#include <stdio.h>
#include <stdbool.h>
// Bonus Question

/* Find if all rows, columns, and diagonals in squares have equals sums.
 * Will create an array to hold sums for each row, column, and diagonal. Arr length is (2 * length) + 2
 * Then check if all sums in array are equal
 */

// Sum of each row in arr
int find_row_sum(const int arr[], int len) {
	int sum = 0;
	for(int i = 0; i < len; i++) {
		sum+=arr[i];
	}
	return sum;
}
// Sum of each column in arr
int find_column_sum(int len, const int arr[len][len],int row) {
	int sum = 0;
	for(int i = 0; i < len; i++) {
		sum+=arr[row][i];
	}
	return sum;
}

// Function to find diagonal sum from top left to bottom right
int find_diagonal_sum(int len, const int arr[len][len]) {
	int sum = 0;
	int j = 0;
	for(int i = 0; i < len; i++) {
		sum+= arr[i][j];
		j++;
	}
	return sum;
}
// Function to find diagonal sum from bottom left to top right
int find_diagonal_sum_the_other_direction(int len, const int arr[len][len]) {
	int sum = 0;
	int j = len - 1;
	for(int i = 0; i < len; i++) {
		sum += arr[i][j];
		j--;
	}
	return sum;
}
// Final function to check if all nums in sum are equal, aka is the square perfect
bool is_perfect_square(const int arr[], int len) {
	bool is_perfect = true;
	for(int i = 0; i < len - 1 && is_perfect; i++) {
		if(arr[i] != arr[i+1])
			is_perfect = false;
	}
	return is_perfect;
}

int main() {
	int M; // Length of squares sides
	printf("Enter square length: ");
	scanf("%d", &M);

	int square[M][M];

	// Input values into matrix
	for(int i = 0; i < M; i++) {
		for(int j = 0; j < M; j++) {
			printf("Enter matrix value %d, %d: ", i, j);
			scanf("%d", &square[i][j]);
		}
	}

	// The array that will hold our calculated sums
	int sums[2*M + 2];
	// Find sum for each row
	for(int i = 0; i < M; i++) {
		sums[i] = find_row_sum(square[i], M);
	}
	// Find sum for each column
	for(int i = 0; i < M; i++) {
		for (int j = M; j < 2 * M; j++) {
			sums[j] = find_column_sum(M, square, i);
		}
	}
	// Find first diagonal
	sums[2*M] = find_diagonal_sum(M, square);
	// Find second diagonal
	sums[2*M+1] = find_diagonal_sum_the_other_direction(M, square);
	//
	if(is_perfect_square(sums, M)) {
		printf("The matrix is a Magic Square");
	}
	else {
		printf("The matrix is not a Magic Square");
	}

	return 0;
}