递归地按行列展开即可

算法：递归，状态压缩

#include <iostream>
#include <cstring>
#include <algorithm>
#include <vector>
#include <map>
#include <cmath>
using namespace std;
typedef long long ll;
const int N = 64;
int g[N][N];
int n;

//dfs参数：行展开所在行的编号，行列子式阶数，子行列式所在列用二进制表示(防止先前已经展开的列再次被使用)
int dfs(int row,int grade,ll col_path) {
    if (grade == 0) return 1;

    int sum = 0,cnt = 0;
    for (int j = 0; j < n;j ++ ) {
        if ((col_path >> j & 1) == 0)  {
            sum += pow(-1,cnt) * g[row + 1][j] * dfs(row + 1,grade - 1,col_path + (1 << j));
            cnt ++;
        }
    }
    return sum;
}
int main() 
{
    //输入行列式的行列数和行列式本身
    cin >> n;
    for (int i = 0;i < n;i ++ ) 
        for (int j = 0;j < n;j ++ ) 
            cin >> g[i][j];

    //计算并输出行列式的值
    int res = 0;
    for (int i = 0;i < n;i ++ ) {
        int val = pow(-1,i) * g[0][i] * dfs(0,n - 1,1 << i);
        res += val;
    }
    cout << "=>  value of determinant equal :" << res << '\n';
    return 0;
}