【C++】RBTree(红黑树)模拟实现

surtr12025-02-12 8:40

文章目录

后续有时间会增加erase

1.红黑树的概念

红黑树 是一种自平衡的二叉搜索树 。每个节点额外存储了一个 color 字段 ("RED" or "BLACK")， 通过对任何一条从根到叶子的路径上各个结点着色方式的限制，红黑树确保没有一条路径会比其他路径长出俩倍，因而是接近平衡。

2.红黑树的性质

一棵合法的红黑树必须遵循以下四条性质：

  1. 节点为红色或黑色
  2. 根节点是黑色的 （在不同的实现下，该条性质并非必须满足）
  3. NIL 节点（空叶子节点）为黑色
  4. 红色节点的子节点为黑色
  5. 从根节点到 NIL节点的每条路径上的黑色节点数量相同

3.红黑树的结点

cpp 复制代码 
enum Colour
{
	RED,
	BLACK
};

template<class K, class V>
struct RBTreeNode
{
	RBTreeNode<K, V>* _left;
	RBTreeNode<K, V>* _right;
	RBTreeNode<K, V>* _parent;

	std::pair<K, V> _kv;
	Colour _col;

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

4.insert函数（插入结点）

新节点的默认颜色是红色 （如果其双亲节点的颜色是黑色，没有违反红黑树任何性质，则不需要调整；但当新插入节点的双亲节点颜色为红色时，就违反了性质4不能有连在一起的红色节点，此时需要对红黑树分情况来讨论）
约定:cur为当前节点，p为父节点，g为祖父节点，u为叔叔节点

所有插入的情况可分为以下三种：

  • 情况一: cur为红，p为红，g为黑，u存在且为红
  • 情况二: cur为红，p为红，g为黑，u不存在/u存在且为黑
  • 情况三: cur为红，p为红，g为黑，u不存在/u存在且为黑
cpp 复制代码 
	bool Insert(const std::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; // 新增节点给红色
		if (parent->_kv.first < kv.first)
		{
			parent->_right = cur;
		}
		else
		{
			parent->_left = cur;
		}
		cur->_parent = parent;

		// parent的颜色是黑色也结束
		while (parent && parent->_col == RED)
		{
			// 关键看叔叔
			Node* grandfather = parent->_parent;
			if (parent == grandfather->_left)
			{
				Node* uncle = grandfather->_right;
				// 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
				{
					if (cur == parent->_left)
					{
						//     g  
						//   p   u
						// c 
						RotateR(grandfather);
						parent->_col = BLACK;
						grandfather->_col = RED;
					}
					else
					{
						//      g  
						//   p     u
						//      c 
						RotateL(parent);
						RotateR(grandfather);
						cur->_col = BLACK;
						grandfather->_col = RED;
					}

					break;
				}
			}
			else
			{
				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;
	}

5.左旋、右旋

这里和AVLTree的旋转一样

cpp 复制代码 
	void RotateR(Node* parent)
	{
		Node* subL = parent->_left;
		Node* subLR = subL->_right;

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

		subL->_right = parent;

		Node* ppNode = parent->_parent;
		parent->_parent = subL;

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

			subL->_parent = ppNode;
		}
	}

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

		parent->_right = subRL;
		if (subRL)
			subRL->_parent = parent;

		subR->_left = parent;
		Node* ppNode = parent->_parent;

		parent->_parent = subR;

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

6.总代码

cpp 复制代码 
#include<vector>

enum Colour
{
	RED,
	BLACK
};

template<class K, class V>
struct RBTreeNode
{
	RBTreeNode<K, V>* _left;
	RBTreeNode<K, V>* _right;
	RBTreeNode<K, V>* _parent;

	std::pair<K, V> _kv;
	Colour _col;

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

template<class K, class V>
class RBTree
{
	typedef RBTreeNode<K, V> Node;
public:
	bool Insert(const std::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; // 新增节点给红色
		if (parent->_kv.first < kv.first)
		{
			parent->_right = cur;
		}
		else
		{
			parent->_left = cur;
		}
		cur->_parent = parent;

		// parent的颜色是黑色也结束
		while (parent && parent->_col == RED)
		{
			// 关键看叔叔
			Node* grandfather = parent->_parent;
			if (parent == grandfather->_left)
			{
				Node* uncle = grandfather->_right;
				// 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
				{
					if (cur == parent->_left)
					{
						//     g  
						//   p   u
						// c 
						RotateR(grandfather);
						parent->_col = BLACK;
						grandfather->_col = RED;
					}
					else
					{
						//      g  
						//   p     u
						//      c 
						RotateL(parent);
						RotateR(grandfather);
						cur->_col = BLACK;
						grandfather->_col = RED;
					}

					break;
				}
			}
			else
			{
				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;
	}

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

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

		subL->_right = parent;

		Node* ppNode = parent->_parent;
		parent->_parent = subL;

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

			subL->_parent = ppNode;
		}
	}

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

		parent->_right = subRL;
		if (subRL)
			subRL->_parent = parent;

		subR->_left = parent;
		Node* ppNode = parent->_parent;

		parent->_parent = subR;

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

	void InOrder()
	{
		_InOrder(_root);
		cout << endl;
	}

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

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

			cur = cur->_left;
		}

		return Check(_root, 0, refNum);
	}

private:
	bool Check(Node* root, int blackNum, const int refNum)
	{
		if (root == nullptr)
		{
			//cout << blackNum << endl;
			if (refNum != blackNum)
			{
				cout << "存在黑色节点的数量不相等的路径" << endl;
				return false;
			}

			return true;
		}

		if (root->_col == RED && root->_parent->_col == RED)
		{
			cout << root->_kv.first << "存在连续的红色节点" << endl;
			return false;
		}

		if (root->_col == BLACK)
		{
			blackNum++;
		}

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

	void _InOrder(Node* root)
	{
		if (root == nullptr)
		{
			return;
		}

		_InOrder(root->_left);
		cout << root->_kv.first << ":" << root->_kv.second << endl;
		_InOrder(root->_right);
	}

private:
	Node* _root = nullptr;
	//size_t _size = 0;
};
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