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=2000+5;
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 = 0; 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, 0, cost));
        edges.push_back(Edge(to, from, 0, 0, -cost));
        m = edges.size();
        G[from].push_back(m - 2);
        G[to].push_back(m - 1);
    }

    bool BellmanFord(int s, int t, int &flow, LL & cost)
    {
        for (int i = 0; i<n; i++) d[i] = INF;
        memset(inq, 0, sizeof(inq));
        d[s] = 0; inq[s] = 1; p[s] = 0; a[s] = INF;

        queue<int> Q;
        Q.push(s);
        while (!Q.empty()){
            int u = Q.front(); Q.pop();
            inq[u] = 0;
            for (int i = 0; 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] = 1; }
                }
            }
        }
        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] ^ 1].flow -= a[t];

        }
        return true;
    }

    int MincostMaxdflow(int s, int t, LL & cost)
    {
        int flow = 0; cost = 0;
        while (BellmanFord(s, t, flow, cost) );
        return flow;
    }
}t;

int n,m;

int main()
{
    //freopen("D:\input.txt", "r", stdin);
    int T;
    int kase=0;
    scanf("%d",&T);
    int u,v,d;
    while(T--)
    {
        memset(map,0,sizeof(map));
        scanf("%d%d",&n,&m);
        int src=0,dst=2*n+1;
        t.init(dst+1);
        for(int i=1;i<=n;i++)
        {
            t.AddEdge(src,i,1,0);
            t.AddEdge(i+n,dst,1,0);
        }
        for(int i=0;i<m;i++)
        {
            scanf("%d%d%d",&u,&v,&d);
            if(map[u][v]==0 || map[u][v]>d)
            {
                t.AddEdge(u,v+n,1,d);
                t.AddEdge(v,u+n,1,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
",cost);
        else printf("NO
");
    }
    return 0;
}