Kth Largest Element in an Array

The usual kth-largest definition counts duplicates. Sorting descending and taking index k-1 is straightforward O(n log n). A size-k min-heap is preferable when k is small or data arrives incrementally: push each number and remove the smallest if heap size exceeds k; the root is the kth largest, costing O(n log k) time and O(k) space. For one in-memory selection, randomized quickselect partitions values around a pivot and continues only into the side containing index n-k in ascending order. It has expected O(n) time but O(n squared) worst case and normally mutates the array. Explain how equal pivot values are handled and avoid promising strict linear time without a deterministic selection algorithm. Test k=1, k=n, all equal, negatives, and invalid k if not guaranteed. Pick the solution based on predictability, memory, and whether the input may be mutated.