BZOJ 1016 [JSOI2008]最小生成树计数 ——Matrix-Tree定理

#include <queue>
#include <cmath>
#include <vector>
#include <cstdio>
#include <cstring>
#include <iostream>
#include <algorithm>
using namespace std;
 
#define F(i,j,k) for (int i=j;i<=k;++i)
#define D(i,j,k) for (int i=j;i>=k;--i)
#define maxn 1005
#define eps 1e-6
const int md=31011;
vector <int> v,to[maxn];
queue <int> q;
struct Edge{int u,v,w;}a[maxn];
int n,m,fa[maxn];
int b[maxn][maxn],inv[maxn];
int vcnt,du[maxn],list[maxn],vis[maxn];
bool cmp(Edge x,Edge y)
{return x.w<y.w;}
int gf(int k)
{if (fa[k]==k) return k; else return fa[k]=gf(fa[k]);}
int gauss(int n)
{
    F(i,1,n) F(j,1,n) b[i][j]%=md;
    int ret=1;
    for (int i=1;i<n;++i)
    {
        for (int j=i+1;j<n;++j)
            while (b[j][i])
            {
                int t=b[i][i]/b[j][i];
                for (int k=i;k<n;++k)
                    b[i][k]=(b[i][k]-b[j][k]*t+md)%md;
                for (int k=i;k<n;++k)
                    swap(b[i][k],b[j][k]);
                ret=-ret;
            }
        if (b[i][i]==0) return 0;
        ret=ret*b[i][i]%md;
    }
    return abs((ret+md)%md);
}
int main()
{
    scanf("%d%d",&n,&m);
    F(i,1,n) fa[i]=i;
    F(i,1,m){scanf("%d%d%d",&a[i].u,&a[i].v,&a[i].w);}
    sort(a+1,a+m+1,cmp);
    int now=1,ans=1;
    while (now<=m)
    {
        int l=now,r=now;
        vcnt=0;
        memset(du,0,sizeof du);
        F(i,1,n) to[i].clear();
        while (a[r+1].w==a[r].w) r++;
        now=r+1;
        F(i,l,r)
        {
            int fl=gf(a[i].u),fr=gf(a[i].v);
            to[fl].push_back(fr);
            to[fr].push_back(fl);
            if (fl!=fr) du[fl]++,du[fr]++;
        }
        memset(vis,0,sizeof vis);
        F(i,1,n)
            if (du[i]&&!vis[i])
            {
                v.clear();
                memset(b,0,sizeof b);
                memset(inv,0,sizeof inv);
                q.push(i);inv[i]=1;vis[i]=1;
                while (!q.empty())
                {
                    int x=q.front();v.push_back(x);q.pop();
                    for (int j=0;j<to[x].size();++j)
                        if (!vis[to[x][j]])
                            q.push(to[x][j]),inv[to[x][j]]=1,vis[to[x][j]]=1;
                }
                for (int j=0;j<v.size();++j) list[v[j]]=j+1;
                for (int j=0;j<v.size();++j)
                    for (int k=0;k<to[v[j]].size();++k)
                        if (inv[to[v[j]][k]])
                        {
                            b[list[v[j]]][list[v[j]]]++,b[list[v[j]]][list[to[v[j]][k]]]--;
                        }
                ans*=gauss(v.size());
                ans%=md;
            }
        F(i,l,r)
        {
            int fl=gf(a[i].u),fr=gf(a[i].v);
            if (fl!=fr){fa[fl]=fr;}
        }
    }
    int cnt=0;
    F(i,1,n) if (fa[i]==i)
    {
        cnt++;
        if (cnt==2) {printf("0\n"); return 0;}
    }
    printf("%d\n",ans);
}