1.红黑树相关迭代器的实现

1.1operator++

在自增/减时要满足红黑树中序遍历的顺序：左子树、根、右子树（符合递增或递减）
++时：
右子树存在，找到右子树中的最左节点
右子树不存在，向上层遍历，直到当前节点是其父节点的左节点，取父节点（左、中）

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;
}

–时同理：
左子树存在，找到左子树中的最右节点
左子树不存在，找到孩子是父亲右节点的祖先节点

1.2operator[]

[k]返回v，map是kv模型，可以实现[],set不能,这里的operator[]在map的封装中实现。

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

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

1.3其他接口

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

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

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

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)
{
	Node* cur = _root;
	while (cur)
	{
		if (cur->_key < key)
		{
			cur = cur->_right;
		}
		else if (cur->_key > key)
		{
			cur = cur->_left;
		}
		else
		{
			return Iterator(cur);
		}
	}

	return End();
}
// 20:10
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<K, V>
		// 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);
}

2.KeyOfT

map和set的底层都是红黑树，但map是kv模型，而set是k模型。在取key值时，set能直接取，但map要取kv.first。这时候我们可以用一个KeyOfT的类去获得map和set里面的k值。

在底层红黑树取k值时分别通过set和map中KetOfT的仿函数取到对应k值。

3.map 封装

#pragma once

#include"RBT.h"
#include<iostream>
using namespace std;
namespace bit
{
	template<class K, class V>
	class Mymap
	{
		struct MapKeyOfT
		{
			const K& operator()(const pair<K, V>& kv)
			{
				return kv.first;
			}
		};
	public:
		typedef typename RBTree<K, 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);
		}

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

		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;
	};

	void test_map()
	{
		Mymap<string, int> m;
		m.insert({ "苹果",1 });
		m.insert({ "菠萝",5 });
		m.insert({ "香蕉",2 });
		m.insert({ "西瓜",3 });

		Mymap<string, int>::iterator it = m.begin();
		while (it != m.end())
		{
			it->second += 1;

			//cout << it.operator->()->first << ":" << it->second << endl;
			cout << it->first << ":" << it->second << endl;
			++it;
		}
		cout << endl;
	}

}

4.set封装

#pragma once

#include"RBT.h"
#include<iostream>
using namespace std;

namespace bit
{
	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);
		}

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

	void PrintSet(const set<int>& s)
	{
		for (auto e : s)
		{
			cout << e << endl;
		}
	}

	void test_set()
	{
		set<int> s;
		s.insert(4);
		s.insert(2);
		s.insert(5);
		s.insert(15);
		s.insert(7);
		s.insert(1);
		s.insert(5);
		s.insert(7);

		PrintSet(s);

		set<int>::iterator it = s.begin();
		while (it != s.end())
		{
			//*it += 5;

			cout << *it << " ";
			++it;
		}
		cout << endl;

		for (auto e : s)
		{
			cout << e << " ";
		}
		cout << endl;

		set<int> copy = s;
		for (auto e : copy)
		{
			cout << e << " ";
		}
		cout << endl;
		//cout << copy._t.IsBalance() << endl;
	}
}

5.测试

#include"mymap.h"
#include"myset.h"
int main()
{
	bit::test_map();
	bit::test_set();
	return 0;
}

6.源码

6.1RBT.h

#pragma once
#include<vector>
#include<iostream>
using namespace std;
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;
	}

	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)
	{
		Node* cur = _root;
		while (cur)
		{
			if (cur->_key < key)
			{
				cur = cur->_right;
			}
			else if (cur->_key > key)
			{
				cur = cur->_left;
			}
			else
			{
				return Iterator(cur);
			}
		}

		return End();
	}
	// 20:10
	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<K, V>
			// 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);
	}

	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:
	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;
	}

	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;
};