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19. Kth Largest Element in an Array

mediumAsked at Chime

Find the kth largest element in an unsorted array without fully sorting it.

By Alex Chen, Founder, InterviewChamp.AI · Last verified

Problem

Given an integer array nums and an integer k, return the kth largest element in the array. Note that it is the kth largest element in sorted order, not the kth distinct element. Solve it without sorting the full array if possible.

Constraints

  • 1 <= k <= nums.length <= 10^5
  • -10^4 <= nums[i] <= 10^4

Examples

Example 1

Input
nums = [3,2,1,5,6,4], k = 2
Output
5

Example 2

Input
nums = [3,2,3,1,2,4,5,5,6], k = 4
Output
4

Approaches

1. Sort the array

Sort descending and return index k-1. Easiest but ignores the constraint.

Time
O(n log n)
Space
O(1)
nums.sort((a, b) => b - a);
return nums[k - 1];

Tradeoff:

2. Min-heap of size k

Maintain a min-heap of size k; the root after processing all elements is the kth largest. Uses O(n log k) time and O(k) extra space.

Time
O(n log k)
Space
O(k)
// pseudo-heap using sorted insert
function findKthLargest(nums, k) {
  const heap = [];
  for (const n of nums) {
    if (heap.length < k) {
      heap.push(n); heap.sort((a,b)=>a-b);
    } else if (n > heap[0]) {
      heap[0] = n; heap.sort((a,b)=>a-b);
    }
  }
  return heap[0];
}

Tradeoff:

Chime-specific tips

Chime asks this when they want to test top-k transaction amounts for fraud heuristics; mention that the heap pattern keeps memory bounded as the stream grows.

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Output

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