转：网络流---Dinic

Dinic算法是在Edmonds-Karp算法上的改进

它与最短路径增值算法不同之处是：在Dinic算法中，我们用一个dfs过程代替多次bfs来寻找阻塞流。下面给出其算法步骤：

算法流程： 

以上转自http://blog.csdn.net/pi9nc/article/details/23339111 

 

#include <queue>
#include <cstdio>
#include <vector>
#include <cstring>
using namespace std;
typedef int Type;
const int MAXNODE = 210;
const int MAXEDGE = 10010;
const Type INF = 0x3f3f3f3f;

struct Edge
{
    int u, v, next;
    Type cap, flow;
    Edge() {}
    Edge(int u, int v, Type cap, Type flow, int next): u(u), v(v), cap(cap), flow(flow), next(next) {} 
};

struct Dinic
{
    int n, m, s, t;
    Edge edges[MAXNODE];
    int head[MAXNODE];
    int cur[MAXNODE], d[MAXNODE];
    bool vis[MAXNODE];
    vector<int> cut;
    
    void init(int n)
    {
        this->n=n;
        memset(head, -1, sizeof(head));
        m=0;
    }  
    
    void addEdge(int u, int v, Type cap)
    {
        edges[m]=Edge(u, v, cap, 0, head[u]);
        head[u]=m++;
        edges[m]=Edge(v, u, 0, 0, head[v]);
        head[v]=m++; 
    }
    
    //bfs构建层次图； 
    bool bfs()
    {
        memset(vis, 0, sizeof(vis));
        queue<int> Q;
        Q.push(s);
        d[s]=0;
        vis[s]=1;
        
        while(!Q.empty())
        {
            int u=Q.front(); Q.pop();
            for(int i=head[u]; i!=-1; i=edges[i].next)
            {
                Edge &e=edges[i];
                if(!vis[e.v] && e.cap > e.flow)
                {
                    vis[e.v]=true;
                    d[e.v]=d[u]+1;
                    Q.push(e.v);    
                }    
            } 
        }
        return vis[t];
    }
    
    Type dfs(int u, Type a)
    {
        if(u==t ||  a==0) return a;
        Type flow=0, f;
        for(int i=cur[u]; ~i; i=edges[i].next)
        {
            Edge &e=edges[i];
            if(d[u]+1==d[e.v] && (f = dfs(e.v, min(a, e.cap-e.flow))) > 0)
            {
                e.flow += f;
                edges[i ^ 1].flow -= f;
                flow += f;
                a -= f;
                if(a==0) break; 
            }
        } 
        return flow;
    }
    
    Type maxFlow(int s, int t)
    {
        this->s=s; this->t=t;
        Type flow=0;
        while(bfs())
        {
            //cur[i]; 表示第i个点已经增广到哪一条边了， 相当于一个剪枝； 
            for(int i=0; i<n; i++)
                cur[i]=head[i];
            flow += dfs(s, INF);
        }
        return flow;
    } 
}dinic;
int main()
{
    return 0;
}