splay模板

对于splay核心是旋转和伸展，其他操作基本都是利用伸展的特性：

#include<bits/stdc++.h>
using namespace std;
#define INF 0x3f3f3f3f
#define M(a, b) memset(a, b, sizeof(a))
const int N = 5e4 + 5;
int ch[N][2], p[N], num[N], sz, rt;

void rotate(int x, int &k) {
    int y = p[x], z = p[y], d = ch[y][1]==x;
    if (y == k) k = x;
    else ch[z][ch[z][1]==y] = x;
    p[ch[x][d^1]] = y; p[y] = x; p[x] = z;
    ch[y][d] = ch[x][d^1]; ch[x][d^1] = y; 
}

void splay(int x, int &k) {
    while (x != k) {
        int y = p[x], z = p[y];
        if (y != k) {
            if ((ch[z][0]==y)^(ch[y][0]==x)) rotate(x, k);
            else rotate(y, k);
        }
        rotate(x, k);
    }
}

void insert(int x, int &k, int fa) {
    if (k == 0) {k = ++sz; num[k] = x; p[k] = fa; splay(k, rt); return;}
    if (x < num[k]) insert(x, ch[k][0], k);
    else insert(x, ch[k][1], k);
}

void split(int &k, int &k1, int nth) {
    splay(nth, k);
    k1 = ch[k][1];
    p[k1] = 0; ch[k][1] = 0;
}