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

Solutions

Approach - Brute Force Technique

public class Solution {
    public int FindKthLargest(int[] nums, int k) {
        
        Array.Sort(nums);
        k=nums.Length-k;
        return nums[k];
        
    }
}

Complexity

Time Complexity: O(n log n)

Space Complexity: O(1)

Approach - Min Heap Technique

public class Solution {
    public int FindKthLargest(int[] nums, int k) {
        // Create a Min Heap
        SortedSet<(int num, int index)> minHeap = new SortedSet<(int num, int index)>();
        int i = 0;
        // Add the first 'k' numbers in the min heap
        for (; i < k; i++)
            minHeap.Add((nums[i], i));

        // Go through the remaining numbers of the array, if the number from the array is bigger than the
        // top (smallest) number of the min-heap, remove the top number from heap and add the number from array
        for (; i < nums.Length; i++) {
            if (nums[i] > minHeap.Min.num) {
                minHeap.Remove(minHeap.Min);
                minHeap.Add((nums[i], i));
            }
        }

        // The root of the heap has the 'Kth' largest number
        return minHeap.Min.num;
    }
}

Complexity

Time Complexity: O(n log k)

Space Complexity: O(k)