hdu 4289(最小割）

题目链接：http://acm.hdu.edu.cn/showproblem.php?pid=4289

思路：求最小花费，最小割应用，将点权转化为边权，拆点，(i,i+n)之间连边，容量为在城市i的花费，然后就是若u,v之间有路，则连边（u+n,v),(v+n,u).最后就是跑最大流了。

#include<iostream>
#include<cstdio>
#include<cstring>
#include<algorithm>
#include<queue>
using namespace std;
#define MAXN 444
#define MAXM 44444444
#define inf 1<<30

struct Edge{
    int v,cap,next;
}edge[MAXM];

int n,m,vs,vt,NE,NV;
int head[MAXN];

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

    edge[NE].v=u;
    edge[NE].cap=0;
    edge[NE].next=head[v];
    head[v]=NE++;
}

int level[MAXN],gap[MAXN];
void bfs(int vt)
{
    memset(level,-1,sizeof(level));
    memset(gap,0,sizeof(gap));
    level[vt]=0;
    gap[level[vt]]++;
    queue<int>que;
    que.push(vt);
    while(!que.empty()){
        int u=que.front();
        que.pop();
        for(int i=head[u];i!=-1;i=edge[i].next){
            int v=edge[i].v;
            if(level[v]!=-1)continue;
            level[v]=level[u]+1;
            gap[level[v]]++;
            que.push(v);
        }
    }
}

int pre[MAXN],cur[MAXN];
int SAP(int vs,int vt)
{
    bfs(vt);
    memset(pre,-1,sizeof(pre));
    memcpy(cur,head,sizeof(head));
    int maxflow=0,aug=inf;
    int u=pre[vs]=vs;
    gap[0]=NV;
    while(level[vs]<NV){
        bool flag=false;
        for(int &i=cur[u];i!=-1;i=edge[i].next){
            int v=edge[i].v;
            if(edge[i].cap>0&&level[u]==level[v]+1){
                flag=true;
                pre[v]=u;
                u=v;
                aug=min(aug,edge[i].cap);
                if(v==vt){
                    maxflow+=aug;
                    for(u=pre[v];v!=vs;v=u,u=pre[u]){
                        edge[cur[u]].cap-=aug;
                        edge[cur[u]^1].cap+=aug;
                    }
                    aug=inf;
                }
                break;
            }
        }
        if(flag)continue;
        int minlevel=NV;
        for(int i=head[u];i!=-1;i=edge[i].next){
            int v=edge[i].v;
            if(edge[i].cap>0&&level[v]<minlevel){
                cur[u]=i;
                minlevel=level[v];
            }
        }
        if(--gap[level[u]]==0)break;
        level[u]=minlevel+1;
        gap[level[u]]++;
        u=pre[u];
    }
    return maxflow;
}

int main()
{
    int u,v,w;
    while(~scanf("%d%d",&n,&m)){
        NE=0,NV=2*n;
        memset(head,-1,sizeof(head));
        scanf("%d%d",&vs,&vt);
        for(int i=1;i<=n;i++){
            scanf("%d",&w);
            Insert(i,i+n,w);
        }
        while(m--){
            scanf("%d%d",&u,&v);
            Insert(u+n,v,inf);
            Insert(v+n,u,inf);
        }
        printf("%d
",SAP(vs,vt+n));
    }
    return 0;
}