BZOJ 1861 Splay伸展树

题目链接

题意：

一个书架有n本书，书本依次编号为1，2，。。。，n，初始有一个给定顺序从上到下摆放，有五种操作：

Top x：将编号为x的书置于最顶上

Bottom x：将编号为x的书置于最底下

Insert x y：将编号为x的书置于x的原位置+y的位置

Ask x：询问编号为x的书上面有多少本书

Query x：询问第x本书的编号

思路：

使用Splay伸展树维护，但是维护的操作都需要加一点细节进去，伸展树总体维护目标将第x本书维护在节点x上以书的标号为权值，但是每次操作都需要先删除再重新添加进伸展树，重新添加就会引进新标号，这个引进的信标号将会对应被抽出的那本书，然后重新赋予节点编号，再次维护进伸展树，也可以看作是删除原书，重新添加一本新书，只不过权值都是相同的而已

插入：因为要具体维护到某一位置，需要为插入多调个参数

插入函数如下：

void Insert( int now , int data , int k )
{
    if ( k==1&&son[now][0]==0 )
        Newnode( data , now ),son[now][0] = sizes;
    else if ( k==2+Getsize(son[now][0])&&son[now][1]==0 )
        Newnode( data , now ),son[now][1] = sizes;
    else if ( k<=1+Getsize(son[now][0]) )
        Insert( son[now][0] , data , k );
    else
        Insert( son[now][1] , data , k-Getsize(son[now][0])-1 );
    Update( now );
}

查找某一节点位置：这样就可以知道节点x是第几本书

int Get( int x )
{
    Splay( x , 0 );
    return Getsize(son[x][0])+1;
}

查找指定位置数据：这样就可以知道第x本书的编号

int Find( int x )
{
    int now = root;
    while ( true )
    {
        if ( x==1+Getsize(son[now][0]) )
            return now;
        if ( x> 1+Getsize(son[now][0]) )
            x -= 1+Getsize(son[now][0]),now = son[now][1];
        else
            now = son[now][0];
    }
}

C++代码：

#include<map>
#include<set>
#include<stack>
#include<cmath>
#include<queue>
#include<vector>
#include<string>
#include<cstdio>
#include<cstring>
#include<complex>
#include<iostream>
#include<algorithm>
using namespace std;
#define lson rt<<1
#define rson rt<<1|1
typedef double DB;
typedef long long LL;
typedef complex<double>CD;
const int maxn = 200010;
const int mod = 1000000;
const int inf = 0x3f3f3f3f;
const int INF = 0x7FFFFFFF;

void Mod( int &x ){ x%=mod; }
int Min( int a , int b ){ return a<b?a:b; }
int Max( int a , int b ){ return a>b?a:b; }
int Abs( int x ){ return x>=0?x:-x; }
int Random(){ static int seed = 703; return seed=(int)(seed*48271LL%2147483647); }

int fa[maxn],son[maxn][2],val[maxn],sz[maxn],a[maxn],pos[maxn],sizes,root;

void Update( int x )
{
    sz[x] = 1;
    if ( son[x][0]!=0 )
        sz[x] += sz[son[x][0]];
    if ( son[x][1]!=0 )
        sz[x] += sz[son[x][1]];
}

void Newnode( int data , int father )
{
    sizes++;
    sz[sizes] = 1;
    fa[sizes] = father;
    son[sizes][0] = 0;
    son[sizes][1] = 0;
    val[sizes] = data;
}

int Getsize( int x )
{
    if ( x==0 )
        return 0;
    else
        return sz[x];
}

void Rotate( int x , int kind )
{
    int y = fa[x];
    int z = fa[y];
    son[y][1-kind] = son[x][kind];
    if ( son[x][kind]!=0 )
        fa[son[x][kind]] = y;
    fa[x] = z;
    if ( z!=0 )
        son[z][son[z][1]==y] = x;
    fa[y] = x,son[x][kind] = y;
    Update( y );
    Update( x );
}

void Splay( int x , int ace )
{
    while ( fa[x]!=ace )
    {
        int y = fa[x];
        int z = fa[y];
        if ( z==ace )
            Rotate( x , son[y][1]!=x );
        else
        {
            if ( son[y][1]==x&&son[z][1]==y )
                Rotate( y , 0 ),Rotate( x , 0 );
            else if ( son[y][1]==x&&son[z][0]==y )
                Rotate( x , 0 ),Rotate( x , 1 );
            else if ( son[y][0]==x&&son[z][0]==y )
                Rotate( y , 1 ),Rotate( x , 1 );
            else
                Rotate( x , 1 ),Rotate( x , 0 );
        }
    }
    if ( ace==0 )
        root = x;
}

void Insert( int now , int data , int k )
{
    if ( k==1&&son[now][0]==0 )
        Newnode( data , now ),son[now][0] = sizes;
    else if ( k==2+Getsize(son[now][0])&&son[now][1]==0 )
        Newnode( data , now ),son[now][1] = sizes;
    else if ( k<=1+Getsize(son[now][0]) )
        Insert( son[now][0] , data , k );
    else
        Insert( son[now][1] , data , k-Getsize(son[now][0])-1 );
    Update( now );
}

void Delete( int x )
{
    Splay( x , 0 );
    if ( son[x][0]==0&&son[x][1]==0 )
        root = 0;
    else if ( son[x][0]==0 )
        root = son[x][1],fa[son[x][1]] = 0;
    else if ( son[x][1]==0 )
        root = son[x][0],fa[son[x][0]] = 0;
    else
    {
        int y = son[x][0];
        while ( son[y][1] )
            y = son[y][1];
        fa[son[x][0]] = 0;
        Splay( y , 0 );
        son[y][1] = son[x][1];
        fa[son[x][1]] = y;
        root = y;
        Update( y );
    }
}

int Find( int x )
{
    int now = root;
    while ( true )
    {
        if ( x==1+Getsize(son[now][0]) )
            return now;
        if ( x> 1+Getsize(son[now][0]) )
            x -= 1+Getsize(son[now][0]),now = son[now][1];
        else
            now = son[now][0];
    }
}

int Get( int x )
{
    Splay( x , 0 );
    return Getsize(son[x][0])+1;
}

int main()
{
    for ( int n,m,t ; scanf ( "%d%d" , &n , &m )==2 ; /*printf ("End\n")*/ )
    {
        for ( int i=1 ; i<=n ; i++ )
            scanf ( "%d" , &a[i] ),pos[a[i]] = i;
        sizes = 0;
        for ( int i=1 ; i<=n ; i++ )
        {
            if ( i==1 )
                Newnode( a[i] , 0 ),root = sizes;
            else
                Insert( root , a[i] , i ),Splay( sizes , 0 );
        }
        for ( int i=1 ; i<=m ; i++ )
        {
            char s[15]; int x,y;
            scanf ( "%s%d" , s , &x );
            if ( s[0]=='I' )
                scanf ( "%d" , &y );
            if ( s[0]=='T' )
                Delete( pos[x] ),Insert( root , x , 1 ),pos[x] = sizes,Splay( sizes , 0 );
            else if ( s[0]=='B' )
                Delete( pos[x] ),Insert( root , x , n ),pos[x] = sizes,Splay( sizes , 0 );
            else if ( s[0]=='I' )
                t = Get(pos[x]),t = t+y,Delete(pos[x]),Insert( root , x , t ),Splay( sizes , 0 ),pos[x] = sizes;
            else if ( s[0]=='A' )
                printf ( "%d\n" , Get(pos[x])-1 );
            else
                printf ( "%d\n" , val[Find(x)] );
        }
    }
    return 0;
}