COGS2479 HZOI2016—偏序

Posted 2020-09-03 MashiroSky

http://cogs.pro/cogs/problem/problem.php?pid=2479 (题目链接)

题意

　　四维偏序。

Solution

　　CDQ套CDQ。

细节

　　第二次分治不能直接按照mid分离两类数了。

代码

// cogs2479
#include<algorithm>
#include<iostream>
#include<cstdlib>
#include<cstring>
#include<cstdio>
#include<cmath>
#define LL long long
#define inf 2147483600
#define Pi acos(-1.0)
#define free(a) freopen(a".in","r",stdin),freopen(a".out","w",stdout)
using namespace std;

const int maxn=50010;
int n,ans,f[maxn],c[maxn];
struct data {int x,y,z,id,op;}q[maxn],nq[maxn],p[maxn],np[maxn];

bool cmp(data a,data b) {return a.id<b.id;}
bool CMP(data a,data b) {return a.y<b.y;}
int lowbit(int x) {
	return x&-x;
}
void modify(int x,int val) {
	for (int i=x;i<=n;i+=lowbit(i)) c[i]+=val;
}
int query(int x) {
	int res=0;
	for (int i=x;i;i-=lowbit(i)) res+=c[i];
	return res;
}
void solve2(int l,int r) {
	if (l==r) return;
	int mid=(l+r)>>1;
	sort(p+l,p+r+1,CMP);
	solve2(l,mid);solve2(mid+1,r);
	for (int i=l,j=mid+1,k=l;i<=mid || j<=r;) {
		if (j>r || (i<=mid && p[i].id<p[j].id)) {
			if (p[i].op==0) modify(p[i].z,1);
			np[k++]=p[i++];
		}
		else {
			if (p[j].op==1) f[p[j].id]+=query(p[j].z-1);
			np[k++]=p[j++];
		}
	}
	for (int i=l;i<=mid;i++) if (p[i].op==0) modify(p[i].z,-1);
	for (int i=l;i<=r;i++) p[i]=np[i];
}
void solve(int l,int r) {
	if (l==r) {ans+=f[q[l].id];return;}
	int mid=(l+r)>>1,l1=l,l2=mid+1;
	for (int i=l;i<=r;i++) q[i].x<=mid ? nq[l1++]=q[i] : nq[l2++]=q[i];
	for (int i=l;i<=r;i++) q[i]=nq[i];
	solve(l,mid);
	for (int i=l;i<=r;i++) p[i]=q[i],p[i].op=i>mid;
	sort(p+l,p+r+1,cmp);
	solve2(l,r);
	solve(mid+1,r);
}
int main() {
	free("partial_order");
	scanf("%d",&n);
	for (int i=1;i<=n;i++) scanf("%d",&q[i].x);
	for (int i=1;i<=n;i++) scanf("%d",&q[i].y);
	for (int i=1;i<=n;i++) scanf("%d",&q[i].z);
	for (int i=1;i<=n;i++) q[i].id=i;
	solve(1,n);
	printf("%d",ans);
	fclose(stdin);fclose(stdout);
	return 0;
}