POJ 2315 最小费用最大流

从1走到N然后从N走回来的最短路程是多少?转换为费用流来建模.

/**

因为e==0所以pe[v]pe[v]^1是两条相对应的边

E[pe[v]].c-=aug;E[pe[v]^1].c+=aug;

*/

#include<queue>

#include<iostream>

#include<string.h>

#include<stdio.h>

#include<map>

usingnamespacestd;

#defineV30010//vertex

#defineE150010//edge

#defineINF0x3F3F3F3F

structMinCostMaxFlow

{

structEdge

{

intv,next,cap,cost;//cap为容量,cost为单位流量费用

}edge[E];

inthead[V],pe[V],pv[V];//每个节点的第一条edge[idx]的编号.

intdis[V];//theshortestpathtothesrc

boolvis[V];//visted

//pe[v]存放在增广路上到达v的边(u,v)在edge[]的位置

//pv[u]存放在增广路上从u出发的边(u,v)在edge[]中的位置

inte,src,sink;//theindexoftheedge

voidaddedge(intu,intv,intcap,intcost)

{

edge[e].v=v,edge[e].cap=cap;

edge[e].cost=cost,edge[e].next=head[u],head[u]=e++;

edge[e].v=u,edge[e].cap=0;

edge[e].cost=-1*cost,edge[e].next=head[v],head[v]=e++;

}

//求最短路,不存在负环的时候,比DFS快

intSPFABFS()

{

memset(vis,0,sizeof(vis));

memset(pv,-1,sizeof(pv));

for(inti=0;i<V;i++)dis[i]=INF;

queue<int>Q;

Q.push(src),vis[src]=1,dis[src]=0;

while(!Q.empty())

{

intu=Q.front();

Q.pop(),vis[u]=0;

for(inti=head[u];i!=-1;i=edge[i].next)

{

intv=edge[i].v;

if(edge[i].cap>0&&dis[v]>dis[u]+edge[i].cost)

{

dis[v]=dis[u]+edge[i].cost;

if(!vis[v])Q.push(v),vis[v]=1;

pv[v]=u,pe[v]=i;

}

}

}

if(dis[sink]==INF)return-2;//can'tfromsrctosink.

returndis[sink];

}

pair<int,int>MCMF()

{

intmaxflow=0,mincost=0;

while(SPFABFS())

{

if(pv[sink]==-1)break;

intaug=INF;

for(inti=sink;i!=src;i=pv[i])

aug=min(aug,edge[pe[i]].cap);

maxflow+=aug;

mincost+=aug*dis[sink];

for(inti=sink;i!=src;i=pv[i])

{

edge[pe[i]].cap-=aug;

edge[pe[i]^1].cap+=aug;

}

}

returnmake_pair(maxflow,mincost);

}

///一定需要初始化的是src,sink

voidsolve()

{

intN,M;

while(scanf("%d%d",&N,&M)!=EOF)

{

e=0;

memset(head,-1,sizeof(head));

for(inti=0;i<M;i++)

{

inta,b,c;

scanf("%d%d%d",&a,&b,&c);

addedge(a,b,1,c);

addedge(b,a,1,c);

}

src=0;

sink=N+1;

addedge(src,1,2,0);

addedge(N,sink,2,0);

pair<int,int>ret=MCMF();

cout<<ret.second<<endl;

}

}

}mcmf;

intmain()

{

mcmf.solve();

return0;

}

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