fhq-Treap

fhq-Treap 是一种非旋转平衡二叉树，代码很好写。

#include <iostream>
#include <algorithm>
#include <cstring>
#include <string>
#include <cstdio>
#include <vector>
#include <ctime>
using namespace std;

#define RG register int
#define LL long long

template<typename elemType>
inline void Read(elemType &T){
    elemType X=0,w=0; char ch=0;
    while(!isdigit(ch)) {w|=ch=='-';ch=getchar();}
    while(isdigit(ch)) X=(X<<3)+(X<<1)+(ch^48),ch=getchar();
    T=(w?-X:X);
}

template<typename elemType,size_t MAX_SIZE=100010>
struct Treap{
    struct TreapNode{
        elemType val;
        int rnd,size,son[2];
        int &operator[](int x){return son[x];}
    }T[MAX_SIZE];
    
    int root,cnt;
    Treap():root(0),cnt(0){}

    void push_up(int u){T[u].size=T[T[u][0]].size+T[T[u][1]].size+1;}

    void split(int u,elemType key,int &x,int &y){
        //将以u为根的树分离成x,y两棵树
        //其中x树的权值均小于等于key,y树的权值均大于key
        if(!u){x=y=0;return;}
        if(T[u].val<=key){x=u;split(T[u][1],key,T[u][1],y);}
        else{y=u;split(T[u][0],key,x,T[u][0]);}
        push_up(u);
    }

    int merge(int x,int y){//合并树x,y
        if(!x) return y;
        if(!y) return x;
        if(T[x].rnd<T[y].rnd){
            T[x][1]=merge(T[x][1],y);
            push_up(x);return x;
        }else{
            T[y][0]=merge(x,T[y][0]);
            push_up(y);return y;
        }
    }

    int new_node(elemType val){//新建值为val的结点
        ++cnt;T[cnt].val=val;
        T[cnt].size=1;T[cnt].rnd=rand();
        return cnt;
    }

    void insert(elemType val){//插入值为val的结点
        if(root==0){root=new_node(val);return;}
        int x,y;split(root,val,x,y);
        root=merge(merge(x,new_node(val)),y);
    }

    void delete_node(elemType val){//删除值为val的结点
        int x,y,z;
        split(root,val,x,z);
        split(x,val-1,x,y);
        y=merge(T[y][0],T[y][1]);
        root=merge(merge(x,y),z);
    }

    int get_rank(elemType val){//查询值val的排名
        int x,y;
        split(root,val-1,x,y);
        int res=T[x].size+1;
        root=merge(x,y);
        return res;
    }

    int get_kth(int u,int kth){//返回第k大的结点
        if(u==0||kth>T[u].size) return 0;
        if(T[T[u][0]].size+1==kth) return u;
        else if(kth<=T[T[u][0]].size) return get_kth(T[u][0],kth);
        return get_kth(T[u][1],kth-T[T[u][0]].size-1);
    }
    elemType get_kth_val(int kth){return T[get_kth(root,kth)].val;}
    //返回第k大的结点的值

    int get_predecessor(elemType val){//返回val的(严格)前驱结点
        int x,y;
        split(root,val-1,x,y);
        int res=get_kth(x,T[x].size);
        root=merge(x,y);
        return res;
    }
    elemType get_predecessor_val(elemType val){return T[get_predecessor(val)].val;}
    //返回val的(严格)前驱结点的值

    int get_successor(elemType val){//返回val的(严格)后继结点
        int x,y;
        split(root,val,x,y);
        int res=get_kth(y,1);
        root=merge(x,y);
        return res;
    }
    elemType get_successor_val(elemType val){return T[get_successor(val)].val;}
    //返回val的(严格)后继结点的值

    void output_tree(int u){//中序遍历Treap
        if(!u) return;
        output_tree(T[u][0]);
        cout<<T[u].val<<" ";
        output_tree(T[u][1]);
    }
};
Treap<int> Tree;
int n;

int main(){
    Read(n);
    for(RG i=1;i<=n;++i){
        int opt,x;
        Read(opt);Read(x);
        if(opt==1) Tree.insert(x);
        else if(opt==2) Tree.delete_node(x);
        else if(opt==3) printf("%d
",Tree.get_rank(x));
        else if(opt==4) printf("%d
",Tree.get_kth_val(x));
        else if(opt==5) printf("%d
",Tree.get_predecessor_val(x));
        else if(opt==6) printf("%d
",Tree.get_successor_val(x));
        else if(opt==7) Tree.output_tree(Tree.root);
    }

    return 0;
}