【C++高阶】深入理解红黑树：数据结构与算法之美

enum Color
{
	RED,
	BLACK
};

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

	RBTreeNode(const pair<K, V>& kv)
		:_left(nullptr)
		, _right(nullptr)
		, _parent(nullptr)
		, _kv(kv)
		, _col(RED)
	{}
};

template<class K, class V>
class RBTTree
{
	typedef BSTreeNode<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)
	{
		if (_root == nullptr)
		{
			_root = new Node(kv);
			_root->_col = BLACK;
			return true;
		}

		Node* parent = nullptr;
		Node* cur = _root;

		while (cur)
		{
			parent = cur;
			if (cur->_kv.first < kv.first)
			{
				cur = cur->_right;
			}
			else if (cur->_kv.first > kv.first)
			{
				cur = cur->_left;
			}
			else
			{
				return false;
			}
		}

		// 新增节点给红色
		cur = new Node(kv);
		cur->_col = RED;
		if (parent->_kv.first < kv.first)
		{
			parent->_right = cur;
		}
		else
		{
			parent->_left = cur;
		}
		cur->_parent = parent;

		// 检测新节点插入后，红黑树的性质是否造到破坏

		return true;
	}

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

			// 继续往上更新处理
			cur = grandfather;
			parent = cur->_parent;
		}
		else
		{
			if (cur == parent->_left)
			{
				// 单旋
				//     g
				//   p
				// c
				RotateR(grandfather);
				parent->_col = BLACK;
				grandfather->_col = RED;
			}
			else
			{
				// 双旋
				//     g
				//   p
				//     c
				RotateL(parent);
				RotateR(grandfather);
				cur->_col = BLACK;
				grandfather->_col = RED;
			}
			break;
		}
	}
	else  // parent == grandfather->_right
	{
		//     g
		//   u   p 
		//          c
		//
		Node* uncle = grandfather->_left;
		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
		{
			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;

void RotateL(Node* parent) // 左旋
{
	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;
	}
}

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

	parent->_left = subLR;
	if (subLR)
	{
		subLR->_parent = parent;
	}

	Node* Parentparent = parent->_parent;

	subL->_right = parent;
	parent->_parent = subL;

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

		subL->_parent = Parentparent;
	}
}

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 Check(Node* root, int blacknum, const int refVal)
{
	if (root == nullptr)
	{
		// 走到null之后，判断refVal和blacknum是否相等
		if (blacknum != refVal)
		{
			cout << "存在黑色节点数量不相等的路径" << endl;
			return false;
		}
		return true;
	}
	
	// 检测当前节点与其双亲是否都为红色
	if (root->_col == RED && root->_parent->_col == RED)
	{
		cout << "有连续的红色节点" << endl;
		return false;
	}
	
	// 统计黑色节点的个数
	if (root->_col == BLACK)
	{
		++blacknum;
	}

	return Check(root->_left, blacknum, refVal)
		&& Check(root->_right, blacknum, refVal);
}

bool IsBalance()
{
	if (_root == nullptr)
	{
		// 空树也是红黑树
		return true;
	}

	if(_root->_col == RED)
	{
		return false;
	}

	// 参考值
	// 检测是否满足红黑树的性质，refVal用来记录路径中黑色节点的个数
	int refVal = 0;
	Node* cur = _root;
	while (cur)
	{
		if (cur->_col == BLACK)
		{
			++refVal;
		}
		cur = cur->_left;
	}
	// 获取任意一条路径中黑色节点的个数
	int blacknum = 0;
	
	return Check(_root, blacknum, refVal);
}

int main()
{
	RBTree<int, int> t;
	int a[] = { 4, 2, 6, 1, 3, 5, 15, 7, 16, 14 };
	for(auto e : a)
	{
		t.Insert(make_pair(e, e));
	}
	t.InOrder();
	cout << t.IsBalance() << endl;
	return 0;
}