Program 3 : Matrix Multiplication

Develop a program to Multiply two Matrices of order n by n. Repeat the experiment for different values of n and plot a graph of the time taken versus n.

To multiply two n x n matrices where:

• The user inputs the size n (max 100).

• Two matrices are filled with random integers.

• The matrices are multiplied using the standard triple loop method.

Version 1: Logic Only

#include <stdio.h>
#include <stdlib.h>
#include <time.h>

#define MAX 100

void fillMatrix(int matrix[MAX][MAX], int n) {
    for (int i = 0; i < n; i++)
        for (int j = 0; j < n; j++)
            matrix[i][j] = rand() % 10;  
            // Random numbers between 0-9
}

void displayMatrix(int matrix[MAX][MAX], int n, const char* name) {
    printf("\nMatrix %s:\n", name);
    for (int i = 0; i < n; i++) {
        for (int j = 0; j < n; j++)
            printf("%4d", matrix[i][j]);
        printf("\n");
    }
}

void multiplyMatrices(int A[MAX][MAX], int B[MAX][MAX], int C[MAX][MAX], int n) {
    for (int i = 0; i < n; i++)
        for (int j = 0; j < n; j++) {
            C[i][j] = 0;
            for (int k = 0; k < n; k++)
                C[i][j] += A[i][k] * B[k][j];
        }
}

int main() {
    int A[MAX][MAX], B[MAX][MAX], C[MAX][MAX];
    int n;

    printf("Enter size of matrix (max %d): ", MAX);
    scanf("%d", &n);
    if (n > MAX || n <= 0) {
        printf("Invalid size.\n");
        return 1;
    }
	
    srand(time(NULL)); // Seed random number generator
	
    fillMatrix(A, n);
    fillMatrix(B, n);
	
    multiplyMatrices(A, B, C, n);
	
    displayMatrix(A, n, "A");
    displayMatrix(B, n, "B");
    displayMatrix(C, n, "C (A x B)");

    return 0;
}

Version 2: With Timing

#include <stdio.h>
#include <stdlib.h>
#include <time.h>

#define MAX 100

void fillMatrix(int matrix[MAX][MAX], int n) {
    for (int i = 0; i < n; i++)
        for (int j = 0; j < n; j++)
            matrix[i][j] = rand() % 10;
}

void displayMatrix(int matrix[MAX][MAX], int n, const char* name) {
    printf("\nMatrix %s:\n", name);
    for (int i = 0; i < n; i++) {
        for (int j = 0; j < n; j++)
            printf("%4d", matrix[i][j]);
        printf("\n");
    }
}

void multiplyMatrices(int A[MAX][MAX], int B[MAX][MAX], int C[MAX][MAX], int n) {
    for (int i = 0; i < n; i++)
        for (int j = 0; j < n; j++) {
            C[i][j] = 0;
            for (int k = 0; k < n; k++)
                C[i][j] += A[i][k] * B[k][j];
        }
}

int main() {
    int A[MAX][MAX], B[MAX][MAX], C[MAX][MAX];
    int n;
    clock_t start, end;
    double cpu_time_used;

    printf("Enter size of matrix (max %d): ", MAX);
    scanf("%d", &n);
    if (n > MAX || n <= 0) {
        printf("Invalid size.\n");
        return 1;
    }
	
    srand(time(NULL)); // Seed RNG
	
    fillMatrix(A, n);
    fillMatrix(B, n);
	
    start = clock();
    multiplyMatrices(A, B, C, n);
    end = clock();
	
    cpu_time_used = ((double)(end - start)) / CLOCKS_PER_SEC;
	
    displayMatrix(A, n, "A");
    displayMatrix(B, n, "B");
    displayMatrix(C, n, "C (A x B)");
	
    printf("\nTime taken for multiplication: %.6f seconds\n", cpu_time_used);

    return 0;
}