BZOJ 1937: [Shoi2004]Mst 最小生成树 [二分图最大权匹配]

#include <iostream>
#include <cstdio>
#include <cstring>
#include <algorithm>
#include <cmath>
using namespace std;
typedef long long ll;
const int N=1005,M=2e5+5,INF=1e9;
inline int read(){
    char c=getchar();int x=0,f=1;
    while(c<‘0‘||c>‘9‘){if(c==‘-‘)f=-1;c=getchar();}
    while(c>=‘0‘&&c<=‘9‘){x=x*10+c-‘0‘;c=getchar();}
    return x*f;
}

int n,m,s,t,g[55][55],u,v,id[55][55],num;
struct data{int u,v,w;}a[M];

int q[N],p;
struct Graph{
    struct edge{int v,ne;}e[M];
    int cnt,h[N];
    inline void ins(int u,int v){
        cnt++;
        e[cnt].v=v;e[cnt].ne=h[u];h[u]=cnt;
        cnt++;
        e[cnt].v=u;e[cnt].ne=h[v];h[v]=cnt;
    }
    bool dfs(int u,int fa,int tar){
        if(u==tar) return true;
        for(int i=h[u];i;i=e[i].ne)
            if(e[i].v!=fa){
                q[++p]=id[u][e[i].v];
                if(dfs(e[i].v,u,tar)) return true;
                p--;
            }
        return false;
    }
}G;

struct Edge{
    int v,ne,w,c,f;
    Edge(){}
    Edge(int v,int w,int c,int f):v(v),w(w),c(c),f(f){}
}e[M];
int cnt,h[N];
inline void ins(int u,int v,int w,int c){//printf("ins %d %d    %d    %d\n",u,v,w,c);
    cnt++;
    e[cnt]=Edge(v,w,c,0);e[cnt].ne=h[u];h[u]=cnt;
    cnt++;
    e[cnt]=Edge(u,-w,0,0);e[cnt].ne=h[v];h[v]=cnt;
}

void build(){
    s=0;t=m+1;
    for(int i=1;i<n;i++) ins(s,i,0,1);
    for(int i=n;i<=m;i++) ins(i,t,0,1);
    for(int i=n;i<=m;i++){
        p=0;
        G.dfs(a[i].u,0,a[i].v);
        //printf("now %d\n",i);
        //for(int j=1;j<=p;j++) printf("%d ",q[j]);puts("");
        for(int j=1;j<=p;j++) ins(q[j],i,a[q[j]].w-a[i].w,1);
    }
}

int d[N],head,tail,inq[N],pre[N],pos[N];
inline void lop(int &x){if(x==N)x=1;}
bool spfa(){
    //memset(d,127,sizeof(d));
    for(int i=s;i<=t;i++) d[i]=-INF,inq[i]=0;
    //memset(inq,0,sizeof(inq));
    head=tail=1;
    d[s]=0;inq[s]=1;q[tail++]=s;
    pre[t]=-1;
    while(head!=tail){
        int u=q[head++];inq[u]=0;lop(head);
        for(int i=h[u];i;i=e[i].ne){
            int v=e[i].v,w=e[i].w;
            if(d[v]<d[u]+w&&e[i].c>e[i].f){
                d[v]=d[u]+w;
                pre[v]=u;pos[v]=i;
                if(!inq[v])q[tail++]=v,inq[v]=1,lop(tail); 
            }
        }
    }
    return pre[t]!=-1;
}
int mcmf(){
    int flow=0,cost=0;
    while(spfa()){
        int f=INF;
        for(int i=t;i!=s;i=pre[i]) f=min(f,e[pos[i]].c-e[pos[i]].f);
        flow+=f; 
        if(d[t]<0) break;
        cost+=d[t]*f;//printf("%d %d %d\n",f,d[t],cost);
        for(int i=t;i!=s;i=pre[i]){
            e[pos[i]].f+=f;
            e[((pos[i]-1)^1)+1].f-=f;
        }
    }
    return cost;
}

int main(){
    freopen("in","r",stdin);
    n=read();m=read(); 
    for(int i=1;i<=m;i++) 
        u=read(),v=read(),g[u][v]=g[v][u]=read();
    for(int i=1;i<n;i++) 
        u=read(),v=read(),id[u][v]=id[v][u]=++num,a[num]=(data){u,v,g[u][v]},G.ins(u,v);
    for(int i=1;i<=n;i++)
        for(int j=i+1;j<=n;j++) 
            if(g[i][j]&&!id[i][j]) id[i][j]=id[j][i]=++num,a[num]=(data){i,j,g[i][j]};
                //printf("lo %d %d %d\n",i,j,num);

    build();
    printf("%d\n",mcmf());
}