Splay入门

这几天了解了一下平衡树，大概有如下几种：

AVL， 红黑， SBT, splay, treap, 后两者不是很严格的平衡。

反正先拿splay练手了，感觉比较热门。。。

平衡树的维护都靠旋转，splay也是。

其核心是Splay(x， goal)操作：把节点x一层层Rotate上去，直到x到达目的地goal下方；

它支持任意区间的更新，查询，插入，删除and翻转，O（lgn）。

模板来源：（盗用自notonlysuccess牛）

　　http://www.notonlysuccess.com/index.php/splay-tree/

用法：（来自Crash牛）

　　http://www.docin.com/p-62465596.html

习题一道：

Play with Chain
此题有splay的最独特的操作 区间插入，删除and翻转

贴个膜板：

#include <iostream>
#include <stdio.h>
#include <string>
#include <algorithm>
#include <string.h>
#include <stdlib.h>
#define MAXN 300500
#define INF 0x3f3f3f3f
#define keyTree  ch[ ch[root][1] ][0]
using namespace std;

int num[MAXN], id;

struct SplayTree{
    int sz[MAXN];        //size
    int ch[MAXN][2];     //child
    int pre[MAXN];        //father 
    int root, top1, top2;
    int ss[MAXN], que[MAXN];
    
    inline void Rotate(int x, int r){    //r：（0，左）；（1，右） 
        int y = pre[x];
        pushDown(y);    
        pushDown(x);    
        ch[y][!r] = ch[x][r];
        if(ch[x][r]) pre[ ch[x][r] ] = y;
        pre[x] = pre[y];
        if(pre[y]) ch[ pre[y] ][ ch[pre[y]][1]==y ] = x;
        ch[x][r] = y;
        pre[y] = x;
        pushUp(y);
    }
    
    inline void Splay(int x, int goal){
        pushDown(x);
        while(pre[x] != goal){
            if(pre[pre[x]] == goal)
                Rotate(x, ch[pre[x]][0] == x);    //左儿则右旋 
            else{
                int y = pre[x], z = pre[y];
                int r = (ch[z][0] == y);
                if(ch[y][r]==x)
                    Rotate(x, !r), Rotate(x, r);    //Rx, Rx
                else
                    Rotate(y, r), Rotate(x, r);    //Ry, Rx 
            }
        }
        pushUp(x);
        if(goal == 0)    root = x;         
    }
    
    //把第k位的数转到goal下边
    inline void RotateTo(int k, int goal){
        int x = root;
        pushDown(x);
        while(sz[ ch[x][0] ] != k){
            if(k < sz[ ch[x][0] ] ) x = ch[x][0];
            else{
                k -= (sz[ ch[x][0] ]+1);
                x = ch[x][1];
            }
            pushDown(x);
        }//找到 第k位的数；
        Splay(x, goal); 
    }
    
    //把以x为祖先结点删掉放进内存池,回收内存
    //bfs(子树x);
    inline void erase(int x){
        int head = 0, tail = 0;
        for(que[tail++]=x; head<tail; head++){
            ss[top2++] = que[head];
            if(ch[ que[head] ][0])    que[tail++] = ch[ que[head] ][0];
            if(ch[ que[head] ][1])    que[tail++] = ch[ que[head] ][1];
        }
    }

    //-------------以上一般不修改-------------------
    void debug( ) { printf("%d
",root); Treaval(root); }
    void Treaval( int x )
    {
        if( x )
        {
            Treaval( ch[x][0] );
            printf("结点%2d:左儿子 %2d 右儿子 %2d 父结点 %2d size = %2d ,val = %2d
",
                    x,ch[x][0],ch[x][1],pre[x],sz[x],val[x]);
            Treaval( ch[x][1] );
        }
    }
    //以上Debug
    
    //以下是题目的特定函数:
    inline void NewNode( int &x, int c ){
        if( top2 ) x = ss[--top2];//用栈手动压的内存池
        else x = ++top1;
        ch[x][0] = ch[x][1] = pre[x] = 0;
        sz[x] = 1, val[x] = c, rev[x] = 0;
    }
    
    inline void pushDown(int x){
        if(rev[x]){
            if(ch[x][0]) rev[ch[x][0]] ^=1;
            if(ch[x][1]) rev[ch[x][1]] ^=1;
            swap(ch[x][0], ch[x][1]);
            rev[x] = 0;
        }
    }
    
    inline void pushUp( int x ) {
        sz[x] = 1 + sz[ ch[x][0] ] + sz[ ch[x][1] ];
    }
    
    inline void makeTree( int &x, int l, int r, int f ){
        if( l > r ) return ;
        int m = ( l + r ) >> 1;
        NewNode( x, num[m] );        
        makeTree( ch[x][0], l, m - 1, x );
        makeTree( ch[x][1], m + 1, r, x );
        pre[x] = f;
        pushUp(x);
    }
    
    inline void init( int n ){
        ch[0][0] = ch[0][1] = pre[0] = sz[0] = 0;
        rev[0] = 0, root = top1 = 0;
        //为了方便处理边界,加两个边界顶点!!        
        NewNode( root , -1 );
        NewNode( ch[root][1], -1 );
        pre[ ch[root][1] ] = root;        

        for( int i = 0; i < n; i++ ) 
            num[i] = i+1;
        makeTree( keyTree, 0, n - 1, ch[root][1] );
        pushUp( ch[root][1] );
        pushUp( root );
    }
    
    inline int del(int l, int r){
        RotateTo(l-1, 0);
        RotateTo(r+1, root);
        int ans = keyTree;
        keyTree = 0;
        pushUp( ch[root][1] );
        pushUp( root );
        return ans;
    }
    
    inline void ins(int d, int s){
        RotateTo(d, 0);
        RotateTo(d+1, root);
        keyTree = s, pre[s] = ch[root][1];
        pushUp( ch[root][1] );
        pushUp( root );
    }
    
    inline void flip(int l, int r){
        RotateTo(l-1, 0);
        RotateTo(r+1, root);
        rev[keyTree] ^= 1;
    }
    
    inline void print(int p){
        if(!p)    return ;
        pushDown(p);
        print(ch[p][0]);
        num[id++] = val[p];
        print(ch[p][1]);
    }
    
    int val[MAXN];
    int rev[MAXN];
}spt;

int main( ) {
    int n, m;
    while(scanf("%d%d",&n,&m) && n>0 && m>0){
        spt.init( n );
        while( m-- ){
            int a, b, c;
            char op[2];
            scanf("%s%d%d", op, &a, &b);
            if( op[0] == 'C' ){
                scanf("%d", &c);
                int s = spt.del(a, b);
                spt.ins(c, s);
            }                
            else
                spt.flip(a, b);
        }
        id = 0;
        spt.print(spt.root);
        for(int i=1; i<=n; i++)
            printf("%d%c", num[i], i!=n? ' ': '
');
    }
    return 0;
}