(史上超级清晰图解分析版)AVL树的实现--C++

template <class K, class V>
struct AVLTreeNode
{
	//需要parent指针,用于平衡因子
	pair<K, V> _kv;
	AVLTreeNode<K, V>* _left;
	AVLTreeNode<K, V>* _right;
	AVLTreeNode<K, V>* _parent;

	int _bf; //balance factor

	AVLTreeNode(const pair<K, V>& kv)
		:_kv(kv)
		, _right(nullptr)
		, _left(nullptr)
		, _parent(nullptr)
		, _bf(0)
	{}
};

template<class K, class V>
class AVLTree
{
	typedef AVLTreeNode<K, V> Node;
public:
	//...
private:
	Node* _root = nullptr;
};

bool Insert(const pair<K, V>& kv)
{
	if (_root == nullptr)
	{
		_root = new Node(kv); 
		return true;
	}
	Node* parent = nullptr;
	Node* cur = _root;
	while (cur)
	{
		if (cur->_kv.first < kv.first)
		{
			parent = cur;
			cur = cur->_right;
		}
		else if (cur->_kv.first > kv.first)
		{
			parent = cur;
			cur = cur->_left;
		}
		else
		{
			return false;
		}
	}
	cur = new Node(kv);
	if (parent->_kv.first < kv.first)
	{
		parent->_right = cur;
	}
	else
	{
		parent->_left = cur;
	}
	//链接父亲
	cur->_parent = parent;

	//控制平衡
	//更新平衡因子
	while (parent)
	{
		//更新平衡因子
		if (cur == parent->_left)
			parent->_bf--;
		else 
			parent->_bf++;
		if (parent->_bf == 0)
		{
			//更新结束
			break;
		}
		else if (parent->_bf == 1 || parent->_bf == -1)
		{
			//继续往上更新
			cur = parent;
			parent = parent->_parent;
		}
		else if (parent->_bf == 2 || parent->_bf == -2)
		{
			//不平衡了,需要旋转处理
			//...
			break;
		}
		else
		{
			assert(false);
		}
	}
	return true;
}

void RotateR(Node* parent)
{
	Node* subL = parent->_left;
	Node* subLR = subL->_right;

	parent->_left = subLR;
	if (subLR)
		subLR->_parent = parent;
	Node* pParent = parent->_parent;
	
	subL->_right = parent;
	parent->_parent = subL;

	if (parent == _root)
	{
		_root = subL;
		subL->_parent = nullptr;
	}
	else
	{
		if (pParent->_left == parent)
		{
			pParent->_left = subL;
		}
		else
		{
			pParent->_right = subL;
		}
		subL->_parent = pParent;
	}
	subL->_bf = 0;
	parent->_bf = 0;
}

void RotateL(Node* parent)
{
	Node* subR = parent->_right;
	Node* subRL = subR->_left;
	parent->_right = subRL;
	if (subRL)
		subRL->_parent = parent;

	Node* parentParent = parent->_parent;
	subR->_left = parent;
	parent->_parent = subR;
	if (parentParent == nullptr)
	{
		_root = subR;
		subR->_parent = nullptr;
	}
	else
	{
		if (parent == parentParent->_left)
		{
			parentParent->_left = subR;
		}
		else
		{
			parentParent->_right = subR;
		}
		subR->_parent = parentParent;
	}

	subR->_bf = 0;
	parent->_bf = 0;
}

void RotateLR(Node* parent)
{
	Node* subL = parent->_left;
	Node* subLR = subL->_right;
	int bf = subLR->_bf;

	RotateL(parent->_left);
	RotateR(parent);

	if (bf == -1)
	{
		subL->_bf = 0;
		subLR->_bf = 0;			
		parent->_bf = 1;
	}
	else if (bf == 1)
	{
		subL->_bf = -1;
		subLR->_bf = 0;		
		parent->_bf = 0;
	}
	else if (bf == 0)
	{
		subL->_bf = 0;
		subLR->_bf = 0;		
		parent->_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);

	if (bf == -1)
	{
		subR->_bf = 1;
		subRL->_bf = 0;
		parent->_bf = 0;
	}
	else if (bf == 1)
	{
		subR->_bf = 0;
		subRL->_bf = 0;
		parent->_bf = -1;
	}
	else if (bf == 0)
	{
		subR->_bf = 0;
		subRL->_bf = 0;		
		parent->_bf = 0;
	}
	else
	{
		assert(false);
	}
}

Node* Find(const K& key)
{
	Node* cur = _root;
	while (cur)
	{
		if (cur->_kv.first < key)
		{
			cur = cur->_right;
		}
		else if (cur->_kv.first > key)
		{
			cur = cur->_left;
		}
		else
		{
			return cur;
		}
	}
	return nullptr;
}

void _InOrder(Node* root)
{
	if (root == nullptr)
	{
		return;
	}
	_InOrder(root->_left);
	cout << root->_kv.first << ":" << root->_kv.second << endl;
	_InOrder(root->_right);
}
int _Height(Node* root)
{
	if (root == nullptr)
		return 0;
	int leftHeight = _Height(root->_left);
	int rightHeight = _Height(root->_right);
	return leftHeight > rightHeight ? leftHeight + 1 : rightHeight + 1;
}

int _Size(Node* root)
{
	if (root == nullptr)
	{
		return 0;
	}
	return _Size(root->_left) + _Size(root->_right) + 1;
}

bool _isBalanceTree(Node* root)
{
	//空树也是AVL树
	if (root == nullptr)
		return true;

	//计算pRoot结点的平衡因子:即pRoot左右子树的高度差
	int leftHeight = _Height(root->_left);
	int rightHeight = _Height(root->_right);
	int diff = rightHeight - leftHeight;

	//如果计算出的平衡因子与pRoot的平衡因子不相等,
	//或者pRoot平衡因子的绝对值超过1,则一定不是AVL树
	if (abs(diff) >= 2)
	{
		cout << root->_kv.first << "高度差异常" << endl;
		return false;
	}
	if (root->_bf != diff)
	{
		cout << root->_kv.first << "平衡因子异常" << endl;
	}
	//pRoot的左和右如果都是AVL树,则该树一定是AVL树
	return _isBalanceTree(root->_left) && _isBalanceTree(root->_right);
}