C Program to multiply two matrices

Given two matrices, the task to multiply them. Matrices can either be square or rectangular.

Examples:

Input : mat1[][] = {{1, 2}, 
                   {3, 4}}
        mat2[][] = {{1, 1}, 
                    {1, 1}}
Output : {{3, 3}, 
          {7, 7}}
Input : mat1[][] = {{2, 4}, 
                    {3, 4}}
        mat2[][] = {{1, 2}, 
                    {1, 3}}       
Output : {{6, 16}, 
          {7, 18}}

Multiplication of Square Matrices : 
The below program multiplies two square matrices of size 4*4, we can change N for different dimensions. 

C

// C program to multiply two square matrices.
#include <stdio.h>
#define N 4

// This function multiplies mat1[][] and mat2[][],
// and stores the result in res[][]
void multiply(int mat1[][N], int mat2[][N], int res[][N])
{
    int i, j, k;
    for (i = 0; i < N; i++) {
        for (j = 0; j < N; j++) {
            res[i][j] = 0;
            for (k = 0; k < N; k++)
                res[i][j] += mat1[i][k] * mat2[k][j];
        }
    }
}

int main()
{
    int mat1[N][N] = { { 1, 1, 1, 1 },
                       { 2, 2, 2, 2 },
                       { 3, 3, 3, 3 },
                       { 4, 4, 4, 4 } };

    int mat2[N][N] = { { 1, 1, 1, 1 },
                       { 2, 2, 2, 2 },
                       { 3, 3, 3, 3 },
                       { 4, 4, 4, 4 } };

    int res[N][N]; // To store result
    int i, j;
    multiply(mat1, mat2, res);

    printf("Result matrix is
");
    for (i = 0; i < N; i++) {
        for (j = 0; j < N; j++)
            printf("%d ", res[i][j]);
        printf("
");
    }

    return 0;
}

Output

Result matrix is 
10 10 10 10 
20 20 20 20 
30 30 30 30 
40 40 40 40

Time complexity: O(n³). It can be optimized using Strassen’s Matrix Multiplication

Auxiliary Space: O(n²)

Multiplication of Rectangular Matrices : 
We use pointers in C to multiply to matrices. Please refer to the following post as a prerequisite of the code.
How to pass a 2D array as a parameter in C?

C

// C program to multiply two rectangular matrices
#include <stdio.h>

// Multiplies two matrices mat1[][] and mat2[][]
// and prints result.
// (m1) x (m2) and (n1) x (n2) are dimensions
// of given matrices.
void multiply(int m1, int m2, int mat1[][m2], int n1,
              int n2, int mat2[][n2])
{
    int x, i, j;
    int res[m1][n2];
    for (i = 0; i < m1; i++)
    {
        for (j = 0; j < n2; j++)
        {
            res[i][j] = 0;
            for (x = 0; x < m2; x++)
            {
                *(*(res + i) + j) += *(*(mat1 + i) + x)
                                     * *(*(mat2 + x) + j);
            }
        }
    }
    for (i = 0; i < m1; i++)
    {
        for (j = 0; j < n2; j++)
        {
            printf("%d ", *(*(res + i) + j));
        }
        printf("
");
    }
}

// Driver code
int main()
{
    int mat1[][2] = { { 2, 4 }, { 3, 4 } };
    int mat2[][2] = { { 1, 2 }, { 1, 3 } };
    int m1 = 2, m2 = 2, n1 = 2, n2 = 2;

    // Function call
    multiply(m1, m2, mat1, n1, n2, mat2);
    return 0;
}

Output

6 16 
7 18

Time complexity: O(n³). It can be optimized using Strassen’s Matrix Multiplication

Auxiliary Space: O(m1 * n2)