【模板】三维偏序

CDQ分治

首先按a排序，分成两段后再分别对两段按b排序，这样就保证了w[x2].a>=w[x1].a,消去一维

按b排序后找到w[x2].b>=w[x1].b的同时满足w[x2].c>=w[x1].c的值

按b排序后有单调性，所以b可以在O(n)时间，对于c，每找到一个w[x1]满足b的条件，则在树状数组中+1

w[x2].ans+=query(w[x2].c)

#include<iostream>
#include<cstdio>
#include<cstring>
#include<algorithm>
using namespace std;
struct Node
{
    int a,b,c,cnt,ans;
}w[100001];
int m,n,c[2000001],ans,f[100001];
bool cmp2(Node a,Node b)
{
    if (a.b==b.b)
     return a.c<b.c;
     else return a.b<b.b;
}
bool cmp1(Node a,Node b)
{
    if (a.a==b.a)
     return cmp2(a,b);
     else return a.a<b.a;
}
void add(int x,int d)
{
    while (x<=m)
    {
     c[x]+=d;
     x+=(x&(-x));
    }
}
int query(int x)
{int s=0;
    while (x)
    {
     s+=c[x];
     x-=(x&(-x));
    }
  return s;
}
void cdq(int l,int r)
{int r1,r2;
    int mid=(l+r)/2;
    if (l==r)
    return;
     cdq(l,mid);cdq(mid+1,r);
     sort(w+l,w+mid+1,cmp2);
     sort(w+mid+1,w+r+1,cmp2);
     r1=l;r2=mid+1;
     while (r2<=r)
     {
        while (r1<=mid&&w[r1].b<=w[r2].b)
         add(w[r1].c,w[r1].cnt),r1++;
         w[r2].ans+=query(w[r2].c);
        r2++;
     }
    for (int i=l;i<=r1-1;i++)
    add(w[i].c,-w[i].cnt);
}
int main()
{int i,j,num=0;
    cin>>n>>m;
    for (i=1;i<=n;i++)
    {
      scanf("%d%d%d",&w[i].a,&w[i].b,&w[i].c);
      w[i].cnt=1;
    }
    sort(w+1,w+n+1,cmp1);
    for (i=1;i<=n;i++)
    {
        int k=i+1;
        while (w[i].a==w[k].a&&w[i].b==w[k].b&&w[i].c==w[k].c)
         k++;
         num++;
         k--;
         w[i].cnt+=k-i;
         w[num]=w[i];
         i=k;
    }
    cdq(1,num);
    for (i=1;i<=num;i++)
    f[w[i].ans+w[i].cnt-1]+=w[i].cnt;
    for (i=0;i<n;i++)
    printf("%d
",f[i]);
}