#include <conio.h>
#include <stdio.h>

int det(int A[100][100], int n)
{
    int Minor[100][100];
    int i,j,k,c1,c2;
    int determinant;
    int c[100];
    int O=1;
determinant = 0;
    if(n == 2)
    {

        determinant = A[0][0]*A[1][1]-A[0][1]*A[1][0];
        return determinant;
    }
    else
    {
        for(i = 0 ; i < n ; i++)
        {
            c1 = 0, c2 = 0;
            for(j = 0 ; j < n ; j++)
            {
                for(k = 0 ; k < n ; k++)
                {
                    if(j != 0 && k != i)
                    {
                        Minor[c1][c2] = A[j][k];
                        c2++;
                        if(c2>n-2)
                        {
                            c1++;
                            c2=0;
                        }
                    }
                }
            }
            determinant = determinant + O*(A[0][i]*det(Minor,n-1));
            O=-1*O;
        }
    }
    return determinant;
}


































double determinantOfMatrix(double mat[3][3])
{
    double ans;
    ans = mat[0][0] * (mat[1][1] * mat[2][2] - mat[2][1] * mat[1][2])
          - mat[0][1] * (mat[1][0] * mat[2][2] - mat[1][2] * mat[2][0])
          + mat[0][2] * (mat[1][0] * mat[2][1] - mat[1][1] * mat[2][0]);
    return ans;
}


void findSolution(double coeff[3][4])
{

    double d[3][3] = {
        { coeff[0][0], coeff[0][1], coeff[0][2] },
        { coeff[1][0], coeff[1][1], coeff[1][2] },
        { coeff[2][0], coeff[2][1], coeff[2][2] },
    };

    double d1[3][3] = {
        { coeff[0][3], coeff[0][1], coeff[0][2] },
        { coeff[1][3], coeff[1][1], coeff[1][2] },
        { coeff[2][3], coeff[2][1], coeff[2][2] },
    };

    double d2[3][3] = {
        { coeff[0][0], coeff[0][3], coeff[0][2] },
        { coeff[1][0], coeff[1][3], coeff[1][2] },
        { coeff[2][0], coeff[2][3], coeff[2][2] },
    };

    double d3[3][3] = {
        { coeff[0][0], coeff[0][1], coeff[0][3] },
        { coeff[1][0], coeff[1][1], coeff[1][3] },
        { coeff[2][0], coeff[2][1], coeff[2][3] },
    };


    double D = determinantOfMatrix(d);
    double D1 = determinantOfMatrix(d1);
    double D2 = determinantOfMatrix(d2);
    double D3 = determinantOfMatrix(d3);


    // Case 1
    if (D != 0) {
        printf("\nMatricea este inversabila!\n");
        double x = D1 / D;
        double y = D2 / D;
        double z = D3 / D;
        printf("Determinatul: %.1lf \n", D);
        printf("DeterminatX : %.1lf \n", D1);
        printf("DeterminatY : %.1lf \n", D2);
        printf("DeterminatZ : %.1lf \n", D3);

        printf("X : %.1lf\n", x);
        printf("Y : %.1lf\n", y);
        printf("Z: %.1lf\n", z);
    }

    else {

        if (D1 == 0 && D2 == 0 && D3 == 0)
        {
            printf("Matricea nu este inversabila!\n");
            printf("Nu se poate rezolva cu metoda Cramer\n");
        }
        else
        {
          if (D1 != 0 || D2 != 0 || D3 != 0)
            printf("Fara solutii\n");
        }
    }
}


int main()
{


double coeff[3][4];
int A[100][100];
int i,j,k,n,res;
printf("Introdu ordinul matricei: ");
scanf("%d",&n);
printf("\nIntrodu elementele matricei: \n");
for(i = 0 ; i < n ; i++)
  {
      for(j = 0 ; j < n ; j++)
      {
          scanf("%d",&A[i][j]);
      }
  }
  for(i = 0 ; i < n ; i++)
  {
      for(j = 0 ; j < n ; j++)
      {
          printf("%5d",A[i][j]);
      }
      printf("\n");
  }

printf("\nIntrodu ecuatiile de forma urmatoare !\n");
printf("\nax+by+cz=du\n");
    for(int i=0;i<3;i++)
          for(int j=0;j<4;j++)
            scanf("%lf",&coeff[i][j]);
printf("\n");
printf("\nMatricea introdusa !\n");
printf("\n\n");
for(int i=0;i<3;i++)
{
    for(int j=0;j<3;j++)
      {
        printf("%3.0lf ",coeff[i][j]);
      }
    printf("\n");
}
printf("Matricea unitate !\n");
for(int i=0,j=3;i<3;i++)
{
        printf("%3.0lf\n",coeff[i][j]);
}
    findSolution(coeff);
    res = det(A,n);
    printf("Determinantul rezultat din prima introducere este Det = %d",res);
    return 0;
}