【数据结构】AVL树

template<class K, class V>
struct AVLTreeNode
{
	// 需要parent指针，后续更新平衡因子可以看到
	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)
		, _left(nullptr)
		, _right(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)//先按二叉搜索树的规则插入
	{
		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;
	}
    //因为节点变为三叉链结构，这里我们需要链接父节点
	cur->_parent = parent;
	// 按照前文规则，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，旋转处理
			break;
		}
		else
		{
			assert(false);
		}
	}
	return true;
}

void RotateR(Node* parent)
{
	Node* subL = parent->_left;
	Node* subLR = subL->_right;
	// 需要注意除了要修改孩子指针指向，还是修改父亲指针指向新父亲
	parent->_left = subLR;
	if (subLR)
		subLR->_parent = parent;

	Node* parentParent = parent->_parent;//记录祖父节点
	subL->_right = parent;
	parent->_parent = subL;

	// parent有可能是整棵树的根，也可能是局部的子树
	// 如果是整棵树的根，要修改_root
	// 如果是局部的指针要跟上一层链接
	if (parentParent == nullptr)
	{
		_root = subL;
		subL->_parent = nullptr;
	}
	else
	{//链接上一层前需要判断父亲节点在祖父节点的左子树还是右子树中
		if (parent == parentParent->_left)
		{
			parentParent->_left = subL;
		}
		else
		{
			parentParent->_right = subL;
		}
		subL->_parent = parentParent;
	}
	parent->_bf = subL->_bf = 0;//更新平衡因子
}

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;

    // parent有可能是整棵树的根，也可能是局部的子树
	// 如果是整棵树的根，要修改_root
	// 如果是局部的指针要跟上一层链接
	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;//平衡因子更新为0
}

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

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

    //根据上文讲解，分情况讨论
	if (bf == 0)
	{//更新平衡因子时，虽然单旋内部也会更新，但是这里我们也需要更新
    //这是一种防御性策略
		subL->_bf = 0;
		subLR->_bf = 0;
		parent->_bf = 0;
	}
	else 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//代码可能由于bug,出现其他值，我们这里是防止意外的防御性代码
	{
		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 == 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);
	}
}

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;
}

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 _IsBalanceTree(Node* root)
{
	// 空树也是AVL树
	if (nullptr == root)
		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;
		return false;
	}
	// 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);
}
// 测试代码
void TestAVLTree1()
{
	AVLTree<int, int> t;
	// 常规的测试用例
	//int a[] = { 16, 3, 7, 11, 9, 26, 18, 14, 15 };
	// 特殊的带有双旋场景的测试用例
	int a[] = { 4, 2, 6, 1, 3, 5, 15, 7, 16, 14 };
	for (auto e : a)
	{
		t.Insert({ e, e });
	}
	t.InOrder();
	cout << t.IsBalanceTree() << endl;
}
// 插入一堆随机值，测试平衡，顺便测试一下高度和性能等
void TestAVLTree2()
{
	const int N = 100000;
	vector<int> v;
	v.reserve(N);
	srand(time(0));
	for (size_t i = 0; i < N; i++)
	{
		v.push_back(rand() + i);
	}
	size_t begin2 = clock();
	AVLTree<int, int> t;
	for (auto e : v)
	{
		t.Insert(make_pair(e, e));
	}
	size_t end2 = clock();
	cout << "Insert:" << end2 - begin2 << endl;
	cout << t.IsBalanceTree() << endl;
	cout << "Height:" << t.Height() << endl;
	cout << "Size:" << t.Size() << endl;
	size_t begin1 = clock();
	// 确定在的值
	/*for (auto e : v)
	{
	t.Find(e);
	}*/
	// 随机值
	for (size_t i = 0; i < N; i++)
	{
		t.Find((rand() + i));
	}
	size_t end1 = clock();
	cout << "Find:" << end1 - begin1 << endl;
}