C Program to sort rows of the Matrix

Given a matrix arr[][] of dimensions N * M, the task is to sort the matrix such that each row is sorted and the first element of each row is greater than or equal to the last element of the previous row.

Examples:

Input: N = 3, M = 3, arr[][] = {{7, 8, 9}, {5, 6, 4}, {3, 1, 2}}
Output:
1 2 3
4 5 6
7 8 9

Approach: Follow the steps below to solve the problem:

1. Traverse the matrix
2. For every matrix element, consider it to be the minimum element in the matrix. Check if there is a smaller element present in the rest of the matrix.
3. If found to be true, swap the current element and the minimum element in the matrix.
4. Finally, print the sorted matrix.

Below is the implementation for the above approach:

C

// C program for the above approach
#include <stdio.h>
#include <stdlib.h>

#define SIZE 100

// Function to sort a matrix
void sort_matrix(int arr[SIZE][SIZE],
                 int N, int M)
{

    // Traverse over the matrix
    for (int i = 0; i < N; i++) {

        for (int j = 0; j < M; j++) {

            // Current minimum element
            int minimum = arr[i][j];

            // Index of the current
            // minimum element
            int z = i;
            int q = j;

            // Check if any smaller element
            // is present in the matrix
            int w = j;

            for (int k = i; k < N; k++) {

                for (; w < M; w++) {

                    // Update the minimum element
                    if (arr[k][w] < minimum) {

                        minimum = arr[k][w];

                        // Update the index of
                        // the minimum element
                        z = k;
                        q = w;
                    }
                }
                w = 0;
            }

            // Swap the current element
            // and the minimum element
            int temp = arr[i][j];
            arr[i][j] = arr[z][q];
            arr[z][q] = temp;
        }
    }
}

// Function to print the sorted matrix
void printMat(int arr[SIZE][SIZE],
              int N, int M)
{
    for (int i = 0; i < N; i++) {

        for (int j = 0; j < M; j++) {

            printf("%d ", arr[i][j]);
        }
        printf("\n");
    }
}

// Driver Code
int main()
{
    int N = 3, M = 3;
    int arr[SIZE][SIZE]
        = { { 7, 8, 9 },
            { 5, 6, 4 },
            { 3, 1, 2 } };

    // Sort the matrix
    sort_matrix(arr, N, M);

    // Print the sorted matrix
    printMat(arr, N, M);

    return 0;
}

Output:

1 2 3 
4 5 6 
7 8 9

Time Complexity: O(N⁴)
Auxiliary Space: O(1)