Step by Step solution about How to resolve the algorithm Quickselect algorithm step by step in the C programming language

This snippet of code implements the quick select algorithm to obtain the kth smallest element in an array. The function qselect takes three parameters: the array, the length of the array and the index of the element to be obtained. It consists of two main loops:

1. The first loop divides the array into two subarrays, one containing elements smaller than the last element of the array, and the other containing the elements that are larger or equal than the last element. The loop iterates over the array and swaps the elements that are smaller than the last element to the beginning of the array, increasing a counter st every time a swap is performed. Once the loop is finished, the last element is swapped with the element at index st.
2. The second loop selects the subarray that contains the kth smallest element based on the value of st and the value of k. If st is equal to k, then the element at index st is the kth smallest element, and it is returned.

If st is greater than k, then the kth smallest element is in the subarray containing the elements smaller than the last element, and the qselect function is called recursively with this subarray and the index k.

If st is smaller than k, then the kth smallest element is in the subarray containing the elements larger than or equal to the last element, and the qselect function is called recursively with this subarray and the index k-st.

The main function calls the qselect function for different values of k and prints the result. The array x is copied into the array y using the memcpy function, as the qselect function modifies the array passed as a parameter.

#include <stdio.h>
#include <string.h>

int qselect(int *v, int len, int k)
{
#	define SWAP(a, b) { tmp = v[a]; v[a] = v[b]; v[b] = tmp; }
	int i, st, tmp;

	for (st = i = 0; i < len - 1; i++) {
		if (v[i] > v[len-1]) continue;
		SWAP(i, st);
		st++;
	}

	SWAP(len-1, st);

	return k == st	?v[st]
			:st > k	? qselect(v, st, k)
				: qselect(v + st, len - st, k - st);
}

int main(void)
{
#	define N (sizeof(x)/sizeof(x[0]))
	int x[] = {9, 8, 7, 6, 5, 0, 1, 2, 3, 4};
	int y[N];

	int i;
	for (i = 0; i < 10; i++) {
		memcpy(y, x, sizeof(x)); // qselect modifies array
		printf("%d: %d\n", i, qselect(y, 10, i));
	}

	return 0;
}