【模板】普通平衡树

#include<cstdio>
#include<cstring>
#include<iostream>
#include<algorithm>
using namespace std;
const int N=100010,INF=1e8;
int n;
struct Node
{
    int l,r;
    int key,val;
    int cnt,size;   
}tr[N];
int root,idx;
void pushup(int p)
{
    tr[p].size=tr[tr[p].l].size+tr[tr[p].r].size+tr[p].cnt;
}
int get_node(int key)
{
    tr[++idx].key=key;
    tr[idx].val=rand();
    tr[idx].cnt=tr[idx].size=1;
    return idx;
}
void build()
{
    get_node(-INF),get_node(INF);
    root=1,tr[1].r=2;
    pushup(root);
}
void zig(int &p)
{
    int q=tr[p].l;
    tr[p].l=tr[q].r,tr[q].r=p,p=q;
    pushup(tr[p].r),pushup(p);
}
void zag(int &p)
{
    int q=tr[p].r;
    tr[p].r=tr[q].l,tr[q].l=p,p=q;
    pushup(tr[p].l),pushup(p);
}
void insert(int &p,int key)
{
    if(!p) p=get_node(key);
    else if(tr[p].key==key) tr[p].cnt++;
    else if(tr[p].key>key)
    {
        insert(tr[p].l,key);
        if(tr[tr[p].l].val>tr[p].val) zig(p);
    }
    else
    {
        insert(tr[p].r,key);
        if(tr[tr[p].r].val>tr[p].val) zag(p);
    }
    pushup(p);
}
void remove(int &p,int key)
{
    if(!p) return;
    if(tr[p].key==key)
    {
        if(tr[p].cnt>1) tr[p].cnt--;
        else if(tr[p].l or tr[p].r)
        {
            if(!tr[p].r or tr[tr[p].l].val>tr[tr[p].r].val)
            {
                zig(p);
                remove(tr[p].r,key);
            }
            else
            {
                zag(p);
                remove(tr[p].l,key);
            }
        }
        else p=0;
    }
    else if(tr[p].key>key) remove(tr[p].l,key);
    else remove(tr[p].r,key);
    pushup(p);
}
int get_rank_by_key(int p,int key)
{
    if(!p) return 0;
    if(tr[p].key==key) return tr[tr[p].l].size+1;
    if(tr[p].key>key) return get_rank_by_key(tr[p].l,key);
    return tr[tr[p].l].size+tr[p].cnt+get_rank_by_key(tr[p].r,key);
}
int get_key_by_rank(int p,int rank)
{
    if(!p) return INF;
    if(tr[tr[p].l].size>=rank) return get_key_by_rank(tr[p].l,rank);
    if(tr[tr[p].l].size+tr[p].cnt>=rank) return tr[p].key;
    return get_key_by_rank(tr[p].r,rank-tr[tr[p].l].size-tr[p].cnt);
}
int get_prev(int p,int key)
{
    if(!p) return -INF;
    if(tr[p].key>=key) return get_prev(tr[p].l,key);
    return max(tr[p].key,get_prev(tr[p].r,key));
}
int get_next(int p,int key)
{
    if(!p) return INF;
    if(tr[p].key<=key) return get_next(tr[p].r,key);
    return min(tr[p].key,get_next(tr[p].l,key));
}
int main()
{
    build();
    scanf("%d",&n);
    while(n--)
    {
        int opt,x;
        scanf("%d%d",&opt,&x);
        if(opt==1) insert(root,x);
        else if(opt==2) remove(root,x);
        else if(opt==3) printf("%d\n",get_rank_by_key(root,x)-1);
        else if(opt==4) printf("%d\n",get_key_by_rank(root,x+1));
        else if(opt==5) printf("%d\n",get_prev(root,x));
        else printf("%d\n",get_next(root,x));
    }
    return 0;
}