离线和简单分治

CDQ分治

【模板】三维偏序 —— bzoj3262

#include<bits/stdc++.h>
using namespace std;
const int N=1e5+5,M=2e5+5;
int n,k,cnt,c[M],ans[N];
struct node {int x,y,z,w,k;}a[N],b[N];
inline int read() {
    int x=0; char c=getchar();
    while(c<'0'||c>'9') c=getchar();
    while(c>='0'&&c<='9') x=(x<<3)+(x<<1)+c-'0',c=getchar();
    return x;
}

int lowbit(int x) {return x&(-x);}
void update(int i,int x) {
    for(;i<=k;i+=lowbit(i)) c[i]+=x; 
}
int query(int i) {
    int h=0;
    for(;i;i-=lowbit(i)) h+=c[i];
    return h;
}

bool cmp1(node x1,node x2) {
    if(x1.x==x2.x) {
        if(x1.y==x2.y) return x1.z<x2.z;
        return x1.y<x2.y;
    } return x1.x<x2.x;
}
bool cmp2(node x1,node x2) {return x1.y<x2.y;}

void CDQ(int l,int r) {
    if(l==r) return ;
    int Mid=(l+r)>>1;
    CDQ(l,Mid); CDQ(Mid+1,r);
    sort(a+l,a+Mid+1,cmp2); sort(a+Mid+1,a+r+1,cmp2);
    int j=l;
    for(int i=Mid+1;i<=r;i++) {
        while(j<=Mid&&a[j].y<=a[i].y)
         update(a[j].z,a[j].w),j++;
        a[i].k+=query(a[i].z);
    }
    for(int i=l;i<j;i++) update(a[i].z,-a[i].w);
}

int main() {
    n=read(),k=read();
    for(int i=1;i<=n;i++)
     b[i].x=read(),b[i].y=read(),b[i].z=read();
    sort(b+1,b+n+1,cmp1); int t=0;
    for(int i=1;i<=n;i++) {
        t++;
        if(b[i].x^b[i+1].x||b[i].y^b[i+1].y||b[i].z^b[i+1].z)
         a[++cnt]=b[i],a[cnt].w=t,t=0;
    }
    CDQ(1,cnt);
    for(int i=1;i<=cnt;i++)
     ans[a[i].k+a[i].w]+=a[i].w;
    for(int i=1;i<=n;i++) printf("%d
",ans[i]);
    return 0;
}