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NULLAVLTreeNode<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;elseparent->_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 << " ";
}