C++AVL樹4種旋轉詳講(左單旋、右單旋、左右雙旋、右左雙旋)

template<class K, class V>
struct AVLtreeNode
{
    //節點建構函式
	AVLtreeNode(const pair<K, V>& kv)
		:_left(nullptr)
		,_right(nullptr)
		,_parent(nullptr)
		,_bf(0)
		,_kv(kv)
	{}
    //節點的成員
    //三叉鏈
	AVLtreeNode<K, V>* _left;
	AVLtreeNode<K, V>* _right;
	AVLtreeNode<K, V>* _parent;
	int _bf;//平衡因子
    //資料使用庫裡面的pair類儲存的kv
	pair<K, V> _kv;
};
template<class K,class V>
class AVLtree
{
	typedef AVLtreeNode<K, V> Node;
public:
    //建構函式
	AVLtree()
		:_root(nullptr)
	{}
    //四種旋轉
	void RotateL(Node* parent)
	void RotateR(Node* parent)
	void RotateLR(Node* parent)
	void RotateRL(Node* parent)
    //插入
	bool Insert(const pair<K, V>& kv)
    //尋找
	Node* Find(const K& kv)
private:
	Node* _root;
};

bool Insert(const pair<K, V>& kv)
	{
		if (_root == nullptr)
		{
			_root = new Node(kv);
			return true;
		}
		Node* parent = _root, *cur = _root;
		while (cur)
		{
			//找nulptr，如果已經有這個key了，二元搜尋樹的特性不支援冗餘，所以返回失敗
			if (cur->_kv.first > kv.first)
			{
				parent = cur;
				cur = cur->_left;
			}
			else if (cur->_kv.first <kv.first)
			{
				parent = cur;
				cur = cur->_right;
			}
			else
			{
				return false;
			}
		}
		//
		cur = new Node(kv);
		//判斷孩子在父親的左邊還是右邊
		if (cur->_kv.first > parent->_kv.first)
		{
			parent->_right = cur;
			cur->_parent = parent;
		}
		else
		{
			parent->_left = cur;
			cur->_parent = parent;
		}
		while (parent)
		{
			//影響一條路徑所有的祖先
			if (parent->_right == cur)
				parent->_bf++;
			else
				parent->_bf--;
			
			if (parent->_bf == 0)
			{
				//左右平衡了不會再影響祖先了
				break;
			}
			if (parent->_bf == 1 || parent->_bf == -1)
			{
				//當前節點所在子樹變了，會影響父親
				// 繼續往上更新
				cur = parent;
				parent = parent->_parent;
			}
			else if (parent->_bf == 2 || parent->_bf == -2)
			{
				//parent所在子樹已經不平衡，需要旋轉處理一下
				if (parent->_bf == -2)
				{
					if (cur->_bf == -1)
						// 右單旋
						RotateR(parent);
					else // cur->_bf == 1
						RotateLR(parent);
				}
				else // parent->_bf  == 2
				{
					if (cur->_bf == 1)
						// 左單旋
						RotateL(parent);
					else // cur->_bf == -1
						RotateRL(parent);
				}
				break;
			}
			else
			{
				// 插入節點之前，樹已經不平衡了，或者bf出錯。需要檢查其他邏輯
				assert(false);
			}
		}
		return true;
	}

void RotateR(Node* parent)
	{
		//軸點的左，孩子節點
		Node* subL = parent->_left;
		//孩子節點的右
		Node* subLR = subL->_right;
		//我的右當你（軸點）的左
		parent->_left = subLR;
		//調整三叉鏈
		if (subLR)
			subLR->_parent = parent;
		//你（軸點）做我的右
		subL->_right = parent;
		//調整三叉鏈
		Node* parentParent = parent->_parent;
		parent->_parent = subL;
 
		if (parent == _root)
		{
			_root = subL;
			_root->_parent = nullptr;
		}
		else
		{
			//軸點的父親新的孩子節點
			if (parentParent->_left == parent)
				parentParent->_left = subL;
			else
				parentParent->_right = subL;
 
			subL->_parent = parentParent;
		}
 
		subL->_bf = parent->_bf = 0;
	}

void RotateL(Node* parent)
	{
		//軸點的右，孩子節點
		Node* subR = parent->_right;
		//孩子節點的左
		Node* subRL = subR->_left;
		//我的左當你（軸點）的右
		parent->_right = subRL;
		//調整三叉鏈
		if (subRL)
		{
			subRL->_parent = parent;
		}
		//你（軸點）做我的左
		subR->_left = parent;
		Node* parentparent = parent->_parent;
 
		parent->_parent = subR;
		if (parent == _root)
		{
			if (parentparent->_left == parent)
				parentparent->_left = subR;
			else
				parentparent->_right = subR;
 
			subR->_parent = parentparent;
		}
		else
		{
			subR->_parent = nullptr;
			_root = subR;
		}
 
		subR->_bf = parent->_bf = 0;
 
	}

void RotateLR(Node* parent)
	{
		Node* subL = parent->_left;
		Node* subLR = subL->_right;
		int bf = subLR->_bf;
 
		RotateL(parent->_left);
		RotateR(parent);
 
		// ...平衡因子調節還需要具體分析
		if (bf == -1)
		{
			subL->_bf = 0;
			parent->_bf = 1;
			subLR->_bf = 0;
		}
		else if (bf == 1)
		{
			parent->_bf = 0;
			subL->_bf = -1;
			subLR->_bf = 0;
		}
		else if (bf == 0)
		{
			parent->_bf = 0;
			subL->_bf = 0;
			subLR->_bf = 0;
		}
		else
		{
			assert(false);
		}
	}

void RotateRL(Node* parent)
	{
		Node* subR = parent->_right;
		Node* subRL = subR->_left;
		int bf = subRL->_bf;
 
		RotateR(parent->_right);
		RotateL(parent);
 
		// 平衡因子更新
		if (bf == 1)
		{
			subR->_bf = 0;
			parent->_bf = -1;
			subRL->_bf = 0;
		}
		else if (bf == -1)
		{
			parent->_bf = 0;
			subR->_bf = 1;
			subRL->_bf = 0;
		}
		else if (bf == 0)
		{
			parent->_bf = 0;
			subR->_bf = 0;
			subRL->_bf = 0;
		}
		else
		{
			assert(false);
		}
	}