Plug It In!(网络流板子)

  1 #include<bits/stdc++.h>
  2 #define INF LLONG_MAX/2
  3 #define N 80500
  4 using namespace std;
  5  
  6 struct ss
  7 {
  8     int v,next;
  9     long long flow;
 10 };
 11 int head[N],now_edge=0,S,T;
 12 ss edg[N*10];
 13  
 14 ss lsedg[N*10];
 15 int lshead[N],lssum_edge;
 16 void init() //初始化
 17 {
 18     now_edge=0;
 19     memset(head,-1,sizeof(head)); 
 20 }
 21  
 22 void addedge(int u,int v,long long flow) //加边,加双向边,反向边为0
 23 {
 24     edg[now_edge]=(ss)
 25     {
 26         v,head[u],flow
 27     };
 28     head[u]=now_edge++;
 29     edg[now_edge]=(ss)
 30     {
 31         u,head[v],0
 32     };
 33     head[v]=now_edge++;
 34 }
 35  
 36 int dis[N];
 37  
 38 int bfs() //这个过程给网络分层，避免循环跑；
 39 {
 40     memset(dis,0,sizeof(dis));
 41     queue<int>q;
 42     q.push(S);
 43     dis[S]=1;
 44  
 45     while(!q.empty())
 46     {
 47         int now=q.front();
 48         q.pop();
 49  
 50         for(int i=head[now]; i!=-1; i=edg[i].next)
 51         {
 52             ss &e=edg[i];
 53             if(e.flow>0&&dis[e.v]==0)
 54             {
 55                 dis[e.v]=dis[now]+1;
 56                 q.push(e.v);
 57             }
 58         }
 59     }
 60  
 61     if(dis[T]==0)return 0;
 62     return 1;
 63 }
 64  
 65 int current[N];//就是记录了当前搜索到了这个点的哪一条边
 66 long long dfs(int x,long long maxflow)
 67 {
 68     if(x==T)return maxflow;
 69     for(int i=current[x]; i!=-1; i=edg[i].next)
 70     {
 71         current[x]=i;//然后接下来直接从这个边搜索就行了
 72  
 73         ss &e=edg[i];
 74         if(e.flow>0&&dis[e.v]==dis[x]+1)  //流量大于0，且在下一层
 75         {
 76             long long flow=dfs(e.v,min(maxflow,e.flow)); //在最大流和当前流取较小值
 77  
 78             if(flow!=0)
 79             {
 80                 e.flow-=flow;
 81                 edg[i^1].flow+=flow;
 82                 return flow;
 83             }
 84         }
 85     }
 86     return 0;
 87 }
 88  
 89 long long dinic()
 90 {
 91     long long ans=0,flow;
 92  
 93     while(bfs())
 94     {
 95         for(int i=0; i<N; i++)current[i]=head[i];
 96         while(flow=dfs(S,INF))ans+=flow;
 97     }
 98     return ans;
 99 }
100  //以上都是板子,用于求最大流
101 //二分图匹配问题，二分图的每条边权值都是1，二分图最大匹配就是最大流
102 int main()
103 {
104     int m,n,k;
105     long long  res=0;
106     scanf("%d%d%d",&m,&n,&k);
107     init();
108     S=n+m+1,T=S+1;
109     for(int i=0; i<k; i++)
110     {
111         int u,v;
112         scanf("%d %d",&u,&v);
113         addedge(u,v+m,1); //把u，v都变成不重复的数值
114     }
115     for(int i=1; i<=m; i++)
116     {
117         addedge(S,i,1); //把起点与二分图的一半连起来
118     }
119     for(int i=1; i<=n; i++)
120     {
121         addedge(i+m,T,1); //与终点连起来
122     }
123     long long nowmax=dinic(); //跑一边最大流
124     long long cancan=0;
125  
126     for(int i=0; i<now_edge; i++)  //将图存起来
127     {
128         lsedg[i].flow=edg[i].flow;
129         lsedg[i].next=edg[i].next;
130         lsedg[i].v=edg[i].v;
131     }
132     for(int i=0;i<=n+m+2;i++)lshead[i]=head[i]; 
133     lssum_edge=now_edge;
134  
135     for(int i=1; i<=m; i++) //然后手动把图复制，枚举起点到二分图的点，且权值为2
136     {
137         now_edge=lssum_edge;
138         for(int i=0; i<now_edge; i++)
139         {
140             edg[i].flow=lsedg[i].flow;
141             edg[i].next=lsedg[i].next;
142             edg[i].v=lsedg[i].v;
143         }
144         for(int i=0;i<=n+m+2;i++)head[i]=lshead[i];
145  
146         addedge(S,i,2);
147         long long dangqiancancan=dinic();
148  
149         cancan=max(cancan,dangqiancancan);//维护一个最大值
150     }
151     printf("%lld\n",cancan+nowmax);
152  
153     return 0;
154 }