最大流最小割模板

Posted 2021-01-03 romalzhih

纯最大流，Dicnic算法：

 1 using namespace std;
 2 const int maxn=650;
 3 const int INF=0x3f3f3f3f;
 4 struct Edge{
 5     int from,to,cap,flow;
 6 };
 7 struct Dinic{
 8     int n,m,s,t;
 9     vector<Edge>edges;
10     vector<int>G[maxn];
11     bool vis[maxn];
12     int d[maxn];
13     int cur[maxn];
14     void AddEdge(int from,int to,int cap){
15         edges.push_back((Edge){from,to,cap,0});
16         edges.push_back((Edge){to,from,0,0});
17         m=edges.size();
18         G[from].push_back(m-2);
19         G[to].push_back(m-1);
20     }
21     bool BFS(){
22         int x,i;
23         memset(vis,0,sizeof(vis));
24         queue<int>Q;
25         Q.push(s);
26         d[s]=0;
27         vis[s]=1;
28         while(!Q.empty()){
29             x=Q.front(),Q.pop();
30             for(i=0;i<G[x].size();i++){
31                 Edge & e =edges[G[x][i]];
32                 if(!vis[e.to]&&e.cap>e.flow){
33                     vis[e.to]=1;
34                     d[e.to]=d[x]+1;
35                     Q.push(e.to);
36                 }
37             }
38         }
39         return vis[t];
40     }
41     int DFS(int x,int a){
42         if(x==t||a==0)
43             return a;
44         int flow=0,f;
45         for(int &i=cur[x];i<G[x].size();i++){
46             Edge & e=edges[G[x][i]];
47             if(d[x]+1==d[e.to]&&(f=DFS(e.to,min(a,e.cap-e.flow)))>0){
48                 e.flow+=f;
49                 edges[G[x][i]^1].flow-=f;
50                 flow+=f;
51                 a-=f;
52                 if(a==0)
53                     break;
54             }
55         }
56         return flow;
57     }
58     int Maxflow(int s,int t){
59         this->s=s,this->t=t;
60         int flow=0;
61         while(BFS()){
62             memset(cur,0,sizeof(cur));
63             flow+= DFS(s,INF);
64         }
65         return flow;
66     }
67 };

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Edmonds Karp模板

 1 const int maxn=;
 2 const int inf=0x3f3f3f3f;
 3 struct Edge
 4 {
 5     int from,to,cap,flow;
 6     Edge(int u,int v,int c,int f): from(u),to(v),cap(c),flow(f) {}
 7 };
 8 
 9 struct EdmondsKarp
10 {
11     int n,m;
12     vector<Edge> edges;
13     vector<int> G[maxn];
14     int a[maxn];
15     int p[maxn];
16 
17     void init(int n)
18     {
19       for(int i=0;i<n;i++) G[i].clear();
20       edges.clear();
21     }
22 
23     void AddEdge(int from,int to,int cap)
24     {
25        edges.push_back(Edge(from,to,cap,0));
26        edges.push_back(Edge(to,from,0,0));
27        m=edges.size();
28        G[from].push_back(m-2);
29        G[to].push_back(m-1);
30     }
31 
32    int Maxflow(int s,int t)
33    {
34      int flow=0;
35      while(1)
36      {
37         memset(a,0,sizeof(a));
38         queue<int> Q;
39         Q.push(s);
40         a[s]=inf;
41         while(!Q.empty())
42         {
43             int x=Q.front();Q.pop();
44             for(int i=0;i<G[x].size();i++)
45             {
46                 Edge& e=edges[G[x][i]];
47                 if(!a[e.to]&&e.cap>e.flow)
48                 {
49                     p[e.to]=G[x][i];
50                     a[e.to]=min(a[x],e.cap-e.flow);
51                     Q.push(e.to);
52                 }
53             }
54             if(a[t]) break;
55         }
56         if(!a[t]) break;
57         for(int u=t;u!=s;u=edges[p[u]].from)
58         {
59             edges[p[u]].flow+=a[t];
60             edges[p[u]^1].flow-=a[t];
61         }
62         flow+=a[t];
63     }
64     return flow;    
65    }
66 };

对于最小割来说，在算法结束后，令已经标号的结点（a[u]>0的结点）集合为S，其他集合为T=V-S，则（S，T）是图 s-t 的最小割