Cranes at VIIT Q3

Matrix Boundary Sum and Diagonal Difference

Write a C program that computes the sum of boundary elements and the absolute difference between the diagonals of a square matrix.

Problem Statement:

• Given a square matrix of size n x n, calculate the sum of all the boundary elements.
• Additionally, calculate the absolute difference between the sum of the two diagonals:
  • Primary Diagonal: Top-left to bottom-right.
  • Secondary Diagonal: Top-right to bottom-left.
• Print the boundary sum and the absolute difference between the diagonal sums.

Input Format:

• n: An integer representing the size of the matrix.
• n lines of input, where each line contains n space-separated integers.

Output Format:

• Print the boundary sum.
• Print the absolute difference between the diagonal sums.

Example Inputs & Outputs:

Enter the size of the matrix: 3
Enter the matrix elements:
1 2 3
4 5 6
7 8 9
Boundary sum: 40
Diagonal difference: 0
            

Enter the size of the matrix: 4
Enter the matrix elements:
5 8 12 3
7 11 4 9
10 6 14 2
3 9 8 15
Boundary sum: 91
Diagonal difference: 29
            

Constraints:

• 2 ≤ n ≤ 100
• -10⁵ ≤ matrix elements ≤ 10⁵

Hint:

To solve this problem, follow these steps:

1. Take Matrix Input:
   • Read an integer n representing the size of the matrix.
   • Read a matrix of size n x n using nested loops.
2. Calculate Boundary Sum:
   • Sum elements from the first and last rows:

     for (j = 0; j < n; j++) {
         boundary_sum += matrix[0][j] + matrix[n-1][j];
     }

   • Sum elements from the first and last columns (excluding corners to avoid double counting):

     for (i = 1; i < n-1; i++) {
         boundary_sum += matrix[i][0] + matrix[i][n-1];
     }

3. Calculate Diagonal Sums:
   • Sum elements of the primary diagonal:

     for (i = 0; i < n; i++) {
         primary_sum += matrix[i][i];
     }

   • Sum elements of the secondary diagonal:

     for (i = 0; i < n; i++) {
         secondary_sum += matrix[i][n-1-i];
     }

4. Calculate Absolute Difference:
   • Compute the absolute difference between the diagonals:

     diagonal_diff = abs(primary_sum - secondary_sum);

5. Print Results:
   • Print the boundary sum.
   • Print the absolute difference between diagonal sums.

Formula Breakdown:

• To calculate boundary sum:

  boundary_sum = sum of first and last rows +
                 sum of first and last columns (excluding corners)
                      

• To calculate diagonal difference:

  diagonal_diff = abs(primary_sum - secondary_sum);
                      

Task: Implement the above logic and write a C program to calculate the boundary sum and diagonal difference.