C Program to print the sum of boundary elements of a matrix

In C programming, finding the sum of boundary elements of a matrix involves identifying elements that are on the first row, last row, first column, or last column. Boundary elements form the outer edge of the matrix.

Syntax

for(i = 0; i < rows; i++){
    for(j = 0; j < cols; j++){
        if(i == 0 || i == rows-1 || j == 0 || j == cols-1){
            // This is a boundary element
        }
    }
}

Example

Consider a 3x3 matrix to understand boundary elements −

Given Matrix

1 2 3
4 5 6
7 8 9

Boundary Elements

1 2 3
4   6
7 8 9

Sum of boundary elements: 1 + 2 + 3 + 4 + 6 + 7 + 8 + 9 = 40

Complete Program

Here is a complete C program to find and display the sum of boundary elements −

#include <stdio.h>

int main() {
    int rows = 3, cols = 3;
    int mat[3][3] = {{1, 2, 3}, {4, 5, 6}, {7, 8, 9}};
    int sum = 0;
    int i, j;
    
    printf("Original Matrix:<br>");
    for(i = 0; i < rows; i++) {
        for(j = 0; j < cols; j++) {
            printf("%d ", mat[i][j]);
        }
        printf("<br>");
    }
    
    printf("\nBoundary Matrix:<br>");
    for(i = 0; i < rows; i++) {
        for(j = 0; j < cols; j++) {
            if(i == 0 || j == 0 || i == rows-1 || j == cols-1) {
                printf("%d ", mat[i][j]);
                sum += mat[i][j];
            }
            else {
                printf("  ");
            }
        }
        printf("<br>");
    }
    
    printf("\nSum of boundary elements: %d<br>", sum);
    return 0;
}

Original Matrix:
1 2 3 
4 5 6 
7 8 9 

Boundary Matrix:
1 2 3 
4   6 
7 8 9 

Sum of boundary elements: 40

How It Works

The algorithm checks each element's position using these conditions:

• First Row: i == 0
• Last Row: i == rows-1
• First Column: j == 0
• Last Column: j == cols-1

If any condition is true, the element is on the boundary and gets added to the sum.

Conclusion

Finding boundary elements involves checking if an element is on the outer edge of the matrix. This technique is useful in image processing and matrix operations where edge elements need special handling.