Rogu P3386 [TEMPLATE] Bipartite Graph Matching Dinic version, p31_dinic

Rogu P3386 [TEMPLATE] Bipartite Graph Matching Dinic version, p31_dinic
Background

Bipartite Graph

Description

Given a bipartite graph, the number of nodes is n, m, and the number of edges is e.

Input/Output Format

Input Format:

 

First line, n, m, e

The second to e + 1 rows have two positive integers u and v, indicating that u and v have a connected edge.

 

Output Format:

 

A total of rows, maximum matching of bipartite graphs

 

Input and Output sample input sample #1: Copy

1 1 11 1

Output example #1: Copy

1

Description

N, m \ leq 1000n, m ≤ 1000, 1 \ leq u \ leq n1 ≤ u ≤ n, 1 \ leq v \ leq m1 ≤ v ≤ m

Due to Data Pitfalls, v> mv> m may occur. Please filter out the v> mv> m data.

Algorithm: Bipartite Graph Matching

 

Create a super source node S

Create a super sink T

Edge connecting n S to 1-n

Connect m edge n + 1-n + 1 + m to T

The weight of all edges is 1.

Maximum stream running

 

 

 1 #include<iostream> 2 #include<cstdio> 3 #include<cstring> 4 #include<cmath> 5 #include<queue> 6 using namespace std; 7 const int MAXN=3*1e6; 8 const int INF=0x7ffff; 9 inline int read()10 {11     char c=getchar();int flag=1,x=0;12     while(c<'0'||c>'9')    {if(c=='-')    flag=-1;c=getchar();}13     while(c>='0'&&c<='9')     x=x*10+c-48,c=getchar();return x*flag;14 }15 struct node16 {17     int u,v,f,nxt;18 }edge[MAXN];19 int head[MAXN];20 int num=0;21 inline void add_edge(int x,int y,int z)22 {23     edge[num].u=x;24     edge[num].v=y;25     edge[num].f=z;26     edge[num].nxt=head[x];27     head[x]=num++;28 }29 int n,m,e;30 int S,T;31 int deep[MAXN],cur[MAXN];32 inline bool BFS()33 {34     memset(deep,0,sizeof(deep));35     deep[S]=1;36     queue<int>q;37     q.push(S);38     while(q.size()!=0)39     {40         int p=q.front();q.pop();41         for(int i=head[p];i!=-1;i=edge[i].nxt)42             if(deep[edge[i].v]==0&&edge[i].f)43                 deep[edge[i].v]=deep[p]+1,q.push(edge[i].v);44     }45     return deep[T];46 }47 int DFS(int now,int nowflow)48 {49     if(nowflow<=0||now==T)    return nowflow;50     int totflow=0;51     for(int &i=cur[now];i!=-1;i=edge[i].nxt)52     {53         if(deep[edge[i].v]==deep[now]+1&&edge[i].f)54         {55             int canflow=DFS(edge[i].v,min(edge[i].f,nowflow));56             totflow+=canflow;57             nowflow-=canflow;58             edge[i].f-=canflow;59             edge[i^1].f+=canflow;    60             if(nowflow<=0)    break;61         }62     }63     return totflow;64 }65 int ans=0;66 inline void Dinic()67 {68     while(BFS())69     {70         memcpy(cur,head,sizeof(head));71         ans+=DFS(S,INF);72     }73         74 }75 int main()76 {77     memset(head,-1,sizeof(head));78     n=read();m=read();e=read();79     for(int i=1;i<=e;i++)80     {81         int x=read(),y=read();82         add_edge(x,y+n,1);83         add_edge(y+n,x,0);84     }85     S=0,T=INF;86     for(int i=1;i<=n;i++)87         add_edge(S,i,1),add_edge(i,S,0);88     for(int i=1;i<=m;i++)89         add_edge(i+n,T,1),add_edge(T,i+n,0);90     Dinic();91     printf("%d",ans);92     return 0;93 }