【C++】map与set的模拟实现

文章目录

  • 1.map和set的底层
  • 2.红黑树的封装
    • 2.1 红黑树的迭代器
    • 2.2 红黑树的begin()、end()
    • 2.3总代码
  • 3.map的封装
  • 4.set的封装

前置知识:RBTree(红黑树)
现已完成删除功能

1.map和set的底层

map和set的底层结构就是红黑树,所以直接在map和set中封装一棵红黑树,然后包装下其接口即可。

2.红黑树的封装

2.1 红黑树的迭代器

template<class T, class Ref, class Ptr>
struct __RBTreeIterator
{
	typedef RBTreeNode<T> Node;
	typedef __RBTreeIterator<T, Ref, Ptr> Self;
	Node* _node;

	__RBTreeIterator(Node* node)
		:_node(node)
	{}

	Ref operator*()
	{
		return _node->_data;
	}

	Ptr operator->()
	{
		return &_node->_data;
	}

	bool operator!=(const Self& s)
	{
		return _node != s._node;
	}

	bool operator==(const Self& other) const
	{
		return _node == other._node;
	}
	Self& operator++()
	{
		if (_node->_right)
		{
			// 下一个,右树最左节点
			Node* leftMin = _node->_right;
			while (leftMin->_left)
			{
				leftMin = leftMin->_left;
			}

			_node = leftMin;
		}
		else
		{
			// 下一个,孩子等于父亲左的那个祖先
			Node* cur = _node;
			Node* parent = cur->_parent;
			while (parent && cur == parent->_right)
			{
				cur = parent;
				parent = parent->_parent;
			}

			_node = parent;
		}

		return *this;
	}
};

2.2 红黑树的begin()、end()

	Iterator Begin()
	{
		Node* leftMin = _root;
		while (leftMin && leftMin->_left)
		{
			leftMin = leftMin->_left;
		}

		return Iterator(leftMin);
	}

	Iterator End()
	{
		return Iterator(nullptr);
	}

	ConstIterator End() const
	{
		return ConstIterator(nullptr);
	}

	ConstIterator Begin() const
	{
		Node* leftMin = _root;
		while (leftMin && leftMin->_left)
		{
			leftMin = leftMin->_left;
		}

		return ConstIterator(leftMin);
	}

2.3总代码

enum Colour
{
	RED,
	BLACK
};

template<class T>
struct RBTreeNode
{
	RBTreeNode<T>* _left;
	RBTreeNode<T>* _right;
	RBTreeNode<T>* _parent;

	T _data;
	Colour _col;

	RBTreeNode(const T& data)
		:_left(nullptr)
		, _right(nullptr)
		, _parent(nullptr)
		, _data(data)
		, _col(RED)
	{}
};

template<class T, class Ref, class Ptr>
struct __RBTreeIterator
{
	typedef RBTreeNode<T> Node;
	typedef __RBTreeIterator<T, Ref, Ptr> Self;
	Node* _node;

	__RBTreeIterator(Node* node)
		:_node(node)
	{}

	Ref operator*()
	{
		return _node->_data;
	}

	Ptr operator->()
	{
		return &_node->_data;
	}

	bool operator!=(const Self& s)
	{
		return _node != s._node;
	}

	bool operator==(const Self& other) const
	{
		return _node == other._node;
	}
	Self& operator++()
	{
		if (_node->_right)
		{
			// 下一个,右树最左节点
			Node* leftMin = _node->_right;
			while (leftMin->_left)
			{
				leftMin = leftMin->_left;
			}

			_node = leftMin;
		}
		else
		{
			// 下一个,孩子等于父亲左的那个祖先
			Node* cur = _node;
			Node* parent = cur->_parent;
			while (parent && cur == parent->_right)
			{
				cur = parent;
				parent = parent->_parent;
			}

			_node = parent;
		}

		return *this;
	}
};

template<class K, class T, class KeyOfT>
class RBTree
{
	typedef RBTreeNode<T> Node;

public:
	typedef __RBTreeIterator<T, T&, T*> Iterator;
	typedef __RBTreeIterator<T, const T&, const T*> ConstIterator;

	RBTree() = default;

	RBTree(const RBTree<K, T, KeyOfT>& t)
	{
		_root = Copy(t._root);
	}

	// t2 = t1
	RBTree<K, T, KeyOfT>& operator=(RBTree<K, T, KeyOfT> t)
	{
		swap(_root, t._root);
		return *this;
	}

	~RBTree()
	{
		Destroy(_root);

		_root = nullptr;
	}

	Iterator Begin()
	{
		Node* leftMin = _root;
		while (leftMin && leftMin->_left)
		{
			leftMin = leftMin->_left;
		}

		return Iterator(leftMin);
	}

	Iterator End()
	{
		return Iterator(nullptr);
	}

	ConstIterator End() const
	{
		return ConstIterator(nullptr);
	}

	ConstIterator Begin() const
	{
		Node* leftMin = _root;
		while (leftMin && leftMin->_left)
		{
			leftMin = leftMin->_left;
		}

		return ConstIterator(leftMin);
	}

	Iterator Find(const K& key)
	{
		KeyOfT kot;
		Node* cur = _root;
		while (cur)
		{
			if (kot(cur->_data) < key)
			{
				cur = cur->_right;
			}
			else if (kot(cur->_data) > key)
			{
				cur = cur->_left;
			}
			else
			{
				return Iterator(cur);
			}
		}

		return End();
	}

	std::pair<Iterator, bool> Insert(const T& data)
	{
		if (_root == nullptr)
		{
			_root = new Node(data);
			_root->_col = BLACK;
			return make_pair(Iterator(_root), true);
		}

		KeyOfT kot;
		Node* parent = nullptr;
		Node* cur = _root;
		while (cur)
		{
			// K
			// pair
			// kot对象,是用来取T类型的data对象中的key
			if (kot(cur->_data) < kot(data))
			{
				parent = cur;
				cur = cur->_right;
			}
			else if (kot(cur->_data) > kot(data))
			{
				parent = cur;
				cur = cur->_left;
			}
			else
			{
				return make_pair(Iterator(cur), false);
			}
		}

		cur = new Node(data);
		Node* newnode = cur;
		cur->_col = RED; // 新增节点给红色
		if (kot(parent->_data) < kot(data))
		{
			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 make_pair(Iterator(newnode), true);
	}


	// 新增:删除接口,按键删除
	bool Erase(const K& key)
	{
		Iterator it = Find(key);
		if (it == End())
			return false;
		Node* z = it._node;
		Node* y = z;             // 真正被删除的节点或移位的节点
		Colour originalColor = y->_col;
		Node* x = nullptr;       // 用于替换 y 的子节点
		Node* xParent = nullptr; // 记录 x 的父节点

		if (z->_left == nullptr)
		{
			x = z->_right;
			xParent = z->_parent;
			transplant(z, z->_right);
		}
		else if (z->_right == nullptr)
		{
			x = z->_left;
			xParent = z->_parent;
			transplant(z, z->_left);
		}
		else
		{
			y = minimum(z->_right);
			originalColor = y->_col;
			x = y->_right;
			if (y->_parent == z)
			{
				if (x)
					x->_parent = y;
				xParent = y;
			}
			else
			{
				transplant(y, y->_right);
				y->_right = z->_right;
				if (y->_right)
					y->_right->_parent = y;
				xParent = y->_parent;
			}
			transplant(z, y);
			y->_left = z->_left;
			if (y->_left)
				y->_left->_parent = y;
			y->_col = z->_col;
		}
		delete z;
		if (originalColor == BLACK)
			eraseFixUp(x, xParent);
		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;
		}
	}

	// 中序遍历(假定 T 为 pair 类型,可以打印 first 与 second)
	void InOrder()
	{
		_InOrder(_root);
		cout << endl;
	}

	// 检查红黑树性质
	bool IsBalance()
	{
		if (_root && _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:
	Node* Copy(Node* root)
	{
		if (root == nullptr)
			return nullptr;

		Node* newroot = new Node(root->_data);
		newroot->_col = root->_col;

		newroot->_left = Copy(root->_left);
		if (newroot->_left)
			newroot->_left->_parent = newroot;

		newroot->_right = Copy(root->_right);
		if (newroot->_right)
			newroot->_right->_parent = newroot;

		return newroot;
	}

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

		Destroy(root->_left);
		Destroy(root->_right);
		delete root;
		root = nullptr;
	}

	// 检查黑色节点数量是否一致
	bool Check(Node* root, int blackNum, const int refNum)
	{
		if (root == nullptr)
		{
			if (refNum != blackNum)
			{
				cout << "存在黑色节点数量不一致的路径" << endl;
				return false;
			}
			return true;
		}
		if (root->_col == RED && root->_parent && root->_parent->_col == RED)
			return false;
		if (root->_col == BLACK)
			blackNum++;
		return Check(root->_left, blackNum, refNum) &&
			Check(root->_right, blackNum, refNum);
	}

	// 中序遍历辅助函数
	void _InOrder(Node* root)
	{
		if (root == nullptr)
			return;
		_InOrder(root->_left);
		// 假定 T 为 pair 类型,如 pair
		cout << root->_data.first << ":" << root->_data.second << " ";
		_InOrder(root->_right);
	}

	// 以下是删除操作所需的辅助函数

	// 用 v 替换 u 子树(不改变 v 的左右孩子)
	void transplant(Node* u, Node* v)
	{
		if (u->_parent == nullptr)
			_root = v;
		else if (u == u->_parent->_left)
			u->_parent->_left = v;
		else
			u->_parent->_right = v;
		if (v)
			v->_parent = u->_parent;
	}

	// 返回以 node 为根的子树中最小节点
	Node* minimum(Node* node)
	{
		while (node && node->_left)
			node = node->_left;
		return node;
	}

	// 删除后修正红黑树性质
	void eraseFixUp(Node* x, Node* parent)
	{
		// 注意:空指针视为黑色节点
		while ((x == nullptr || x->_col == BLACK) && x != _root)
		{
			if (x == parent->_left)
			{
				Node* w = parent->_right;
				if (w == nullptr)
				{
					x = parent;
					parent = x->_parent;
					continue;
				}
				if (w->_col == RED)
				{
					w->_col = BLACK;
					parent->_col = RED;
					RotateL(parent);
					w = parent->_right;
				}
				if ((w->_left == nullptr || w->_left->_col == BLACK) &&
					(w->_right == nullptr || w->_right->_col == BLACK))
				{
					w->_col = RED;
					x = parent;
					parent = x->_parent;
				}
				else
				{
					if (w->_right == nullptr || w->_right->_col == BLACK)
					{
						if (w->_left)
							w->_left->_col = BLACK;
						w->_col = RED;
						RotateR(w);
						w = parent->_right;
					}
					w->_col = parent->_col;
					parent->_col = BLACK;
					if (w->_right)
						w->_right->_col = BLACK;
					RotateL(parent);
					x = _root;
					break;
				}
			}
			else // 对称情况:x 为右孩子
			{
				Node* w = parent->_left;
				if (w == nullptr)
				{
					x = parent;
					parent = x->_parent;
					continue;
				}
				if (w->_col == RED)
				{
					w->_col = BLACK;
					parent->_col = RED;
					RotateR(parent);
					w = parent->_left;
				}
				if ((w->_right == nullptr || w->_right->_col == BLACK) &&
					(w->_left == nullptr || w->_left->_col == BLACK))
				{
					w->_col = RED;
					x = parent;
					parent = x->_parent;
				}
				else
				{
					if (w->_left == nullptr || w->_left->_col == BLACK)
					{
						if (w->_right)
							w->_right->_col = BLACK;
						w->_col = RED;
						RotateL(w);
						w = parent->_left;
					}
					w->_col = parent->_col;
					parent->_col = BLACK;
					if (w->_left)
						w->_left->_col = BLACK;
					RotateR(parent);
					x = _root;
					break;
				}
			}
		}
		if (x)
			x->_col = BLACK;
	}
private:
	Node* _root = nullptr;
	//size_t _size = 0;
};

3.map的封装

namespace my_std
{
	template<class K, class V>
	class map
	{
		struct MapKeyOfT
		{
			const K& operator()(const pair<K, V>& kv)
			{
				return kv.first;
			}
		};
	public:
		//在没有示例化的类模板里取内嵌类型的时候要加typename
		//typename 让编译器等到实例化后再识别这个类型
		typedef typename RBTree<K, std::pair<const K, V>, MapKeyOfT>::Iterator iterator;
		typedef typename RBTree<K, const K, MapKeyOfT>::ConstIterator const_iterator;

		const_iterator begin() const
		{
			return _t.Begin();
		}

		const_iterator end() const
		{
			return _t.End();
		}

		iterator begin()
		{
			return _t.Begin();
		}

		iterator end()
		{
			return _t.End();
		}

		iterator find(const K& key)
		{
			return _t.Find(key);
		}

		std::pair<iterator, bool> insert(const std::pair<K, V>& kv)
		{
			return _t.Insert(kv);
		}
		
		bool erase(const K& key) {
			return _t.Erase(key);
		}

		V& operator[](const K& key)
		{
			pair<iterator, bool> ret = _t.Insert(make_pair(key, V()));
			return ret.first->second;
		}

	private:
		RBTree<K, pair<const K, V>, MapKeyOfT> _t;
	};

4.set的封装

namespace my_std
{
	template<class K>
	class set
	{
		struct SetKeyOfT
		{
			const K& operator()(const K& key)
			{
				return key;
			}
		};
	public:
		typedef typename RBTree<K, const K, SetKeyOfT>::Iterator iterator;
		typedef typename RBTree<K, const K, SetKeyOfT>::ConstIterator const_iterator;

		const_iterator begin() const
		{
			return _t.Begin();
		}

		const_iterator end() const
		{
			return _t.End();
		}

		iterator begin()
		{
			return _t.Begin();
		}

		iterator end()
		{
			return _t.End();
		}

		iterator find(const K& key)
		{
			return _t.Find(key);
		}

		pair<iterator, bool> insert(const K& key)
		{
			return _t.Insert(key);
		}
		
		bool erase(const K& key) 
		{
			return _t.Erase(key);
		}

	private:
		RBTree<K, const K, SetKeyOfT> _t;
	};

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