How do I reduce the running time of my program?

Question

I was solving a problem on HackerEarth but as I submitted my solution most of the test cases were passed and the rest showed 'Time Limit Exceeded'. I would be very grateful if you could help me improve the algorithm of my code to reduce the runtime.

Following is the problem: Alice works as a restaurant manager. The restaurant has prepared 'N' lunch boxes and Alice plans to distribute them to some schools. Consider that there are 'M' schools and an i-th school orders A[i] lunch boxes.

She wants to distribute lunch boxes to as many schools as possible. Also, she has the following rule:

For an i-th school, she gives either zero or A[i] lunch boxes

Your task is to help Alice to determine the maximum number of schools that can get lunch boxes.

My code-

#include <stdio.h>

int main() {
    int t;
    scanf("%d", &t);
    while (t--) {
        int n, m;
        scanf("%d", &n); 
        scanf("%d", &m); 
        int a[m];
        
        for (int i = 0; i < m; i++) {
            scanf("%d", &a[i]);   
        }
        
        for (int i = 0; i < m; i++) {
            for (int j = i + 1; j < m; j++) {
                if (a[i] > a[j]) {
                    int temp = a[i];
                    a[i] = a[j];
                    a[j] = temp;
                }
            }
        }
       
        int sum = 0, count = 0;
        for (int i = 0; i < m; i++) {
            sum = sum + a[i];
            if (sum > n) {
                break;
            } else {
                while (sum <= n) {
                    count++;
                    break;
                }
            }
        }
        printf("%d\n", count);
    }
}

Answer 1

The final loop should be simplified: the while (sum <= n) { count++; break; } is fully redundant and equivalent to count++;.

You can simply use i at the end of the loop:

    int i;
    int sum = 0;
    for (i = 0; i < m; i++) {
        sum = sum + a[i];
        if (sum > n) {
            break;
        }
    }
    printf("%d\n", i);

Regarding the time limit, it is possible that the test cases use large amounts of data, and the sort method you use has quadratic time complexity O(m²), causing the program to exceed the time limit.

You can use qsort to reduce the complexity to O(m*log(m)).

Here is a modified version:

#include <stdio.h>

int compare_ints(const void *a1, const void *a2) {
    const int *p1 = a1;
    const int *p2 = a2;
    return (*p1 > *p2) - (*p1 < *p2);
}

int main() {
    int t;
    if (scanf("%d", &t) != 1)
        return 1;

    while (t-- > 0) {
        int i, n, m;
        if (scanf("%d %d", &n, &m) != 2)
            return 1;

        int a[m];
        int sum = 0;
        for (i = 0; i < m; i++) {
            if (scanf("%d", &a[i]) != 1)
                return 1;
            sum += a[i];
        }

        if (sum > n) {
            /* all orders cannot be delivered: lets sort the array
             * to determine how many of the lowest orders can be delivered.
             * Optimisation inspired by EdHeal.
             */        
            qsort(t, sizeof(t[0]), m, compare_ints)
            sum = 0;
            for (i = 0; i < m; i++) {
                sum = sum + a[i];
                if (sum > n)
                    break;
            }
        }
        printf("%d\n", i);
    }
    return 0;
}