玩转红黑树：算法背后的平衡与旋转技巧

// 枚举值表⽰颜⾊ 
enum Colour
{
 	RED,
 	BLACK
};
// 这⾥我们默认按key/value结构实现 
template<class K, class V>
struct RBTreeNode
{
	 // 这⾥更新控制平衡也要加⼊parent指针 
	 pair<K, V> _kv;
	 RBTreeNode<K, V>* _left;
	 RBTreeNode<K, V>* _right;
	 RBTreeNode<K, V>* _parent;
	 Colour _col;
	 RBTreeNode(const pair<K, V>& kv)
		 :_kv(kv)
		 , _left(nullptr)
		 , _right(nullptr)
		 , _parent(nullptr)
	 {}
};
template<class K, class V>
class RBTree{
 	typedef RBTreeNode<K, V> Node;
public:
private:
 	Node* _root = nullptr;
};

bool Insert(const pair<K, V>& kv)
	{
		if (_root == nullptr)
		{
			_root = new Node(kv);
			_root->_col = BLACK;
			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);
		cur->_col = RED;
		if (parent->_kv.first < kv.first)
		{
			parent->_right = cur;
		}
		else
		{
			parent->_left = cur;
		}

		cur->_parent = parent;
		//...进行旋转、调整等操作

void RotateR(Node* parent)
{
	Node* cur = parent->_left;
	Node* curright = cur->_right;

	parent->_left = curright;

	if (curright)
	{
		curright->_parent = parent;
	}

	cur->_right = parent;

	Node* ppnode = parent->_parent;

	parent->_parent = cur;

	if (ppnode == nullptr)
	{
		_root = cur;
		cur->_parent = nullptr;
	}
	else
	{
		if (ppnode->_left == parent)
		{
			ppnode->_left = cur;
		}
		else
		{
			ppnode->_right = cur;
		}

		cur->_parent = ppnode;
	}
}

void RotateL(Node* parent)
{

	Node* cur = parent->_right;

	Node* curleft = cur->_left;

	parent->_right = curleft;

	if (curleft)
	{
		curleft->_parent = parent;
	}

	cur->_left = parent;

	Node* ppnode = parent->_parent;

	parent->_parent = cur;

	if (parent == _root)
	{
		_root = cur;
		cur->_parent = nullptr;
	}
	else
	{
		if (ppnode->_left == parent)
		{
			ppnode->_left = cur;
		}
		else
		{
			ppnode->_right = cur;
		}

		cur->_parent = ppnode;
	}
}

template<class K, class V>
class RBTree
{
	typedef RBTreeNode<K, V> Node;
public:
	bool Insert(const pair<K, V>& kv)
	{
		if (_root == nullptr)
		{
			_root = new Node(kv);
			_root->_col = BLACK;
			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);
		cur->_col = RED;
		if (parent->_kv.first < kv.first)
		{
			parent->_right = cur;
		}
		else
		{
			parent->_left = cur;
		}

		cur->_parent = parent;

		while (parent && parent->_col == RED)
		{
			Node* grandfather = parent->_parent;
			if (grandfather->_left == parent)
			{
				//   g
				// p   u
				//
				Node* uncle = grandfather->_right;
				// uncle存在且为红
				if (uncle && uncle->_col == RED)
				{
					// 变色
					parent->_col = uncle->_col = BLACK;
					grandfather->_col = RED;

					// 继续往上处理
					cur = grandfather;
					parent = cur->_parent;
				}
				else  // uncle不存在，或者存在且为黑
				{
					if (cur == parent->_left)
					{
						// 旋转+变色
						//    g
						//  p   u
						//c
						RotateR(grandfather);
						parent->_col = BLACK;
						grandfather->_col = RED;
					}
					else
					{
						// 旋转+变色
						//    g
						//  p   u
						//    c
						RotateL(parent);
						RotateR(grandfather);
						cur->_col = BLACK;
						grandfather->_col = RED;
					}

					break;
				}
			}
			else
			{
				//	 g
				// u   p
				Node* uncle = grandfather->_left;
				// 叔叔存在且为红，-》变色即可
				if (uncle && uncle->_col == RED)
				{
					parent->_col = uncle->_col = BLACK;
					grandfather->_col = RED;
					// 继续往上处理
					cur = grandfather;
					parent = cur->_parent;
				}
				else // 叔叔不存在，或者存在且为黑
				{
					// 情况二：叔叔不存在或者存在且为黑
					// 旋转+变色
					//    g
					//  u   p
					// c
					if (cur == parent->_right)
					{
						RotateL(grandfather);
						parent->_col = BLACK;
						grandfather->_col = RED;
					}
					else
					{
						//    g
						//  u   p
						// c
						RotateR(parent);
						RotateL(grandfather);
						cur->_col = BLACK;
						grandfather->_col = RED;
					}

					break;
				}
			}
		}

		_root->_col = BLACK;

		return true;
	}

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;
}

bool Check(Node* root, int blackNum, const int refNum)
{
    if (root == nullptr)
    {
        // 前序遍历⾛到空时，意味着⼀条路径⾛完了 
        //cout << blackNum << endl;
        if (refNum != blackNum)
        {
            cout << "存在⿊⾊结点的数量不相等的路径" << endl;
            return false;
        }
        return true;
    }

    // 检查孩⼦不太⽅便，因为孩⼦有两个，且不⼀定存在，反过来检查⽗亲就⽅便多了 
    if (root->_col == RED && root->_parent->_col == RED)
    {
        cout << root->_kv.first << "存在连续的红⾊结点" << endl;
        return false;
    }
    if (root->_col == BLACK)
    {
        blackNum++;
    }

    return Check(root->_left, blackNum, refNum) && Check(root->_right, blackNum, refNum);
}

bool IsBalance()
{
    if (_root == nullptr)
        return true;
    if (_root->_col == RED)
        return false;

    // 参考值 
    int refNum = 0;
    Node* cur = _root;
    while (cur)
    {
        if (cur->_col == BLACK)
        {
            ++refNum;
        }
        cur = cur->_left;
    }

    return Check(_root, 0, refNum);
}