Solve array modulo and parentheses tasks
Problem Description
This task consists of two independent algorithmic problems, each with specific requirements for time and space complexity.
1. Count Subarrays by Modulo Remainder
Given an integer array nums of length n, and two integers K (where 1 ≤ K ≤ 10^4) and R (where 0 ≤ R < K).
Your objective is to determine the total number of subarrays [i..j] (where 0 ≤ i ≤ j < n) such that the sum of elements within that subarray, sum(nums[i..j]), when taken modulo K, equals R.
Requirements:
- The solution must achieve
O(n)time complexity. - The solution must use
O(K)space complexity. - You must describe your chosen approach, provide a clear justification for its correctness, and analyze its time and space complexity.
- Provide a complete implementation for a function named
countSubarraysByRemainder(nums, K, R).
2. Remove Minimum Parentheses to Balance a String
Given a string s which contains lowercase English letters and parentheses ('(' and ')').
Your objective is to return any string that can be formed by deleting the minimum possible number of parentheses, such that the resulting string is a valid, balanced parentheses string. The relative order of the remaining characters must be preserved.
Requirements:
- The solution must achieve
O(n)time complexity. - The solution must use
O(1)extra space beyond the output string itself. - You must describe your algorithm and provide a complete implementation.
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Core dilemma
The central challenge is demonstrating broad algorithmic mastery and efficient problem-solving under pressure by tackling two distinct medium-difficulty problems, each with specific time and space constraints, within a typical interview slot. It tests the candidate's ability to quickly switch contexts, apply appropriate optimized techniques, and deliver robust code for different algorithmic paradigms.
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Solve array modulo and parentheses tasks
Problem Description
This task consists of two independent algorithmic problems, each with specific requirements for time and space complexity.
1. Count Subarrays by Modulo Remainder
Given an integer array nums of length n, and two integers K (where 1 ≤ K ≤ 10^4) and R (where 0 ≤ R < K).
Your objective is to determine the total number of subarrays [i..j] (where 0 ≤ i ≤ j < n) such that the sum of elements within that subarray, sum(nums[i..j]), when taken modulo K, equals R.
Requirements:
- The solution must achieve
O(n)time complexity. - The solution must use
O(K)space complexity. - You must describe your chosen approach, provide a clear justification for its correctness, and analyze its time and space complexity.
- Provide a complete implementation for a function named
countSubarraysByRemainder(nums, K, R).
2. Remove Minimum Parentheses to Balance a String
Given a string s which contains lowercase English letters and parentheses ('(' and ')').
Your objective is to return any string that can be formed by deleting the minimum possible number of parentheses, such that the resulting string is a valid, balanced parentheses string. The relative order of the remaining characters must be preserved.
Requirements:
- The solution must achieve
O(n)time complexity. - The solution must use
O(1)extra space beyond the output string itself. - You must describe your algorithm and provide a complete implementation.