AVL树的操作——郁闷的出纳员，平衡树解法
今天学习了一下AVL，顺便用AVL树 A掉了这道经典的题，以前用树状数组解过这个题，今天记录一下AVL的解法。如有错误之处欢迎指正，各位大牛不要笑话我。
该题需要用平衡树：定义这样的一颗平衡树，根节点大于等于左儿子节点，小于右儿子节点。（也可以规范的定义左儿子小于根，小于右儿子，但是要加入新的数据域）
为了球第K小，除了原本的height域以外加入一个size域，表示以当前节点为跟的子树有多少个节点。
操作1：数据域的维护
首先要在旋转前维护该节点的子树的height和size，然后才能根据更新的数据，判断该树是否平衡，然后旋转
void fix(node* &R)
{
R->h = max(R->rchild->h,R->lchild->h) + 1;
R->size = R->rchild->size + R->lchild->size + 1;
}
操作2:旋转化操作
插入和删除的时候用同样的旋转维护该树
void rightsinglerotate(node* &R)//LL型旋转,单旋一次
{
node * lc = R->lchild;
R->lchild = lc->rchild;
fix(R);
lc->rchild = R;
R = lc;
fix(R);
}
void leftsinglerotate(node* &R)//RR型旋转,单选一次
{
node * rc = R->rchild;
R->rchild = rc->lchild;
fix(R);
rc->lchild = R;
R = rc;
fix(R);
}
void leftdoublerotate(node* &R)//RL型旋转,双旋
{
rightsinglerotate(R->rchild);
leftsinglerotate(R);
}
void rightdoublerotate(node* &R)//LR型旋转,双旋
{
leftsinglerotate(R->lchild);
rightsinglerotate(R);
}
void maintain(node* &R)
{
if(R->lchild != MYNULL)
{
if(R->lchild->lchild->h == R->rchild->h + 1)
rightsinglerotate(R);
else if(R->lchild->rchild->h == R->rchild->h + 1)
rightdoublerotate(R);
}
if(R->rchild != MYNULL)
{
if(R->rchild->rchild->h == R->lchild->h + 1)
leftsinglerotate(R);
else if(R->rchild->lchild->h == R->lchild->h + 1)
leftdoublerotate(R);
}
}
操作3：求第K小的操作，也就是size域的用途
int findK(node* &R,int k)
{
if(k == R->lchild->size + 1)
return R->value;
else if(k <= R->lchild->size)
return findK(R->lchild,k);
else if(k > R->size - R->rchild->size)
return findK(R->rchild,k + R->rchild->size - R->size);
}
操作4：erase函数，要完成该题的统计功能，看erase了多少次
void erase(node* &R,T value)
{
if(R == MYNULL)
return;
if(R->value == value)
{
if(R->rchild == MYNULL)
{
node * tmp = R;
R = tmp->lchild;
}
else
{
node *tmp = R->rchild;
while(tmp->lchild != MYNULL)
tmp = tmp->lchild;
R->value = tmp->value;
erase(R->rchild,tmp->value);
fix(R);
}
return;
}
else if(value < R->value)
erase(R->lchild,value);
else if(value < R->value)
erase(R->rchild,value);
fix(R);
maintain(R);
}
最后在调整树使其不失衡。
有了这些操作就可以轻松的完成题目的要求了，
完整的代码如下
/*
* =====================================================================================
*
* Filename: AVLtree.cpp
*
* Description: AVLtree with template
*
* Version: 1.0
* Created: 2010年12月27日 09时45分44秒
* Revision: none
* Compiler: gcc
*
* Author: ronaflx
* Company: hit-acm-group
*
* =====================================================================================
*/
#include <iostream>
#include <cstring>
#include <cstdio>
using namespace std;
int delta;
const int INF = 10000000;
template<typename T>
class AVL
{
public:
AVL()
{
pp = pool;
TMP = node(0,0,NULL,NULL);
MYNULL = &TMP;
roof = MYNULL;
}
void insert(T k)
{
insert(roof,k);
}
void erase(T k)
{
erase(roof,k);
}
bool empty()
{
return roof == MYNULL;
}
int findK(int k)
{
if(k <= 0)
return -INF;
return findK(roof,k);
}
struct node
{
node *lchild,*rchild;
T value;
int h,size;
node(){}
node (int h,int size,node * lchild,node *rchild)
{
this->size = size;
this->h = h;
this->lchild = lchild;
this->rchild = rchild;
}
};
node* roof;
private:
#define max(a,b) ((a) < (b) ? (b) : (a))
static const int N = 1000000;
node* MYNULL,TMP;
//为了快速方便的求高度而设立的虚空节点
node pool[N],*pp;
int findK(node* &R,int k)
{
if(k == R->lchild->size + 1)
return R->value;
else if(k <= R->lchild->size)
return findK(R->lchild,k);
else if(k > R->size - R->rchild->size)
return findK(R->rchild,k + R->rchild->size - R->size);
}
void fix(node* &R)
{
R->h = max(R->rchild->h,R->lchild->h) + 1;
R->size = R->rchild->size + R->lchild->size + 1;
}
void rightsinglerotate(node* &R)//LL型旋转,单旋一次
{
node * lc = R->lchild;
R->lchild = lc->rchild;
fix(R);
lc->rchild = R;
R = lc;
fix(R);
}
void leftsinglerotate(node* &R)//RR型旋转,单选一次
{
node * rc = R->rchild;
R->rchild = rc->lchild;
fix(R);
rc->lchild = R;
R = rc;
fix(R);
}
void leftdoublerotate(node* &R)//RL型旋转,双旋
{
rightsinglerotate(R->rchild);
leftsinglerotate(R);
}
void rightdoublerotate(node* &R)//LR型旋转,双旋
{
leftsinglerotate(R->lchild);
rightsinglerotate(R);
}
void maintain(node* &R)
{
if(R->lchild != MYNULL)
{
if(R->lchild->lchild->h == R->rchild->h + 1)
rightsinglerotate(R);
else if(R->lchild->rchild->h == R->rchild->h + 1)
rightdoublerotate(R);
}
if(R->rchild != MYNULL)
{
if(R->rchild->rchild->h == R->lchild->h + 1)
leftsinglerotate(R);
else if(R->rchild->lchild->h == R->lchild->h + 1)
leftdoublerotate(R);
}
}
void insert(node* &R,T value)
{
if(R == MYNULL)
{
R = mynew(value);
return;
}
else if(value <= R->value)
insert(R->lchild,value);
else if(value > R->value)
insert(R->rchild,value);
fix(R);
maintain(R);
}
void erase(node* &R,T value)
{
if(R == MYNULL)
return;
if(R->value == value)
{
if(R->rchild == MYNULL)
{
node * tmp = R;
R = tmp->lchild;
}
else
{
node *tmp = R->rchild;
while(tmp->lchild != MYNULL)
tmp = tmp->lchild;
R->value = tmp->value;
erase(R->rchild,tmp->value);
fix(R);
}
return;
}
else if(value < R->value)
erase(R->lchild,value);
else if(value < R->value)
erase(R->rchild,value);
fix(R);
maintain(R);
}
node* mynew(T value)
{
pp->lchild = pp->rchild = MYNULL;
pp->size = pp->h = 1;
pp->value = value;
return pp++;
}
#undef max
};
AVL<int> avltree;
int main()
{
int n,minn;
char cmd;
int f,cnt = 0;
while(scanf("%d %d",&n,&minn) == 2)
{
delta = 0;
cnt = 0;
while(!avltree.empty())
{
avltree.erase(avltree.roof->value);
}
for(int i = 0;i < n;i++)
{
scanf(" %c %d",&cmd,&f);
if(cmd == 'I')
{
if(f < minn)
continue;
avltree.insert(f - delta);
}
else if(cmd == 'A')
delta += f;
else if(cmd == 'F')
{
int tmp = avltree.findK(avltree.roof->size - f + 1);
if(tmp == -INF)
printf("-1\n");
else
printf("%d\n",tmp + delta);
}
else if(cmd == 'S')
{
delta -= f;
while(!avltree.empty())
{
int tmp = avltree.findK(1);
tmp += delta;
if(tmp >= minn)
break;
else
{
cnt++;
avltree.erase(tmp - delta);
}
}
}
}
printf("%d\n",cnt);
}
return 0;
}