LeetCode //C - 215. Kth Largest Element in an Array

215. Kth Largest Element in an Array

Given an integer array nums and an integer k, return the $k^{th}$ largest element in the array.

Note that it is the $k^{th}$ largest element in the sorted order, not the $k^{th}$ 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:

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

From: LeetCode
Link: 215. Kth Largest Element in an Array

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Solution:

Ideas：

This function initializes a min heap with the first k elements of the array, then iterates through the rest of the array, maintaining the heap property and ensuring that only the k largest elements are in the heap. The $k^{th}$ largest element is then the smallest element in this heap.

Code:

void minHeapify(int* heap, int heapSize, int i) {
    int smallest = i;
    int left = 2 * i + 1;
    int right = 2 * i + 2;

    if (left < heapSize && heap[left] < heap[smallest])
        smallest = left;

    if (right < heapSize && heap[right] < heap[smallest])
        smallest = right;

    if (smallest != i) {
        int temp = heap[i];
        heap[i] = heap[smallest];
        heap[smallest] = temp;

        minHeapify(heap, heapSize, smallest);
    }
}

void buildMinHeap(int* heap, int heapSize) {
    for (int i = heapSize / 2 - 1; i >= 0; i--)
        minHeapify(heap, heapSize, i);
}

int findKthLargest(int* nums, int numsSize, int k) {
    int heap[k];
    for (int i = 0; i < k; i++)
        heap[i] = nums[i];

    buildMinHeap(heap, k);

    for (int i = k; i < numsSize; i++) {
        if (nums[i] > heap[0]) {
            heap[0] = nums[i];
            minHeapify(heap, k, 0);
        }
    }

    return heap[0];
}