Question 3 of 8: Programming

Question 3: Programming

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. Square size $n$, followed by $n^2$ integers filling the array row by row. Find. Whether every row sum, column sum, and both diagonal sums are equal.

Approach. Dynamically allocate the $n \times n$ array, take the first row's sum as the target, then check every row, every column, and both diagonals against that one target — a single early mismatch is enough to reject the square.

int is_magic(int **sq, int n) {
    int target = 0;
    for (int j = 0; j < n; j++) target += sq[0][j];   /* row 0 sets the target */

    for (int i = 0; i < n; i++) {
        int row_sum = 0, col_sum = 0;
        for (int j = 0; j < n; j++) {
            row_sum += sq[i][j];
            col_sum += sq[j][i];
        }
        if (row_sum != target || col_sum != target) return 0;
    }

    int diag1 = 0, diag2 = 0;
    for (int 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;
    printf("Enter n: ");
    scanf("%d", &n);

    int **sq = malloc(n * sizeof(int *));
    for (int i = 0; i < n; i++) {
        sq[i] = malloc(n * sizeof(int));
        for (int j = 0; j < n; j++) scanf("%d", &sq[i][j]);
    }

    printf(is_magic(sq, n) ? "Magic square.\n" : "Not a magic square.\n");
    for (int i = 0; i < n; i++) free(sq[i]);
    free(sq);
    return 0;
}

Applying is_magic to the given 4×4 example: every row sums to 34 (16+3+2+13, 5+10+11+8, 9+6+7+12, 4+15+14+1), every column sums to 34, and both diagonals (16+10+7+1 and 13+11+6+4) sum to 34, so the check returns true.