(第十一步) STL: stl_rb_tree容器实现

RB-tree

红黑树的重要性,不言而喻,是一种插入和删除都为 O ( l o g ( N ) ) O(log(N)) O(log(N))的数据结构,具体原理可以看这个:红黑树插入和删除分析

之后程序的编写,和注释红黑树重平衡的情况也是对照上文的情况的,这里就不多做介绍,直接开始程序设计

设计的重点

首先根据侯捷书,所述的迭代器之间的关系图,但是我这里直接放在一起,没有分的很细致,设计迭代器

(第十一步) STL: stl_rb_tree容器实现_第1张图片

然后红黑树结构设计,引入了一个header结点,来表示根节点的父节点且为红色

  • 当红黑树处于初始状态时,只有header节点(为红色),它的左右子节点初始状态指向自己

  • 当插入节点时,header的父节点指向根结点,左子节点指向最小的节点,右子节点指向最大的节点

  • 当不止一个结点存在时,header->left指向最小值,即最左节点,header->right指向最大值,即最右节点

(第十一步) STL: stl_rb_tree容器实现_第2张图片

实现功能

  • begin()
  • end()
  • size()
  • empty()
  • insert_unique(val); 插入元素不重复
  • clear();
  • erase(val);
  • find(val);

额外补充

红黑树是为后面的set、map准备,需要有键值,所以在Functional.h添加了一个仿函数identity(证同)

//********** [identity] ****************
	template<class T>
	struct identity {
		const T& operator()(const T& x)const { return x; }
	};

stl_rb_tree.h

#ifndef _RB_TREE_H_
#define _RB_TREE_H_

#include "../Includes/Allocator.h"
#include "../Includes/Algorithm.h"
#include "../Includes/Construct.h"
#include "../Includes/Iterator.h"
#include "../Includes/Utility.h"
#include "../Includes/Functional.h"

namespace mySTL {
	template<class Key, class Value, class KeyOfValue, class Compare>
	class rb_tree;

	// 结点颜色
	typedef bool rbtree_node_color;	
	const rbtree_node_color rbtree_red = true;
	const rbtree_node_color rbtree_black = false;

	namespace detail {	
		// 定义红黑树的结构体
		template<class T>
		struct rbtree_node
		{
			typedef rbtree_node_color color_type;
			typedef rbtree_node<T>* base_ptr;

			T			val;			// 值
			color_type	color;			// 红黑树颜色
			base_ptr	parent;			// 红黑树非常有必要知道父节点情况
			base_ptr	left;			//
			base_ptr	right;			//

			rbtree_node() :val(0),color(rbtree_red), parent(0), left(0), right(0) { }
			rbtree_node(const T&val) :val(val), color(rbtree_red), parent(0), left(0), right(0) { }
		};


		// 迭代器
		template<class T>
		class rbtree_iterator:public iterator<bidirectional_iterator_tag, T>
		{
			template<class Key, class Value, class KeyOfValue, class Compare>
			friend class rb_tree;

		public:
			typedef rbtree_iterator<T>				iterator;
			typedef rbtree_iterator<const T>		const_iterator;

			typedef ptrdiff_t						difference_type;
			typedef T								value_type;
			typedef T*								pointer;
			typedef T&								reference;
			typedef bidirectional_iterator_tag		iterator_category;

			typedef rbtree_node<T>					node_type;
			typedef rbtree_node<T>*					node_ptr;

		public:
			node_ptr ptr; // 与容器之间的连接

			rbtree_iterator(){}
			rbtree_iterator(node_ptr p) :ptr(p) {};
			rbtree_iterator(const_iterator& x) :ptr(x.ptr) {};

		public:
			reference operator*()const { return ptr->val; }
			pointer operator->()const { return &(ptr->val); }

			rbtree_iterator& operator++();
			rbtree_iterator operator++(int);

			rbtree_iterator& operator--();
			rbtree_iterator operator--(int);


			template<class T>
			friend bool operator==(const rbtree_iterator<T>& lhs, const rbtree_iterator<T>& rhs);
			template<class T>
			friend bool operator!=(const rbtree_iterator<T>& lhs, const rbtree_iterator<T>& rhs);

			

			
		private:
			// 辅助迭代器函数

			// 搜索树的自加 it++
			void increment();
			// 搜索树的自减 it--
			void decrement();
		};
		
	}

	/* 首先我们应该注意的是模板的参数
	 * key代表红黑树上存储节点时依据的值
	 * value即节点的值
	 * KeyOfValue是仿函数,用于通过value获取到key
	 * Compare为比较key大小的标准
	 * Alloc是空间配置器
	 */

	template<class Key, class Value, class KeyOfValue, class Compare>
	class rb_tree
	{
	private:
		friend class detail::rbtree_iterator<Value>;

	public:

		typedef rbtree_node_color					color_type;
		typedef ptrdiff_t							difference_type;
		typedef size_t								size_type;
		typedef Key									key_type;
		typedef Value								value_type;
		typedef value_type*							pointer;
		typedef value_type&							reference;
		typedef const value_type*					const_pointer;
		typedef const value_type&					const_reference;

		typedef detail::rbtree_node<value_type>				rbtreeNode;
		typedef rbtreeNode*									rbtree_node_ptr;

		typedef allocator<detail::rbtree_node<value_type>>	rbtreeAllocator;

	public:
		typedef detail::rbtree_iterator<value_type>			iterator;
		typedef detail::rbtree_iterator<value_type>			const_iterator;


	private:
		rbtree_node_ptr		header;
		size_type			node_count;
		Compare				key_compare;

	protected:
		//construct / destroy / init
		rbtree_node_ptr getNode();
		rbtree_node_ptr createNode(const Value& val = Value());

		void putNode(rbtree_node_ptr ptr);
		void deleteNode(rbtree_node_ptr ptr);

		void init();

	public:
		rb_tree(const Compare& comp = Compare());
		//复制节点,包括颜色
		rbtree_node_ptr clone_node(rbtree_node_ptr x);
		~rb_tree();

	protected:
		// 定义header节点属性
		// header的左孩子指向key值最小的节点
		rbtree_node_ptr& root()const { return (rbtree_node_ptr&)header->parent; }
		rbtree_node_ptr& leftmost() const { return (rbtree_node_ptr&)header->left; }
		rbtree_node_ptr& rightmost() const { return (rbtree_node_ptr&)header->right; }

		// 使用6个函数,方便获取x的节点成员
		static rbtree_node_ptr& left(rbtree_node_ptr x)
		{
			return (rbtree_node_ptr&)(x->left);
		}
		static rbtree_node_ptr& right(rbtree_node_ptr x)
		{
			return (rbtree_node_ptr&)(x->right);
		}
		static rbtree_node_ptr& parent(rbtree_node_ptr x)
		{
			return (rbtree_node_ptr&)(x->parent);
		}
		static reference value(rbtree_node_ptr x)
		{
			return x->val;
		}
		static const key_type& key(rbtree_node_ptr x)
		{
			return KeyOfValue()(value(x));
		}
		static color_type& color(rbtree_node_ptr x)
		{
			return (color_type&)(x->color);
		}

	public:
		iterator begin() { return leftmost(); }
		//const_iterator begin()const { return const_iterator(leftmost()); }

		iterator end() { return header; }
		//const_iterator end()const { return const_iterator(header); }

		size_type size()const { return node_count; }
		size_type max_size() const { return size_type(-1); }
		bool empty() const { return node_count == 0; }




	public:
		pair<iterator, bool> insert_unique(const Value& val);	// 插入元素不重复
		void clear();
		void erase(iterator position);
		void erase(const Value& val);
		iterator find(const Value& val);
		
	protected:

		iterator insert(rbtree_node_ptr x, rbtree_node_ptr p, const Value& val);	// 实现插入
		void rbtree_rebalance_for_insert(rbtree_node_ptr z, rbtree_node_ptr& root);			// 实现插入重平衡
		void rbtree_rotate_left(rbtree_node_ptr x, rbtree_node_ptr& root);			// 左旋
		void rbtree_rotate_right(rbtree_node_ptr x, rbtree_node_ptr& root);			// 右旋
		void recurErase(rbtree_node_ptr x);
		// 删除的重平衡
		rbtree_node_ptr rbtree_rebalance_for_erase(rbtree_node_ptr z, rbtree_node_ptr& root);
		rbtree_node_ptr findRBTree(const Value& val, bool& isFind);

		rbtree_node_ptr RBTreeMinimum(rbtree_node_ptr p);
		rbtree_node_ptr RBTreeMaximum(rbtree_node_ptr p);

	};

}


#include "../Detail/stl_rb_tree.impl.h"

#endif

stl_rb_tree.impl.h

#ifndef _RB_TREE_IMPL_H_
#define _RB_TREE_IMPL_H_


namespace mySTL {
	namespace detail {	
		// 搜索树的自加 it++
		template<class T>
		void rbtree_iterator<T>::increment()
		{
			if (ptr->right != nullptr)
			{
				// 情况1:存在右节点,后继结点为右子树的最左结点
				ptr = ptr->right;
				while (ptr->left != nullptr)
					ptr = ptr->left;
			}
			else
			{
				// 情况2:不存在右节点
				node_ptr parent_node = ptr->parent;
				// 如果ptr是右节点,向上找出不为右节点的节点
				// 如果ptr为最右节点,此时会返回至ptr = root,
				while (ptr == parent_node->right)
				{
					ptr = parent_node;
					parent_node = parent_node->parent;
				}

				// ==出现的特殊情况3:ptr结点为root结点,
				// 同时不存在右子树时,header == root->parent == ptr->parent == ptr->right == nullptr
				// 为了处理当node为root时并且root无右子树的特殊情况

				if (ptr->right != parent_node)
					ptr = parent_node;

			}
		}

		// 搜索树的自减 it--
		template<class T>
		void rbtree_iterator<T>::decrement()
		{	// 情况1:ptr指向header时
			// 此时是为end(),应该返回最右值,header->right
			if (ptr->color == rbtree_red &&
				ptr->parent->parent == ptr)
			{
				ptr = ptr->right;
			}
			else if (ptr->left != nullptr)
			{
				// 情况2:存在左节点,前继结点为左子树的最右结点
				ptr = ptr->left;
				while (ptr->right != nullptr)
					ptr = ptr->right;
			}
			else
			{	// 情况3:不存在左节点					
				node_ptr parent_node = ptr->parent;
				// 如果ptr是左节点,向上找出不为左节点的节点
				while (ptr == parent_node->left)
				{
					ptr = parent_node;
					parent_node = parent_node->parent;
				}

				ptr = parent_node;
			}
		}

		template<class T>
		inline rbtree_iterator<T>& rbtree_iterator<T>::operator++()
		{
			increment();
			return *this;
		}

		template<class T>
		inline rbtree_iterator<T> rbtree_iterator<T>::operator++(int)
		{
			auto tmp = *this;
			++(*this);
			return tmp;
		}

		template<class T>
		inline rbtree_iterator<T>& rbtree_iterator<T>::operator--()
		{
			decrement();
			return *this;
		}

		template<class T>
		inline rbtree_iterator<T> rbtree_iterator<T>::operator--(int)
		{
			auto tmp = *this;
			--(*this);
			return tmp;
		}

		template<class T>
		bool operator==(const rbtree_iterator<T>& lhs, const rbtree_iterator<T>& rhs)
		{
			return lhs.ptr == rhs.ptr;
		}

		template<class T>
		bool operator!=(const rbtree_iterator<T>& lhs, const rbtree_iterator<T>& rhs)
		{
			return !(lhs == rhs);
		}

	}

	template<class Key, class Value, class KeyOfValue, class Compare>
	inline typename rb_tree<Key, Value, KeyOfValue, Compare>::rbtree_node_ptr 
		rb_tree<Key, Value, KeyOfValue, Compare>::getNode()
	{
		return rbtreeAllocator::allocate();
	}

	template<class Key, class Value, class KeyOfValue, class Compare>
	inline typename rb_tree<Key, Value, KeyOfValue, Compare>::rbtree_node_ptr 
		rb_tree<Key, Value, KeyOfValue, Compare>::createNode(const Value& val)
	{
		rbtree_node_ptr tmp = getNode();		// 开辟空间
		mySTL::construct(&(tmp->val), val);		// 赋值
		return tmp;								// 返回指针
	}

	template<class Key, class Value, class KeyOfValue, class Compare>
	inline void rb_tree<Key, Value, KeyOfValue, Compare>::putNode(rbtree_node_ptr ptr)
	{
		rbtreeAllocator::deallocate(ptr);
	}

	template<class Key, class Value, class KeyOfValue, class Compare>
	inline void rb_tree<Key, Value, KeyOfValue, Compare>::deleteNode(rbtree_node_ptr ptr)
	{
		mySTL::destroy(&ptr->val);
		putNode(ptr);
	}

	template<class Key, class Value, class KeyOfValue, class Compare>
	inline void rb_tree<Key, Value, KeyOfValue, Compare>::init()
	{
		header = createNode();
		leftmost() = header;		// 令header左节点为自己
		rightmost() = header;		// 令header右节点为自己
		color(header) = rbtree_red;	// 用来区分header和root,在operator--中
		root() = nullptr;			// header的父节点,红黑树的root为nullptr

		// 这里体现一个技巧:插入root结点时,header和root互为对方的父节点
	}

	/***********************init 结束,开始构造和析构**********************/ 

	template<class Key, class Value, class KeyOfValue, class Compare>
	inline rb_tree<Key, Value, KeyOfValue, Compare>::rb_tree(const Compare& comp)
		:node_count(0), key_compare(comp)
	{
		init();
	}

	template<class Key, class Value, class KeyOfValue, class Compare>
	inline typename rb_tree<Key, Value, KeyOfValue, Compare>::rbtree_node_ptr 
		rb_tree<Key, Value, KeyOfValue, Compare>::clone_node(rbtree_node_ptr x)
	{
		{
			rbtree_node_ptr tmp = createNode(x->val);
			tmp->color = x->color;
			tmp->left = nullptr;
			tmp->right = nullptr;
			return tmp;
		}
	}

	template<class Key, class Value, class KeyOfValue, class Compare>
	inline rb_tree<Key, Value, KeyOfValue, Compare>::~rb_tree()
	{
		clear();
		putNode(header);
	}

	/***********************插入的实现**********************/
	template<class Key, class Value, class KeyOfValue, class Compare>
	inline pair<typename  rb_tree<Key, Value, KeyOfValue, Compare>::iterator, bool> 
		rb_tree<Key, Value, KeyOfValue, Compare>::insert_unique(const Value& val)
	{
		rbtree_node_ptr p = header;	// 根节点的父节点
		rbtree_node_ptr x = root(); // 从根节点开始
		bool comp = true;
		while (x != nullptr)		// 从根节点开始往下寻找合适的插入点
		{
			p = x;
			comp = key_compare(KeyOfValue()(val), key(x));	// 对比

			x = comp ? left(x) : right(x);		// 遇大往左,小往右
		}// 离开while循环后,p就为插入点(叶子结点)

		// 如果当前x树为空树,直接插入val结点
		if (p == header)
		{
			return pair<iterator, bool>(insert(x, p, val), true);
		}

		iterator j = iterator(p);	// j 指向插入结点的父节点p
		if (comp)					// comp为真,遇大插左侧
		{
			if (j == begin())		// 插入为最左结点,即最小结点
			{
				return pair<iterator, bool>(insert(x, p, val), true);
			}
			else
			{
				--j;	// 调整j,回头测试
			}
		}

		if (key_compare(key(j.ptr), KeyOfValue()(val)))	// 新值不与键值重复,插入
		{
			return pair<iterator, bool>(insert(x, p, val), true);
		}

		// 重复,不插入
		return pair<iterator, bool>(j, false);
	}

	template<class Key, class Value, class KeyOfValue, class Compare>
	inline typename  rb_tree<Key, Value, KeyOfValue, Compare>::iterator 
		rb_tree<Key, Value, KeyOfValue, Compare>::insert(rbtree_node_ptr x, rbtree_node_ptr p, const Value& val)
	{
		// x新值插入点,p插入点的父节点,val插入的新值
		rbtree_node_ptr z;

		if (p == header || key_compare(KeyOfValue()(val), key(p)))
		{
			z = createNode(val);
			left(p) = z;
			if (p == header)	// p为header时,即当前为空树, leftmost = z;
			{
				root() = z;					// header父节点指向root
				rightmost() = z;			// header右节点指向z,也就是rightmost = z;
			}
			else if (p == leftmost()) // 插入结点的父节点为最左结点
			{
				leftmost() = z;	// 维护leftmost(),永远指向最左结点
			}

		}
		else	
		{	// 树不为空,且comp为false,val小于ptr->val,存放右边
			z = createNode(val);
			right(p) = z;			// 将p的右孩子设置为z
			if (rightmost() == p)
			{
				rightmost() = z; // 维护rightmost(),永远指向最右结点
			}
		}

		// 设定新节点z的父节点、和子节点
		parent(z) = p;	
		left(z) = nullptr;
		right(z) = nullptr;
		// 重平衡
		rbtree_rebalance_for_insert(z, parent(header));
		++node_count;

		return iterator(z);
	}

	/***********************插入重平衡**********************/
	template<class Key, class Value, class KeyOfValue, class Compare>
	inline void rb_tree<Key, Value, KeyOfValue, Compare>::rbtree_rebalance_for_insert(rbtree_node_ptr z, rbtree_node_ptr& root)
	{
		// z 插入的新节点,root树的根节点
		z->color = rbtree_red;	// 插入节点必为红色


		
		while (z != root && z->parent->color == rbtree_red)
		{
			// 情景4:插入结点的父结点为红结点
			if (z->parent == z->parent->parent->left)
			{
				// 情景:插入结点的父亲结点是祖父结点的左子结点
				rbtree_node_ptr u = z->parent->parent->right; // 叔叔结点
				
				if (u != nullptr && u->color == rbtree_red)
				{
					// 情景4.1:叔叔结点存在并且为红结点
					u->color					=	rbtree_black;
					z->parent->color			=	rbtree_black;
					z->parent->parent->color	=	rbtree_red;
					z = z->parent->parent;			// 更新插入结点,直到更新至root
				}
				else
				{
					// 插入情景4.2:叔叔结点不存在或为黑结点,并且插入结点的父亲结点是祖父结点的左子结点
					// 插入情景4.2.2:插入结点是其父结点的右子结点,双旋,先P结点左旋,变成情形4.2.1
					if (z == z->parent->right)
					{
						z = z->parent;
						rbtree_rotate_left(z, root);
					}
					
					// 插入情景4.2.1:插入结点是其父结点的左子结点,单旋,PP结点右旋
					z->parent->parent->color = rbtree_red;
					z->parent->color = rbtree_black;
					rbtree_rotate_right(z->parent->parent, root);
				}
			}
			else
			{	
				// 情景:插入结点的父亲结点是祖父结点的右子结点
				// 和4.2处理只是进行对称镜像
				rbtree_node_ptr u = z->parent->parent->left;

				if (u != 0 && u->color == rbtree_red)
				{
					// 情景4.1:叔叔结点存在并且为红结点
					u->color					=	rbtree_black;
					z->parent->color			=	rbtree_black;
					z->parent->parent->color	=	rbtree_red;
					z = z->parent->parent;
				}
				else
				{
					//  插入情景4.3.2:插入结点是其父结点的左子结点,双旋,先P结点右旋,至情景4.3.1
					if (z == z->parent->left)
					{
						z = z->parent;
						rbtree_rotate_right(z, root);
					}

					// 插入情景4.3.1:插入结点是其父结点的右子结点,单旋
					z->parent->parent->color = rbtree_red;
					z->parent->color = rbtree_black;
					rbtree_rotate_left(z->parent->parent, root);

				}
			}
		}

		// 情景1,3:直接插入,无需操作即可
		root->color = rbtree_black; //	根节点永远为黑
	}


	/***********************左旋和右旋**********************/
	template<class Key, class Value, class KeyOfValue, class Compare>
	inline void rb_tree<Key, Value, KeyOfValue, Compare>::rbtree_rotate_left(rbtree_node_ptr x, rbtree_node_ptr& root)
	{
		// x为旋转节点
		rbtree_node_ptr y = x->right;
		x->right = y->left;
		if (y->left != nullptr)
			y->left->parent = x;	
		// 完成x结点,除x->parent参数的更新
		// 开始y节点的更新
		y->parent = x->parent;
		if (x == root)
		{
			root = y;
		}			
		else if (x->parent->left == x)
		{
			x->parent->left = y;
		}
		else
		{
			x->parent->right = y;
		}
		x->parent = y;
		y->left = x;
	}

	template<class Key, class Value, class KeyOfValue, class Compare>
	inline void rb_tree<Key, Value, KeyOfValue, Compare>::rbtree_rotate_right(rbtree_node_ptr x, rbtree_node_ptr& root)
	{
		// 原理同左旋
		rbtree_node_ptr y = x->left;
		x->left = y->right;
		if (y->right != 0)
			y->right->parent = x;

		y->parent = x->parent;
		if (x == root)
		{
			root = y;
		}			
		else if (x->parent->left == x)
		{
			x->parent->left = y;
		}
		else
		{
			x->parent->right = y;
		}

		x->parent = y;
		y->right = x;
	}

	// 查找函数
	template<class Key, class Value, class KeyOfValue, class Compare>
	inline typename rb_tree<Key, Value, KeyOfValue, Compare>::rbtree_node_ptr
		rb_tree<Key, Value, KeyOfValue, Compare>::RBTreeMinimum(rbtree_node_ptr p)
	{
		while (p->left != nullptr)
			p = p->left;
		return p;
	}


	template<class Key, class Value, class KeyOfValue, class Compare>
	inline typename rb_tree<Key, Value, KeyOfValue, Compare>::rbtree_node_ptr
		rb_tree<Key, Value, KeyOfValue, Compare>::RBTreeMaximum(rbtree_node_ptr p)
	{
		while (p->right != nullptr)
			p = p->right;
		return p;
	}

	template<class Key, class Value, class KeyOfValue, class Compare>
	inline typename rb_tree<Key, Value, KeyOfValue, Compare>::rbtree_node_ptr
		rb_tree<Key, Value, KeyOfValue, Compare>::findRBTree(const Value& val, bool& isFind)
	{
		rbtree_node_ptr res = parent(header);
		isFind = false;
		while (res != 0)
		{
			if (key_compare(KeyOfValue()(val), key(res)))
			{
				res = left(res);
			}
			else
			{
				if (key_compare(key(res), KeyOfValue()(val)))
				{
					res = right(res);
				}
				else
				{
					isFind = true;
					break;
				}
			}
		}
		return res;
	}

	template<class Key, class Value, class KeyOfValue, class Compare>
	inline typename rb_tree<Key, Value, KeyOfValue, Compare>::iterator
		rb_tree<Key, Value, KeyOfValue, Compare>::find(const Value& val)
	{
		bool isFind = false;
		rbtree_node_ptr res = findRBTree(val, isFind);

		if (isFind)
		{
			return iterator(res);
		}
		else
		{
			return end();
		}
	}

	// 递归删除值
	template<class Key, class Value, class KeyOfValue, class Compare>
	inline void rb_tree<Key, Value, KeyOfValue, Compare>::recurErase(rbtree_node_ptr x)
	{
		if (x != 0)
		{
			recurErase(left(x));
			recurErase(right(x));
			deleteNode(x);
		}
	}

	template<class Key, class Value, class KeyOfValue, class Compare>
	inline void rb_tree<Key, Value, KeyOfValue, Compare>::clear()
	{
		recurErase(root());
		left(header) = header;
		right(header) = header;
		parent(header) = nullptr;
	}


	// 删除
	template<class Key, class Value, class KeyOfValue, class Compare>
	inline void rb_tree<Key, Value, KeyOfValue, Compare>::erase(iterator position)
	{
		rbtree_node_ptr to_be_delete = rbtree_rebalance_for_erase(position.ptr, root());
		deleteNode(to_be_delete);
		--node_count;
	}

	template<class Key, class Value, class KeyOfValue, class Compare>
	inline void rb_tree<Key, Value, KeyOfValue, Compare>::erase(const Value& val)
	{
		auto positon = find(val);
		rbtree_node_ptr to_be_delete = rbtree_rebalance_for_erase(positon.ptr, root());
		deleteNode(to_be_delete);
		--node_count;
	}

	// 删除重平衡
	template<class Key, class Value, class KeyOfValue, class Compare>
	inline typename rb_tree<Key, Value, KeyOfValue, Compare>::rbtree_node_ptr
		rb_tree<Key, Value, KeyOfValue, Compare>::rbtree_rebalance_for_erase(rbtree_node_ptr z, rbtree_node_ptr& root)
	{	// z删除节点位置
		rbtree_node_ptr del_node = z;			// 删除的节点
		rbtree_node_ptr replace_node = 0;		// 替代del_node的节点,真正需要删除的节点
		rbtree_node_ptr replace_node_parent;	// 删除之后 x 的父节点

		// 查找实际需要删除的del_node节点的替换节点replace_node
		if (del_node->left == nullptr)
		{
			// 删除情景1或2:删除结点无子节点或只有一个右子结点
			replace_node = del_node->right;
		}
		else if (del_node->right == nullptr)
		{
			// 删除情景2:删除结点只有一个左子结点
			replace_node = del_node->left;
		}
		else
		{
			// 删除情景3:删除结点有两个子结点
			// 采用后继结点法,删除节点的右节点的,最左节点
			del_node = del_node->right;
			while (del_node->left != nullptr)
				del_node = del_node->left;

			//replace_node = del_node;
			replace_node = del_node->right;
		}

		// 开始我们的大工程,自平衡
		// 首先,删除结点值,和替代结点值的交换
		if (del_node == z)
		{
			// 情景1或2,del_node保持不变,== z,步骤如下
			// 1.删除结点z的父节点z->parent指向,replace_node替换节点(此时为z的子节点)
			// 2.然后替换节点replace_node->parent删除结点z父节点
			// 3.保持header->left、header->right的指向,即最小最大的指向,不变
			replace_node_parent = del_node->parent;
			if (z == root)
			{
				// 删除结点为根节点
				root = replace_node;	
			}
			else if (z == z->parent->left)
			{
				// 删除结点为父节点的左子结点
				z->parent->left = replace_node;
			}
			else
			{
				// 删除结点为父节点的右子结点
				z->parent->right = replace_node;
			}

			// 替代结点,代替删除结点
			if (replace_node != nullptr) replace_node->parent = z->parent;

			if (z == leftmost())
			{
				// 删除结点为最左节点,更新最左节点,保持最小值
				if (z->right == nullptr)
					leftmost() = z->parent;
				else
					leftmost() = RBTreeMinimum(replace_node);
			}

			if (z == rightmost())
			{
				// 删除结点为最右节点,更新最右节点,保持最大值
				if (z->left == 0)
					rightmost() = z->parent;
				else
					rightmost() = RBTreeMaximum(replace_node);
			}
		}
		else
		{
			// 情景3,此时del_node != z,del_node == 替换节点位置上
			// replace_node = del_node->right;

			// 更新del_node左半部分
			del_node->left = z->left;
			z->left->parent = del_node;

			if (z->right != del_node)
			{	// 删除结点z的右子结点,有左子结点
				// del_node->right 与 del_node->parent之间的更新,即移除del_node结点
				replace_node_parent = del_node->parent;

				if (replace_node != nullptr) 
					replace_node->parent = del_node->parent;
				del_node->parent->left = replace_node;

				// 更新del_node 右半部分
				del_node->right = z->right;
				z->right->parent = del_node;
			}
			else
			{	// 删除结点z的右子结点,无左子结点
				// 此时右半部分保持不变,维持原状即可
				replace_node_parent = del_node;
			}

			// 更新删除结点的父节点
			if (z == root)
			{
				root = del_node;
			}
			else if (z == z->parent->left)
			{
				z->parent->left = del_node;
			}
			else
			{
				z->parent->right = del_node;
			}
			del_node->parent = z->parent;

			// 完成交换值,并保持删除结点颜色不变,此时删除结点变成删除替换节点
			swap(del_node->color, z->color);
			// 后面只需要根据颜色进行调整红黑树,所以获取del_node的颜色,即现在的z的颜色
			del_node = z;	
		}

		// del_node:				待删节点   
		// replace_node:			替换del_node的节点,此时replace_node也成为标记节点   
		// replace_node_parent:		replace_node的父节点
		// 此时开始调动颜色,如果del_node为红色直接删除即可,为黑色需要分析
		// D 待删节点  S 是D的兄弟节点
		if (del_node->color == rbtree_black)
		{
			while (replace_node != root && (replace_node == nullptr || replace_node->color == rbtree_black))  
			{	
				// 为双黑色节点
				if (replace_node == replace_node_parent->left)
				{
					// del_node结点是其父结点的左子结点
					rbtree_node_ptr s = replace_node_parent->right;
					if (s->color == rbtree_red)
					{
						// 删除情景1.2.2:D结点的兄弟结点S是红结点
						s->color = rbtree_black;
						replace_node_parent->color = rbtree_red;
						rbtree_rotate_left(replace_node_parent, root);
						s = replace_node_parent->right;
						// 此时变为情景1.2.1.1
					}

					if ((s->left == nullptr || s->left->color == rbtree_black) 
						&& (s->right == nullptr || s->right->color == rbtree_black))
					{
						// 删除情景1.2.1.1:D结点的兄弟结点S的子结点SL 、SR都为黑结点null
						s->color = rbtree_red;
						// 向上更新
						replace_node = replace_node_parent;
						replace_node_parent = replace_node_parent->parent;
					}
					else
					{
						if (s->right == nullptr || s->right->color == rbtree_black)
						{
							// 删除情景1.2.1.2:D结点的兄弟结点S的子结点SL为红,SR为黑、null
							if (s->left != nullptr)
								s->left->color = rbtree_black;

							s->right->color = rbtree_red;	// 变红后,后就操作了
							rbtree_rotate_right(s, root);	// 右旋后,近似变为删除情景1.2.1.3,比较抽象
							s = replace_node_parent->right;
						}
						// 删除情景1.2.1.3:D结点的兄弟结点的子结点SL为黑null(或者红),SR为红
						s->color = replace_node_parent->color;
						replace_node_parent->color = rbtree_black;
						if (s->right != nullptr)
							s->right->color = rbtree_black;
						rbtree_rotate_left(replace_node_parent, root);
						break;
					}

				}
				else
				{
					// del_node结点是其父结点的右子结点,镜像处理
					rbtree_node_ptr s = replace_node_parent->left;
					if (s->color == rbtree_red)
					{
						s->color = rbtree_black;
						replace_node_parent->color = rbtree_red;
						rbtree_rotate_right(replace_node_parent, root);
						s = replace_node_parent->left;
					}

					if ((s->left == nullptr || s->left->color == rbtree_black)
						&& (s->right == nullptr || s->right->color == rbtree_black))
					{
						s->color = rbtree_red;
						replace_node = replace_node_parent;
						replace_node_parent = replace_node_parent->parent;
					}
					else
					{
						if (s->left == nullptr || s->left->color == rbtree_black)
						{
							if (s->right != nullptr)
								s->right->color = rbtree_black;
							s->color = rbtree_red;
							rbtree_rotate_left(s, root);
							s = replace_node_parent->left;
						}
						s->color = replace_node_parent->color;
						replace_node_parent->color = rbtree_black;
						if (s->left != nullptr)
							s->left->color = rbtree_black;
						rbtree_rotate_right(replace_node_parent, root);
						break;
					}


				}
			}
			if (replace_node != nullptr) replace_node->color = rbtree_black;
		}

		return del_node;

	}

}

#endif

插入测试程序

顺序插入:10,7,8,15,5,6,11,13,12

(第十一步) STL: stl_rb_tree容器实现_第3张图片

删除顺序测试:10,11,15
(第十一步) STL: stl_rb_tree容器实现_第4张图片

(第十一步) STL: stl_rb_tree容器实现_第5张图片
(第十一步) STL: stl_rb_tree容器实现_第6张图片

stl_rb_tree_test.h

#pragma once
#include "../p2_STL_Source/stl_rb_tree.h"

namespace mySTL
{
	namespace rbtreeTest
	{
		template<class Key, class Value>
		using myRBTree = mySTL::rb_tree<Key, Value, mySTL::identity<int>, mySTL::less<int>>;

		void test01();

	}
}

stl_rb_tree_test.cpp

#include "stl_rb_tree_test.h"
#include 

using namespace std;

namespace mySTL
{
	namespace rbtreeTest
	{

		void test01()
		{
			myRBTree<int, int> itree;

			cout << "size = " << itree.size() << endl;

			itree.insert_unique(10); 
			itree.insert_unique(7); 
			itree.insert_unique(8);
			itree.insert_unique(15); 
			itree.insert_unique(5); 
			itree.insert_unique(6);
			itree.insert_unique(11);
			itree.insert_unique(13); 
			itree.insert_unique(12);

			cout << "size = " << itree.size() << endl;
			// 顺序
			cout << "顺序输出val 测试++" << endl;
			for (auto it = itree.begin(); it != itree.end(); ++it)
			{
				cout << *it << " ";
			}
			cout << endl << endl;

			// 倒序
			cout << "倒序输出val 测试-- " << endl;
			for (auto it = itree.end() ; it != itree.begin(); --it)
			{
				cout << *it << " ";
			}
			cout << endl;
			cout << "end 为 0,抵达begin即刻停止, 所以多个0,少个begin" << endl << endl;


			// 顺序
			cout << "顺序输出val(color)" << endl;
			for (auto it = itree.begin(); it != itree.end(); ++it)
			{
				cout << *it << "(" << it.ptr->color <<")" << " ";
			}
			cout << endl;

			itree.erase(10);
			// erase顺序
			cout << "erase 10 顺序输出val(color)" << endl;
			for (auto it = itree.begin(); it != itree.end(); ++it)
			{
				cout << *it << "(" << it.ptr->color << ")" << " ";
			}
			cout << endl;

			itree.erase(11);
			// erase顺序
			cout << "erase 11 顺序输出val(color)" << endl;
			for (auto it = itree.begin(); it != itree.end(); ++it)
			{
				cout << *it << "(" << it.ptr->color << ")" << " ";
			}
			cout << endl;

			itree.erase(15);
			// erase顺序
			cout << "erase 15 顺序输出val(color)" << endl;
			for (auto it = itree.begin(); it != itree.end(); ++it)
			{
				cout << *it << "(" << it.ptr->color << ")" << " ";
			}
			cout << endl;
		}

	}
}

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