hdu 1532 Drainage Ditches（最大流 三种模板：EK、Dinic、isap）

http://acm.split.hdu.edu.cn/showproblem.php?pid=1532

题目大意：
给出边数N,点数M，每条边都是单向的，问从1点到M的最大流是多少。

最大流的三种模板EK，Dinic和isap

第一种：EK算法

#include<iostream>#include<cstdio>#include<cstring>#include<vector>#include<queue>#define INF 0x3f3f3f3fusing namespace std;const int maxn=205;struct Edge{    int from,to,cap,flow;    Edge(int u,int v,int c,int f):from(u),to(v),cap(c),flow(f){}};struct Edmonds_Karp{    int n,m;    vector<Edge> edges;      //边数的两倍     vector<int> g[maxn];    //邻接表 g[i][j]表示节点i的第j条边在e数组中的序号     int a[maxn];      //当源点到i的可改进量     int p[maxn];       //最短路树上p的入弧编号     void Init(int 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);    }     int Maxflow(int s,int t)    {        int flow=0;        for(;;)        {            memset(a,0,sizeof(a));            queue<int> q;            q.push(s);            a[s]=INF;            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(!a[e.to]&&e.cap>e.flow)                    {                        p[e.to]=g[x][i];                        a[e.to]=min(a[x],e.cap-e.flow);                        q.push(e.to);                    }                }                if(a[t])                  break;            }                   if(!a[t])              break;            for(int u=t;u!=s;u=edges[p[u]].from)            {                edges[p[u]].flow+=a[t];                edges[p[u]^1].flow-=a[t];            }                   flow+=a[t];         }        return flow;    }}EK;int main(){    int n,m,a,b,c;    while(~scanf("%d%d",&n,&m))    {        EK.Init(m);        for(int i=0;i<n;i++)        {            scanf("%d%d%d",&a,&b,&c);            a--;            b--;            EK.addedge(a,b,c);        }        printf("%d\n",EK.Maxflow(0,m-1));    }    return 0;}

第二种：Dinic算法

#include<iostream>#include<cstdio>#include<cstring>#include<vector>#include<queue>#define INF 0x3f3f3f3fusing namespace std;const int maxn=205;struct Edge{    int from,to,cap,flow;    Edge(int u,int v,int c,int f):from(u),to(v),cap(c),flow(f){}};struct Dinic{    int n,m,s,t;    vector<Edge> edges;    vector<int> g[maxn];    bool vis[maxn];    int d[maxn];    int cur[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()    {        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)))>0)            {                edges[g[x][i]].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(){    int n,m,a,b,c;    while(~scanf("%d%d",&n,&m))    {        DC.Init(m);        while(n--)        {            scanf("%d%d%d",&a,&b,&c);            a--;            b--;            DC.addedge(a,b,c);         }        printf("%d\n",DC.Maxflow(0,m-1));    }    return 0;}

第三种：isap算法

#include<iostream>#include<cstdio>#include<cstring>#include<vector>#include<queue>#define INF 0x3f3f3f3fusing namespace std;const int maxn=1005;int src,sink,num_nodes;           //源点 汇点 int p[maxn];           //可增广路上的上一条弧的编号 int num[maxn];         //和t的最短距离等于i的节点数量 int cur[maxn];          //当前弧下标 int d[maxn];          //残量网络中节点i到汇点t的最短距离bool vis[maxn]; struct Edge{    int from,to,cap,flow;    Edge(int u,int v,int c,int f):from(u),to(v),cap(c),flow(f){}};vector<int> g[maxn];vector<Edge> edges;void Init(){    edges.clear();    for(int i=0;i<num_nodes;i++)      g[i].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));    int m=edges.size();    g[from].push_back(m-2);    g[to].push_back(m-1);}int augment(){    int u=sink,flow=INF;    //从汇点到源点通过追踪增广路径  flow为路上最小的残量     while(u!=src)    {        Edge &e=edges[p[u]];        flow=min(flow,e.cap-e.flow);        u=edges[p[u]].from;    }    u=sink;    //从汇点到源点更新流量     while(u!=src)    {        edges[p[u]].flow+=flow;        edges[p[u]^1].flow-=flow;        u=edges[p[u]].from;    }    return flow;}bool bfs(){    memset(vis,0,sizeof(vis));    queue<int> q;    q.push(sink);    vis[sink]=1;    d[sink]=0;    while(!q.empty())    {        int u=q.front();        q.pop();        for(int i=0;i<g[u].size();i++)        {            Edge &e=edges[g[u][i]^1];            if(!vis[e.from]&&e.cap>e.flow)            {                vis[e.from]=1;                d[e.from]=d[u]+1;                q.push(e.from);            }        }    }     return vis[src];}int isap(){    int flow=0,u=src;    bfs();      memset(num,0,sizeof(num));    memset(cur,0,sizeof(cur));      for(int i=0;i<num_nodes;i++)      num[d[i]]++;    while(d[src]<num_nodes)    {        if(u==sink)        {            flow+=augment();            u=src;        }        bool advanced=false;        for(int i=cur[u];i<g[u].size();i++)        {            Edge &e=edges[g[u][i]];            if(d[u]==d[e.to]+1&&e.cap>e.flow)            {                advanced=true;                p[e.to]=g[u][i];                cur[u]=i;                u=e.to;                break;            }        }        if(!advanced)    //retreat        {            int m=num_nodes-1;            for(int i=0;i<g[u].size();i++)              if(edges[g[u][i]].cap>edges[g[u][i]].flow)                m=min(m,d[edges[g[u][i]].to]);            if(--num[d[u]]==0)       //gap优化               break;            num[d[u]=m+1]++;            cur[u]=0;            if(u!=src)              u=edges[p[u]].from;        }    }    return flow;}int main(){    int n,a,b,c;    while(~scanf("%d%d",&n,&num_nodes))    {        Init();        src=0;        sink=num_nodes-1;        for(int i=0;i<n;i++)        {            scanf("%d%d%d",&a,&b,&c);            a--;            b--;            addedge(a,b,c);        }         printf("%d\n",isap());    }    return 0;}