Farm Tour POJ - 2135 （最小费用流）

Posted 2021-02-04 smallhester

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

题意：节点1把所有的节点都要跑一遍，然后回到节点1，每个边智能跑一次，问最短距离
思路：流量为2的最小费用流

#include<cstdio>
#include<iostream>
#include<algorithm>
#include<cstring>
#include<sstream>
#include<cmath>
#include<stack>
#include<cstdlib>
#include <vector>
#include<queue>
using namespace std;

#define ll long long
#define llu unsigned long long
#define INF 0x3f3f3f3f
#define PI acos(-1.0)
const int maxn =  1e4+5;
const int  mod = 1e9+7;

typedef  pair<int,int>P;
struct edge{
    int to,cap,cost,rev;
};

int V;
vector<edge> G[maxn];
int h[maxn];
int dist[maxn];
int prevv[maxn],preve[maxn];

void addedge(int from,int to,int cap,int cost)
{
    G[from].push_back((edge){to,cap,cost,G[to].size()});
    G[to].push_back((edge){from,0,-cost,G[from].size() -1});
}

int min_cost_flow(int s,int t,int f)
{
    int res =0;
    fill(h,h+V,0);
    while (f>0)
    {
        priority_queue<P,vector<P>,greater<P> > que;
        fill(dist,dist+V,INF);
        dist[s] =0;
        que.push(P(0,s));
        while(!que.empty())
        {
            P p=que.top();
            que.pop();
            int v=p.second;
            if(dist[v]<p.first)
                continue;
            for(int i=0;i<G[v].size();i++) {
                edge &e = G[v][i];
                if(e.cap>0 && dist[e.to]>dist[v]+e.cost+h[v]-h[e.to])
                {
                    dist[e.to] = dist[v] + e.cost + h[v] -h[e.to];
                    prevv[e.to] = v;
                    preve[e.to] = i;
                    que.push(P(dist[e.to],e.to));
                }
            }

        }
        if(dist[t] == INF)
        {
            return -1;
        }
        for(int v=0;v<V;v++)
            h[v] += dist[v];
        int d=f;
        for(int v=t;v!=s;v=prevv[v])
        {
            d=min(d,G[prevv[v]][preve[v]].cap);
        }
        f -= d;
        res += d*h[t];
        for(int v=t;v!=s;v=prevv[v])
        {
            edge &e = G[prevv[v]][preve[v]];
            e.cap -= d;
            G[v][e.rev].cap += d;
        }
    }
    return res;
}

int N,M;
int a[maxn],b[maxn],c[maxn];

void solve()
{
    int s=0,t=N-1;
    V=N;
    for(int i=0;i<M;i++)
    {
        addedge(a[i]-1,b[i]-1,1,c[i]);
        addedge(b[i]-1,a[i]-1,1,c[i]);
    }
    printf("%d
",min_cost_flow(s,t,2));
}

int main()
{
    cin>>N>>M;
    for(int i=0;i<M;i++)
    {
        scanf("%d%d%d",&a[i],&b[i],&c[i]);
    }
    solve();
}

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