A Story of One Country (Hard) CodeForces - 1181E2 (分治)

#include <iostream>
#include <sstream>
#include <algorithm>
#include <cstdio>
#include <cmath>
#include <set>
#include <map>
#include <queue>
#include <string>
#include <cstring>
#include <bitset>
#include <functional>
#include <random>
#define REP(i,a,n) for(int i=a;i<=n;++i)
#define PER(i,a,n) for(int i=n;i>=a;--i)
#define hr putchar(10)
#define pb push_back
#define lc (o<<1)
#define rc (lc|1)
#define mid ((l+r)>>1)
#define ls lc,l,mid
#define rs rc,mid+1,r
#define x first
#define y second
#define io std::ios::sync_with_stdio(false)
#define endl ‘\n‘
#define DB(a) ({REP(__i,1,n) cout<<a[__i]<<‘ ‘;hr;})
using namespace std;
typedef long long ll;
typedef pair<int,int> pii;
const int P = 1e9+7, INF = 0x3f3f3f3f;
ll gcd(ll a,ll b) {return b?gcd(b,a%b):a;}
ll qpow(ll a,ll n) {ll r=1%P;for (a%=P;n;a=a*a%P,n>>=1)if(n&1)r=r*a%P;return r;}
ll inv(ll x){return x<=1?1:inv(P%x)*(P-P/x)%P;}
inline int rd() {int x=0;char p=getchar();while(p<‘0‘||p>‘9‘)p=getchar();while(p>=‘0‘&&p<=‘9‘)x=x*10+p-‘0‘,p=getchar();return x;}
//head



const int N = 1e6+10;
struct _ {
	int l,r,id;
	bool operator < (const _ &rhs) const {
		if (l==rhs.l) return id<rhs.id;
		return l<rhs.l;
	}
} a[N][4];
set<_> s[4];

int dfs(set<_> L[4]) {
	if (L[0].size()<=1) return 1;
	set<_> R[4];
	set<_>::iterator it[4];
	int m[4];
	REP(i,0,3) {
		it[i] = L[i].begin();
		m[i] = it[i]++->r;
	}
	int sz = L[0].size();
	REP(i,1,sz-1) REP(j,0,3) {
		if (it[j]->l>=m[j]) {
			for (auto t=L[j].begin(); t!=it[j]; ) {
				int id = t++->id;
				REP(k,0,3) R[k].insert(a[id][k]),L[k].erase(a[id][k]);
			}
			return dfs(L)&&dfs(R);
		}
		m[j] = max(m[j], it[j]++->r);
	}
	return 0;
}

int main() {
	int n=rd();
	REP(i,1,n) {
		int x1=rd(),y1=rd(),x2=rd(),y2=rd();
		a[i][0] = {x1,x2,i};
		a[i][1] = {-x2,-x1,i};
		a[i][2] = {y1,y2,i};
		a[i][3] = {-y2,-y1,i};
		REP(j,0,3) s[j].insert(a[i][j]);
	}
	cout<<(dfs(s)?"YES":"NO")<<endl;
}