NOI2015 小园丁与老司机

#include<cstdio>
#include<cstdlib>
#include<iostream>
#include<fstream>
#include<algorithm>
#include<cstring>
#include<string>
#include<cmath>
#include<queue>
#include<stack>
#include<map>
#include<utility>
#include<set>
#include<bitset>
#include<vector>
#include<functional>
#include<deque>
#include<cctype>
#include<climits>
#include<complex>
//#include<bits/stdc++.h>适用于CF,UOJ，但不适用于poj
 
using namespace std;

typedef long long LL;
typedef double DB;
typedef pair<int,int> PII;
typedef complex<DB> CP;

#define mmst(a,v) memset(a,v,sizeof(a))
#define mmcy(a,b) memcpy(a,b,sizeof(a))
#define re(i,a,b)  for(i=a;i<=b;i++)
#define red(i,a,b) for(i=a;i>=b;i--)
#define fi first
#define se second
#define m_p(a,b) make_pair(a,b)
#define SF scanf
#define PF printf
#define two(k) (1<<(k))

template<class T>inline T sqr(T x){return x*x;}
template<class T>inline void upmin(T &t,T tmp){if(t>tmp)t=tmp;}
template<class T>inline void upmax(T &t,T tmp){if(t<tmp)t=tmp;}

const DB EPS=1e-9;
inline int sgn(DB x){if(abs(x)<EPS)return 0;return(x>0)?1:-1;}
const DB Pi=acos(-1.0);

inline void clear(vector<int> *A,int a,int b){int i,j;A->clear();re(i,0,a)re(j,0,b)A[i].push_back(0);}

inline int gint()
  {
        int res=0;bool neg=0;char z;
        for(z=getchar();z!=EOF && z!=‘-‘ && !isdigit(z);z=getchar());
        if(z==EOF)return 0;
        if(z==‘-‘){neg=1;z=getchar();}
        for(;z!=EOF && isdigit(z);res=res*10+z-‘0‘,z=getchar());
        return (neg)?-res:res; 
    }
inline LL gll()
  {
      LL res=0;bool neg=0;char z;
        for(z=getchar();z!=EOF && z!=‘-‘ && !isdigit(z);z=getchar());
        if(z==EOF)return 0;
        if(z==‘-‘){neg=1;z=getchar();}
        for(;z!=EOF && isdigit(z);res=res*10+z-‘0‘,z=getchar());
        return (neg)?-res:res; 
    }

const int maxN=50000;
const int INF=1<<30;

int N;
struct Tpoint{int x,y,id;}p[maxN+100];
int pos[maxN+100];
PII lr[maxN+100];

inline bool cmp1(Tpoint a,Tpoint b){return (a.y!=b.y)?a.y>b.y:a.x<b.x;}
inline bool cmp2(Tpoint a,Tpoint b){return (a.x!=b.x)?a.x<b.x:a.y>b.y;}
inline bool cmp3(Tpoint a,Tpoint b){return (a.y-a.x!=b.y-b.x)?a.y-a.x<b.y-b.x:a.x>b.x;}
inline bool cmp4(Tpoint a,Tpoint b){return (a.y+a.x!=b.y+b.x)?a.y+a.x<b.y+b.x:a.x<b.x;}

int now,first[maxN+100];
struct Tedge{int v,next;}edge[3*maxN+100];

inline void addedge(int u,int v)
  {
      now++;
      edge[now].v=v;
      edge[now].next=first[u];
      first[u]=now;
  }

int G[maxN+100],F[maxN+100];
int toG[maxN+100],toF[maxN+100];
int isonlyG[maxN+100],isonlyF[maxN+100];

inline int walk(int head,int tail,int st,int en)
  {
      if(st==en) return 0;
      if(st<en) return en-head; 
      if(st>en) return tail-en;
  }

inline void outputpoint(int x){if(x!=1)PF("%d ",x-1);}
inline void outputwalk(int head,int tail,int st,int en)
  {
      int x;
      if(st==en)
          {
              outputpoint(p[st].id);
              return;
            }
        if(st<en)
          {
              for(x=st;x!=head;x--)outputpoint(p[x].id);
                outputpoint(p[x].id);
                for(x=st+1;x!=en;x++)outputpoint(p[x].id);
                outputpoint(p[x].id);
                return;
            }
        if(st>en)
          {
              for(x=st;x!=tail;x++)outputpoint(p[x].id);
                outputpoint(p[x].id);
              for(x=st-1;x!=en;x--)outputpoint(p[x].id);
                outputpoint(p[x].id);
                return;
            }
  }
inline void outputway()
  {
      int u=1,v;
      while(u!=-1)
        {
            v=toF[u];
            outputwalk(lr[pos[u]].fi,lr[pos[u]].se,pos[u],pos[v]);
            u=toG[v];
        }
      PF("\n");
  }

int flagF[maxN+100],flagG[maxN+100];
vector<int> V[maxN+100];

int S,T,superS,superT;
int intot[maxN+100],outtot[maxN+100];
int tol,info[maxN+100];
struct Tedge2{int v,flow,next;}E[10000000];

inline void addedge2(int u,int v,int flow)
  {
      tol++;
        E[tol].v=v;
        E[tol].flow=flow;
        E[tol].next=info[u];
        info[u]=tol;
  }

inline void Flow_build()
  {
      int i,j;
      S=N+1;T=N+2;superS=N+3;superT=N+4;
      mmst(info,-1);tol=-1;
      re(i,1,N)re(j,0,int(V[i].size())-1)outtot[i]++,intot[V[i][j]]++;
      re(i,1,N+2)
        {
            addedge2(superS,i,intot[i]);addedge2(i,superS,0);
            addedge2(i,superT,outtot[i]);addedge2(superT,i,0);
        }
      re(i,1,N)
        addedge2(S,i,INF),addedge2(i,S,0);
      re(i,1,N)
        addedge2(i,T,INF),addedge2(T,i,0);
      re(i,1,N)re(j,0,int(V[i].size())-1)
        addedge2(i,V[i][j],INF),addedge2(V[i][j],i,0);
  }

int level[maxN+100],last[maxN+100];
int head,tail,que[maxN+100];
inline int Dinic_Build()
  {
      int i;
      mmst(level,0);
      level[que[head=tail=1]=superS]=1;
      while(head<=tail)
        {
            int u=que[head++],v,flow;
            for(i=info[u],v=E[i].v,flow=E[i].flow;i!=-1;i=E[i].next,v=E[i].v,flow=E[i].flow)
              if(!level[v] && flow>0)level[que[++tail]=v]=level[u]+1;
        }
      return level[superT];
  }
inline int Dinic(int u,int delta)
  {
      if(u==superT) return delta;
      int res=0,&i=last[u],v,flow;
      for(v=E[i].v,flow=E[i].flow;i!=-1;i=E[i].next,v=E[i].v,flow=E[i].flow)
        if(level[u]+1==level[v] && flow>0)
          {
              int tmp=Dinic(v,min(delta,flow));
              delta-=tmp;
              res+=tmp;
              E[i].flow-=tmp;
              E[i^1].flow+=tmp;
              if(delta==0) return res;
          }
      return res;
  }

inline int check()
  {
      int u=1;
      while(u!=-1)
        {
            if(!isonlyF[u])return 0;
            u=toF[u];
            if(!isonlyG[u])return 0;
            u=toG[u];
        }
      int cnt=0,f=0;
      u=1;
      while(u!=-1)
        {
            if(toF[u]!=u) f=0;
            u=toF[u];
            if(toG[u]==-1)break;
            if(!f){cnt++;f=1;}
            u=toG[u];
        }
      PF("%d\n",cnt);
      return 1;
  }

int main()
  {
      freopen("farm.in","r",stdin);
      freopen("farm.out","w",stdout);
      int i,j,k;
      N=gint()+1;
      p[1].x=0,p[1].y=0,p[1].id=1;
      re(i,2,N)p[i].x=gint(),p[i].y=gint(),p[i].id=i;
      
      mmst(first,-1);now=-1;
      sort(p+1,p+N+1,cmp2);
      re(i,2,N)if(p[i].x==p[i-1].x)addedge(p[i].id,p[i-1].id);
      sort(p+1,p+N+1,cmp3);
      re(i,2,N)
          if(p[i].y-p[i].x==p[i-1].y-p[i-1].x)
              addedge(p[i].id,p[i-1].id);
      sort(p+1,p+N+1,cmp4);
      re(i,2,N)if(p[i].y+p[i].x==p[i-1].y+p[i-1].x)addedge(p[i].id,p[i-1].id);
      
      sort(p+1,p+N+1,cmp1);
      re(i,1,N)pos[p[i].id]=i;
      int head,tail;
      for(head=1;head<=N;head=tail+1)
        {
            for(tail=head;tail+1<=N && p[tail+1].y==p[head].y;tail++);
            re(j,head,tail)lr[j]=PII(head,tail);
            re(j,head,tail)
              {
                  int u=p[j].id,v;
                  G[u]=1;toG[u]=-1;isonlyG[u]=1;
                  for(i=first[u],v=edge[i].v;i!=-1;i=edge[i].next,v=edge[i].v)
                          if(F[v]+1>G[u])
                              G[u]=F[v]+1,toG[u]=v,isonlyG[u]=1;
                            else
                              if(F[v]+1==G[u]) isonlyG[u]=0;
                        F[u]=G[u],toF[u]=u,isonlyF[u]=1;
              }
            /*re(j,head,tail)
              {
                  int u=p[j].id;
                  F[u]=G[u];toF[u]=u;
                  re(k,head,tail)
                    {
                        int v=p[k].id,dis=walk(head,tail,j,k);
                                if(G[v]+dis>F[u])F[u]=G[v]+dis,toF[u]=v;
                            }
                    }*/
                int t=0,tot=0,isonly=1;
                re(j,head+1,tail)
                  {
                      int u=p[j].id,v=p[j-1].id;
                      if(G[v]+tail-(j-1)>t)
                        t=G[v]+tail-(j-1),tot=v,isonly=1;
                      else
                        if(G[v]+tail-(j-1)==t) isonly=0;
                      if(t>F[u])
                          F[u]=t,toF[u]=tot,isonlyF[u]=isonly;
                      else
                        if(t==F[u])
                          if(isonly==0)
                                  isonlyF[u]=0;
                  }
                t=0,tot=0,isonly=1;
                red(j,tail-1,head)
                  {
                      int u=p[j].id,v=p[j+1].id;
                      if(G[v]+j+1-head>t)
                        t=G[v]+j+1-head,tot=v,isonly=1;
                      else
                        if(G[v]+j+1-head==t) isonly=0;
                      if(t>F[u])
                        F[u]=t,toF[u]=tot,isonlyF[u]=isonly;
                      else
                        if(t==F[u])
                          if(isonly==0)
                            isonlyF[u]=0;
                  }
            }
            
        cout<<F[1]-1<<endl;
        outputway();
        
        if(check())return 0;
        
        mmst(flagG,0);mmst(flagF,0);
        flagF[1]=1;
        for(tail=N;tail>=1;tail=head-1)
          {
              for(head=tail;head-1>=1 && p[head-1].y==p[tail].y;head--);
              re(j,head,tail)if(flagF[p[j].id])
                {
                    int u=p[j].id;
                    re(k,head,tail)
                      {
                          int v=p[k].id,dis=walk(head,tail,j,k);
                          if(G[v]+dis==F[u])flagG[v]=1;
                      }
                }
              re(j,head,tail)if(flagG[p[j].id])
                {
                    int u=p[j].id,v;
                    for(i=first[u],v=edge[i].v;i!=-1;i=edge[i].next,v=edge[i].v)
                          if(F[v]+1==G[u])
                              V[u].push_back(v),flagF[v]=1;
                }
            }
        
        Flow_build();
        int fullflow=0,maxflow=0,v,flow;
        for(i=info[superS],v=E[i].v,flow=E[i].flow;i!=-1;i=E[i].next,v=E[i].v,flow=E[i].flow)fullflow+=flow;
        while(Dinic_Build())
          {
              re(i,1,N+4)last[i]=info[i];
              maxflow+=Dinic(superS,INF);
            }
        cout<<fullflow-maxflow<<endl;
        return 0;
    }