生成树记数 Matrix-Tree定理

//By BLADEVIL
#include <cstdio>
#include <cstring>
#define maxn 20

using namespace std;

int a[maxn][maxn];
double g[maxn][maxn];

bool zero(double x)
{
    return (((x<0)?-x:x)<1e-15);
}

void swap(double &a,double &b)
{double c=a;a=b;b=c;}

double delte(double a[maxn][maxn],int n)
{
    int sign=0;
    double ans=1;
    for (int i=1;i<=n;i++)
    {
        if (zero(a[i][i]))
        {
            int j;
            for (j=i+1;(j<=n)&&(zero(a[j][i]));j++);
            if (j>n) return 0;
            for (int k=i+1;k<=n;k++) swap(a[i][k],a[j][k]);
            sign++;
        }
        ans*=a[i][i];
        for (int j=i+1;j<=n;j++) a[i][j]/=a[i][i];
        for (int j=i+1;j<=n;j++)
            for (int k=i+1;k<=n;k++)
                a[j][k]-=a[i][j]*a[k][i];
    }
    if (sign&1) ans=-ans;
    return ans;
}

void solve()
{
    int n,m;
    scanf("%d%d",&n,&m);
    memset(g,0,sizeof g); memset(a,0,sizeof a);
    for (int i=1;i<=m;i++)
    {
        int x,y;
        scanf("%d%d",&x,&y);
        a[x][y]=a[y][x]=1;
        g[x][x]++; g[y][y]++;
    }
    n--;
    for (int i=1;i<=n;i++)
        for (int j=1;j<=n;j++)
            if (a[i][j]) g[i][j]=-1;
    printf("%.0f\n",delte(g,n));
}

int main()
{
    int task;
    scanf("%d",&task);
    while (task--) solve();
    return 0;
}