Codeforces Round #567 (Div. 2) E2 A Story of One Country (Hard)

https://codeforces.com/contest/1181/problem/E2

想到了划分的方法跟题解一样，但是没理清楚复杂度，很难受。

看了题解觉得很有道理，还是自己太菜了。

然后直接开始写，四个if写的太难受了180+行。

ac之后看了红名大佬的代码，简直woc，好短，四个sort我分开写了，但是红名大佬写的很巧妙，借鉴了一下代码长度缩短到110行左右，红名大佬np，特此记录。

使用静态链表，复杂度计算 T(n) = T(a1)+T(a2)+T(a3) ... + O(nlogn)   ( ai<=n/2)

傻逼版

#include<bits/stdc++.h>
#include<ext/rope>
#include<ext/pb_ds/assoc_container.hpp>
#include<ext/pb_ds/tree_policy.hpp>
#define mst(a,b) memset(a,b,sizeof(a))
#define lowbit(x) (x&(-x))
#define lson        (rt<<1)
#define rson        (rt<<1|1)
using namespace __gnu_pbds;
using namespace __gnu_cxx;
using namespace std;
typedef long long ll;
typedef unsigned long long ull;
typedef pair<ll,ll> pll;
typedef pair<ull,ull> pull;
typedef pair<int,int> pii;
const int mod = 1e9+;
ll qpow(ll a,ll b){ll res=;for(;b;b>>=,a=a*a%mod)if(b&)res=res*a%mod;return res; }
const int inf = 0x3f3f3f3f;
const ll INF = 0x3f3f3f3f3f3f3f3f;
const int maxn = 2e5+;
void co(){
    cout<<"NO";exit();
}
int x1[maxn],x2[maxn],y1[maxn],y2[maxn];
bool cmp0(const int&le,const int&ri){
    return x1[le]<x1[ri];
}
bool cmp1(const int&le,const int&ri){
    return y1[le]<y1[ri];
}
bool cmp2(const int&le,const int&ri){
    return x2[le]>x2[ri];
}
bool cmp3(const int&le,const int&ri){
    return y2[le]>y2[ri];
}
int pre[][maxn],nx[][maxn];
void store(int *f){
    for(int i=;i<;++i)
        f[i]=nx[i][];
}
void read(int *f){
    for(int i=;i<;++i)
        nx[i][]=f[i];
}
void init(vector<int>&use){
    sort(use.begin(),use.end(),cmp0);
    int p=;
    for(int v:use){
        nx[][p]=v;
        pre[][v]=p;
        p=v;
    }
    nx[][p]=;
    sort(use.begin(),use.end(),cmp1);
    p=;
    for(int v:use){
        nx[][p]=v;
        pre[][v]=p;
        p=v;
    }
    nx[][p]=;
    sort(use.begin(),use.end(),cmp2);
    p=;
    for(int v:use){
        nx[][p]=v;
        pre[][v]=p;
        p=v;
    }
    nx[][p]=;
    sort(use.begin(),use.end(),cmp3);
    p=;
    for(int v:use){
        nx[][p]=v;
        pre[][v]=p;
        p=v;
    }
    nx[][p]=;
}
void del(int p){
    for(int i=;i<;++i){
        int a=pre[i][p],b=nx[i][p];
        nx[i][a]=b;pre[i][b]=a;
    }
}
void solve(vector<int>&use){
    if(use.size()<=)return;
    init(use);
//    for(int i=0;i<4;++i){
//        int p=nx[i][0];
//        while(p!=0){
//            cout<<p<<" ";
//            p=nx[i][p];
//        }
//        cout<<endl;
//    }
//    exit(0);
    int sz=use.size();
    while(sz>){
        int now[];
        store(now);
        int v[]={x2[now[]],y2[now[]],x1[now[]],y1[now[]]};
        bool ok=false;
        for(int i=;i<sz;++i){
            for(int d=;d<;++d)
                now[d]=nx[d][now[d]];
            if(x1[now[]]>=v[]){
                vector<int>son;
                for(int j=nx[][];j!=now[];j=nx[][j])
                    son.push_back(j);
                for(int v:son)
                    del(v);
                store(now);
                solve(son);
                sz-=i;
                read(now);
                ok=true;
                break;
            }else v[]=max(v[],x2[now[]]);
            if(y1[now[]]>=v[]){
                vector<int>son;
                for(int j=nx[][];j!=now[];j=nx[][j])
                    son.push_back(j);
                for(int v:son)
                    del(v);
                store(now);
                solve(son);
                sz-=i;
                read(now);
                ok=true;
                break;
            }else v[]=max(v[],y2[now[]]);
            if(x2[now[]]<=v[]){
                vector<int>son;
                for(int j=nx[][];j!=now[];j=nx[][j])
                    son.push_back(j);
                for(int v:son)
                    del(v);
                store(now);
                solve(son);
                sz-=i;
                read(now);
                ok=true;
                break;
            }else v[]=min(v[],x1[now[]]);
            if(y2[now[]]<=v[]){
                vector<int>son;
                for(int j=nx[][];j!=now[];j=nx[][j])
                    son.push_back(j);
                for(int v:son)
                    del(v);
                store(now);
                solve(son);
                sz-=i;
                read(now);
                ok=true;
                break;
            }else v[]=min(v[],y1[now[]]);
        }
        if(!ok)co();
    }
}
vector<int>a;
int main() {
#ifdef local
    freopen("in.txt","r",stdin);
//    freopen("out.txt","w",stdout);
#endif
    ios::sync_with_stdio(false);
    cin.tie();
    cout.tie();
    int n;
    cin>>n;
    for(int i=;i<=n;++i)
        cin>>x1[i]>>y1[i]>>x2[i]>>y2[i];
    for(int i=;i<=n;++i)
        a.push_back(i);
    solve(a);
    cout<<"YES";

    return ;
}

借鉴大佬代码改良版

#include<bits/stdc++.h>
#include<ext/rope>
#include<ext/pb_ds/assoc_container.hpp>
#include<ext/pb_ds/tree_policy.hpp>
#define mst(a,b) memset(a,b,sizeof(a))
#define lowbit(x) (x&(-x))
#define lson        (rt<<1)
#define rson        (rt<<1|1)
using namespace __gnu_pbds;
using namespace __gnu_cxx;
using namespace std;
typedef long long ll;
typedef unsigned long long ull;
typedef pair<ll,ll> pll;
typedef pair<ull,ull> pull;
typedef pair<int,int> pii;
const int mod = 1e9+;
ll qpow(ll a,ll b){ll res=;for(;b;b>>=,a=a*a%mod)if(b&)res=res*a%mod;return res; }
const int inf = 0x3f3f3f3f;
const ll INF = 0x3f3f3f3f3f3f3f3f;
const int maxn = 2e5+;
void co(){
    cout<<"NO";exit();
}
pii a[][maxn];
int pre[][maxn],nx[][maxn];
void store(int *f){
    for(int i=;i<;++i)
        f[i]=nx[i][];
}
void read(int *f){
    for(int i=;i<;++i)
        nx[i][]=f[i];
}
void init(vector<int>&use){
    for(int i=;i<;++i){
        sort(use.begin(),use.end(),[&](const int &le,const int&ri){
            return a[i][le]<a[i][ri];
        });
        int p=;
        for(int v:use){
            nx[i][p]=v;
            pre[i][v]=p;
            p=v;
        }
        nx[i][p]=;
    }
}
void del(int p){
    for(int i=;i<;++i){
        int a=pre[i][p],b=nx[i][p];
        nx[i][a]=b;pre[i][b]=a;
    }
}
void solve(vector<int>&use){
    if(use.size()<=)return;
    init(use);
    int sz=use.size();
    while(sz>){
        int now[],v[];
        store(now);
        for(int i=;i<;++i)
            v[i]=a[i][now[i]].second;
        bool ok=false;
        for(int i=;i<sz and !ok;++i){
            for(int d=;d< and !ok;++d){
                now[d]=nx[d][now[d]];
                if(a[d][now[d]].first>=v[d]){
                    vector<int>son;
                    for(int j=nx[d][];j!=now[d];j=nx[d][j])
                        son.push_back(j);
                    for(int v:son)
                        del(v);
                    store(now);
                    solve(son);
                    sz-=i;
                    read(now);
                    ok=true;
                }else v[d]=max(v[d],a[d][now[d]].second);
            }
        }
        if(!ok)co();
    }
}
vector<int>uu;
int main() {
#ifdef local
    freopen("in.txt","r",stdin);
//    freopen("out.txt","w",stdout);
#endif
    ios::sync_with_stdio(false);
    cin.tie();
    cout.tie();
    int n;
    cin>>n;
    for(int i=;i<=n;++i){
        int x1,y1,x2,y2;
        cin>>x1>>y1>>x2>>y2;
        a[][i]=pii(x1,x2);
        a[][i]=pii(y1,y2);
        a[][i]=pii(-x2,-x1);
        a[][i]=pii(-y2,-y1);
    }
    for(int i=;i<=n;++i)
        uu.push_back(i);
    solve(uu);
    cout<<"YES";

    return ;
}