最大密度子图

BZOJ1312

转换为最大权闭合子图

#include <cstdio>
#include <cstring>
#define LDB long double
using namespace std;

  const LDB eps=1e-6;

  int cnt,nd[4001],dep[4001],sor,dl[4001],sta[1000001],tar,cur[4001],n,m,x[4001],y[4001],b[4001],ans;

  struct edge{
      int next,des,fr;
      LDB cap;
  }sid[1000001];

  void addedge(int u,int v,LDB cap){
      sid[cnt].next=nd[u];sid[cnt].des=v;sid[cnt].cap=cap;nd[u]=cnt;sid[cnt].fr=u;cnt++;
      sid[cnt].next=nd[v];sid[cnt].des=u;sid[cnt].cap=0;nd[v]=cnt;sid[cnt].fr=v;cnt++;
  }
   
   int bfs(){
      memset(dep,-1,sizeof(dep));
      
      int head=1,tail=1;
      dep[sor]=0;dl[head]=sor;
      while (head<=tail){
        for (int p=nd[dl[head]];p!=-1;p=sid[p].next)
          if ((dep[sid[p].des]==-1)&&(sid[p].cap>eps)) dep[sid[p].des]=dep[dl[head]]+1,dl[++tail]=sid[p].des;
        head++;  
    }
    
    if (dep[tar]==-1) return(0);else return(1);
  }
  
  LDB dinic(){
      LDB maxflow=0;
      while (bfs()){
          for (int i=0;i<=tar;i++) cur[i]=nd[i];
          
          int u=sor,top=0;
          while(1){
              if (u==tar){
                  LDB mi=1e9;int last;
                  for (int i=1;i<=top;i++)
                    if (sid[sta[i]].cap<mi)
                    {mi=sid[sta[i]].cap;last=i;}
                    
                  for (int i=1;i<=top;i++) 
                  sid[sta[i]].cap-=mi,sid[sta[i]^1].cap+=mi;
                u=sid[sta[last]].fr;cur[u]=sid[cur[u]].next;top=last-1;
                maxflow+=mi;
                continue;
            }
            
            while((cur[u]!=-1)&&((sid[cur[u]].cap<eps)||(dep[sid[cur[u]].des]!=dep[u]+1)))
              cur[u]=sid[cur[u]].next;
              
            if (cur[u]!=-1){sta[++top]=cur[u];u=sid[cur[u]].des;continue;}
            else{
                if (u==sor) break;
                dep[u]=-1;
                u=sid[sta[top--]].fr;
                continue;
            }       
          }
      }
      return(maxflow);
  }
  
  void build(LDB mid){
      sor=0,tar=n+m+1;
      for (int i=sor;i<=tar;i++) nd[i]=-1;
      for (int i=1;i<=m;i++) addedge(0,i,1),addedge(i,m+x[i],1e9),addedge(i,m+y[i],1e9);
      for (int i=1;i<=n;i++) addedge(m+i,tar,mid);
  }
  
  void dfs(int po){
      b[po]=1;
      if (po>m&&po<n+m+1) ans++;
      for (int p=nd[po];p!=-1;p=sid[p].next)
        if (!b[sid[p].des]&&sid[p].cap>eps)
          dfs(sid[p].des);
  }

  int main(){
      scanf("%d%d",&n,&m);
      if (m==0){
        printf("1\n");return(0);
    }
      for (int i=1;i<=m;i++) scanf("%d%d",&x[i],&y[i]);
      
      LDB l=0,r=m;
      while (r-l>1.0/n/n){
        LDB mid=(l+r)/2;
      build(mid);
      LDB ans=m-dinic();
      if (ans<eps) r=mid;else l=mid;    
    }
    
    build(l);
    dinic();
    dfs(0);
    
    printf("%d\n",ans);
  }