「Luogu3369」【模板】普通平衡树 - Splay

题目链接：传送门

Description

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)

Input

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( )

Output

对于操作3,4,5,6每行输出一个数，表示对应答案

Sample Input

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

Sample Output

106465 84185 492737

Solution

才学Splay，一道Splay的模板题 第一次写200+行的代码，打了2h，调了一天才A掉 看来我还是太弱了。。。 就把板子放这里算了

Code

#include <iostream>
#include <cstdio>
#include <cstring>
#include <cmath>
#include <algorithm>

#define root Tree[0].ch[1]
const int Maxn = 100000 + 100;
using namespace std;

struct node
{
    int val, ch[2], size, cnt, fa;
}Tree[Maxn];
int M, N;
int points;

inline void update(int x)
{
    Tree[x].size = Tree[Tree[x].ch[0]].size + Tree[Tree[x].ch[1]].size + Tree[x].cnt;
    return ;
}

inline int judge_dir(int x)
{
    return Tree[Tree[x].fa].ch[1] == x;
}

inline void Connect(int x, int f, int dir)
{
    Tree[x].fa = f;
    Tree[f].ch[dir] = x;
    return ;
}

inline void Rotate(int x)
{
    int f = Tree[x].fa; 
    int dirx = judge_dir(x);
    int anc = Tree[f].fa;
    int dirf = judge_dir(f);
    Connect(Tree[x].ch[dirx ^ 1], f, dirx);
    Connect(f, x, (dirx ^ 1));
    Connect(x, anc, dirf);
    update(f); update(x);
    return ;
}

inline void Splay (int x, int y)
{
    while (Tree[x].fa != y)
    {
        int f = Tree[x].fa;
        int dirx = judge_dir(x), dirf = judge_dir(f);
        if (Tree[f].fa == y) Rotate(x);
        else if (dirx == dirf) Rotate(f), Rotate(x);
        else Rotate(x), Rotate(x);
    }
    return ;
}

inline int Insert (int x, int f)
{
    Tree[++N].val = x;
    Tree[N].size = Tree[N].cnt = 1;
    Tree[N].fa = f;
    return N;
}

inline void Clear(int x)
{
    Tree[x].val = 0, Tree[x].fa = 0;
    Tree[x].size = 0, Tree[x].cnt = 0;
    Tree[x].ch[0] = 0, Tree[x].ch[1] = 0;
    return ;
}

inline int Find (int x)
{
    int now = root;
    while (1)
    {
        if (Tree[now].val == x)
        {
            Splay(now, 0);
            return now;
        }
        int dir = (x > Tree[now].val);
        if (!Tree[now].ch[dir]) return 0;
        now = Tree[now].ch[dir];
    }
    return 0;
}
inline void Create (int x)
{
    points++;
    if (!N)
    {
        root = 1;
        Insert(x, 0);
        return ;
    }
    int now = root;
    while (1)
    {
        Tree[now].size ++;
        if (Tree[now].val == x)
        {
            Tree[now].cnt ++;
            Splay(now, 0);
            return ;
        }
        int dir = (x > Tree[now].val);
        if (!Tree[now].ch[dir])
        {
            Insert(x, now);
            Tree[now].ch[dir] = N;
            Splay(N, 0);
            return ;
        }
        now = Tree[now].ch[dir];
    }
    return ;
}

inline void Delete(int v)
{
    int x = Find(v);
    if (!x) return ;
    points--;
    if (Tree[x].cnt > 1)
    {
        Tree[x].cnt --;
        Tree[x].size --;
        return ;
    }
    if (!Tree[x].ch[0])
    {
        root = Tree[x].ch[1];
        Tree[root].fa = 0;
        Clear(x);
//      cout<<"*"<<root<<endl;
        return ;
    }
    int now = Tree[x].ch[0];
    while (Tree[now].ch[1]) now = Tree[now].ch[1];
    Splay(now, x);
    Connect(Tree[x].ch[1], now, 1);
    Connect(now, 0, 1);
//  root = now;
    update(now);
    Clear(x);
    return ;
}

inline int Rank(int v)
{
    int now = root;
    int Ans = 0;
    while (1)
    {
    //  cout<<"*"<<now<<endl;
        if (Tree[now].val == v) return Ans + Tree[Tree[now].ch[0]].size + 1;
        if (now == 0) break;
        if (Tree[now].val > v)
            now = Tree[now].ch[0];
        else Ans += (Tree[Tree[now].ch[0]].size + Tree[now].cnt), now = Tree[now].ch[1];
    }
    return Ans;
}

inline int Rerank(int x)
{
    if (x > points) return -(0x3f3f3f3f);
    int now = root;
    while (1)
    {
        int Sum = Tree[now].size - Tree[Tree[now].ch[1]].size;
        if (Tree[Tree[now].ch[0]].size < x && x <= Sum)
            break;
        if (x < Sum)
            now = Tree[now].ch[0];
        else x -= Sum, now = Tree[now].ch[1];
    }
    Splay(now, 0);
    return Tree[now].val;
}

inline int Pre(int v)
{
    int Sum = -(0x3f3f3f3f);
    int now = root;
    while (1)
    {
        if (!now) break;
        if (Tree[now].val < v && Tree[now].val > Sum) Sum = Tree[now].val;
        if (Tree[now].val < v) now = Tree[now].ch[1];
        else now = Tree[now].ch[0];
    }
    return Sum;
}

inline int Next(int v)
{
    int Sum = 0x3f3f3f3f;
    int now = root;
    while (1)
    {
        if (!now) break;
        if (Tree[now].val > v && Tree[now].val < Sum) Sum = Tree[now].val;
        if (Tree[now].val > v) now = Tree[now].ch[0];
        else now = Tree[now].ch[1];
    }
    return Sum;
}

int main()
{
#ifndef ONLINE_JUDGE
    freopen("A.in", "r", stdin);
    freopen("A.out", "w", stdout);
#endif
    scanf("%d", &M);
    int tot = 0;
    while (M --)
    {
        int op, x;
        scanf("%d%d", &op, &x);
        if (op == 1) Create(x);
        if (op == 2) Delete(x);
        if (op == 3) printf("%d\n", Rank(x));
        if (op == 4) printf("%d\n", Rerank(x));
        if (op == 5) printf("%d\n", Pre(x));
        if (op == 6) printf("%d\n", Next(x));
    }
    return 0;
}