[JSOI2008]最小生成树计数

JSOI2008 最小生成树计数

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阴间消消乐（躺

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先给代码，之后补题解

#include<cstdio>
#include<iostream>
#include<cmath>
#include<cstring>
#include<algorithm>
#include<vector>
using namespace std;
typedef long long ll;
const int maxn=1010;
const ll mod=10337;
const ll mod1=31011;
struct edge{
    int from,to,dis;
}g[maxn<<1];
bool cmp(edge a,edge b)
{
    return a.dis<b.dis;
}
int inv[mod<<1];
int n,m;
int _max=0;
struct BCJ{
    int f[maxn];
    void init()
    {
        for(int i=1;i<maxn;i++)f[i]=i;
    }
    int gf(int x)
    {
        if(f[x]!=x)f[x]=gf(f[x]);
        return f[x];
    }
    bool merge(int x,int y)
    {
        x=gf(x),y=gf(y);
        if(x==y)return 0;
        f[y]=x;
        return 1;
    }
}s1,s2;
ll ans=1;
ll a[120][120];
bool mark[maxn];
int id[maxn];
ll HLS(int n)
{
	n--;
    int i,j,k,l;
    int pos=1;
    int s=1;
    bool fu=0;
    for(i=1;i<=n;i++,pos++)
    {
        int _max=i;
        for(j=i+1;j<=n;j++)
        {
            if(abs(a[j][pos])>abs(a[_max][pos]))_max=j;
        }
        if(!a[_max][pos])continue;
        if(_max!=i)
        {
            for(j=pos;j<=n+1;j++)swap(a[i][j],a[_max][j]);
            fu^=1;
        }
        for(j=i+1;j<=n;j++)
        {
            if(a[j][pos]){
            	int ori=a[j][pos];
            	s=(s*a[i][pos])%mod;
                for(k=pos;k<=n+1;k++)
                {
                    a[j][k]=a[j][k]*a[i][pos]-ori*a[i][k];
                }
            }
        }
    }
    ll res=1;
    if(s<0)res*=-1;
    if(fu)res*=-1;
    for(i=1;i<=n;i++)res=(res*a[i][i])%mod;
//    printf("---%d\n",s);
    return res*inv[abs(s)]%mod;
}
bool use[maxn];

ll col(int val)
{
    memset(mark,0,sizeof(mark));
    memset(a,0,sizeof(a));
    int i,j;
    s1.init();
    vector<edge>q;
    for(i=1;g[i].dis<=_max&&i<=m;i++)
    {
        if(g[i].dis!=val){
        	if(use[i])
        	s1.merge(g[i].from,g[i].to);
		}
        else q.push_back(g[i]);
    }
    int num=0;
    for(i=1;i<=n;i++)
    {
        if(!mark[s1.gf(i)])id[s1.gf(i)]=++num,mark[s1.gf(i)]=1;
    }
    for(i=0;i<q.size();i++)
    {
        int f=q[i].from,t=q[i].to;
        f=id[s1.gf(f)],t=id[s1.gf(t)];
//        printf("--%d %d\n",f,t);
        a[f][f]+=1;
        a[t][t]+=1;
        a[f][t]-=1;
        a[t][f]-=1;
    }
//    printf("--%d\n",_max);
    return HLS(num);
}
int main()
{
    int i,j;
    inv[1]=1;
    for(i=2;i<mod;i++)inv[i]=(mod-mod/i)*inv[mod%i]%mod;
	scanf("%d%d",&n,&m);
    s1.init();
    
    for(i=1;i<=m;i++)
    {
        scanf("%d%d%d",&g[i].from,&g[i].to,&g[i].dis);
    }
    sort(g+1,g+m+1,cmp);
    int k=n-1;
    i=1;
    while(k&&(i<=m)){
        if(s1.merge(g[i].from,g[i].to)){
        	use[i]=1;
            _max=g[i].dis;
            k--;
        }
        i++;
    }
    if(k){
    	printf("0\n");
    	return 0;
	}
    for(i=1;i<=m;i++)
    {
        if(g[i].dis>_max)break;
        if(g[i].dis==g[i-1].dis)continue;
//        cout<<g[i].dis<<endl;
        ans=(ans*col(g[i].dis))%mod1;
    }
    printf("%lld\n",ans);
}