BZOJ 1497: [NOI2006]最大获利（最大权闭合图）

http://www.lydsy.com/JudgeOnline/problem.php?id=1497

题意：

思路：

论文题，只要看过论文的话就是小菜一碟啦~

每个用户群i作为一个结点分别向相应的中转站ai和中转站bi连有向边。

#include<iostream>
#include<algorithm>
#include<cstring>
#include<cstdio>
#include<vector>
#include<stack>
#include<queue>
#include<cmath>
#include<map>
#include<set>
using namespace std;
typedef long long ll;
typedef pair<int,int> pll;
const int INF = 0x3f3f3f3f;
const int maxn = 55000 + 5;

int n, m;
int val[maxn];

struct Edge
{
    int from,to,cap,flow;
    Edge(int u,int v,int w,int f):from(u),to(v),cap(w),flow(f){}
};

struct Dinic
{
    int n,m,s,t;
    vector<Edge> edges;
    vector<int> G[maxn];
    bool vis[maxn];
    int cur[maxn];
    int d[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)
    {
        edges.push_back( Edge(from,to,cap,0) );
        edges.push_back( Edge(to,from,0,0) );
        m=edges.size();
        G[from].push_back(m-2);
        G[to].push_back(m-1);
    }

    bool BFS()
    {
        queue<int> Q;
        memset(vis,0,sizeof(vis));
        vis[s]=true;
        d[s]=0;
        Q.push(s);
        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]=true;
                    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[e.to]==d[x]+1 && (f=DFS(e.to,min(a,e.cap-e.flow) ) )>0)
            {
                e.flow +=f;
                edges[G[x][i]^1].flow -=f;
                flow +=f;
                a -=f;
                if(a==0) break;
            }
        }
        return flow;
    }

    int Maxflow(int s,int t)
    {
        this->s=s; this->t=t;
        int flow=0;
        while(BFS())
        {
            memset(cur,0,sizeof(cur));
            flow +=DFS(s,INF);
        }
        return flow;
    }
}DC;

int main()
{
    //freopen("in.txt","r",stdin);
    while(~scanf("%d%d",&n,&m))
    {
        int src = 0, dst = n+m+1;
        DC.init(dst+1);
        for(int i=1;i<=n;i++)
        {
            scanf("%d",&val[i]);
            DC.AddEdge(i,dst,val[i]);
        }
        int sum = 0;
        for(int i=1;i<=m;i++)
        {
            int a,b,c;
            scanf("%d%d%d",&a,&b,&c);
            DC.AddEdge(src,i+n,c);
            DC.AddEdge(i+n,a,INF);
            DC.AddEdge(i+n,b,INF);
            sum+=c;
        }
        int ans = sum-DC.Maxflow(src,dst);
        printf("%d
",ans);
    }
    return 0;
}