AVLTree

#include <iostream>
using namespace std;

struct TreeNode
{
    char data;
    int heigth;
    TreeNode* rchild;
    TreeNode* lchild;
};

class AVLTree
{
public:
    AVLTree(){top = NULL;}
    TreeNode* MakeEmpty();
    void Delete(char elem,TreeNode* &position,bool& isdel);
    TreeNode* Insert(char elem,TreeNode* &position);
    TreeNode* IsExist(char elem);
    void Create();

    //处理之后position指向原position的左根
    TreeNode* SingleRotateWithLeft(TreeNode* &position);
    //处理之后position指向原position的右根
    TreeNode* SingleRotateWithRight(TreeNode* &position);
    TreeNode* DoubleRotateWithLeft(TreeNode* &position);
    TreeNode* DoubleRotateWithRight(TreeNode* &position);
    int Max(int n1,int n2);
    int Heigth(TreeNode* position);


private:
    TreeNode* top;

};

//判断节点高度
int AVLTree::Heigth(TreeNode* position)
{
    if (position == NULL)
    {
        return -1;
    }
    else
    {
        int n = position->heigth;
        return n;
    }
}

//判断大小、
int AVLTree::Max(int n1,int n2)
{
    return (n1>n2)?n1:n2;
}

//左旋,左孩子作为新的根节点,新根的右孩子成为原根的左孩子，原根成为新根的右孩子
TreeNode* AVLTree::SingleRotateWithLeft(TreeNode* &position)
{
    TreeNode* pos = (position)->lchild;
    (position)->lchild = pos->rchild;
    pos->rchild = position;

    (position)->heigth = Max(Heigth((position)->lchild),Heigth((position)->rchild)) + 1;
    (pos)->heigth = Max(Heigth((pos)->lchild),Heigth((pos)->rchild)) + 1;
    return pos;
}

//右旋,右孩子作为新的根节点,新根的左孩子成为原根的右孩子，原根成为新根的左孩子
TreeNode* AVLTree::SingleRotateWithRight(TreeNode* &position)
{
    TreeNode* pos = (position)->rchild;
    (position)->rchild = pos->lchild;
    pos->lchild = position;

    (position)->heigth = Max(Heigth((position)->lchild),Heigth((position)->rchild)) + 1;
    (pos)->heigth = Max(Heigth((pos)->lchild),Heigth((pos)->rchild)) + 1;
    return pos;
}

//左侧双旋
TreeNode* AVLTree::DoubleRotateWithLeft(TreeNode* &position)
{
    position->lchild = SingleRotateWithRight(position->lchild);
    return SingleRotateWithLeft(position);
}

//右侧双旋
TreeNode* AVLTree::DoubleRotateWithRight(TreeNode* &position)
{
    position->rchild = SingleRotateWithLeft(position->rchild);
    return SingleRotateWithRight(position);
}

TreeNode* AVLTree::Insert(char elem,TreeNode* &position)
{
    if (position == NULL)
    {
        position = new TreeNode;
        position->data = elem;
        position->lchild = position->rchild = NULL;
        position->heigth = 0;
    }
    else if (elem < position->data)
    {
        position->lchild = Insert(elem,position->lchild);
        if (Heigth(position->lchild) - Heigth(position->rchild) == 2)
        {
            if (elem < position->lchild->data)
            {
                position = SingleRotateWithLeft(position);
            } 
            else
            {
                position = DoubleRotateWithLeft(position);
            }
        }
    } 
    else if(elem > position->data)
    {
        position->rchild = Insert(elem,position->rchild);
        if (Heigth(position->rchild) - Heigth(position->lchild) == 2)
        {
            if (elem < position->rchild->data)
            {
                position = DoubleRotateWithRight(position);
            } 
            else
            {
                position = SingleRotateWithRight(position);
            }
        }
    }
    else
    {
        //数据已存在
    }

    position->heigth = Max(Heigth(position->lchild) , Heigth(position->rchild)) + 1;
    return position;
}

void AVLTree::Delete(char elem,TreeNode* &position,bool& isdel)
{
    bool is_left = false;
    //寻找值并删除
    if (position == NULL)
    {
        cout<<"This elem is not existed!"<<endl;
        isdel = false;
    }
    else if (position->data == elem)
    {
        if (position->lchild == NULL)//包括右孩子为空和右孩子不为空
        {
            TreeNode* temp = position;
            position = position->rchild;
            delete temp;
            temp = NULL;
        }
        else if (position->rchild == NULL)//右孩子为空做孩子不为空
        {
            TreeNode* temp = position;
            position = position->lchild;
            delete temp;
            temp = NULL;
        }
        else//做右孩子都不为空
        {
            TreeNode* temp = position;
            temp = temp->lchild;
            while (temp->rchild)
            {
                temp = temp->rchild;
            }
            position->data = temp->data;
            Delete(temp->data,position->lchild,isdel);
            is_left = true;
        }
        isdel = true;
    }
    else if (position->data > elem)
    {
        Delete(elem,position->lchild,isdel);
        is_left = true;
    } 
    else if(position->data < elem)
    {
        Delete(elem,position->rchild,isdel);
        is_left = false;
    }

    //平衡并重新制定高度
    if (isdel && position)
    {
        if (is_left)//删除的为左子树部分
        {
            if (Heigth(position->rchild) - Heigth(position->lchild) == 2)
            {
                if (elem < position->rchild->data)
                {
                    position = DoubleRotateWithRight(position);
                } 
                else
                {
                    position = SingleRotateWithRight(position);
                }
            }
        } 
        else//删除为右子树部分
        {
            if (Heigth(position->lchild) - Heigth(position->rchild) == 2)
            {
                if (elem < position->lchild->data)
                {
                    position = SingleRotateWithLeft(position);
                } 
                else
                {
                    position = DoubleRotateWithLeft(position);
                }
            }
        }
        //重新制定高度，position ！= NULL
        position->heigth = Max(Heigth(position->lchild) , Heigth(position->rchild)) + 1;
    }
}

void AVLTree::Create()
{
    char a[10] = {'a','b','c','d','e','f','g','p','o','n'};
    for (int i = 0;i < 10; i++)
    {
        Insert(a[i],top);
    }

    //test
    bool bl;
    //     Delete('e',top,bl);
    //     Delete('f',top,bl);
    Delete('d',top,bl);
}