Splay P3369 【模板】普通平衡树（Treap/SBT）

题目描述

您需要写一种数据结构（可参考题目标题），来维护一些数，其中需要提供以下操作：

1. 插入x数

2. 删除x数(若有多个相同的数，因只删除一个)

3. 查询x数的排名(排名定义为比当前数小的数的个数+1。若有多个相同的数，因输出最小的排名)

4. 查询排名为x的数

5. 求x的前驱(前驱定义为小于x，且最大的数)

6. 求x的后继(后继定义为大于x，且最小的数)

输入输出格式

输入格式：

第一行为n，表示操作的个数,下面n行每行有两个数opt和x，opt表示操作的序号( 1 leq opt leq 61≤opt≤6 )

输出格式：

对于操作3,4,5,6每行输出一个数，表示对应答案

输入输出样例

输入样例#1： 复制

10
1 106465
4 1
1 317721
1 460929
1 644985
1 84185
1 89851
6 81968
1 492737
5 493598

输出样例#1： 复制

106465
84185
492737

说明

时空限制：1000ms,128M

1.n的数据范围： n leq 100000n≤100000

2.每个数的数据范围： [-{10}^7, {10}^7][−107,107]

来源：Tyvj1728 原名：普通平衡树

在此鸣谢

#include<iostream>
#include<cstdio>
#include<cmath>
#include<algorithm>
using namespace std;

const int N = 1e5+5;
const int INF = 599518803;

int n, opt, x;
struct NODE
{
    NODE *fa;
    NODE *son[2];
    int siz;
    int num, cnt;
}node[N];

typedef NODE* Tree;
Tree Root, now_node, null;

inline void init()
{
    Root = now_node = null = node;
    null->son[0] = null->son[1] = null;
}

inline int read()
{
    char c = getchar(); int num = 0, f = 1;
    for(; !isdigit(c); c = getchar())
        f = c == '-' ? -1 : f;
    for(; isdigit(c); c = getchar())
        num = num * 10 + c - '0';
    return num * f;
}


inline Tree new_node(int num, Tree fa)
{
    ++ now_node;
    now_node->siz = 1;
    now_node->num = num;
    now_node->fa = fa;
    now_node->son[0] = now_node->son[1] = null;
    return now_node;
}

inline bool getgx(Tree root)
{
    return root->fa->son[1] == root;
}

inline void connect(Tree root, Tree fa, bool flag)
{
    if(fa != null)
        fa->son[flag] = root;
    else
        Root = root;
    root->fa = fa;
}

inline void update(Tree root)
{
    root->siz = root->son[0]->siz + root->son[1]->siz + root->cnt;
}

inline void rotate(Tree root)
{
    Tree fa = root->fa;
    bool a = getgx(root), b = !a;
    connect(root->son[b], fa, a);
    connect(root, fa -> fa, getgx(fa));
    connect(fa, root, b);
    update(fa);
    update(root);
    if(root->fa == null)
        Root = root;
}

inline void splay(Tree root, Tree goal)
{
    for(; root->fa != goal; rotate(root))
        if(root->fa->fa != goal)
            rotate(getgx(root) == getgx(root->fa) ? root->fa : root);
}

void insert(int num)
{
    if(Root == null)
    {
        Root = new_node(num, null);
        Root->cnt = 1;
    }
    else
    {
        Tree root = Root;
        for(; root->num != num; root = root->son[num > root->num])
        {
            ++ (root->siz);
            if(root->son[num > root->num] == null)
                root->son[num > root->num] = new_node(num, root);
        }
        ++ (root->cnt);
        splay(root, null);
    }
}

void erase(int num)
{
    if(Root == null)
        return;
    else
    {
        Tree root = Root;
        for(;root != null && root->num != num; root = root->son[num > root->num]);
        if(root == null)
            return;
        splay(root, null);
        -- (root->cnt);
        if(!root->cnt)
        {
            if(root->son[0] != null)
            {
                Tree tmp = root->son[0];
                for(;tmp->son[1] != null; tmp = tmp->son[1]);
                splay(tmp, null);
                Root->son[1] = root->son[1];
                if(Root->son[1] != null)
                    Root->son[1]->fa = Root;
            }
            else
            {
                Root = root->son[1];
                Root->fa = null;
            }
        }
    }
}

inline int query_rank(int num)
{
    int rank = 0;
    for(Tree root = Root; root != null; root = root->son[num > root->num])
    {
        if(num == root->num)
            return rank + root->son[0]->siz + 1;
        if(num > root->num)
            rank += root->son[0]->siz + root->cnt;
    }
    return rank;
}

inline int query_num(int rank)
{
    for(Tree root = Root; root != null; )
    {
        if(rank <= root->son[0]->siz)
            root = root->son[0];
        else if(rank > root->son[0]->siz + root->cnt)
            rank -= root->son[0]->siz + root->cnt, root = root->son[1];
        else
            return root->num;
    }
}

inline int query_pre(int x)
{
    int pre = -INF;
    for(Tree root = Root; root != null; root = root->son[x > root->num])
    {
        if(x > root->num)
            pre = max(pre, root->num);
    }
    return pre;
}

inline int query_nxt(int x)
{
    int nxt = INF;
    for(Tree root = Root; root != null; root = root->son[x >= root->num])
    {
        if(root->num > x)
            nxt = min(nxt, root->num);
    }
    return nxt;
}

int main()
{
    init();
    n = read();
    for(int i = 1; i <= n; ++ i)
    {
        opt = read(), x = read();
        switch(opt)
        {
            case 1:
                insert(x); break;
            case 2:
                erase(x); break;
            case 3:
                printf("%d
", query_rank(x)); break;
            case 4:
                printf("%d
", query_num(x)); break;
            case 5:
                printf("%d
", query_pre(x)); break;
            default:
                printf("%d
", query_nxt(x));
        }
    }
    return 0;
}