[luoguP3317] [SDOI2014]重建（矩阵树定理）

#include <cstdio>
#include <cmath>
#include <iostream>

using namespace std;

int n;
double a[101][101];
double ans = 1, tmp = 1, eps = 1e-9;

inline void gs()
{
	int i, j, k;
	double div;
	for(j = 1; j < n; j++)
	{
		k = j;
		for(i = j + 1; i < n; i++)
			if(fabs(a[i][j]) > fabs(a[k][j])) k = i;
		if(j != k) swap(a[j], a[k]);
		if(fabs(a[j][j]) < eps)
		{
			ans = 0;
			return;
		}
		for(i = j + 1; i < n; i++)
		{
			div = a[i][j] / a[j][j];
			for(k = j; k < n; k++)
				a[i][k] -= a[j][k] * div;
		}
	}
	for(i = 1; i < n; i++) ans *= a[i][i];
	ans = fabs(ans);
}

int main()
{
	int i, j;
	scanf("%d", &n);
	for(i = 1; i <= n; i++)
		for(j = 1; j <= n; j++)
		{
			scanf("%lf", &a[i][j]);
			if(fabs(a[i][j]) < eps) a[i][j] = eps;
			if(fabs(1 - a[i][j]) < eps) a[i][j] = 1 - eps;
			if(i < j) tmp *= 1.0 - a[i][j];
			a[i][j] /= 1.0 - a[i][j];
		}
	for(i = 1; i <= n; i++)
	{
		a[i][i] = 0;
		for(j = 1; j <= n; j++)
			if(i != j)
			{
				a[i][i] += a[i][j];
				a[i][j] = -a[i][j];
			}
	}
	gs();
	printf("%.5lf\n", ans * tmp);
	return 0;
}