POJ2987 Firing 最大权闭合图

详情请参考http://www.cnblogs.com/kane0526/archive/2013/04/05/3001557.html

值得注意的地方，割边会把图分成两部分，一部分和起点相连，另一部分和汇点相连

我们只需要关注和起点相连的点的点就好，如何统计呢？

只需要从起点开始搜索，只要边不是满流，一直搜就好

然后，答案就是总权值-最小割

注：对于dinic网络流，我还是喜欢LRJ白书上的，用起来方便

#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <cmath>
#include <iostream>
#include <algorithm>
#include <map>
#include <queue>
#include <vector>
using namespace std;
typedef  long long LL;
const int N = 20;
const int INF = 0x3f3f3f3f;
const LL mod = 1e9+7;
const int maxn=5e3+5;
struct Edge
{
    int from,to,cap,flow;
    Edge(int u,int v,int c,int d):from(u),to(v),cap(c),flow(d) {}
};
struct dinic
{
    int s,t;
    vector<Edge>edges;
    vector<int>G[maxn];
    int d[maxn];
    int cur[maxn];
    bool vis[maxn];
    void init(){
      for(int i=0;i<maxn;++i)G[i].clear();
      edges.clear();
    }
    bool bfs()
    {
        memset(vis,0,sizeof(vis));
        queue<int>q;
        q.push(s);
        d[s]=0;
        vis[s]=1;
        while(!q.empty())
        {
            int x=q.front();
            q.pop();
            for(int i=0; i<G[x].size(); i++)
            {
                Edge &e= edges[G[x][i]];
                if(!vis[e.to]&&e.cap>e.flow)
                {
                    vis[e.to]=1;
                    d[e.to]=d[x]+1;
                    q.push(e.to);
                }
            }
        }
        return vis[t];
    }
    int dfs(int x,int a)
    {
        if(x==t||a==0)return a;
        int flow=0,f;
        for(int &i=cur[x]; i<G[x].size(); i++)
        {
            Edge &e=edges[G[x][i]];
            if(d[x]+1==d[e.to]&&(f=dfs(e.to,min(a,e.cap-e.flow))))
            {
                e.flow+=f;
                edges[G[x][i]^1].flow-=f;
                flow+=f;
                a-=f;
                if(a==0)break;
            }
        }
        return flow;
    }
    LL maxflow(int s,int t)
    {
        this->s=s;
        this->t=t;
        LL flow=0;
        while(bfs())
        {
            memset(cur,0,sizeof(cur));
            flow+=dfs(s,INF);
        }
        memset(vis,false,sizeof(vis));
        return flow;
    }
    void addedge(int u,int v,int c)
    {
        Edge x(u,v,c,0),y(v,u,0,0);
        edges.push_back(x);
        edges.push_back(y);
        int l=edges.size();
        G[u].push_back(l-2);
        G[v].push_back(l-1);
    }
    int search(int u){
       int ret=1;vis[u]=true;
       for(int i=0;i<G[u].size();++i){
          Edge &e=edges[G[u][i]];
          if(vis[e.to]||e.flow==e.cap)continue;
          ret+=search(e.to);
       }
       return ret;   
    }
}solve;
int main(){
  int n,m;
  while(~scanf("%d%d",&n,&m)){
     solve.init();LL sum=0;
     for(int i=1;i<=n;++i){
       int w;scanf("%d",&w);
       if(w>0)sum+=w,solve.addedge(0,i,w);
       else if(w<0)solve.addedge(i,n+1,-w); 
     }
     for(int i=0;i<m;++i){
      int u,v;scanf("%d%d",&u,&v);
      solve.addedge(u,v,INF);
     }
     LL mxf=solve.maxflow(0,n+1);
     printf("%d %I64d\n",solve.search(0)-1,sum-mxf);
  }
  return 0;
}