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Grokking the Coding Interview Patterns in Python

Solution: Find the K-Sum of an Array

Explore how to find the kth largest sum of an array's subsequences by leveraging sorting and min heap data structures. Understand the approach to transform the problem to track losses from the maximum sum and apply a heap-based method to efficiently compute the result without generating all subsequences.

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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 ≤103\leq 10^3

  • −103≤-10^3 \leq nums[i] ...