【Luogu】P3317重建（高斯消元+矩阵树定理）

#include<cstdio>
#include<cstdlib>
#include<cctype>
#include<algorithm>
#include<cstring>
#include<cmath>
#define eps 1e-8
#define maxn 100
using namespace std;
inline long long read(){
    long long num=0,f=1;
    char ch=getchar();
    while(!isdigit(ch)){
        if(ch==‘-‘)    f=-1;
        ch=getchar();
    }
    while(isdigit(ch)){
        num=num*10+ch-‘0‘;
        ch=getchar();
    }
    return num*f;
}

double s[maxn][maxn];

int main(){
    int n=read();
    double tmp=1;
    for(int i=1;i<=n;++i)
        for(int j=1;j<=n;++j){
            scanf("%lf",&s[i][j]);
            if(fabs(s[i][j])<eps)    s[i][j]=eps;
            if(fabs(1-s[i][j])<eps)    s[i][j]=1-eps;
            if(i<j)    tmp*=(1.0-s[i][j]);
            s[i][j]/=(1-s[i][j]);
        }
    for(int i=1;i<=n;++i){
        s[i][i]=0;
        for(int j=1;j<=n;++j)
            if(i^j)    s[i][i]-=s[i][j];
    }
    for(int i=1;i<n;++i){
        int now=i;
        for(int j=i+1;j<n;++j)
            if(fabs(s[j][i])>fabs(s[now][i]))    now=j;
        if(now!=i)    swap(s[now],s[i]);
        for(int j=i+1;j<n;++j){
            double ret=s[j][i]/s[i][i];
            for(int k=i;k<n;++k)    s[j][k]-=s[i][k]*ret;
        }
    }
    double now=1;
    for(int i=1;i<n;++i)    now*=s[i][i];
    now=fabs(now)*tmp;
    printf("%.10lf",now);
    return 0;
}