readme.md

Kth Largest Element in an Array

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 the sorted order, not the kth distinct element.

Can you solve it without sorting?

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

Constraints:

• 1 <= k <= nums.length <= 105
• -104 <= nums[i] <= 104

Solution

import heapq

class Solution:
    def findKthLargest(self, nums: list[int], k: int) -> int:
        min_heap = nums[:k]
        heapq.heapify(min_heap)
        for num in nums[k:]:
            if num > min_heap[0]:
                heapq.heapreplace(min_heap, num)
        return min_heap[0]

# Example usage
sol = Solution()
print(sol.findKthLargest([3,2,1,5,6,4], 2))  # Output: 5
print(sol.findKthLargest([3,2,3,1,2,4,5,5,6], 4))  # Output: 4

Thoughts

Time Complexity

O(n log k), where n is the number of elements in the input array. We insert each element into the min heap, which takes O(log k) time, and we do this for all n elements.

Space Complexity

O(k) for the min heap.