平衡二叉树

#include <iostream>

#include <algorithm>

using namespace std;

//平衡二叉树结点

template <typename T>

struct AvlNode

{

    T data;

    int height; //结点所在高度

    AvlNode<T> *left;

    AvlNode<T> *right;

    AvlNode<T>(const T theData) : data(theData), left(NULL), right(NULL), height(0){}

};

 

//AvlTree

template <typename T>

class AvlTree

{

public:

    AvlTree<T>(){}

    ~AvlTree<T>(){}

    AvlNode<T> *root;

    //插入结点

    void Insert(AvlNode<T> *&t, T x);

    //删除结点

    bool Delete(AvlNode<T> *&t, T x);

    //查找是否存在给定值的结点

    bool Contains(AvlNode<T> *t, const T x) const;

    //中序遍历

    void InorderTraversal(AvlNode<T> *t);

    //前序遍历

    void PreorderTraversal(AvlNode<T> *t);

    //最小值结点

    AvlNode<T> *FindMin(AvlNode<T> *t) const;

    //最大值结点

    AvlNode<T> *FindMax(AvlNode<T> *t) const;

private:

    //求树的高度

    int GetHeight(AvlNode<T> *t);

    //单旋转 左

    AvlNode<T> *LL(AvlNode<T> *t);

    //单旋转 右

    AvlNode<T> *RR(AvlNode<T> *t);

    //双旋转 右左

    AvlNode<T> *LR(AvlNode<T> *t);

    //双旋转 左右

    AvlNode<T> *RL(AvlNode<T> *t);

};

 

template <typename T>

AvlNode<T> * AvlTree<T>::FindMax(AvlNode<T> *t) const

{

    if (t == NULL)

        return NULL;

    if (t->right == NULL)

        return t;

    return FindMax(t->right);

}

 

template <typename T>

AvlNode<T> * AvlTree<T>::FindMin(AvlNode<T> *t) const

{

    if (t == NULL)

        return NULL;

    if (t->left == NULL)

        return t;

    return FindMin(t->left);

}

 

 

template <typename T>

int AvlTree<T>::GetHeight(AvlNode<T> *t)

{

    if (t == NULL)

        return -1;

    else

        return t->height;

}

 

 

//单旋转

//左左插入导致的不平衡

template <typename T>

AvlNode<T> * AvlTree<T>::LL(AvlNode<T> *t)

{

    AvlNode<T> *q = t->left;

    t->left = q->right;

    q->right = t;

    t = q;

    t->height = max(GetHeight(t->left), GetHeight(t->right)) + 1;

    q->height = max(GetHeight(q->left), GetHeight(q->right)) + 1;

    return q;

}

 

//单旋转

//右右插入导致的不平衡

template <typename T>

AvlNode<T> * AvlTree<T>::RR(AvlNode<T> *t)

{

    AvlNode<T> *q = t->right;

    t->right = q->left;

    q->left = t;

    t = q;

    t->height = max(GetHeight(t->left), GetHeight(t->right)) + 1;

    q->height = max(GetHeight(q->left), GetHeight(q->right)) + 1;

    return q;

}

 

//双旋转

//插入点位于t的左儿子的右子树

template <typename T>

AvlNode<T>* AvlTree<T>::LR(AvlNode<T> *t)

{

//双旋转可以通过两次单旋转实现

//对t的左结点进行RR旋转,再对根节点进行LL旋转

AvlNode<T> * q = RR(t->left);

t->left = q;

return LL(t);

}

 

//双旋转

//插入点位于t的右儿子的左子树

template <typename T>

AvlNode<T> * AvlTree<T>::RL(AvlNode<T> *t)

{

AvlNode<T> *q = LL(t->right);

t->right = q;

return RR(t);

}

 

 

template <typename T>

void AvlTree<T>::Insert(AvlNode<T> *&t, T x)

{

    if (t == NULL)

        t = new AvlNode<T>(x);

    else if (x < t->data)

    {

        Insert(t->left, x);

        //判断平衡情况

        if (GetHeight(t->left) - GetHeight(t->right) > 1)

        {

            //分两种情况 左左或左右

 

            if (x < t->left->data)//左左

                t = LL(t);

            else                  //左右

                t = LR(t);

        }

    }

    else if (x > t->data)

    {

        Insert(t->right, x);

        if (GetHeight(t->right) - GetHeight(t->left) > 1)

        {

            if (x > t->right->data)

                t = RR(t);

            else

                t = RL(t);

        }

    }

    else

        ;//数据重复

    t->height = max(GetHeight(t->left), GetHeight(t->right)) + 1;

}

 

template <typename T>

bool AvlTree<T>::Delete(AvlNode<T> *&t, T x)

{

    //t为空 未找到要删除的结点

    if (t == NULL)

        return false;

    //找到了要删除的结点

    else if (t->data == x)

    {

        //左右子树都非空

        if (t->left != NULL && t->right != NULL)

        {//在高度更大的那个子树上进行删除操作

 

            //左子树高度大,删除左子树中值最大的结点,将其赋给根结点

            if (GetHeight(t->left) > GetHeight(t->right))

            {

                t->data = FindMax(t->left)->data;

                Delete(t->left, t->data);

            }

            else//右子树高度更大,删除右子树中值最小的结点,将其赋给根结点

            {

                t->data = FindMin(t->right)->data;

                Delete(t->right, t->data);

            }

        }

        else

        {//左右子树有一个不为空,直接用需要删除的结点的子结点替换即可

            AvlNode<T> *old = t;

            t = t->left ? t->left: t->right;//t赋值为不空的子结点

            delete old;

        }

    }

    else if (x < t->data)//要删除的结点在左子树上

    {

        //递归删除左子树上的结点

        Delete(t->left, x);

        //判断是否仍然满足平衡条件

        if (GetHeight(t->right) - GetHeight(t->left) > 1)

        {

            if (GetHeight(t->right->left) > GetHeight(t->right->right))

            {

                //RL双旋转

                t = RL(t);

            }

            else

            {//RR单旋转

                t = RR(t);

            }

        }

        else//满足平衡条件 调整高度信息

        {

            t->height = max(GetHeight(t->left), GetHeight(t->right)) + 1;

        }

    }

    else//要删除的结点在右子树上

    {

        //递归删除右子树结点

        Delete(t->right, x);

        //判断平衡情况

        if (GetHeight(t->left) - GetHeight(t->right) > 1)

        {

            if (GetHeight(t->left->right) > GetHeight(t->left->left))

            {

                //LR双旋转

                t = LR(t);

            }

            else

            {

                //LL单旋转

                t = LL(t);

            }

        }

        else//满足平衡性 调整高度

        {

            t->height = max(GetHeight(t->left), GetHeight(t->right)) + 1;

        }

    }

   

    return true;

}

 

//查找结点

template <typename T>

bool AvlTree<T>::Contains(AvlNode<T> *t, const T x) const

{

    if (t == NULL)

        return false;

    if (x < t->data)

        return Contains(t->left, x);

    else if (x > t->data)

        return Contains(t->right, x);

    else

        return true;

}

 

//中序遍历

template <typename T>

void AvlTree<T>::InorderTraversal(AvlNode<T> *t)

{

    if (t)

    {

        InorderTraversal(t->left);

        cout << t->data << ' ';

        InorderTraversal(t->right);

    }

}

 

//前序遍历

template <typename T>

void AvlTree<T>::PreorderTraversal(AvlNode<T> *t)

{

    if (t)

    {

        cout << t->data << ' ';

        PreorderTraversal(t->left);

        PreorderTraversal(t->right);

    }

}

 

posted @ 2019-03-24 08:05  WanTong  阅读(146)  评论(0编辑  收藏  举报