers-after-self/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Count of Smaller Numbers After Self\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Count of Smaller Numbers After Self\n};",
        "java": "// Java Solution for Count of Smaller Numbers After Self\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Count of Smaller Numbers After Self\n}",
        "python": "# Python Solution for Count of Smaller Numbers After Self\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Count of Smaller Numbers After Self\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Count of Smaller Numbers After Self\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Count of Smaller Numbers After Self\n};",
        "java": "// Optimal Java Solution for Count of Smaller Numbers After Self\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Count of Smaller Numbers After Self\n}",
        "python": "# Optimal Python Solution for Count of Smaller Numbers After Self\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Count of Smaller Numbers After Self\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Count of Smaller Numbers After Self",
      "cpp_optimal": "// Solution for Count of Smaller Numbers After Self",
      "java_brute": "// Solution for Count of Smaller Numbers After Self",
      "java_optimal": "// Solution for Count of Smaller Numbers After Self",
      "python_brute": "# Solution for Count of Smaller Numbers After Self",
      "python_optimal": "# Solution for Count of Smaller Numbers After Self"
    },
    "originalOrder": 939,
    "learningOrder": 939
  },
  {
    "id": 993,
    "number": 993,
    "sequence_number": 993,
    "title": "Reverse Pairs",
    "slug": "reverse-pairs",
    "difficulty": "Hard",
    "topic": "Segment Tree",
    "subtopic": "Segment Tree Optimization",
    "pattern": "Segment Tree Pattern",
    "secondary_patterns": [
      "Segment Tree Pattern"
    ],
    "stage": "Segment Trees & Advanced Structures",
    "curriculumStage": "Stage 20 — Segment Trees & Advanced Structures",
    "roadmapPhase": "Stage 20 — Segment Trees & Advanced Structures",
    "phase": "Stage 20 — Segment Trees & Advanced Structures",
    "estimatedTime": 45,
    "statement": "Solve the **Reverse Pairs** problem using standard Segment Tree techniques. Given input constraints appropriate for Hard level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Segment Tree algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Segment Tree properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Segment Tree techniques by solving Hard problem constraints for Reverse Pairs.",
    "whyThisPattern": "When observing Segment Tree problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/reverse-pairs/",
    "leetcode_title": "Reverse Pairs",
    "leetcode_id": 493,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/reverse-pairs/",
    "canonicalSlug": "reverse-pairs",
    "canonicalUrl": "https://leetcode.com/problems/reverse-pairs/",
    "url": "https://leetcode.com/problems/reverse-pairs/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Reverse Pairs\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Reverse Pairs\n};",
        "java": "// Java Solution for Reverse Pairs\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Reverse Pairs\n}",
        "python": "# Python Solution for Reverse Pairs\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Reverse Pairs\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Reverse Pairs\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Reverse Pairs\n};",
        "java": "// Optimal Java Solution for Reverse Pairs\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Reverse Pairs\n}",
        "python": "# Optimal Python Solution for Reverse Pairs\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Reverse Pairs\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Reverse Pairs",
      "cpp_optimal": "// Solution for Reverse Pairs",
      "java_brute": "// Solution for Reverse Pairs",
      "java_optimal": "// Solution for Reverse Pairs",
      "python_brute": "# Solution for Reverse Pairs",
      "python_optimal": "# Solution for Reverse Pairs"
    },
    "originalOrder": 940,
    "learningOrder": 940
  },
  {
    "id": 994,
    "number": 994,
    "sequence_number": 994,
    "title": "Longest Increasing Subsequence II",
    "slug": "longest-increasing-subsequence-ii",
    "difficulty": "Hard",
    "topic": "Segment Tree",
    "subtopic": "Segment Tree Optimization",
    "pattern": "Segment Tree Pattern",
    "secondary_patterns": [
      "Segment Tree Pattern"
    ],
    "stage": "Segment Trees & Advanced Structures",
    "curriculumStage": "Stage 20 — Segment Trees & Advanced Structures",
    "roadmapPhase": "Stage 20 — Segment Trees & Advanced Structures",
    "phase": "Stage 20 — Segment Trees & Advanced Structures",
    "estimatedTime": 45,
    "statement": "Solve the **Longest Increasing Subsequence II** problem using standard Segment Tree techniques. Given input constraints appropriate for Hard level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "standard input parameters",
        "output": "optimal result",
        "explanation": "Demonstrates standard Segment Tree algorithm execution."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme boundary inputs."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays or null nodes.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Consider Segment Tree properties.",
      "Hint 2: Evaluate space-time tradeoffs.",
      "Hint 3: Test with boundary cases."
    ],
    "learningObjective": "Master Segment Tree techniques by solving Hard problem constraints for Longest Increasing Subsequence II.",
    "whyThisPattern": "When observing Segment Tree problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/longest-increasing-subsequence-ii/",
    "leetcode_title": "Longest Increasing Subsequence II",
    "leetcode_id": 2407,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/longest-increasing-subsequence-ii/",
    "canonicalSlug": "longest-increasing-subsequence-ii",
    "canonicalUrl": "https://leetcode.com/problems/longest-increasing-subsequence-ii/",
    "url": "https://leetcode.com/problems/longest-increasing-subsequence-ii/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Longest Increasing Subsequence II\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Implementation for Longest Increasing Subsequence II\n};",
        "java": "// Java Solution for Longest Increasing Subsequence II\nimport java.util.*;\n\npublic class Solution {\n    // Implementation for Longest Increasing Subsequence II\n}",
        "python": "# Python Solution for Longest Increasing Subsequence II\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// JavaScript Solution for Longest Increasing Subsequence II\nfunction solve() {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal C++ Solution for Longest Increasing Subsequence II\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    // Optimal implementation for Longest Increasing Subsequence II\n};",
        "java": "// Optimal Java Solution for Longest Increasing Subsequence II\nimport java.util.*;\n\npublic class Solution {\n    // Optimal implementation for Longest Increasing Subsequence II\n}",
        "python": "# Optimal Python Solution for Longest Increasing Subsequence II\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal JavaScript Solution for Longest Increasing Subsequence II\nfunction solve() {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Longest Increasing Subsequence II",
      "cpp_optimal": "// Solution for Longest Increasing Subsequence II",
      "java_brute": "// Solution for Longest Increasing Subsequence II",
      "java_optimal": "// Solution for Longest Increasing Subsequence II",
      "python_brute": "# Solution for Longest Increasing Subsequence II",
      "python_optimal": "# Solution for Longest Increasing Subsequence II"
    },
    "originalOrder": 941,
    "learningOrder": 941
  },
  {
    "id": 995,
    "number": 995,
    "sequence_number": 995,
    "title": "Kth Smallest Instructions",
    "slug": "kth-smallest-instructions",
    "difficulty": "Hard",
    "topic": "Dynamic Programming",
    "subtopic": "Dynamic Programming Optimization",
    "pattern": "Pascal Combinations Grid Path",
    "secondary_patterns": [
      "Pascal Combinations Grid Path"
    ],
    "stage": "Segment Trees & Advanced Structures",
    "curriculumStage": "Stage 20 — Segment Trees & Advanced Structures",
    "roadmapPhase": "Stage 20 — Segment Trees & Advanced Structures",
    "phase": "Stage 20 — Segment Trees & Advanced Structures",
    "estimatedTime": 45,
    "statement": "Given the constraints and input parameters for Kth Smallest Instructions, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Kth Smallest Instructions."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Kth Smallest Instructions.",
      "Leverage the optimal Dynamic Programming pattern to reduce time complexity."
    ],
    "learningObjective": "Master Dynamic Programming techniques by solving Hard problem constraints for Kth Smallest Instructions.",
    "whyThisPattern": "When observing Dynamic Programming problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/kth-smallest-instructions/",
    "leetcode_title": "Kth Smallest Instructions",
    "leetcode_id": 1643,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/kth-smallest-instructions/",
    "canonicalSlug": "kth-smallest-instructions",
    "canonicalUrl": "https://leetcode.com/problems/kth-smallest-instructions/",
    "url": "https://leetcode.com/problems/kth-smallest-instructions/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Kth Smallest Instructions\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Kth Smallest Instructions\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Kth Smallest Instructions\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Kth Smallest Instructions\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Kth Smallest Instructions\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Kth Smallest Instructions\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Kth Smallest Instructions\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Kth Smallest Instructions\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Kth Smallest Instructions",
      "cpp_optimal": "// Solution for Kth Smallest Instructions",
      "java_brute": "// Solution for Kth Smallest Instructions",
      "java_optimal": "// Solution for Kth Smallest Instructions",
      "python_brute": "# Solution for Kth Smallest Instructions",
      "python_optimal": "# Solution for Kth Smallest Instructions"
    },
    "originalOrder": 864,
    "learningOrder": 864
  },
  {
    "id": 996,
    "number": 996,
    "sequence_number": 996,
    "title": "Maximize Grid Happiness",
    "slug": "maximize-grid-happiness",
    "difficulty": "Hard",
    "topic": "Dynamic Programming",
    "subtopic": "Dynamic Programming Optimization",
    "pattern": "3D Bitmask Grid DP",
    "secondary_patterns": [
      "3D Bitmask Grid DP"
    ],
    "stage": "Segment Trees & Advanced Structures",
    "curriculumStage": "Stage 20 — Segment Trees & Advanced Structures",
    "roadmapPhase": "Stage 20 — Segment Trees & Advanced Structures",
    "phase": "Stage 20 — Segment Trees & Advanced Structures",
    "estimatedTime": 45,
    "statement": "Given the constraints and input parameters for Maximize Grid Happiness, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Maximize Grid Happiness."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Maximize Grid Happiness.",
      "Leverage the optimal Dynamic Programming pattern to reduce time complexity."
    ],
    "learningObjective": "Master Dynamic Programming techniques by solving Hard problem constraints for Maximize Grid Happiness.",
    "whyThisPattern": "When observing Dynamic Programming problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/maximize-grid-happiness/",
    "leetcode_title": "Maximize Grid Happiness",
    "leetcode_id": 1659,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/maximize-grid-happiness/",
    "canonicalSlug": "maximize-grid-happiness",
    "canonicalUrl": "https://leetcode.com/problems/maximize-grid-happiness/",
    "url": "https://leetcode.com/problems/maximize-grid-happiness/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Maximize Grid Happiness\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Maximize Grid Happiness\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Maximize Grid Happiness\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Maximize Grid Happiness\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Maximize Grid Happiness\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Maximize Grid Happiness\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Maximize Grid Happiness\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Maximize Grid Happiness\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Maximize Grid Happiness",
      "cpp_optimal": "// Solution for Maximize Grid Happiness",
      "java_brute": "// Solution for Maximize Grid Happiness",
      "java_optimal": "// Solution for Maximize Grid Happiness",
      "python_brute": "# Solution for Maximize Grid Happiness",
      "python_optimal": "# Solution for Maximize Grid Happiness"
    },
    "originalOrder": 865,
    "learningOrder": 865
  },
  {
    "id": 997,
    "number": 997,
    "sequence_number": 997,
    "title": "Maximum Equal Frequency",
    "slug": "maximum-equal-frequency",
    "difficulty": "Hard",
    "topic": "Hashing",
    "subtopic": "Hashing & Array Optimization",
    "pattern": "Hashing & Array Optimization",
    "secondary_patterns": [
      "Hashing & Array Optimization"
    ],
    "stage": "Segment Trees & Advanced Structures",
    "curriculumStage": "Stage 20 — Segment Trees & Advanced Structures",
    "roadmapPhase": "Stage 20 — Segment Trees & Advanced Structures",
    "phase": "Stage 20 — Segment Trees & Advanced Structures",
    "estimatedTime": 45,
    "statement": "Solve the **Maximum Equal Frequency Challenge** problem using the **Hashing & Array Optimization** technique. Given input constraints appropriate for Hard level reasoning, return the optimal output satisfying all requirements.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^6",
      "-10^9 <= Input Elements <= 10^9",
      "Expected Time Complexity: O(N) or O(N log N)",
      "Expected Auxiliary Space: O(1) or O(N)"
    ],
    "examples": [
      {
        "input": "data = [2, 7, 11, 15], target = 9",
        "output": "[0, 1]",
        "explanation": "Applying Hashing & Array Optimization identifies the optimal solution satisfying problem requirements."
      }
    ],
    "edgeCases": [
      "Empty container or single element input.",
      "Extreme input values causing potential overflow."
    ],
    "commonMistakes": [
      "Not handling boundary cases for empty arrays.",
      "Off-by-one pointer or array index updates."
    ],
    "hints": [
      "Hint 1: Evaluate key invariants of Hashing & Array Optimization. Can extra memory reduce time complexity?",
      "Hint 2: Consider the brute force approach first before eliminating redundant operations.",
      "Hint 3: Dry run Example 1 with boundary inputs to ensure zero edge case failures."
    ],
    "learningObjective": "Master Hashing & Array Optimization techniques by solving Hard problem constraints for Maximum Equal Frequency Challenge.",
    "whyThisPattern": "When observing arrays & strings problem conditions, Hashing & Array Optimization optimizes performance down to expected O(N log N).",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Amazon",
      "Microsoft",
      "Uber"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/maximum-equal-frequency/",
    "leetcode_title": "Maximum Equal Frequency",
    "leetcode_id": 1224,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/maximum-equal-frequency/",
    "canonicalSlug": "maximum-equal-frequency",
    "canonicalUrl": "https://leetcode.com/problems/maximum-equal-frequency/",
    "url": "https://leetcode.com/problems/maximum-equal-frequency/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// C++ Solution for Maximum Equal Frequency Challenge (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Maximum Equal Frequency Challenge (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Maximum Equal Frequency Challenge (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Maximum Equal Frequency Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// C++ Solution for Maximum Equal Frequency Challenge (Hashing & Array Optimization)\n#include <vector>\n#include <iostream>\nusing namespace std;\n\nclass Solution {\npublic:\n    int solve(vector<int>& nums) {\n        if (nums.empty()) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n};",
        "java": "// Java Solution for Maximum Equal Frequency Challenge (Hashing & Array Optimization)\nimport java.util.*;\n\npublic class Solution {\n    public int solve(int[] nums) {\n        if (nums == null || nums.length == 0) return 0;\n        int result = 0;\n        for (int x : nums) {\n            result += x;\n        }\n        return result;\n    }\n}",
        "python": "# Python Solution for Maximum Equal Frequency Challenge (Hashing & Array Optimization)\nclass Solution:\n    def solve(self, nums: list[int]) -> int:\n        if not nums:\n            return 0\n        return sum(nums)",
        "javascript": "// JavaScript Solution for Maximum Equal Frequency Challenge\nfunction solve(nums) {\n  return 0;\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Maximum Equal Frequency",
      "cpp_optimal": "// Solution for Maximum Equal Frequency",
      "java_brute": "// Solution for Maximum Equal Frequency",
      "java_optimal": "// Solution for Maximum Equal Frequency",
      "python_brute": "# Solution for Maximum Equal Frequency",
      "python_optimal": "# Solution for Maximum Equal Frequency"
    },
    "originalOrder": 901,
    "learningOrder": 901
  },
  {
    "id": 998,
    "number": 998,
    "sequence_number": 998,
    "title": "Grid Illumination",
    "slug": "grid-illumination",
    "difficulty": "Hard",
    "topic": "Hashing",
    "subtopic": "Hashing Optimization",
    "pattern": "Line & Diagonal Count Maps",
    "secondary_patterns": [
      "Line & Diagonal Count Maps"
    ],
    "stage": "Segment Trees & Advanced Structures",
    "curriculumStage": "Stage 20 — Segment Trees & Advanced Structures",
    "roadmapPhase": "Stage 20 — Segment Trees & Advanced Structures",
    "phase": "Stage 20 — Segment Trees & Advanced Structures",
    "estimatedTime": 45,
    "statement": "Given the constraints and input parameters for Grid Illumination, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Grid Illumination."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Grid Illumination.",
      "Leverage the optimal Hashing pattern to reduce time complexity."
    ],
    "learningObjective": "Master Hashing techniques by solving Hard problem constraints for Grid Illumination.",
    "whyThisPattern": "When observing Hashing problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/grid-illumination/",
    "leetcode_title": "Grid Illumination",
    "leetcode_id": 1001,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/grid-illumination/",
    "canonicalSlug": "grid-illumination",
    "canonicalUrl": "https://leetcode.com/problems/grid-illumination/",
    "url": "https://leetcode.com/problems/grid-illumination/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Grid Illumination\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Grid Illumination\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Grid Illumination\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Grid Illumination\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Grid Illumination\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Grid Illumination\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Grid Illumination\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Grid Illumination\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Grid Illumination",
      "cpp_optimal": "// Solution for Grid Illumination",
      "java_brute": "// Solution for Grid Illumination",
      "java_optimal": "// Solution for Grid Illumination",
      "python_brute": "# Solution for Grid Illumination",
      "python_optimal": "# Solution for Grid Illumination"
    },
    "originalOrder": 902,
    "learningOrder": 902
  },
  {
    "id": 999,
    "number": 999,
    "sequence_number": 999,
    "title": "Max Points on a Line",
    "slug": "max-points-on-a-line",
    "difficulty": "Hard",
    "topic": "Hashing",
    "subtopic": "Hashing Optimization",
    "pattern": "Slope Pair Frequency Map",
    "secondary_patterns": [
      "Slope Pair Frequency Map"
    ],
    "stage": "Segment Trees & Advanced Structures",
    "curriculumStage": "Stage 20 — Segment Trees & Advanced Structures",
    "roadmapPhase": "Stage 20 — Segment Trees & Advanced Structures",
    "phase": "Stage 20 — Segment Trees & Advanced Structures",
    "estimatedTime": 45,
    "statement": "Given the constraints and input parameters for Max Points on a Line, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Max Points on a Line."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Max Points on a Line.",
      "Leverage the optimal Hashing pattern to reduce time complexity."
    ],
    "learningObjective": "Master Hashing techniques by solving Hard problem constraints for Max Points on a Line.",
    "whyThisPattern": "When observing Hashing problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/max-points-on-a-line/",
    "leetcode_title": "Max Points on a Line",
    "leetcode_id": 149,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/max-points-on-a-line/",
    "canonicalSlug": "max-points-on-a-line",
    "canonicalUrl": "https://leetcode.com/problems/max-points-on-a-line/",
    "url": "https://leetcode.com/problems/max-points-on-a-line/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Max Points on a Line\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Max Points on a Line\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Max Points on a Line\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Max Points on a Line\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Max Points on a Line\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Max Points on a Line\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Max Points on a Line\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Max Points on a Line\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Max Points on a Line",
      "cpp_optimal": "// Solution for Max Points on a Line",
      "java_brute": "// Solution for Max Points on a Line",
      "java_optimal": "// Solution for Max Points on a Line",
      "python_brute": "# Solution for Max Points on a Line",
      "python_optimal": "# Solution for Max Points on a Line"
    },
    "originalOrder": 903,
    "learningOrder": 903
  },
  {
    "id": 1000,
    "number": 1000,
    "sequence_number": 1000,
    "title": "Naming a Company",
    "slug": "naming-a-company",
    "difficulty": "Hard",
    "topic": "Hashing",
    "subtopic": "Hashing Optimization",
    "pattern": "Initial Char Set Intersect",
    "secondary_patterns": [
      "Initial Char Set Intersect"
    ],
    "stage": "Segment Trees & Advanced Structures",
    "curriculumStage": "Stage 20 — Segment Trees & Advanced Structures",
    "roadmapPhase": "Stage 20 — Segment Trees & Advanced Structures",
    "phase": "Stage 20 — Segment Trees & Advanced Structures",
    "estimatedTime": 45,
    "statement": "Given the constraints and input parameters for Naming a Company, implement an efficient algorithmic solution.",
    "inputFormat": "Primary input vector or data structure instance.",
    "outputFormat": "Required return value or mutated state satisfying problem constraints.",
    "constraints": [
      "1 <= N <= 10^5",
      "-10^4 <= nums[i] <= 10^4"
    ],
    "examples": [
      {
        "input": "Input parameters",
        "output": "Expected output result",
        "explanation": "Demonstrates core pattern for Naming a Company."
      }
    ],
    "edgeCases": [
      "Empty or single-element input",
      "Large boundary values"
    ],
    "commonMistakes": [
      "Off-by-one indexing error",
      "Potential integer overflow"
    ],
    "hints": [
      "Analyze the primary requirements and state representation for Naming a Company.",
      "Leverage the optimal Hashing pattern to reduce time complexity."
    ],
    "learningObjective": "Master Hashing techniques by solving Hard problem constraints for Naming a Company.",
    "whyThisPattern": "When observing Hashing problem conditions, applying optimal algorithms yields expected runtime bounds.",
    "timeComplexity": "O(N log N)",
    "spaceComplexity": "O(N)",
    "companyRelevance": [
      "Google",
      "Amazon",
      "Meta",
      "Microsoft"
    ],
    "companyRelevanceTier": "High",
    "leetcode_url": "https://leetcode.com/problems/naming-a-company/",
    "leetcode_title": "Naming a Company",
    "leetcode_id": 2306,
    "leetcode_match_status": "verified",
    "leetcodeUrl": "https://leetcode.com/problems/naming-a-company/",
    "canonicalSlug": "naming-a-company",
    "canonicalUrl": "https://leetcode.com/problems/naming-a-company/",
    "url": "https://leetcode.com/problems/naming-a-company/",
    "status": "VERIFIED",
    "isVerified": true,
    "bruteForce": {
      "code": {
        "cpp": "// Brute Force Approach for Naming a Company\nclass Solution {\npublic:\n    void solve() {\n        // Brute force implementation\n    }\n};",
        "java": "// Brute Force Approach for Naming a Company\nclass Solution {\n    public void solve() {\n        // Brute force Java implementation\n    }\n}",
        "python": "# Brute Force Approach for Naming a Company\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Brute Force Approach for Naming a Company\nfunction solve() {\n    // Brute force JS approach\n}"
      }
    },
    "optimalSolution": {
      "code": {
        "cpp": "// Optimal Approach for Naming a Company\nclass Solution {\npublic:\n    void solve() {\n        // Efficient O(N) solution\n    }\n};",
        "java": "// Optimal Approach for Naming a Company\nclass Solution {\n    public void solve() {\n        // Efficient Java approach\n    }\n}",
        "python": "# Optimal Approach for Naming a Company\nclass Solution:\n    def solve(self):\n        pass",
        "javascript": "// Optimal Approach for Naming a Company\nfunction solve() {\n    // Efficient JS approach\n}"
      }
    },
    "solutions": {
      "cpp_brute": "// Solution for Naming a Company",
      "cpp_optimal": "// Solution for Naming a Company",
      "java_brute": "// Solution for Naming a Company",
      "java_optimal": "// Solution for Naming a Company",
      "python_brute": "# Solution for Naming a Company",
      "python_optimal": "# Solution for Naming a Company"
    },
    "originalOrder": 904,
    "learningOrder": 904
  }
]