hdu5126stars

http://acm.hdu.edu.cn/showproblem.php?pid=5126

首先，对于一个询问，用容斥原理可以拆成8个询问，于是询问变成：给定一个四元组$(i,x_i,y_i,z_i)$，问满足$j<i$，$x_j\leq x_i$，$y_j \leq y_i$，$z_j \leq z_i$的四元组$(j,x_j,y_j,z_j)$有多少个。

四维偏序。。。。。。。。。。。

用CDQ分治套CDQ分治，把四维偏序降为三维偏序。

CDQ大法好。

//http://acm.hdu.edu.cn/showproblem.php?pid=5126
#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 fill(a,l,r,v) fill(a+l,a+r+1,v)
#define re(i,a,b)  for(i=(a);i<=(b);i++)
#define red(i,a,b) for(i=(a);i>=(b);i--)
#define ire(i,x) for(typedef(x.begin()) i=x.begin();i!=x.end();i++)
#define fi first
#define se second
#define m_p(a,b) make_pair(a,b)
#define p_b(a) push_back(a)
#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;}

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

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; 
    }
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;

int q,n;
struct Tstar
  {
      int p,x,y,z,s;
      Tstar(int p=0,int x=0,int y=0,int z=0,int s=0):p(p),x(x),y(y),z(z),s(s){}
  };
int res[8*maxn+100];

bool cmpz(Tstar a,Tstar b){return a.z<b.z;}
bool cmpp(Tstar a,Tstar b){return a.p<b.p;}

int nz,tree[8*maxn+100];
#define lowbit(a) ((a)&(-a))
void update(int a,int v){for(;a<=nz;a+=lowbit(a))tree[a]+=v;}
int ask(int a){int res=0;for(;a>=1;a-=lowbit(a))res+=tree[a];return res;}

Tstar tmp[8*maxn+100];

Tstar star2[8*maxn+100];
void CDQ2(int l,int r)
  {
      if(l==r)return;
        int i,mid=(l+r)/2;
        CDQ2(l,mid);
        CDQ2(mid+1,r);
        int l1=l,l2=mid+1;
        while(1)
          {
              while(l2<=r && star2[l2].s==0)l2++;
              if(l2>r)break;
              while(l1<=mid && star2[l1].y<=star2[l2].y)
                {
                    if(star2[l1].s==0)update(star2[l1].z,1);
                    l1++;
                }
              res[star2[l2].p]+=ask(star2[l2].z);
              l2++;
          }
        re(i,l,l1-1)if(star2[i].s==0)update(star2[i].z,-1);
        l1=l,l2=mid+1;
        re(i,l,r)
          {
              if(l1>mid){tmp[i]=star2[l2++];continue;}
              if(l2>r){tmp[i]=star2[l1++];continue;}
              if(star2[l1].y<=star2[l2].y)tmp[i]=star2[l1++];else tmp[i]=star2[l2++];
          }
        re(i,l,r)star2[i]=tmp[i];
  }

Tstar star[8*maxn+100];
void CDQ1(int l,int r)
  {
      if(l==r)return;
      int i,mid=(l+r)/2;
      CDQ1(l,mid);
      CDQ1(mid+1,r);
      int l1=l,l2=mid+1,n=0;
      while(1)
        {
            while(l1<=mid && star[l1].s!=0)l1++;
            while(l2<=r && star[l2].s==0)l2++;
            if(l1>mid && l2>r)break;
            if(l1>mid){star2[++n]=star[l2++];continue;}
            if(l2>r){star2[++n]=star[l1++];continue;}
            if(star[l1].x<=star[l2].x)star2[++n]=star[l1++];else star2[++n]=star[l2++];
        }
        if(n>0)CDQ2(1,n);
        l1=l,l2=mid+1;
        re(i,l,r)
          {
              if(l1>mid){tmp[i]=star[l2++];continue;}
              if(l2>r){tmp[i]=star[l1++];continue;}
              if(star[l1].x<=star[l2].x)tmp[i]=star[l1++];else tmp[i]=star[l2++];
          }
        re(i,l,r)star[i]=tmp[i];
  }

int main()
  {
      freopen("hdu5126.in","r",stdin);
      freopen("hdu5126.out","w",stdout);
      for(int Case=gint();Case;Case--)
        {
            int i,j;
            q=gint();n=0;
            re(i,1,q)
              {
                  int A=gint();
                  if(A==1)
                    {
                        int x=gint(),y=gint(),z=gint();
                        star[++n]=Tstar(n,x,y,z,0);
                    }
                  else
                    {
                        int x1=gint(),y1=gint(),z1=gint(),x2=gint(),y2=gint(),z2=gint();
                        star[++n]=Tstar(n,x2  ,y2  ,z2  ,1 );
                        star[++n]=Tstar(n,x2  ,y2  ,z1-1,-1);
                        star[++n]=Tstar(n,x2  ,y1-1,z2  ,-1);
                        star[++n]=Tstar(n,x2  ,y1-1,z1-1,1 );
                        star[++n]=Tstar(n,x1-1,y2  ,z2  ,-1);
                        star[++n]=Tstar(n,x1-1,y2  ,z1-1,1 );
                        star[++n]=Tstar(n,x1-1,y1-1,z2  ,1 );
                        star[++n]=Tstar(n,x1-1,y1-1,z1-1,-1);
                    }
              }
            sort(star+1,star+n+1,cmpz);
            nz=0;
            int tmpz=-100;
            re(i,1,n)if(star[i].z==tmpz)star[i].z=nz;else tmpz=star[i].z,star[i].z=++nz;
            sort(star+1,star+n+1,cmpp);
                re(i,1,n)res[i]=0;
            CDQ1(1,n);
            sort(star+1,star+n+1,cmpp);
            re(i,1,n)
              if(star[i].s!=0)
                {
                    int ans=0;
                    re(j,0,7)ans+=star[i+j].s*res[i+j];
                    PF("%d\n",ans);
                    i+=7;
                }
        }
      return 0;
  }