【HDU 4408】Minimum Spanning Tree（矩阵树定理 / 最小生成树）

传送门

考虑 $Kruscal$的过程
按权值从小到大
对每个权值的每个连通块做一次矩阵树

注意判 $不连通,n=1且m=0，mod=1$的情况

#include<bits/stdc++.h>
using namespace std;
#define cs const
#define re register
#define pb push_back
#define pii pair<int,int>
#define ll long long
#define fi first
#define se second
#define bg begin
cs int RLEN=1<<20|1;
inline char gc(){
    static char ibuf[RLEN],*ib,*ob;
    (ib==ob)&&(ob=(ib=ibuf)+fread(ibuf,1,RLEN,stdin));
    return (ib==ob)?EOF:*ib++;
}
inline int read(){
    char ch=gc();
    int res=0;bool f=1;
    while(!isdigit(ch))f^=ch=='-',ch=gc();
    while(isdigit(ch))res=(res+(res<<2)<<1)+(ch^48),ch=gc();
    return f?res:-res;
}
inline ll readll(){
    char ch=gc();
    ll res=0;bool f=1;
    while(!isdigit(ch))f^=ch=='-',ch=gc();
    while(isdigit(ch))res=(res+(res<<2)<<1)+(ch^48),ch=gc();
    return f?res:-res;
}
inline void readstring(char *s){
    int top=0;char ch=gc();
    while(isspace(ch))ch=gc();
    while(!isspace(ch)&&ch!=EOF)s[++top]=ch,ch=gc();
}
template<class tp>inline void chemx(tp &a,tp b){a<b?a=b:0;}
template<class tp>inline void chemn(tp &a,tp b){a>b?a=b:0;}
int mod;
inline int add(int a,int b){return (a+=b)>=mod?(a-mod):a;}
inline int dec(int a,int b){a-=b;return a+(a>>31&mod);}
inline int mul(int a,int b){static ll r;r=1ll*a*b;return (r>=mod)?(r%mod):r;}
inline void Add(int &a,int b){(a+=b)>=mod?(a-=mod):0;}
inline void Dec(int &a,int b){a-=b,a+=a>>31&mod;}
inline void Mul(int &a,int b){static ll r;r=1ll*a*b;a=(r>=mod)?(r%mod):r;}
inline int ksm(int a,int b,int res=1){for(;b;b>>=1,Mul(a,a))(b&1)&&(Mul(res,a),1);return res;}
inline int Inv(int x){return ksm(x,mod-2);}
inline int fix(int x){return (x<0)?x+mod:x;}
cs int N=105;
int n,m;
vector<pii> e[12],in[N];
vector<int> son[N];
int id[N],pos[N];
int fa[N],a[N][N],ans;
inline int find(int x){return fa[x]==x?x:fa[x]=find(fa[x]);}
inline void addedge(int i,int j){
    Add(a[i][i],1),Add(a[j][j],1);
    Dec(a[i][j],1),Dec(a[j][i],1);
}
inline int calc(int n){
    int res=1;
    for(int i=1;i<=n;i++){
        int pos=i;
        for(;pos<=n;pos++)if(a[pos][i])break;
        if(pos!=i)swap(a[pos],a[i]),res=dec(0,res);
        for(int j=i+1;j<=n;j++){
            while(a[j][i]){
                if(a[j][i]<a[i][i])swap(a[j],a[i]),res=dec(0,res);
                int mt=a[j][i]/a[i][i];
                for(int k=i;k<=n;k++)Dec(a[j][k],mul(a[i][k],mt));
            }
        }
        Mul(res,a[i][i]);
    }
    for(int i=1;i<=n+1;i++)
    memset(a[i],0,sizeof(int)*(n+2));
    return res;
}
inline void calc(cs vector<pii>&a,int t){
    for(pii x:a){
        int f1=find(x.fi),f2=find(x.se);
        if(f1!=f2)fa[f1]=f2;
    }
    for(pii x:a)in[find(x.fi)].pb(x);
    for(int i=1;i<=n;i++)son[find(i)].pb(i);
    int cnt=0;
    for(int i=1;i<=n;i++)if(find(i)==i){
        pos[i]=++cnt;int tot=0;
        for(int u:son[i])id[u]=++tot;
        for(pii x:in[i])addedge(id[x.fi],id[x.se]);
        Mul(ans,calc(tot-1));
    }
    for(int i=t+1;i<=10;i++)
    for(pii &x:e[i])x.fi=pos[find(x.fi)],x.se=pos[find(x.se)];
    for(int i=1;i<=n;i++)in[i].clear(),son[i].clear();
    n=cnt;for(int i=1;i<=n;i++)fa[i]=i;
}
int main(){
    #ifdef Memoria
    freopen("lx.in","r",stdin);
    #endif
    n=read(),m=read(),mod=read();
    while(n||m||mod){
    //    if(m==0){cout<<(n==1)%mod<<'\n';n=read(),m=read(),mod=read();continue;}
        ans=1;int pn=n;
        for(int i=1;i<=n;i++)fa[i]=i;
        for(int i=1;i<=m;i++){
            int u=read(),v=read(),w=read();
            e[w].pb(pii(u,v));
        }
        for(int i=1;i<=10;i++)if(e[i].size())calc(e[i],i);
        for(int i=1;i<=10;i++)e[i].clear();
        for(int i=1;i<=pn;i++)id[i]=pos[i]=0,son[i].clear(),in[i].clear();
        memset(a,0,sizeof(a));
        if(n==1)cout<<ans%mod<<'\n';
        else cout<<0<<'\n';
        n=read(),m=read(),mod=read();
    }
}