K-th Largest Element Efficiently

CrowdStrike Falcon may need to identify a score threshold among a large, unsorted set of detections. Given an unsorted integer array nums and an integer k, return the K-th largest value in the array.

You should design an efficient solution that avoids fully sorting the array. Duplicate values count as separate elements, so the largest value is the 1st largest, and the smallest value is the nums.length-th largest.

Formal Specification

Implement find_kth_largest(nums, k).

• Input: nums, a list of integers, and k, an integer.
• Output: The integer that is the K-th largest element in nums.
• You may modify nums during execution.