Solution: Find the K-Sum of an Array

Explore the efficient approach to finding the kth largest subsequence sum in an integer array. Learn to transform the problem by focusing on smallest losses using absolute values, sorting, and a min heap to navigate subsequences without exhaustive enumeration. This lesson helps you implement a time-effective solution and understand its complexity.

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Statement
Solution
- Time complexity
- Space complexity

Statement

You are given an integer array, nums, and a positive integer k. Your task is to determine and return the $k^{th}$ 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 $0$ .
Duplicate subsequence sums are allowed and counted separately when determining the $k^{th}$ largest.

Constraints:

$n ==$ nums.length
$1 \leq$ n $\leq 10^3$
$-10^3 \leq$ nums[i] ...