Poj(2135)，MCMF，模板

题目链接：http://poj.org/problem?id=2135

Farm Tour

Description

When FJ‘s friends visit him on the farm, he likes to show them around. His farm comprises N (1 <= N <= 1000) fields numbered 1..N, the first of which contains his house and the Nth of which contains the big barn. A total M (1 <= M <= 10000) paths that connect the fields in various ways. Each path connects two different fields and has a nonzero length smaller than 35,000.

To show off his farm in the best way, he walks a tour that starts at his house, potentially travels through some fields, and ends at the barn. Later, he returns (potentially through some fields) back to his house again.

He wants his tour to be as short as possible, however he doesn‘t want to walk on any given path more than once. Calculate the shortest tour possible. FJ is sure that some tour exists for any given farm.

Input

* Line 1: Two space-separated integers: N and M.

* Lines 2..M+1: Three space-separated integers that define a path: The starting field, the end field, and the path‘s length.

Output

A single line containing the length of the shortest tour.

Sample Input

4 5
1 2 1
2 3 1
3 4 1
1 3 2
2 4 2

Sample Output

6

Source

USACO 2003 February Green

代码几乎是找的，太难了，我以后就用模板吧，不过还是要把模板理解清楚。

题意：不走重边，1->n->1的最少步数。

分析：见注释。

#include <iostream>
#include <cstring>
#include <cstdio>
#include <queue>

using namespace std;
int sumFlow;
const int MAXN = 1010;
const int MAXM = 1000200;
#define INF 0x3f3f3f3f

struct Edge
{
    int u;
    int v;
    int cap;
    int cost;
    int next;
} edge[MAXM<<2];

int NE;
int head[MAXN], dist[MAXN], pre[MAXN];
bool vis[MAXN];

void addedge(int u,int v,int cap,int cost)
{
    edge[NE].u=u;
    edge[NE].v=v;
    edge[NE].cap=cap;
    edge[NE].cost=cost;
    edge[NE].next=head[u];
    head[u]=NE++;

    edge[NE].u=v;       ///反的容量图
    edge[NE].v=u;
    edge[NE].cap=0;
    edge[NE].cost=-cost;
    edge[NE].next=head[v];
    head[v]=NE++;
}

bool SPFA(int s,int t,int n)
{
    int i,u,v;
    queue<int>Q;
    memset(vis,false,sizeof(vis));
    memset(pre,-1,sizeof(pre));
    for(i=0; i<=n; i++)
        dist[i]=INF;
    vis[s]=true;
    dist[s]=0;
    Q.push(s);
    while(!Q.empty())
    {
        u=Q.front();
        Q.pop();
        vis[u]=false;
        for(i=head[u]; i!=-1; i=edge[i].next)
        {
            v=edge[i].v;
            if(edge[i].cap&&dist[v]>dist[u]+edge[i].cost)
            {
                dist[v]=dist[u]+edge[i].cost;
                pre[v]=i;
                if(!vis[v])
                {
                    Q.push(v);
                    vis[v]=true;
                }
            }
        }
    }
    if(dist[t]==INF)
        return false;
    return true;
}

int MCMF(int s,int t,int n)
{
    int flow=0; /// 总流量
    int minflow,mincost;
    mincost=0;
    while(SPFA(s,t,n))
    {
        minflow=INF+1;      ///容量瓶颈
        for(int i=pre[t]; i!=-1; i=pre[edge[i].u])
            if(edge[i].cap<minflow)
                minflow=edge[i].cap;
        flow+=minflow;
        for(int i=pre[t]; i!=-1; i=pre[edge[i].u])
        {
            edge[i].cap-=minflow;
            edge[i^1].cap+=minflow;     ///更新残余网络，^1处理，因为0,是正边，1是反边，做^1，就能找到反边
        }
        mincost+=dist[t]*minflow;       ///这里和书上有点不一样，就是相当于一个合并同类项了，dist[t]到汇点的最少花费*瓶颈容量
    }
    sumFlow=flow; /// 最大流
    return mincost;
}

int main()
{
    int n,m;
    int u,v,c;
    while(~scanf("%d%d",&n,&m))
    {
        NE=0;
        memset(head,-1,sizeof(head));
        int S=0;
        int T=n+1;
        while(m--)
        {
            scanf("%d%d%d",&u,&v,&c);
            addedge(u,v,1,c);
            addedge(v,u,1,c);   ///建反图，这样在SPFA里面就能回来了，
        }
        addedge(S,1,2,0);
        addedge(n,T,2,0);
        int ans=MCMF(S,T,T+1);
        printf("%d\n",ans);
    }
    return 0;
}