用红黑树封装实现map与set

bool IsBalance()
	{
		//检查根节点
		if (_root == nullptr)
			return true;

		if (_root->_col == RED)
			return false;
		//检查是否有连续的红节点+每条路径的黑色节点数目是否一样
		
		int refVal = 0;//参考值
		Node* cur = _root;
		while (cur)//以最左边的路径上的黑色节点数目为参考值
		{
			if (cur->_col == BLACK)
				refVal++;
			cur = cur->_left;
		}

		int blacknum = 0;
		return  Check(_root, refVal, blacknum);

	}

	bool Check(Node* root, const int refVal,int blacknum)
	{
		if (root == nullptr)
		{
			if (blacknum != refVal)
			{
				cout << "存在黑色节点数量不相等的路径" << endl;
				return false;
			}
			return true;
		}

		if (root->_col == BLACK)//节点为黑色--统计
		{
			blacknum++;
		}
		
		if(root->_col == RED && root->_parent->_col == RED)//节点为红色--检查
		{
			
			cout << "有连续的红色节点" << endl;
			return false;
		}

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

红黑树模拟实现map与set

代码：

MyMap.h

#pragma once
#include"RBTree.h"

namespace djx
{
	template<class K,class V>
	class map
	{
	public:
		struct MapKeyOfT//获取关键字K，map存储的是pair<K,V>
		{
			const K& operator()(const pair<K, V>&kv)
			{
				return kv.first;
			}
		};

		// 对类模板取内嵌类型，加typename告诉编译器这里是类型
		typedef typename RBTree<K, pair<const K, V> ,MapKeyOfT>::iterator iterator;
		typedef typename RBTree<K, pair<const K, V> ,MapKeyOfT>::const_iterator const_iterator;

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

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

		V& operator[](const K&key)
		{
			pair<iterator, bool> ret = insert(make_pair(key, V()));
			return ret.first->second;//ret.first是迭代器，能够找到节点
		}

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

	private:
		RBTree<K, pair<const K, V> ,MapKeyOfT> _t;//封装红黑树
	};
}

MySet.h

#pragma once
#include"RBTree.h"

namespace djx
{
	template<class K>
	class set
	{
	public:
		struct SetKeyOfT//仿函数，返回关键字K，set存储的就是K
		{
			const K& operator()(const K& key)
			{
				return key;
			}
		};

		typedef typename RBTree<K, K,SetKeyOfT>::const_iterator iterator;//set中的元素不可被修改，所以普通迭代器就用const_iterator来实现
		typedef typename RBTree<K, K, SetKeyOfT>::const_iterator const_iterator;

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

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

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

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

RBTree.h

#pragma once

// set ->key
// map ->key/value
enum Colour
{
	RED,
	BLACK
};

template<class T>
struct RBTreeNode//节点
{
	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 __TreeIterator//迭代器
{
	typedef RBTreeNode<T> Node;
	typedef __TreeIterator<T, Ref, Ptr> Self;
	Node* _node;

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


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

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

	Self& operator++()
	{
		//顺序：左 中 右
		if (_node->_right)//这颗子树没有走完--找右子树的最左节点
		{
			Node* cur = _node->_right;
			while (cur->_left)
			{
				cur = cur->_left;
			}
			_node = cur;
		}
		else//这颗子树已经走完--找一个祖先（这个子树是它左孩子的祖先）
		{
			Node* cur = _node;
			Node* parent = cur->_parent;
			while (parent && parent->_right == cur)
			{
				cur = parent;
				parent = cur->_parent;
			}
			_node = parent;
		}
		return *this;
	}

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

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

template<class K,class T,class KeyOfT>
class RBTree
{
	typedef RBTreeNode<T> Node;
public:
	typedef __TreeIterator<T, T&, T*> iterator;
	typedef __TreeIterator<T, const T&, const T*> const_iterator;

	iterator begin()//红黑树中序序列得到有序序列，begin()可设计成最左节点的迭代器
	{
		Node* cur = _root;
		while (cur && cur->_left)
		{
			cur = cur->_left;
		}
		return iterator(cur);
	}

	iterator end()
	{
		return iterator(nullptr);
	}

	const_iterator begin()const
	{

		Node* cur = _root;
		while (cur&& cur->_left)
		{
			cur = cur->_left;
		}
		return const_iterator(cur);
	}

	const_iterator end()const
	{
		return const_iterator(nullptr);
	}
    
    //返回值不能是pair<iterator, bool>，因为set的普通迭代器实际也是const_iterator，set设计insert时要返回的pair<iterator, bool> 实际是pair<const_iterator, bool> ，而封装红黑树，复用红黑树的Insert（返回值若是pair<iterator, bool>，红黑树的普通迭代器就是普通迭代器，那么因为普通迭代器iterator不能转成const_iterator，所以代码会报错）
设计成pair<Node*, bool>就很好，节点指针Node*可以通过const_iterator迭代器的构造函数完成转变
	pair<Node*, bool> Insert(const T& data)
	{
		//插入一个红色节点
		if (_root == nullptr)
		{
			_root = new Node(data);
			_root->_col = BLACK;
			return make_pair(_root, true);
		}
			
		Node* cur = _root;
		Node* parent = nullptr;
		KeyOfT kot;

		while (cur)
		{
			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(cur, false);
			}
		}

		//新增节点给红色
		cur = new Node(data);
		Node* newnode = cur;
		if (kot(parent->_data)>kot(data))
		{
			parent->_left = cur;
			cur->_parent = parent;
		}
		else
		{
			parent->_right = cur;
			cur->_parent = parent;
		}

		//红黑树调整--有连续的红节点
		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)//uncle存在且为红--变色
				{
					parent->_col = uncle->_col = BLACK;
					grandfather->_col = RED;

					//继续向上调整
					cur = grandfather;
					parent = cur->_parent;
				}
				else//uncle不存在或者存在且为黑--旋转+变色
				{
					if (cur == parent->_left)//右单旋
					{
						//     g
						//   p
						// c
						RotateR(grandfather);
						parent->_col = BLACK;
						grandfather->_col = RED;
					}
					else//左右双旋
					{
						//     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)//uncle存在且为红--变色
				{
					parent->_col = uncle->_col = BLACK;
					grandfather->_col = RED;

					//继续向上调整
					cur = grandfather;
					parent = cur->_parent;
				}
				else//uncle不存在或者存在且为黑--旋转+变色
				{
					if (cur == parent->_right)//左单旋
					{
						RotateL(grandfather);
						parent->_col = BLACK;
						grandfather->_col = RED;
					}
					else//右左双旋
					{
						//     g
						//   u   p 
						//     c
						RotateR(parent);
						RotateL(grandfather);
						cur->_col = BLACK;
						grandfather->_col = RED;
					}
					break;
				}
			}
		}
		_root->_col = BLACK;
		return make_pair(newnode, true);
	}

	iterator Find(const K& key)
	{
		//...

		return end();
	}

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

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

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

	void RotateR(Node* parent)
	{
		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 (parentParent->_left == parent)
			{
				parentParent->_left = subL;
			}
			else
			{
				parentParent->_right = subL;
			}
			subL->_parent = parentParent;
		}
	}



	bool IsBalance()//红黑树的验证
	{
		//检查根节点
		if (_root == nullptr)
			return true;

		if (_root->_col == RED)
			return false;
		//检查是否有连续的红节点+每条路径的黑色节点数目是否一样
		
		int refVal = 0;//参考值
		Node* cur = _root;
		while (cur)//以最左边的路径上的黑色节点数目为参考值
		{
			if (cur->_col == BLACK)
				refVal++;
			cur = cur->_left;
		}

		int blacknum = 0;
		return  Check(_root, refVal, blacknum);

	}

	bool Check(Node* root, const int refVal,int blacknum)
	{
		if (root == nullptr)
		{
			if (blacknum != refVal)
			{
				cout << "存在黑色节点数量不相等的路径" << endl;
				return false;
			}
			return true;
		}

		if (root->_col == BLACK)//节点为黑色--统计
		{
			blacknum++;
		}
		
		if(root->_col == RED && root->_parent->_col == RED)//节点为红色--检查
		{
			
			cout << "有连续的红色节点" << endl;
			return false;
		}

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

	int Height()
	{
		return _Height(_root);
	}

	int _Height(Node* root)
	{
		if (root == nullptr)
			return 0;

		int leftHeight = _Height(root->_left);
		int rightHeight = _Height(root->_right);
		return leftHeight > rightHeight ? leftHeight + 1 : rightHeight + 1;
	}

	size_t Size()
	{
		return _Size(_root);
	}

	size_t _Size(Node* root)
	{
		if (root == nullptr)
			return 0;

		return _Size(root->_left) + _Size(root->_right) + 1;
	}
private:
	Node* _root = nullptr;
};

处理设计红黑树Insert函数返回值的细节：