FJ省队集训DAY3 T2

思路:如果一个DAG要的路径上只要一条边去切掉，那么要怎么求？很容易就想到最小割，但是如果直接做最小割会走出重复的部分，那我们就这样:反向边设为inf，这样最小割的时候就不会割到了，判断无解我们直接用tarjan

 #include<cstdio>
 #include<iostream>
 #include<cmath>
 #include<cstring>
 #include<algorithm>
 #define ll long long
 const ll inf = 1ll << ;
 struct edge{
     int u,v,w;
 }e[];
 ll flow[];
 int op[],dis[],cnt[],a[][],pd[];
 int tot,go[],next[],first[],S,T,nodes,sz;
 int n,m,vis[],instack[],c[],top,dfn[],low[],belong[],num;
 int read(){
     int t=,f=;char ch=getchar();
     while (ch<''||ch>''){if (ch=='-')f=-;ch=getchar();}
     while (''<=ch&&ch<=''){t=t*+ch-'';ch=getchar();}
     return t*f;
 }
 void insert(int x,int y){
     tot++;
     go[tot]=y;
     next[tot]=first[x];
     first[x]=tot;
 }
 void insert(int x,int y,ll z){
     tot++;
     go[tot]=y;
     next[tot]=first[x];
     first[x]=tot;
     flow[tot]=z;
 }
 void add(int x,int y,ll z){
     insert(x,y,z);op[tot]=tot-;
     insert(y,x,inf);op[tot]=tot+;
 }
 void tarjan(int x){
     vis[x]=instack[x]=;
     c[++top]=x;dfn[x]=low[x]=++sz;
     for (int i=first[x];i;i=next[i]){
         int pur=go[i];
         if (!vis[pur]){
             tarjan(pur);
             low[x]=std::min(low[x],low[pur]);
         }else if (instack[pur]){
             low[x]=std::min(low[x],dfn[pur]);
         }
     }
     if (low[x]==dfn[x]){
         num++;
         while (c[top]!=x){
             belong[c[top]]=num;
             instack[c[top]]=;
             top--;
         }
             belong[c[top]]=num;
             instack[c[top]]=;
             top--;
     }
 }
 ll dfs(int x,ll f){
     if (x==T) return f;
     int mn=nodes;ll sum=;
     for (int i=first[x];i;i=next[i]){
         int pur=go[i];
         if (flow[i]&&dis[pur]+==dis[x]){
             ll F=std::min(f-sum,flow[i]);
             ll save=dfs(pur,F);
             flow[i]-=save;
             flow[op[i]]+=save;
             sum+=save;
             if (dis[S]>=nodes||f==sum) return sum;
         }
         if (flow[i]) mn=std::min(mn,dis[pur]);
     }
     if (sum==){
         cnt[dis[x]]--;
         if (cnt[dis[x]]==){
             dis[S]=nodes;
         }else{
             dis[x]=mn+;
             cnt[dis[x]]++;
         }
     }
     return sum;
 }
 int main(){
     n=read();m=read();
     for (int i=;i<=m;i++){
         e[i].u=read()+,e[i].v=read()+,e[i].w=read();
         a[e[i].u][e[i].v]=;
         insert(e[i].u,e[i].v);
     }
     for (int i=;i<=n;i++)
      if (!vis[i]) tarjan(i);
     if (belong[]==belong[n]){
         puts("-1");
         return ;
     }
     for (int i=;i<=n;i++)
      a[i][i]=;
     for (int k=;k<=n;k++)
      for (int i=;i<=n;i++)
       for (int j=;j<=n;j++)
        a[i][j]|=a[i][k]&&a[k][j];
     for (int i=;i<=n;i++)
      if (a[][i]&&a[i][n]) pd[i]=;
     for (int i=;i<=m;i++)
      if (pd[e[i].u]&&pd[e[i].v])
       add(e[i].u,e[i].v,e[i].w);
     S=;T=n;nodes=n;
     int ans=;
     while (dis[S]<nodes&&ans<inf) ans+=dfs(S,inf);
     if (ans==) printf("-1");
     else printf("%d\n",ans);
 }