215. Kth Largest Element in an Array (22/06/2022)

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 the sorted order, not the kth distinct element.

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 <= 104
• -104 <= nums[i] <= 104

Solution:

Using sorting

Algorithm

• Sort nums array.
• Element present at index nums.length - k would be kth largest.

class Solution {
    public int findKthLargest(int[] nums, int k) {
        Arrays.sort(nums);
        return nums[nums.length - k];
    }
}

Time complexity: O(n log n) where n is size of nums array

Space complexity: O(1) as we are not using any extra data structure

Using Heap

Algorithm

In a min-heap, top element is smallest among all the elements present.

• Iterate through nums array and place each element num in a min heap (heap).
• If heap size is greater than k then pop element from heap

• After iteration is completed, top element in heap would be kth largest

  class Solution {
    public int findKthLargest(int[] nums, int k) {
        PriorityQueue<Integer> heap = new PriorityQueue<>();
  
        for(int num: nums) {
            heap.offer(num);
            if(heap.size() > k) {
                heap.poll();
            }
        }
        return heap.peek();
    }
  }
  

  Time complexity: O(n log k) where n is size of nums array

Space complexity: O(k) as we are using min-heap to store k elements