POJ 2135

Farm Tour

Time Limit: 1000MS		Memory Limit: 65536K
Total Submissions: 10840		Accepted: 4011

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

 

最小费用流

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

using namespace std;

const int MAX_N = 1005;
const int INF = 1e9;
struct Edge {int from, to, cap, flow, cost; };
int N,M;
vector<Edge> edges;
vector<int> G[MAX_N];
int dist[MAX_N],prevv[MAX_N],preve[MAX_N];
bool inq[MAX_N];

void add_edge(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});
        int m = edges.size();
        G[from].push_back(m - 2);
        G[to].push_back(m - 1);
}

int min_cost_flow(int s, int t, int f) {
        int res = 0;
        while(f > 0) {
                fill(dist, dist + N, INF);
                dist[s] = 0;
                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 && dist[e.to] > dist[u] + e.cost) {
                                        dist[e.to] = dist[u] + e.cost;
                                        prevv[e.to] = u;
                                        preve[e.to] = i;
                                        if(!inq[e.to]) {
                                                inq[e.to] = 1;
                                                q.push(e.to);
                                        }
                                }
                        }

                }
                if(dist[t] == INF) {
                        return -1;
                }

        int d = f;
        for (int v = t; v != s; v = prevv[v]) {
                Edge& e = edges[ G[ prevv[v] ][preve[v]] ];
                d = min(d,e.cap - e.flow);
        }

        //printf("d = %d dis = %d\n",d,dist[t]);
        f -= d;
        res += d * dist[t];

        for (int v = t; v != s; v = prevv[v]) {
                Edge& e = edges[ G[prevv[v]][ preve[v] ] ];
                e.flow += d;
                edges[ G[prevv[v]][ preve[v] ] ^ 1].flow -= d;
        }

        }

        return res;
}


int main()
{
    //freopen("sw.in","r",stdin);

    scanf("%d%d",&N,&M);
    for(int i = 1; i <= M; ++i) {
            int a,b,cost;
            scanf("%d%d%d",&a,&b,&cost);
            add_edge(a - 1,b - 1,1,cost);
            add_edge(b - 1,a - 1,1,cost);
    }

    printf("%d\n",min_cost_flow(0,N - 1,2));
    //cout << "Hello world!" << endl;
    return 0;
}