// 3ddt 
// find the determinant of any size matrix

#include <stdio.h>

#define DIM  4

int minor(int matrix[DIM][DIM], int r, int c1, int c2) {
  //printf("r=%d, c1=%d, c2=%d\n", r, c1, c2);
  //printf(" a=%d, b=%d, c=%d, d =%d\n", matrix[r][c1],
  //	 matrix[r][c2], matrix[r+1][c1], matrix[r+1][c2]);
  return(matrix[r][c1]*matrix[r+1][c2] - 
	 matrix[r+1][c1]*matrix[r][c2]);
}

int det3(int matrix[DIM][DIM], int start){
  int i,d, sig;
  int dim =3;
  int m[dim];
  // calcualte minors 
  for(i=0; i < dim; i++) {
    m[i]=minor(matrix, DIM-2, 
	       (start+((i+1)%dim))%DIM, 
	       (start+((i+2)%dim))%DIM);
    //printf("Minor i=%d m[i]=%d\n", i, m[i]);
  }
  d=0;
  for(i=0; i < 3; i++){
    sig = (-1)^(i+1);
    //printf("index %d value \n", (start+((i)%dim))%DIM );
    d = d + matrix[dim-2][(start+((i)%dim))%DIM]*m[i];	
  }
  printf("det3 = %d (start=%d)\n", d, start);
  return d;
}

int det4(int matrix[DIM][DIM], int dim){
  int i,d, sig;
  int m[DIM];
  for(i=0; i < dim; i++){
    m[i] = det3(matrix, (i+1)%DIM);
  }
  d=0;
  for(i=0; i < dim; i++){
    sig = (i%2) ? -1 : 1;
    printf("sig %d coeff %d\n", sig, matrix[0][i]);
    d = d + sig*matrix[0][i]*m[i];	
  }
  printf("det4 = %d\n", d);
  return d;
}

int main() {
  int d, i, j, dim;
  int matrix[DIM][DIM] = { 20, 50, 70, 90,
		           6,  5,  4,  3,
			   11, 234, 11, 357,
                           7,  11, 13, 17}; 
  dim =DIM;
  for(i=0; i< dim; i++){
    for(j=0; j<dim; j++)
      printf("%d ", matrix[i][j]);
    printf("\n");
  }
  d =0;
  d = det4(matrix, 4); 
  printf("result = %d\n", d);
  return(0);
}