Update 最大流.md

板子加上当前弧优化

docs/Graph/最大流.md

@@ -41,7 +41,7 @@ $O(V^2E)$，如果用在二分图，是 $O(E\sqrt V)$
 二分图最小路径覆盖=原图节点数-最大匹配.
 ## 板子
 ```c++
-const int N=2e2+5;
+const int N=3.2e3;
 const int M=1e6+3;
 const ll INF=1e18;
 namespace Dinic
@@ -50,67 +50,38 @@ namespace Dinic
     {
         int v,nxt;
         ll cap;
-    };
-    int n,s,t,tot;
-    int head[N],dep[N];
-    Edge e[M];
+    }e[M];
+    int n,s,t,tot,hd[N],dep[N],cur[N];
     queue<int> q;
-    void init(int nn,int ss,int tt)
+    void init(int nn)
     {
-        n=nn;
-        s=ss;
-        t=tt;
-        memset(head,0,sizeof(int)*(n+1));
-        head[s]=head[t]=0;
+        n=nn,s=nn+1,t=nn+2;
+        memset(hd,0,sizeof(int)*(n+3));
         tot=1;
     }
     void addEdge(int x,int y,ll cap)
     {
-        e[++tot]={y,head[x],cap};
-        head[x]=tot;
-        e[++tot]={x,head[y],0};
-        head[y]=tot;
-    }
-    bool level()
-    {
-        memset(dep,0,sizeof(int)*(n+1));
-        dep[t]=0;
-        dep[s]=1;
-        int u,v;
-        q.push(s);
-        while(!q.empty())
-        {
-            u=q.front();
-            q.pop();
-            for(int i=head[u];i;i=e[i].nxt)
-            {
-                v=e[i].v;
-                if(e[i].cap && !dep[v])
-                {
-                    dep[v]=dep[u]+1;
-                    q.push(v);
-                }
-            }
-        }
-        return dep[t];
+        e[++tot]={y,hd[x],cap};
+        hd[x]=tot;
+        e[++tot]={x,hd[y],0};
+        hd[y]=tot;
     }
     ll findpath(int u,ll in)
     {
         if(u==t)
             return in;
-        ll out=0,res;
-        int v;
-        for(int i=head[u];i && in;i=e[i].nxt)
+        ll out=0;
+        for(int i=cur[u];i && in;i=e[i].nxt)
         {
-            v=e[i].v;
-            if(e[i].cap && dep[v]==dep[u]+1)
-            {
-                res=findpath(v,min(in,e[i].cap));
-                e[i].cap-=res;
-                e[i^1].cap+=res;
-                out+=res;
-                in-=res;
-            }
+            cur[u]=i;
+            int v=e[i].v;
+            if(!e[i].cap || dep[v]!=dep[u]+1)
+                continue;
+            ll res=findpath(v,min(in,e[i].cap));
+            e[i].cap-=res;
+            e[i^1].cap+=res;
+            out+=res;
+            in-=res;
         }
         if(!out)
             dep[u]=0;
@@ -119,12 +90,32 @@ namespace Dinic
     ll dinic()
     {
         ll res=0;
-        while(level())
+        while(1)
+        {
+            memset(dep,0,sizeof(int)*(n+3));
+            memcpy(cur,hd,sizeof(int)*(n+3));
+            dep[s]=1;
+            q.push(s);
+            while(!q.empty())
+            {
+                int u=q.front();
+                q.pop();
+                for(int i=hd[u];i;i=e[i].nxt)
+                {
+                    int v=e[i].v;
+                    if(!e[i].cap || dep[v])
+                        continue;
+                    dep[v]=dep[u]+1;
+                    q.push(v);
+                }
+            }
+            if(!dep[t])
+                return res;
             res+=findpath(s,INF);
-        return res;
+        }
     }
 };
-Dinic::init(n,s,t);
+Dinic::init(n);//源点为n+1，汇点为n+2
 Dinic::addEdge(u,v,w);//边的顺序一定是源点-中间点-汇点
 Dinic::dinic();
 ```