Matrix Boundary and Diagonal Properties in C

Summary: This C program calculates the sum of boundary elements, the sum of the primary and secondary diagonals, and computes the absolute difference between the diagonals in a square matrix.

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

void calculateMatrixProperties(int n, int matrix[n][n]) {
    int boundary_sum = 0, primary_sum = 0, secondary_sum = 0;

    // Calculate boundary sum and diagonal sums
    for (int i = 0; i < n; i++) {
        for (int j = 0; j < n; j++) {
            // Boundary elements
            if (i == 0 || i == n - 1 || j == 0 || j == n - 1) {
                boundary_sum += matrix[i][j];
            }
            // Primary diagonal
            if (i == j) {
                primary_sum += matrix[i][j];
            }
            // Secondary diagonal
            if (j == n - 1 - i) {
                secondary_sum += matrix[i][j];
            }
        }
    }

    // Calculate absolute difference between the diagonals
    int diagonal_diff = abs(primary_sum - secondary_sum);

    // Print results
    printf("Boundary sum: %d\n", boundary_sum);
    printf("Diagonal difference: %d\n", diagonal_diff);
}

int main() {
    int n;

    // Get the size of the matrix
    printf("Enter the size of the matrix: ");
    scanf("%d", &n);

    // Check constraints
    if (n < 2 || n > 100) {
        printf("Invalid matrix size! Please enter a value between 2 and 100.\n");
        return 1;
    }

    int matrix[n][n];

    // Get matrix elements
    printf("Enter the matrix elements:\n");
    for (int i = 0; i < n; i++) {
        for (int j = 0; j < n; j++) {
            scanf("%d", &matrix[i][j]);
        }
    }

    // Calculate and print results
    calculateMatrixProperties(n, matrix);

    return 0;
}

Explanation:

Program Overview:

This program calculates properties of a square matrix such as the sum of boundary elements, the sum of diagonals, and the absolute difference between the diagonals.

Function - calculateMatrixProperties():

The function calculateMatrixProperties() performs the following tasks:

• Boundary Sum:
  • The sum of elements along the first row, last row, first column, and last column is computed.
  • Conditions used: i == 0 || i == n - 1 || j == 0 || j == n - 1
• Primary Diagonal Sum:
  • The primary diagonal consists of elements where i == j.
• Secondary Diagonal Sum:
  • The secondary diagonal consists of elements where j == n - 1 - i.
• Diagonal Difference:
  • The absolute difference between the primary and secondary diagonals is calculated using abs(primary_sum - secondary_sum).

Main Function Workflow:

1. Input Matrix Size:
   • The user inputs the size of the matrix n.
   • A validation check ensures that n is between 2 and 100.
2. Input Matrix Elements:
   • The user inputs the matrix elements.
3. Calculate and Print Results:
   • The calculateMatrixProperties() function is called to compute and print the required results.

Edge Cases and Error Handling:

• Matrix Size Less Than 2: An error message is shown if the matrix size is less than 2.
• Matrix Size Greater Than 100: An error message is shown if the matrix size exceeds 100.

Time Complexity:

• O(n^2) because all elements of the matrix are traversed once.

Space Complexity:

• O(1) since no additional space is used other than the matrix and constant variables.