网络流 KM dinic

study from：

https://blog.csdn.net/A_Comme_Amour/article/details/79356220

1.

Edmonds-Karp 无优化

最坏时间复杂度O(n*m*m) n为点数，m为边数

 #include <cstdio>
 #include <cstdlib>
 #include <cmath>
 #include <ctime>
 #include <cstring>
 #include <string>
 #include <map>
 #include <set>
 #include <list>
 #include <queue>
 #include <stack>
 #include <vector>
 #include <bitset>
 #include <algorithm>
 #include <iostream>
 using namespace std;
 #define ll long long
 const int maxn=1e4+;
 const int inf=1e9;

 struct node
 {
     int d,len;
     node *next,*opp;
 }*e[maxn],*pre[maxn];

 int sum=,s,t,add[maxn];
 queue<int> st;
 bool vis[maxn];

 void add_edge(int x,int y,int len)
 {
     node *p1=(node*) malloc (sizeof(node));
     node *p2=(node*) malloc (sizeof(node));

     p1->d=y;
     p1->len=len;
     p1->next=e[x];
     p1->opp=p2;
     e[x]=p1;

     p2->d=x;///注意
     p2->len=;///注意
     p2->next=e[y];
     p2->opp=p1;
     e[y]=p2;
 }

 void bfs()
 {
     int d,dd,v;
     node *p;
     while ()
     {
         memset(add,,sizeof(add));
         ///vis不用初始化
         add[s]=inf;
         vis[s]=;
         st.push(s);
         while (!st.empty())
         {
             d=st.front();
             st.pop();
             p=e[d];
             while (p)
             {
                 dd=p->d;
                 v=min(add[d],p->len);
                 if (add[dd]<v)
                 {
                     add[dd]=v;
                     pre[dd]=p->opp;
                     if (!vis[dd])
                     {
                         vis[dd]=;
                         st.push(dd);
                     }
                 }
                 p=p->next;
             }
             vis[d]=;
         }

         if (add[t]==)
             break;

         sum+=add[t];
         d=t;
         while (d!=s)
         {
             pre[d]->len+=add[t];
             pre[d]->opp->len-=add[t];
             d=pre[d]->d;
         }
     }
 }

 int main()
 {
     int n,m,x,y,z;
     scanf("%d%d%d%d",&n,&m,&s,&t);
     while (m--)
     {
         scanf("%d%d%d",&x,&y,&z);
         add_edge(x,y,z);
     }
     bfs();
     printf("%d",sum);
     return ;
 }

2.

study from https://www.luogu.org/problemnew/solution/P3376 第一个题解的dinic

dinic

 #include <cstdio>
 #include <cstdlib>
 #include <cmath>
 #include <ctime>
 #include <cstring>
 #include <string>
 #include <map>
 #include <set>
 #include <list>
 #include <queue>
 #include <stack>
 #include <vector>
 #include <bitset>
 #include <algorithm>
 #include <iostream>
 using namespace std;
 #define ll long long
 const int maxn=1e4+;
 const int inf=1e9;

 struct node
 {
     int d,len;
     node *next,*opp;
 }*e[maxn];

 int sum=,s,t;
 int q[maxn],dep[maxn];
 bool vis[maxn];

 void add_edge(int x,int y,int len)
 {
     node *p1=(node*) malloc (sizeof(node));
     node *p2=(node*) malloc (sizeof(node));

     p1->d=y;
     p1->len=len;
     p1->next=e[x];
     p1->opp=p2;
     e[x]=p1;

     p2->d=x;
     p2->len=;///注意
     p2->next=e[y];
     p2->opp=p1;
     e[y]=p2;
 }

 ///前面的网络流算法，每进行一次增广，都要做 一遍BFS，十分浪费。能否少做几次BFS?

 bool bfs()
 {
     int head=,tail=,d,dd;
     node *p;
     memset(vis,,sizeof(vis));
     vis[s]=;
     dep[s]=;
     q[]=s;

     while (head<tail)
     {
         head++;
         d=q[head];
         p=e[d];
         while (p)
         {
             dd=p->d;
             if (p->len> && !vis[dd])
             {
                 tail++;
                 q[tail]=dd;
                 vis[dd]=;
                 dep[dd]=dep[d]+;
             }
             p=p->next;
         }
     }
     if (vis[t])
         return ;
     return ;
 }

 ///DFS找到一条增广路径后，并不立即结束，而是回溯后继续DFS寻找下一个增广路径

 int dfs(int d,int add)
 {
     if (!add || d==t)
         return add;
     int totf=,f,dd;
     node *p=e[d];
     while (p)
     {
         dd=p->d;
         if (dep[dd]==dep[d]+ && (f=dfs(dd,min(add,p->len)))>)///注意
         {
             totf+=f;
             add-=f;///注意
             p->len-=f;
             p->opp->len+=f;
         }
         p=p->next;
     }
     return totf;
 }

 int main()
 {
     int n,m,x,y,z;
     scanf("%d%d%d%d",&n,&m,&s,&t);
     while (m--)
     {
         scanf("%d%d%d",&x,&y,&z);
         add_edge(x,y,z);
     }
     while (bfs())
         sum+=dfs(s,inf);
     printf("%d",sum);
     return ;
 }