/*
#include <math.h>
#include <stdio.h>
#define N 100
#define LIM -100000000
float det(float a[N][N],int n){
    if(n==1)
        return a[0][0];
    if(n==2)
        return a[0][0]*a[1][1]-a[0][1]*a[1][0];// the base situation
    else{
        int j,i,flag=1;
        float ret=0;
        for(j=0;j<n;j++){//j is the column
            int st_c=0,st_r=0;
            float a0j=a[0][j];
            flag=-flag;
            a[0][j]=LIM;
            for(i=1;i<n;i++){//compose the trans_a
                a[i][j]=LIM;
            }//end reseting a
            float trans_a[N][N];
            for(i=1;i<n;i++){
                for(j=0;j<n;j++){
                    if(a[i][j]!=LIM){
                        if(st_c==n-1){
                            st_r++;
                            st_c=0;
                        }
                        trans_a[st_r][st_c]=a[i][j];
                        st_c++;
                    }
                }//end composing
            }
            ret+=det(trans_a,n-1)*a0j*flag;
            printf("%f\n",ret);
        }

    return det(a,n-1);
    }

}
int main(){
    printf("Please enter matrix size n(1<=n<20):");
    int n;
    scanf("%d",&n);
    printf("Please input matrix line by line:\n");
    float a[N][N];
    int i,j;
    for(i=0;i<n;i++)
        for(j=0;j<n;j++)
            scanf("%f",&a[i][j]);
    printf("matrix a:\n");
    for(i=0;i<n;i++){
        for(j=0;j<n;j++)
            printf("%6.1f",a[i][j]);//the elements
        printf("\n");
    }
    printf("result = %f\n",det(a,n));//the res
    return 0;
}*/

#include <math.h>
#include <stdio.h>
 
#define  CONST 1e-6
#define  SIZE 20
 
void InputMatrix (double a[][SIZE], int n);
double DeterminantValue(double a[][SIZE], int n);
void SubMatrix(double a[][SIZE], double b[][SIZE], int n, int row, int col);
void PrintMatrix(double a[][SIZE], int n);
int main(void)
{
    double  a[SIZE][SIZE];
    int     n;
    double  result;
    printf("Please enter matrix size n(1<=n<%d):", SIZE);
    scanf("%d", &n);
    printf("Please input matrix line by line:\n");
    InputMatrix(a, n);
    printf("matrix a:\n");
    PrintMatrix(a, n);
    printf("\n");
    result = DeterminantValue(a, n);
    printf("result = %f\n", result);
    return 0;
}
//  函数功能： 输入一个n×n矩阵的元素
void InputMatrix (double a[][SIZE], int n)
{
    int i, j;
    for (i = 0; i < n; i++)
    {
        for (j = 0; j < n; j++)
        {
            scanf("%lf", &a[i][j]);
        }
    }
}
//  函数功能： 计算n×n矩阵的行列式的值
double DeterminantValue(double a[][SIZE], int n)
{
    int    i = 0, j = 0;
    double temp, result, b[SIZE][SIZE];
    if (n == 1)
    {
        result = a[0][0];
    }
    else if (n == 2)
    {
        result = a[0][0] * a[1][1] - a[0][1] * a[1][0];
    }
    else
    {
        result = 0.0;
        for (j = 0; j < n; j++)//遍历列
        {
            SubMatrix(a, b, n, i, j);//the key
            printf("Submatrix:\n");
            PrintMatrix(b, n - 1);
            temp = DeterminantValue(b, n - 1);        //递归
            result += pow(-1, i + j) * a[0][j] * temp;
            printf("DValue of the Submatrix is %6.1f\n", temp);
        }
    }
    return result;
}
//  函数功能： 计算n×n矩阵a中第row行col列元素的(n-1)×(n-1)子矩阵b
void SubMatrix(double a[][SIZE], double b[][SIZE], int n, int row,
               int col)
{
    int i, j, ii = 0, jj = 0;
    for (i = 0; i < n; i++)
    {
        jj = 0;//回归0
        for (j = 0; j < n; j++)//复制第j列的数
        {
            if (i != row && j != col)//过滤行列为i j的项
            {
                b[ii][jj] = a[i][j];
                jj++;
            }
        }
        if (i != row && j != col)//复制完后向下推进一行
        {
            ii++;////////////////////////////////////////////////////////
        }        ///////两次的i!=row&&...直接不考虑row,col上的数/////////
    }            ////////////////////////////////////////////////////////
}
//  函数功能： 输出一个n×n矩阵的元素
void PrintMatrix(double a[][SIZE], int n)
{
    int i, j;
    for (i = 0; i < n; i++)
    {
        for (j = 0; j < n; j++)
        {
            printf("%6.1f\t", a[i][j]);
        }
        printf("\n");
    }
}