数据结构 —— AVL树

//节点
template<class K, class V>
struct AVLTreeNode
{
    //需要parent指针，后续更新平衡因?可以看到 
    pair<K, V> _kv;
    AVLTreeNode<K, V>* _left;
    AVLTreeNode<K, V>* _right;
    AVLTreeNode<K, V>* _parent;//加上一个_parent构成三叉列
    int _bf; // balance factor 平衡因子
    AVLTreeNode(const pair<K, V>& kv)
        :_kv(kv)
        , _left(nullptr)
        , _right(nullptr)
        , _parent(nullptr)
        , _bf(0)
    {}
};

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

//按二叉搜索树规则进行插入
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;
	}
	//链接父节点
	cur->_parent = parent;

    return true;
}

//如果更新后的parent平衡因子为0，那么就不更新
if (parent->_bf == 0)
{
	break;
}
else if (parent->_bf == 1 || parent->_bf == -1)
{
	//如果更新后的parent平衡因子为1/-1，那么就继续向上更新
	cur = parent;
	parent = parent->parent;
}
else if (parent->_bf == 2 || parent->_bf == -2)
{
	//如果更新后的parent平衡因子为2/-2，那么就不符合平衡要求，需要继续旋转
	// 旋转

	break;
}
else
{
	//如果更新之后的平衡因子不为上面三种情况中的其中一种
	assert(false);
}

//右单旋
void RotateR(Node* parent)
{
	//起始位置
	//subL是parent的左节点
	Node* subL = parent->_left;
	Node* subLR = subL->_right;

	//开始旋转
	//parent的左节点是subLR
	parent->_left = subLR;
	//如果subLR不为空  对subLR和parent的父节点进行更新
	if (subLR)
		subLR->_parent = parent;//subLR的父节点为parent

	//如果传入的根节点是一个子树的根节点则需要将旋转后的根节点重新接入原来的节点
	Node* pParent = parent->_parent;

	//subL作为新的根节点
	subL->_right = parent;
	parent->_parent = subL;//parent的根节点为subL

	//旋转的树可能是一个整棵树的子树，还需要和上一层进行链接
	//两种情况：1.parent之前就是根
	if (parent == _root)
	{
		_root = subL;//subL作为新的根
		subL->_parent = nullptr;//subL为根，指向的parent置为空
	}
	else//不是根，那么就一定有parent的parent（pparent）
	{
		//判断之前parent是pparent的左还是右
		if (pParent->_left == parent)
		{
			pParent->_left = subL;
		}
		else
		{
			pParent->_right = subL;
		}

		//链接完之后将subL的Parent指向pParent
		subL->_parent = pParent;
	}

	//更新平衡因子
	subL->_bf = 0;
	parent->_bf = 0;

}

//左单旋
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;
	}

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

//左右双旋  先进行左旋再进行右旋
void RotateLR(Node* parent)
{
	Node* subL = parent->_left;
	Node* subLR = subL->_right;
	//双旋需要记录subLR的平衡因子
	int bf = subLR->_bf;

	//调用左右单旋
	RotateL(parent->_left);
	RotateR(parent);

	//按照图上的三种情况讨论 
	if (bf == -1)//如果节点8的平衡因子为-1（结合图看）
	{
		//旋转之后
		subLR->_bf = 0;
		subL->_bf = 0;
		parent->_bf = 1;
	}
	else if (bf == 1)
	{
		subLR->_bf = 0;
		subL->_bf = -1;
		parent->_bf = 0;
	}
	else if (bf == 0)
	{
		subLR->_bf = 0;
		subL->_bf = 0;
		parent->_bf = 0;
	}
	else//出现错误直接断言，避免调试
	{
		assert(false);
	}

}

//右左双旋
void RotateRL(Node* parent)
{
	Node* subR = parent->_right;
	Node* subRL = subR->_left;

	int bf = subRL->_bf;

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

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

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;
}

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

	int leftheight = _Heighr(root->_left);
	int rightheight = _Height(root->_right);
	int diff = rightheight - leftheight;

	if (abs(diff) >= 2)
	{
		cout << root->_kv.first << "高度差异常" << endl;
		return false;
	}
	if (diff != root->_bf)
	{
		cout << root->_kv.first << "平衡因子异常" << endl;
	}

	return _IsAVLTree(root->_left) && _IsAVLTree(root->_right);
}

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;
}