Question 3 of 9: Programming — Magic Square Checker

Question 3: Programming — Magic Square Checker (20 marks)

Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.

Given. A square size $n$ followed by $n^2$ integers read row by row.

Find. Whether every row sum, column sum, and both diagonal sums are equal.

Approach. Dynamically allocate the $n\times n$ array (an array of $n$ row pointers, since a runtime-sized true 2-D array is not portable pre-C99), take row 0's sum as the target, and check every row, column and diagonal against that one target; a single mismatch is enough to reject the square.

1. Write the checker.

   #include <stdio.h>
   #include <stdlib.h>
   
   int is_magic(int **sq, int n)
   {
       int target = 0, i, j, diag1 = 0, diag2 = 0;
       for (j = 0; j < n; j++) target += sq[0][j];   /* row 0 sets the target */
   
       for (i = 0; i < n; i++) {
           int row_sum = 0, col_sum = 0;
           for (j = 0; j < n; j++) {
               row_sum += sq[i][j];
               col_sum += sq[j][i];
           }
           if (row_sum != target || col_sum != target) return 0;
       }
       for (i = 0; i < n; i++) {
           diag1 += sq[i][i];
           diag2 += sq[i][n - 1 - i];
       }
       return (diag1 == target && diag2 == target);
   }
   
   int main(void)
   {
       int n, i, j;
       printf("Enter n: ");
       if (scanf("%d", &n) != 1 || n <= 0) return 1;
   
       int **sq = malloc(n * sizeof(int *));
       for (i = 0; i < n; i++) {
           sq[i] = malloc(n * sizeof(int));
           for (j = 0; j < n; j++) scanf("%d", &sq[i][j]);
       }
   
       printf(is_magic(sq, n) ? "Magic square.\n" : "Not a magic square.\n");
   
       for (i = 0; i < n; i++) free(sq[i]);
       free(sq);
       return 0;
   }

2. Apply it to the paper's example. Row 0 sets the target: $$\text{target} = 16+3+2+13 = 34$$ $$\boxed{\text{target} = 34}$$ Every remaining row (5+10+11+8, 9+6+7+12, 4+15+14+1), every column (16+5+9+4, 3+10+6+15, 2+11+7+14, 13+8+12+1) and both diagonals (16+10+7+1, 13+11+6+4) also sum to 34, so the checker returns true.