【C++高阶】掌握AVL树：构建与维护平衡二叉搜索树的艺术

template<class K,class V>
struct AVLTreeNode
{
	AVLTreeNode<K, V>* _left; // 该节点的左孩子
	AVLTreeNode<K, V>* _right; // 该节点的右孩子
	AVLTreeNode<K, V>* _parent; // 该节点的父亲
	
	pair<K, V> _kv;  // pair

	int _bf; // balance factor 该节点的平衡因子

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

template<class K,class V>
class AVLTree
{
	typedef AVLTreeNode<K, V> Node;
public:
	// 其他未实现的成员函数
private:
	Node* _root = nullptr;
};

bool Insert(const pair<K, V>& kv)
{
	// 当根节点为空时直接插入
	if (_root == nullptr)
	{
		_root = new Node(kv);
		return true;
	}
	Node* parent = nullptr;
	Node* cur = _root;
		
	// 寻找插入位置
	while (cur)
	{
		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;
		}
	}
	// 链接新节点
	cur = new Node(kv);
	if (parent->_kv.first > kv.first)
	{
		parent->_left = cur;
		cur->_parent = parent;
	}
	else
	{
		parent->_right = cur;
		cur->_parent = parent;
	}
	// 更改平衡因子
	while (parent)
	{
		if (cur == parent->_left)
		{
			parent->_bf--;
		}
		else
		{
			parent->_bf++;
		} 

		if (parent->_bf == 0)
		{
			break;
		}
		// 向上遍历，判断祖先是否受到影响
		else if (parent->_bf == 1 || parent->_bf == -1)
		{
			cur = parent;
			parent = parent->_parent;
		}
		// 平衡出现问题，需要进行修理
		else if(parent->_bf == 2 || parent->_bf == -2)
		{
			// 旋转
			if (parent->_bf == 2 && cur->_bf == 1)
			{
				RotateL(parent);
			}
			else if (parent->_bf == -2 && cur->_bf == -1)
			{
				RotateR(parent);
			}
			else if (parent->_bf == -2 && cur->_bf == 1)
			{
				RotateLR(parent);
			}
			else if (parent->_bf == 2 && cur->_bf == -1)
			{
				RotateRL(parent);
			}
			break;
		}
		else
		{
			assert(false);
		}
	}
	return true;
}

void RotateR(Node* parent)
{
	// 定义parent的左孩子 和 parent的左孩子的右孩子
	Node* subL = parent->_left;
	Node* subLR = subL->_right;

	parent->_left = subLR;
	if (subLR)
	{
		subLR->_parent = parent;
	}
	// 当旋转点是子树时，保留父亲节点
	Node* Parentparent = parent->_parent;

	subL->_right = parent;
	parent->_parent = subL;
	// 当旋转点是根时，跟新根节点
	if (_root == parent)
	{
		_root = subL;
		subL->_parent = nullptr;
	}
	// 当旋转点是子树时，更新链接
	else
	{
		if (parent == Parentparent->_left)
		{
			Parentparent->_left = subL;
		}
		else
		{
			Parentparent->_right = subL;
		}

		subL->_parent = Parentparent;
	}
	// 更新平衡因子为0
	parent->_bf = subL->_bf = 0;
}

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

	parent->_right = subRL;
	subR->_left = parent;

	Node* Parentparent = parent->_parent;

	parent->_parent = subR;
	if (subRL)
	{
		subRL->_parent = parent;
	}

	// 判断parent是不是根节点
	if (_root == parent)
	{
		_root = subR;
		subR->_parent = nullptr;
	}
	else
	{
		if (parent == Parentparent->_left)
		{
			Parentparent->_left = subR;
		}
		else
		{
			Parentparent->_right = subR;
		}
   		subR->_parent = Parentparent;
	}
	parent->_bf = subR->_bf = 0;
}

void RotateLR(Node* parent)
{
	Node* subL = parent->_left;
	Node* subLR = subL->_right;
	int bf = subLR->_bf; // 根据右子树的右孩子的平衡因子，判断旋转后的平衡因子情况

	// 复用单旋
	RotateL(parent->_left);
	RotateR(parent);

	// subLR就是新插入节点
	if (bf == 0)
	{
		parent->_bf = subL->_bf = subLR->_bf = 0;
	}
	else if (bf == 1)
	{
		subLR->_bf = 0;
		parent->_bf = 0;
		subL->_bf = -1;
	}
	else if (bf == -1)
	{
		subLR->_bf = 0;
		parent->_bf = 1;
		subL->_bf = 0;
	}
	else
	{
		assert(false);
	}
}

void RotateRL(Node* parent)
	{
	Node* subR = parent->_right;
	Node* subRL = subR->_left;
	int bf = subRL->_bf;
	
	// 复用单旋
	RotateR(parent->_right);
	RotateL(parent);

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

// 中序遍历
void InOrder()
{
	_InOrder(_root);
	cout << endl;
}

void _InOrder(Node* root)
{
	if (root == nullptr)
	{
		return;
	}
	_InOrder(root->_left);
	cout << root->_kv.first << " ";
	_InOrder(root->_right);
}

bool IsBalance()
{
	return _IsBalance(_root);
}

int _Height(Node* root)
{
	if (root == nullptr)
	{
		return;
	}
	int rightHeight = _Height(root->_right);
	int leftHeight = _Height(root->_left);

	return rightHeight > leftHeight ? rightHeight + 1 : leftHeight + 1;
}

bool _IsBalance(Node* root)
{
	if (root == nullptr)
	{
		return true;
	}

	int rightHeight = _Height(root->_right);
	int leftHeight = _Height(root->_left);

	if (rightHeight - leftHeight != root->_bf)
	{
		cout << root->_kv.first << "平衡因子有误" << endl;
		return false;
	}

	return abs(rightHeight - leftHeight) < 2
		&& _IsBalance(root->_left)
		&& _IsBalance(root->_right);
}

int main()
{
	// 这里会进行双旋
	int a[] = { 4, 2, 6, 1, 3, 5, 15, 7, 16, 14 };
	AVLTree<int, int> t;
	
	for (auto e : a)
	{
		t.Insert(make_pair(e, e));
	}
	t.InOrder();
	cout << t.IsBalance() << endl;

	return 0;
}