POJ2455Secret Milking Machine（无向图网络流）

http://www.cnblogs.com/markliu/archive/2012/05/18/2508392.html

题意：有N个农场，P条无向路连接。要从1到N不重复走T条路，求所经过的直接连接两个区域的道路中最长道路中的最小值，。

构图：源点向1连容量T的边。二分最小长度，长度超过mid的边容量为0，否则为1，用最大流判可行性。

注意:1.该题有重边，切忌用邻接矩阵删除重边(重边要用邻接表来处理以保留)。2.无向图在addedge中要进行处理(处理方式见代码)。

// File Name: 2455.cpp
// Author: zlbing
// Created Time: 2013/3/3 16:46:48

#include<iostream>
#include<string>
#include<algorithm>
#include<cstdlib>
#include<cstdio>
#include<set>
#include<map>
#include<vector>
#include<cstring>
#include<stack>
#include<cmath>
#include<queue>
using namespace std;
#define CL(x,v); memset(x,v,sizeof(x));
#define INF 0x3f3f3f3f
#define LL long long
#define MAXN 205
#define MAXM 40005
struct Edge{
    int from,to,cap,flow;
};
bool cmp(const Edge& a,const Edge& b){
    return a.from < b.from || (a.from == b.from && a.to < b.to);
}
struct Dinic{
    int n,m,s,t;
    vector<Edge> edges;
    vector<int> G[MAXN];
    bool vis[MAXN];
    int d[MAXN];
    int cur[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){
        edges.push_back((Edge){from,to,cap,0});
        edges.push_back((Edge){to,from,cap,0});//当是无向图时，反向边容量也是cap,有向边时，反向边容量是0
        m=edges.size();
        G[from].push_back(m-2);
        G[to].push_back(m-1);
    }
    bool BFS(){
        CL(vis,0);
        queue<int> Q;
        Q.push(s);
        d[s]=0;
        vis[s]=1;
        while(!Q.empty()){
            int x=Q.front();
            Q.pop();
            for(int i=0;i<G[x].size();i++){
                Edge& e=edges[G[x][i]];
                if(!vis[e.to]&&e.cap>e.flow){
                    vis[e.to]=1;
                    d[e.to]=d[x]+1;
                    Q.push(e.to);
                }
            }
        }
        return vis[t];
    }
    int DFS(int x,int a){
        if(x==t||a==0)return a;
        int flow=0,f;
        for(int& i=cur[x];i<G[x].size();i++){
            Edge& e=edges[G[x][i]];
            if(d[x]+1==d[e.to]&&(f=DFS(e.to,min(a,e.cap-e.flow)))>0){
                e.flow+=f;
                edges[G[x][i]^1].flow-=f;
                flow+=f;
                a-=f;
                if(a==0)break;
            }
        }
        return flow;
    }
    //当所求流量大于need时就退出，降低时间
    int Maxflow(int s,int t,int need){
        this->s=s;this->t=t;
        int flow=0;
        while(BFS()){
            CL(cur,0);
            flow+=DFS(s,INF);
            if(flow>need)return flow;
        }
        return flow;
    }
    //最小割割边
    vector<int> Mincut(){
        BFS();
        vector<int> ans;
        for(int i=0;i<edges.size();i++){
            Edge& e=edges[i];
            if(vis[e.from]&&!vis[e.to]&&e.cap>0)ans.push_back(i);
        }
        return ans;
    }
    void Reduce(){
        for(int i = 0; i < edges.size(); i++) edges[i].cap -= edges[i].flow;
    }
    void ClearFlow(){
        for(int i = 0; i < edges.size(); i++) edges[i].flow = 0;
    }
};
Edge E[MAXM];
Dinic solver;
int main(){
    int n,m,t;
    while(~scanf("%d%d%d",&n,&m,&t))
    {
        int minn=INF,maxn=-1;
        for(int i=0;i<m;i++)
        {
            scanf("%d%d%d",&E[i].from,&E[i].to,&E[i].cap);
            minn=min(minn,E[i].cap);
            maxn=max(maxn,E[i].cap);
        }
        int L=minn,R=maxn;
        while(L<R){
            solver.init(n);
            int mid=L+(R-L+1)/2;
            for(int i=0;i<m;i++)
            {
                if(E[i].cap<=mid)
                    solver.AddEdge(E[i].from,E[i].to,1);
            }
            if(solver.Maxflow(1,n,INF)>=t)R=mid-1;
            else L=mid;
        }
        printf("%d\n",L+1);
    }
    return 0;
}