[最小费用最大流]UVa1658

来源：互联网发布：督促自己的软件编辑：程序博客网时间：2024/04/29 23:17
这种问题难点仅在于建模
理解透彻原模型！
#include<bits/stdc++.h>using namespace std;const int maxn  = 10000 + 100;const int INF  = 0x7f7f7f7f;typedef long long LL;struct Edge{    int from,to,cap,flow,cost;    Edge(int u,int v,int c,int f,int w):from(u),to(v),cap(c),flow(f),cost(w) {}};struct MCMF{    int n,m;    vector<Edge> edges;    vector<int> G[maxn];    int inq[maxn];    int d[maxn];    int p[maxn];    int a[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,int cost){        edges.push_back(Edge(from,to,cap,0,cost));        edges.push_back(Edge(to,from,0,0,-cost));        m=edges.size();        G[from].push_back(m-2);        G[to].push_back(m-1);    }    bool BellmanFord(int s,int t,int &flow,LL & cost){        for(int i=0;i<n;i++) d[i]=INF;        memset(inq,0,sizeof(inq));        d[s]=0; inq[s]=1; p[s]=0; a[s]=INF;        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 && d[e.to]>d[u]+e.cost){                    d[e.to]=d[u]+e.cost;                    p[e.to]=G[u][i];                    a[e.to]=min(a[u],e.cap-e.flow);                    if(!inq[e.to]) { Q.push(e.to); inq[e.to]=1; }                }            }        }        if(d[t]==INF) return false;        flow+=a[t];        cost+=(LL) d[t]*(LL)a[t];        for(int u=t;u!=s;u=edges[p[u]].from){            edges[p[u] ].flow+=a[t];            edges[p[u]^1 ].flow-=a[t];        }        return true;    }    int MincostMaxdflow(int s,int t,int limit,LL & cost){        int flow=0; cost=0;        while(flow<limit && BellmanFord(s,t,flow,cost));        return flow;    }}g;int main(){    int n,m;    while(~scanf("%d%d",&n,&m)){        g.init(2*n-2);        for(int i=2;i<=n-1;i++){            g.AddEdge(i-1,n-2+i,1,0);        }        for(int i=0;i<m;i++){            int u,v,w;            scanf("%d%d%d",&u,&v,&w); v-=1;            if(u!=1&&u!=n) u+=n-2;            else u-=1;            g.AddEdge(u,v,1,w);        }        LL cost;        g.MincostMaxdflow(0,n-1,2,cost);        printf("%lld\n",cost);    }    return 0;}
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