HDU 3435 A new Graph Game（最小费用流：有向环权值最小覆盖）

http://acm.hdu.edu.cn/showproblem.php?pid=3435

题意：
有n个点和m条边，你可以删去任意条边，使得所有点在一个哈密顿路径上，路径的权值得最小。

思路：

费用流，注意判断重边，否则会超时。

 #include<iostream>
 #include<cstdio>
 #include<cmath>
 #include<cstring>
 #include<queue>
 using namespace std;
 typedef long long LL;

 const int maxn=+;
 const int INF=0x3f3f3f3f;

 int map[maxn][maxn];

 struct Edge
 {
     int from, to, cap, flow, cost;
     Edge(int u, int v, int c, int f, int w) :from(u), to(v), cap(c), flow(f), cost(w) {}
 };

 struct MCMF
 {
     int n, m;
     vector<Edge> edges;
     vector<int> G[maxn];
     int inq[maxn];
     int d[maxn];
     int p[maxn];
     int a[maxn];

     void init(int n)
     {
         this->n = n;
         for (int i = ; i<n; i++) G[i].clear();
         edges.clear();
     }

     void AddEdge(int from, int to, int cap, int cost)
     {
         edges.push_back(Edge(from, to, cap, , cost));
         edges.push_back(Edge(to, from, , , -cost));
         m = edges.size();
         G[from].push_back(m - );
         G[to].push_back(m - );
     }

     bool BellmanFord(int s, int t, int &flow, LL & cost)
     {
         for (int i = ; i<n; i++) d[i] = INF;
         memset(inq, , sizeof(inq));
         d[s] = ; inq[s] = ; p[s] = ; a[s] = INF;

         queue<int> Q;
         Q.push(s);
         while (!Q.empty()){
             int u = Q.front(); Q.pop();
             inq[u] = ;
             for (int i = ; i<G[u].size(); i++){
                 Edge& e = edges[G[u][i]];
                 if (e.cap>e.flow && d[e.to]>d[u] + e.cost){
                     d[e.to] = d[u] + e.cost;
                     p[e.to] = G[u][i];
                     a[e.to] = min(a[u], e.cap - e.flow);
                     if (!inq[e.to]) { Q.push(e.to); inq[e.to] = ; }
                 }
             }
         }
         if (d[t] == INF) return false;
         flow += a[t];
         cost += (LL)d[t] * (LL)a[t];
         for (int u = t; u != s; u = edges[p[u]].from){
             edges[p[u]].flow += a[t];
             edges[p[u] ^ ].flow -= a[t];

         }
         return true;
     }

     int MincostMaxdflow(int s, int t, LL & cost)
     {
         int flow = ; cost = ;
         while (BellmanFord(s, t, flow, cost) );
         return flow;
     }
 }t;

 int n,m;

 int main()
 {
     //freopen("D:\\input.txt", "r", stdin);
     int T;
     int kase=;
     scanf("%d",&T);
     int u,v,d;
     while(T--)
     {
         memset(map,,sizeof(map));
         scanf("%d%d",&n,&m);
         int src=,dst=*n+;
         t.init(dst+);
         for(int i=;i<=n;i++)
         {
             t.AddEdge(src,i,,);
             t.AddEdge(i+n,dst,,);
         }
         for(int i=;i<m;i++)
         {
             scanf("%d%d%d",&u,&v,&d);
             if(map[u][v]== || map[u][v]>d)
             {
                 t.AddEdge(u,v+n,,d);
                 t.AddEdge(v,u+n,,d);
                 map[u][v]=map[v][u]=d;
             }
         }
         long long cost;
         int flow=t.MincostMaxdflow(src,dst,cost);
         printf("Case %d: ",++kase);
         if(flow==n)  printf("%d\n",cost);
         else printf("NO\n");
     }
     return ;
 }