POJ-2455-Secret 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;
}