初识splay

　　这东西都没什么板子着实让我很难受啊，只能到网上抄抄补补，

　　记下两个用到的博客

https://blog.csdn.net/clove_unique/article/details/50630280

https://blog.csdn.net/ophunter_lcm/article/details/18157185

　　BZOJ 3224

　　复制粘贴？...

 #include <iostream>
 #include <string.h>
 #include <cstdio>
 #include <vector>
 #include <queue>
 #include <math.h>
 #include <string>
 #include <algorithm>
 #include <time.h>
 
 #define SIGMA_SIZE 26
 #define lson rt<<1
 #define rson rt<<1|1
 #define lowbit(x) (x&-x)
 #define foe(i, a, b) for(int i=a; i<=b; i++)
 #define fo(i, a, b) for(int i=a; i<b; i++);
 #pragma warning ( disable : 4996 )
 
 using namespace std;
 typedef long long LL;
 inline LL LMax(LL a, LL b) { return a>b ? a : b; }
 inline LL LMin(LL a, LL b) { return a>b ? b : a; }
 inline LL lgcd(LL a, LL b) { return b ==  ? a : lgcd(b, a%b); }
 inline LL llcm(LL a, LL b) { return a / lgcd(a, b)*b; }  //a*b = gcd*lcm
 inline int Max(int a, int b) { return a>b ? a : b; }
 inline int Min(int a, int b) { return a>b ? b : a; }
 inline int gcd(int a, int b) { return b ==  ? a : gcd(b, a%b); }
 inline int lcm(int a, int b) { return a / gcd(a, b)*b; }  //a*b = gcd*lcm
 const LL INF = 0x3f3f3f3f3f3f3f3f;
 const LL mod = ;
 const double eps = 1e-;
 const int inf = 0x3f3f3f3f;
 const int maxk = 1e6 + ;
 const int maxn = 1e5 + ;
 
 int Size, root;
 int ch[maxn<<][];
 int f[maxn<<];
 int key[maxn<<];
 int cnt[maxn<<];
 int siz[maxn<<];
 
 inline void clear(int x)
 { ch[x][] = ch[x][] = f[x] = cnt[x] = key[x] = siz[x] = ; }
 
 //判断当前点是它父节点的左儿子还是右儿子
 inline int get(int x)
 { return ch[f[x]][] == x; }
 
 //更新当前点size值(用于修改之后)
 inline void update(int x)
 {
     if (x) {
         siz[x] = cnt[x];
         if (ch[x][]) siz[x] += siz[ch[x][]];
         if (ch[x][]) siz[x] += siz[ch[x][]];
     }
 }
 
 inline void rotate(int x)
 {
     int old = f[x], oldf = f[old], which = get(x);
     ch[old][which] = ch[x][which^]; f[ch[old][which]] = old;
     f[old] = x; ch[x][which^] = old;
     f[x] = oldf;
     if (oldf)
         ch[oldf][ch[oldf][]==old] = x;
     update(old); update(x);
 }
 
 inline void splay(int x)
 {
     for( int fa; (fa=f[x]); rotate(x))
         if ( f[fa] )
             rotate((get(x)==get(fa) ? fa : x));
     root = x;
 }
 
 inline void insert(int v)
 {
     if ( root ==  )
     {
         Size++; ch[Size][] = ch[Size][] = f[Size] = ; key[Size] = v;
         cnt[Size] = ; siz[Size] = ; root = Size; return;
     }
 
     int now = root, fa = ;
     while ()
     {
         if (key[now] == v) {
             cnt[now]++;
             update(now); update(fa);
             splay(now);
             break;
         }
         fa = now;
         now = ch[now][key[now]<v];
         if (now == ) {
             Size++;
             ch[Size][] = ch[Size][] = ;
             key[Size] = v; siz[Size] = ;
             cnt[Size] = ; f[Size] = fa;
             ch[fa][key[fa]<v] = Size;
             update(fa);
             splay(Size);
             break;
         }
     }
 }
 
 inline int find(int v)
 {
     int ans = , now = root;
     while ()
     {
         if ( v < key[now] )
             now = ch[now][];
         else {
             ans += (ch[now][] ? siz[ch[now][]] : );
             if ( v == key[now] ) { splay(now); return ans+; }
 
             ans += cnt[now];
             now = ch[now][];
         }
     }
 }
 
 inline int findx(int x)
 {
     int now = root;
     while ()
     {
         if ( ch[now][] && x <= siz[ch[now][]] )
             now = ch[now][];
         else {
             int tmp = ( ch[now][] ? siz[ch[now][]] : ) + cnt[now];
 
             if ( x <= tmp )
                 return key[now];
             x -= tmp;
             now = ch[now][];
         }
     }
 }
 
 inline int pre()
 {
     int now = ch[root][];
     while ( ch[now][] ) now = ch[now][];
     return now;
 }
 
 inline int next()
 {
     int now = ch[root][];
     while ( ch[now][] ) now = ch[now][];
     return now;
 }
 
 inline void del(int x) {
     int whatever = find(x);
     if (cnt[root]>) { cnt[root]--; return; }
     //Only One Point
     if (!ch[root][] && !ch[root][]) { clear(root); root = ; return; }
     //Only One Child
     if (!ch[root][]) {
         int oldroot = root; root = ch[root][]; f[root] = ; clear(oldroot); return;
     }
     else if (!ch[root][]) {
         int oldroot = root; root = ch[root][]; f[root] = ; clear(oldroot); return;
     }
     //Two Children
     int leftbig = pre(), oldroot = root;
     splay(leftbig);
     f[ch[oldroot][]] = root;
     ch[root][] = ch[oldroot][];
     clear(oldroot);
     update(root);
     return;
 }
 
 int main()
 {
     int n, opt, x;
     scanf("%d", &n);
     for (int i = ; i <= n; ++i) {
         scanf("%d%d", &opt, &x);
         switch (opt) {
         case : insert(x); break;
         case : del(x); break;
         case : printf("%d\n", find(x)); break;
         case : printf("%d\n", findx(x)); break;
         case : insert(x); printf("%d\n", key[pre()]); del(x); break;
         case : insert(x); printf("%d\n", key[next()]); del(x); break;
         }
     }
 
     return ;
 }

　　BZOJ 1251(区间翻转和区间增加一个值V)

　　这份代码比较清晰易懂

　　https://blog.csdn.net/whai362/article/details/47298133（加了一些注释

/*bzoj 1251 序列终结者
题意：
给定一个长度为N的序列，每个序列的元素是一个整数。要支持以下三种操作：
1. 将[L,R]这个区间内的所有数加上V;
2. 将[L,R]这个区间翻转，比如1 2 3 4变成4 3 2 1;
3. 求[L,R]这个区间中的最大值;
最开始所有元素都是0。
限制：
N <= 50000, M <= 100000
思路：
伸展树
关键点：
1. 伸展树为左小右大的二叉树，所以旋转操作不会影响树的性质
2. 区间操作为：
int u = select(L - 1), v = select(R + 1);
splay(u, 0); splay(v, u);    //通过旋转操作把询问的区间聚集到根的右子树的左子树下
因为伸展树为左小右大的二叉树，旋转操作后的所以对于闭区间[L, R]之间的所有元素都聚集在根的右子树的左子树下
因为闭区间[L, R]，
1) 所以每次都要查开区间(L - 1, R + 1)，
2) 所以伸展树元素1对应的标号为2，
3) 所以node[0]对应空节点，node[1]对应比所以元素标号都小的点，node[2 ~ n + 1]对应元素1 ~ n，node[n + 2]对应比所有元素标号都打的点，其中node[0], node[1], node[n + 2]都是虚节点，不代表任何元素。
*/
#include <iostream>
#include <string.h>
#include <cstdio>
#include <vector>
#include <queue>
#include <math.h>
#include <string>
#include <algorithm>
#include <time.h>
 
#define SIGMA_SIZE 26
#define lson rt<<1
#define rson rt<<1|1
#define lowbit(x) (x&-x)
#define foe(i, a, b) for(int i=a; i<=b; i++)
#define fo(i, a, b) for(int i=a; i<b; i++);
#pragma warning ( disable : 4996 )
 
using namespace std;
typedef long long LL;
inline LL LMax(LL a, LL b) { return a>b ? a : b; }
inline LL LMin(LL a, LL b) { return a>b ? b : a; }
inline LL lgcd(LL a, LL b) { return b ==  ? a : lgcd(b, a%b); }
inline LL llcm(LL a, LL b) { return a / lgcd(a, b)*b; }  //a*b = gcd*lcm
inline int Max(int a, int b) { return a>b ? a : b; }
inline int Min(int a, int b) { return a>b ? b : a; }
inline int gcd(int a, int b) { return b ==  ? a : gcd(b, a%b); }
inline int lcm(int a, int b) { return a / gcd(a, b)*b; }  //a*b = gcd*lcm
const LL INF = 0x3f3f3f3f3f3f3f3f;
const LL mod = ;
const double eps = 1e-;
const int inf = 0x3f3f3f3f;
const int maxk = 1e6 + ;
const int maxn = 1e5 + ;
 
#define LS(n) node[(n)].ch[0]
#define RS(n) node[(n)].ch[1]
 
struct Splay {
    struct Node {
        int fa, ch[];
        bool rev;
        int val, add, maxx, size;
        void init(int _val) {
            val = maxx = _val;
            size = ;
            add = rev = ch[] = ch[] = ;
        }
    } node[maxn];
    int root;
 
    ///相当于线段树的pushup和pushdown
    void pushUp(int n) {
        node[n].maxx = Max(node[n].val, Max(node[LS(n)].maxx, node[RS(n)].maxx));
        node[n].size = node[LS(n)].size + node[RS(n)].size + ;
    }
 
    void pushDown(int n) {
        if (n == ) return;
        if (node[n].add) {
            if (LS(n)) {
                node[LS(n)].val += node[n].add;
                node[LS(n)].maxx += node[n].add;
                node[LS(n)].add += node[n].add;
            }
            if (RS(n)) {
                node[RS(n)].val += node[n].add;
                node[RS(n)].maxx += node[n].add;
                node[RS(n)].add += node[n].add;
            }
            node[n].add = ;
        }
        if (node[n].rev) {
            if (LS(n)) node[LS(n)].rev ^= ;
            if (RS(n)) node[RS(n)].rev ^= ;
            swap(LS(n), RS(n));
            node[n].rev = ;
        }
    }
 
    ///kind = 0为左旋
    ///kind = 1为右旋
    void rotate(int n, bool kind) {
        int fn = node[n].fa;
        int ffn = node[fn].fa;
        node[fn].ch[!kind] = node[n].ch[kind];
        node[node[n].ch[kind]].fa = fn;
 
        node[n].ch[kind] = fn;
        node[fn].fa = n;
 
        node[ffn].ch[RS(ffn) == fn] = n;
        node[n].fa = ffn;
        pushUp(fn);
    }
 
    void splay(int n, int goal) {
        while (node[n].fa != goal) {
            int fn = node[n].fa;
            int ffn = node[fn].fa;
            //三连pushDown
            pushDown(ffn); pushDown(fn); pushDown(n);
            bool rotate_n = (LS(fn) == n);
            bool rotate_fn = (LS(ffn) == fn);
            if (ffn == goal) rotate(n, rotate_n);
            else {
                if (rotate_n == rotate_fn) rotate(fn, rotate_fn);
                else rotate(n, rotate_n);
                rotate(n, rotate_fn);
            }
        }
        pushUp(n);
        if (goal == ) root = n;
    }
 
    ///通过数组中的位置找在树中的位置
    int select(int pos) {
        int u = root;
        pushDown(u);
        while (node[LS(u)].size != pos) {
            if (pos < node[LS(u)].size)
                u = LS(u);
            else {
                pos -= node[LS(u)].size + ;
                u = RS(u);
            }
            pushDown(u);
        }
        return u;
    }
 
    int query(int L, int R) {
        int u = select(L - ), v = select(R + );
        splay(u, ); splay(v, u);    ///通过旋转操作把询问的区间聚集到根的右子树的左子树下
        return node[LS(v)].maxx;
    }
 
    void pushUpdate(int L, int R, int val) {
        int u = select(L - ), v = select(R + );
        splay(u, ); splay(v, u);
        node[LS(v)].val += val;
        node[LS(v)].maxx += val;
        node[LS(v)].add += val;
    }
 
    void reverse(int L, int R) {
        int u = select(L - ), v = select(R + );
        splay(u, ); splay(v, u);
        node[LS(v)].rev ^= ;
    }
 
    ///返回子树的根节点
    int build(int L, int R) {
        if (L > R) return ;
        if (L == R) return L;
        int mid = (L + R) >> ;
        int r_L, r_R;
        LS(mid) = r_L = build(L, mid - );
        RS(mid) = r_R = build(mid + , R);
        node[r_L].fa = node[r_R].fa = mid;
        pushUp(mid);
        return mid;
    }
 
    ///按照数组的下标顺序作为建树依据
    ///而不是按照数组内的元素大小做依据
    void init(int n) {
        ///0号节点最大值和值都是负无穷
        node[].init(-inf); node[].size = ;
        node[].init(-inf);
        node[n + ].init(-inf);
        for (int i = ; i <= n + ; ++i)
            node[i].init();
 
        root = build(, n + );
        node[root].fa = ;
 
        node[].fa = ;
        LS() = root;
    }
} splay_tree;
 
int main() {
    int n, m;
    scanf("%d%d", &n, &m);
    splay_tree.init(n);
    for (int i = ; i < m; ++i) {
        int op, l, r, v;
        scanf("%d", &op);
        if (op == ) {
            scanf("%d%d%d", &l, &r, &v);
            splay_tree.pushUpdate(l, r, v);
        }
        else if (op == ) {
            scanf("%d%d", &l, &r);
            splay_tree.reverse(l, r);
        }
        else {
            scanf("%d%d", &l, &r);
            printf("%d\n", splay_tree.query(l, r));
        }
    }
    return ;
}