#include <stdio.h>

#define N 100

float determinant();
void copy_matrix();
void add_row(float *, float *, float, int);
int find_nonzero_row();
void read_matrix();


/* Computes the determinant of size n matrix
 * stored in array A using recursion. 
 */
float determinant(float A[][N], int n)
{
	int i;
	float B[N][N]; // stores a submatrix of A

	if (n == 1) // 1 x 1 matrix
		return A[0][0];

	if (A[0][0] == 0) {
		i = find_nonzero_row(A, n);
		if (i >= n) // no non-zero row
			return 0; // determinant is 0
		add_row(A[0], A[i], 1, n); // add row #i to row #0
	}

	for (int t = 1; t < n; t++) // make first column of A[t] zero
		add_row(A[t], A[0], -A[t][0] / A[0][0], n);

	// Drop the first row and column of A
	copy_matrix(B, A, 1, n-1);

	/* The determinant of A equals the determinant of B times
	 * A[0][0].
	 */
	return A[0][0] * determinant(B, n-1);
}

/* Returns the first row of B whose first element is non-zero */
int find_nonzero_row(float B[][N], int m)
{
	int i;

	for (i = 0; i < m; i++)
		if (B[i][0] != 0.0)
			return i;
	
	return i;
}

/* Copies matrix B to A by dropping the first i rows and columns of
 * A first. The size of matrix B is m.
 */
void copy_matrix(float A[][N], float B[][N], int i, int m)
{
	int j, k;

	for (k = 0; k < m; k++)
		for (j = 0; j < m; j++)
			A[k][j] = B[k+i][j+i];
}

/* Adds row_2 to row_1 by first multiplying it with factor. The
 * size of rows is m.
 */
void add_row(float *row_1, float *row_2, float factor, int m)
{
	for (int i = 0; i < m; i++)
		row_1[i] = row_1[i] + factor * row_2[i];
}


int main()
{
	int n;
	float A[N][N];

	read_matrix(A, &n);

	printf("Determinant of the matrix = %f\n", determinant(A, n));
}


void read_matrix(float A[][N], int *ptr_n)
{
	printf("Input the size of the matrix: ");
	scanf("%d", ptr_n);

	printf("Input the %d x %d matrix:\n", *ptr_n, *ptr_n);
	for (int i = 0; i < *ptr_n; i++)
		for (int j = 0; j < *ptr_n; j++)
			scanf("%f", &A[i][j]);
}