C++实现平衡二叉树

template<class K, class V>
struct AVLTreeNode
{
    K _key;                //树权值
    V _value;
    int  _bf;            //平衡因子 -1,0,1        (每个节点的平衡因子等于左子树的高度减去右子树的高度) 
                        //有的教材定义平衡度是左子树高度减去右子树，都是可以的
    AVLTreeNode<K, V>* _parent;    //指向父节点的指针
    AVLTreeNode<K, V>* _left;            //指向左孩子的指针
    AVLTreeNode<K, V>* _right;        //指向右孩子的指针

    AVLTreeNode(const K& key = K(), const V& value = V())
        :_key(key)
        , _value(value)
        , _bf(0)
        , _parent(NULL)
        , _left(NULL)
        , _right(NULL)
    {}
};

//左改组LL型
template<class K, class V>
void AVLTree<K, V>::_RotateLL(AVLTreeNode<K, V>*&  parent)
{
    AVLTreeNode<K, V>* subL = parent->_left; //构造的左子树
    AVLTreeNode<K, V>* subLR = subL->_right;//subL的右子树
    AVLTreeNode<K, V>* ppNode = parent->_parent;//标记祖先节点
    //1.构建parent子树 将parent和subLR链接起来
    parent->_left = subLR;
    if (subLR) subLR->_parent = parent;
    //2.构建subL子树 将subL与parent链接起来
    subL->_right = parent;
    parent->_parent = subL;
    //3.将祖先节点与subL链接起来
    if (ppNode == NULL)
    {    //如果祖先为NULL，说明当前subL节点为根节点
        subL->_parent = NULL;
        _root = subL;
    }
    else
    {
        subL->_parent = ppNode;
        if (ppNode->_left == parent)
            ppNode->_left = subL;
        else if (ppNode->_right == parent)
            ppNode->_right = subL;
    }
    //4.重置平衡因子
    parent->_bf = 0;
    subL->_bf = 0;
    //5.更新subL为当前父节点
    parent = subL;
}

//左改组LR型
template<class K, class V>
void AVLTree<K, V>::_RotateLR(AVLTreeNode<K, V>*&  parent)
{
    AVLTreeNode<K, V>* pNode = parent;
    AVLTreeNode<K, V>* subR = parent->_right;
    AVLTreeNode<K, V>* subLR = subR->_left;
    int bf = subLR->_bf;

    _RotateLL(parent->_right);
    _RotateRR(parent);
    //LR(b)型
    if (bf == -1)
    {
        pNode->_bf = 0;
        subR->_bf = 1;
    }
    //LR(a)型
    else if (bf == 1)
    {
        pNode->_bf = -1;
        subR->_bf = 0;
    }
    //LR(c)型
    else
    {
        pNode->_bf = 0;
        subR->_bf = 0;
    }
}

template<class K, class V>
bool AVLTree<K, V>::Insert(const K& key, const V& value)
{
    //1.空树
    if (_root == NULL)
    {
        _root = new AVLTreeNode<K, V>(key, value);
        return true;
    }

    //2.AVL树不为NULL
    AVLTreeNode<K, V>* parent = NULL;
    AVLTreeNode<K, V>* cur = _root;
    //找到数据插入位置
    while (cur)
    {
        if (cur->_key < key)
        {
            parent = cur;
            cur = cur->_right;
        }
        else if (cur->_key > key)
        {
            parent = cur;
            cur = cur->_left;
        }
        else
        {
            return false;
        }
    }
    //插入数据
    cur = new AVLTreeNode<K, V>(key, value);
    cur->_parent = parent;
    if (parent->_key > key)
        parent->_left = cur;
    else
        parent->_right = cur;

    while (parent)
    {
        //更新平衡因子
        if (cur == parent->_left)
            parent->_bf++;
        else if (cur == parent->_right)
            parent->_bf--;

        //检验平衡因子是否合法
        if (parent->_bf == 0)
            break;
        else if (parent->_bf == -1 || parent->_bf == 1)
        {    // 回溯上升 更新祖父节点的平衡因子并检验合法性
            cur = parent;
            parent = cur->_parent;
        }
        //    2 -2 平衡因子不合法 需要进行旋转 降低高度
        else   
        {
            if (parent->_bf == -2)
            {
                if (cur->_bf == -1)
                    _RotateRR(parent);
                else
                    _RotateLR(parent);
            }
            else if (parent->_bf == 2)
            {
                if (cur->_bf == 1)
                    _RotateLL(parent);
                else
                    _RotateRL(parent);
            }
            break;
        }
    }
}

//中序遍历
template<class K, class V>
void AVLTree<K, V>::_InOrder(AVLTreeNode<K, V>* root)
{
    if (root == NULL)
        return;
    _InOrder(root->_left);
    cout << root->_key << " ";
    _InOrder(root->_right);
}
//前序遍历
template<class K, class V>
void AVLTree<K, V>::_PreOrder(AVLTreeNode<K, V>* root)
{
    if (root == NULL)
        return;
    cout << root->_key << " ";
    _PreOrder(root->_left);
    _PreOrder(root->_right);
}
//后序遍历
template<class K, class V>
void AVLTree<K, V>::_PostOrder(AVLTreeNode<K, V>* root)
{
    if (root == NULL)
        return;
    _PostOrder(root->_left);
    _PostOrder(root->_right);
    cout << root->_key << " ";
}