Luogu3369普通平衡树

Posted 2021-01-28 wifimonster

#include<bits/stdc++.h>
using namespace std;
const int maxn=1e5+4;
int n,rt,pool=0;
struct node{
    int lc,rc,fa,size,key,pri,cnt;
}a[maxn];
inline void zig(int &k){
    int y=a[k].lc;
    a[k].lc=a[y].rc;
    a[y].rc=k;
    a[y].size=a[a[y].lc].size+a[a[y].rc].size+a[y].cnt;
    a[k].size=a[a[k].lc].size+a[a[k].rc].size+a[k].cnt;
    k=y;
}
inline void zag(int &k){
    int y=a[k].rc;
    a[k].rc=a[y].lc;
    a[y].lc=k;
    a[y].size=a[a[y].lc].size+a[a[y].rc].size+a[y].cnt;
    a[k].size=a[a[k].lc].size+a[a[k].rc].size+a[k].cnt;
    k=y;
}
inline void insert(int &k,int key){
    if(!k){
        k=++pool;
        a[k].key=key;a[k].pri=rand();
        a[k].cnt=a[k].size=1;
        a[k].lc=a[k].rc=0;
        return;
    }
    if(a[k].key==key) ++a[k].cnt;
    else if(key<a[k].key){
        insert(a[k].lc,key);
        if(a[a[k].lc].pri<a[k].pri) zig(k);
    }else{
        insert(a[k].rc,key);
        if(a[a[k].rc].pri<a[k].pri) zag(k);
    }
    a[k].size=a[a[k].lc].size+a[a[k].rc].size+a[k].cnt;
    return;
}
inline void delete1(int &k,const int &key){
    if(!k) return;
    if(a[k].key==key){
        if(a[k].cnt>1) a[k].cnt--;
        else if (!a[k].lc||!a[k].rc) k=a[k].lc+a[k].rc;
        else if(a[a[k].lc].pri<a[a[k].rc].pri) zig(k),delete1(k,key);
        else zag(k),delete1(k,key);
    }
    else if(key<a[k].key) delete1(a[k].lc,key);
    else delete1(a[k].rc,key);
    a[k].size=a[a[k].lc].size+a[a[k].rc].size+a[k].cnt;
    return;
}
inline int queryRank(const int &key){
    int x=rt,res=0,lc,rc;
    while(x){
        lc=a[x].lc,rc=a[x].rc;
        if(a[x].key==key) return res+a[lc].size+1;
        if(key<a[x].key) x=lc;
        else res+=a[lc].size+a[x].cnt,x=rc;
    }
    return res;
}
inline int queryKey(int k){
    int x=rt,lc,rc;
    while(x){
        lc=a[x].lc,rc=a[x].rc;
        if(a[lc].size<k&&a[lc].size+a[x].cnt>=k) return a[x].key;
        else if(a[lc].size>=k) x=lc;
        else k-=a[lc].size+a[x].cnt,x=rc;
    }
    return 0;
}
inline int queryQian(int key){
    int x=rt,res=-0x3f3f3f3f;
    while(x){
        if(a[x].key<key) {
            res=a[x].key;
            x=a[x].rc;
        }else x=a[x].lc;
    }
    return res;
}
inline int queryHou(int key){
    int x=rt,res=0x3f3f3f3f;
    while(x){
        if(a[x].key>key) {
            res=a[x].key;
            x=a[x].lc;
        }else x=a[x].rc;
    }
    return res;
}
int main(){
    cin>>n;
    for(int i=1;i<=n;i++){
        int opt,x;scanf("%d%d",&opt,&x);
        if(opt==1){
            insert(rt,x);
        }else if(opt==2){
            delete1(rt,x);
        }else if(opt==3){
            printf("%d
",queryRank(x));
        }else if(opt==4){
            printf("%d
",queryKey(x));
        }else if(opt==5){
            printf("%d
",queryQian(x));
        }else if(opt==6){
            printf("%d
",queryHou(x));
        }
    }
}