【Treap】[BZOJ 3224]Tyvj 1728 普通平衡树

平衡树的入门题目，也可以用Treap来实现，我觉得Treap的核心就是那个rand()了用来保证树不退化成链，同时还是有平衡树的特性。。总体来说我觉得比较好些，而且比较快

#include <cstdio>
#include <cstring>
#include <cmath>
#include <algorithm>
#include <cctype>
#include <iostream>
using namespace std;
const int MAXN = 500000;
struct node{
    int r, v, sz, number;
    node *ch[2];
    void rz(){sz = ch[0]->sz + ch[1]->sz + number;}
}Edges[MAXN+10], *ecnt = Edges, Tnull, *nil = &Tnull;
node *newnode(node *lch, node *rch, int v, int r){
    ++ecnt;
    ecnt->ch[0] = lch;
    ecnt->ch[1] = rch;
    ecnt->v = v;
    ecnt->r = r;
    return ecnt;
}
node *retu;
int ret;
struct Treap{
    node *root;
    Treap(){root = nil; nil->ch[0] = nil->ch[1] = nil;}
    void rotate(node *&n, bool d){
        node *a = n->ch[d];
        n->ch[d] = a->ch[!d]; n->rz();
        a->ch[!d] = n; a->rz();
        n = a;
    }
    void Insert(node *&rt, int val){
        if(rt == nil){
            rt = newnode(nil, nil, val, rand());
            rt->number = 1;
            rt->rz();
            return ;
        }
        rt->sz++;
        if(val == rt->v){
            rt->number++;
        }else if(val < rt->v){
            Insert(rt->ch[0], val);
            if(rt->ch[0]->r < rt->r)
                rotate(rt, false);
        }else if(val > rt->v){
            Insert(rt->ch[1], val);
            if(rt->ch[1]->r < rt->r)
                rotate(rt, true);
        }
    }
    void del(node *&rt, int val){
        if(rt == nil) return ;
        rt->sz--;
        if(rt->v == val){
            if(rt->number > 1){
                rt->number--;
            }
            else if(rt->ch[0] == nil || rt->ch[1] == nil){
                if(rt->ch[0]!=nil)
                    rt = rt->ch[0];
                else
                    rt = rt->ch[1];
            }
            else{
                if(rt->ch[0]->r > rt->ch[1]->r){
                    rotate(rt, false);
                    del(rt->ch[1], val);
                    rt->rz();
                }else{
                    rotate(rt, true);
                    del(rt->ch[0], val);
                    rt->rz();
                }
            }
        }else if(val < rt->v)
            del(rt->ch[0], val);
        else
            del(rt->ch[1], val);
    }
    int Rank(node *rt, int val){
        if(rt == nil) return ret+1;
        if(rt->v == val)
            return ret+rt->ch[0]->sz+1;
        if(val < rt->v)
            return Rank(rt->ch[0], val);
        ret += rt->ch[0]->sz+rt->number;
        return Rank(rt->ch[1], val);
    }
    void pre(node *rt, int val){
        if(rt == nil) return ;
        else if(rt->v <= val){
            retu = rt;
            pre(rt->ch[1], val);
        }else
            pre(rt->ch[0], val);
    }
    void bak(node *rt, int val){
        if(rt == nil) return ;
        else if(rt->v >= val){
            retu = rt;
            bak(rt->ch[0], val);
        }else
            bak(rt->ch[1], val);
    }
    int order(node *rt, int rk){
        if(rt->sz < rk) return 0;
        if(rk <= rt->ch[0]->sz)
            return order(rt->ch[0], rk);
        else if(rk > rt->ch[0]->sz+rt->number)
            return order(rt->ch[1], rk-rt->ch[0]->sz-rt->number);
        return rt->v;
    }
}tp;
int main(){
    //freopen("data10.in", "r", stdin);
    int n;
    scanf("%d", &n);
    for(int i=0;i<n;i++){
        int o, x;
        scanf("%d %d", &o, &x);
        switch(o){
            case 1: tp.Insert(tp.root, x); break;
            case 2: tp.del(tp.root, x); break;
            case 3: ret = 0; printf("%d\n", tp.Rank(tp.root, x)); break;
            case 4: printf("%d\n", tp.order(tp.root, x)); break;
            case 5: retu = nil;tp.pre(tp.root, x-1); printf("%d\n", retu->v); break;
            case 6: retu = nil;tp.bak(tp.root, x+1); printf("%d\n", retu->v); break;
        }
    }

    return 0;
}