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By using a Min-Heap, we can efficiently keep track of the k largest elements. Maintain a heap of size k, and for each element in the array, decide whether to add it to the heap. If you add an element to the heap when it is full, remove the minimum element to maintain the size of the heap as k. At the end, the root of the heap will be the kth largest element.
Time Complexity: O(n log n), where n is the size of the array, because of the sorting operation.
Space Complexity: O(1), as we are modifying the input array in-place.
1#include <stdio.h>
2#include <stdlib.h>
3
4int cmpfunc (const void * a, const void * b) {
5 return (*(int*)a - *(int*)b);
6}
7
8int findKthLargest(int* nums, int numsSize, int k) {
9 qsort(nums, numsSize, sizeof(int), cmpfunc);
10 return nums[numsSize - k];
11}
12
13int main() {
14 int nums[] = {3,2,1,5,6,4};
15 int k = 2;
16 int numsSize = sizeof(nums) / sizeof(nums[0]);
17 printf("%d\n", findKthLargest(nums, numsSize, k));
18 return 0;
19}We first define a comparison function cmpfunc that is used by the C library function qsort to sort the array. After sorting, the kth largest element is located at index numsSize - k.
Quickselect is an efficient selection algorithm to find the kth smallest element in an unordered list. The algorithm is related to the quicksort sorting algorithm. It works by partitioning the data, similar to the partitioning step of quicksort, and is based on the idea of reducing the problem size through partitioning.
Average-case Time Complexity: O(n), but worst-case O(n²).
Space Complexity: O(1) for iterative solution, O(log n) for recursive calls due to stack depth.
1import random
The Python method takes advantage of Python's dynamic lists and absence of static partitioning constraints. A randomized pivot helps further eliminate edge case pitfalls akin to performance degradation prevalent in non-randomized variants of Quickselect.