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Solution: Find the K-Sum of an Array

Explore how to find the kth largest sum of subsequences in an integer array without brute forcing all combinations. Learn to transform the problem by calculating losses, sorting absolute values, and using a min heap to efficiently identify the kth largest sum. This lesson helps you understand the approach that balances time and space complexity in solving the problem.

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Statement

You are given an integer array, nums, and a positive integer k. Your task is to determine and return the kthk^{th} largest possible sum among all subsequences of the array. A subsequence is formed by deleting no or more elements from the array without changing the order of the remaining elements. The sum of a subsequence is the total of its elements.

Remember: For valid subsequences:

  • The empty subsequence is valid, and its sum is considered 00.

  • Duplicate subsequence sums are allowed and counted separately when determining the kthk^{th} largest.

Constraints:

  • n==n == nums.length

  • 1≤1 \leq n ...