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【C++进阶】封装红黑树实现map和set

【C++进阶】封装红黑树实现map和set

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🌼文章目录🌼

1. 源码及框架分析

2. 模拟实现map和set

    2.1 实现出复用红黑树的框架,并支持insert

    2.2 支持iterator的实现

    2.3 map支持[]

    2.4 Mymap和myset代码实现

1. 源码及框架分析

  SGI-STL30版本源代码,map和set的源代码在map/set/stl_map.h/stl_set.h/stl_tree.h等几个头文件中。

  map和set的实现结构框架核心部分截取出来如下:

// set
#ifndef __SGI_STL_INTERNAL_TREE_H
#include <stl_tree.h>
#endif
#include <stl_set.h>
#include <stl_multiset.h>
// map
#ifndef __SGI_STL_INTERNAL_TREE_H
#include <stl_tree.h>
#endif
#include <stl_map.h>
#include <stl_multimap.h>
// stl_set.h
template <class Key, class Compare = less<Key>, class Alloc = alloc>
class set {
public:
	// typedefs:
	typedef Key key_type;
	typedef Key value_type;
private:
	typedef rb_tree<key_type, value_type,
		identity<value_type>, key_compare, Alloc> rep_type;
	rep_type t; // red-black tree representing set
};
// stl_map.h
template <class Key, class T, class Compare = less<Key>, class Alloc = alloc>
class map {
public:
	// typedefs:
	typedef Key key_type;
	typedef T mapped_type;
	typedef pair<const Key, T> value_type;
private:
	typedef rb_tree<key_type, value_type,
		select1st<value_type>, key_compare, Alloc> rep_type;
	rep_type t; // red-black tree representing map
};
// stl_tree.h
struct __rb_tree_node_base
{
	typedef __rb_tree_color_type color_type;
	typedef __rb_tree_node_base* base_ptr;
	color_type color;
	base_ptr parent;
	base_ptr left;
	base_ptr right;
};
// stl_tree.h
template <class Key, class Value, class KeyOfValue, class Compare, class Alloc
	= alloc>
class rb_tree {
protected:
	typedef void* void_pointer;
	typedef __rb_tree_node_base* base_ptr;
	typedef __rb_tree_node<Value> rb_tree_node;
	typedef rb_tree_node* link_type;
	typedef Key key_type;
	typedef Value value_type;
public:
	// insert⽤的是第⼆个模板参数左形参
	pair<iterator, bool> insert_unique(const value_type& x);
	// erase和find⽤第⼀个模板参数做形参
	size_type erase(const key_type& x);
	iterator find(const key_type& x);
protected:
	size_type node_count; // keeps track of size of tree
	link_type header;
};
template <class Value>
struct __rb_tree_node : public __rb_tree_node_base
{
	typedef __rb_tree_node<Value>* link_type;
	Value value_field;
};

   ① 通过下图对框架的分析,我们可以看到源码中rb_tree用了⼀个巧妙的泛型思想实现,rb_tree是实现key的搜索场景,还是key/value的搜索场景不是直接写死的,而是由第⼆个模板参数Value决定_rb_tree_node中存储的数据类型。

  ② set实例化rb_tree时第二个模板参数给的是key,map实例化rb_tree时第二个模板参数给的是
pair<const key, T>,这样⼀颗红黑树既可以实现key搜索场景的set,也可以实现key/value搜索场景的map。

  ③ 要注意⼀下,源码里面模板参数是用T代表value,而内部写的value_type不是我们我们日常
key/value场景中说的value,源码中的value_type反⽽是红黑树结点中存储的真实的数据的类型。

  ④ rb_tree第⼆个模板参数Value已经控制了红黑树结点中存储的数据类型,为什么还要传第⼀个模板参数Key呢?尤其是set,两个模板参数是⼀样的,这是很多同学这时的⼀个疑问。要注意的是对于map和set,find/erase时的函数参数都是Key,所以第⼀个模板参数是传给find/erase等函数做形参的类型的。对于set而言两个参数是⼀样的,但是对于map而言就完全不⼀样了,map insert的是pair对象,但是find和ease的是Key对象。

2. 模拟实现map和set
    2.1 实现出复用红黑树的框架,并支持insert

  ① 参考源码框架,map和set复用之前我们实现的红黑树。

  ② 我们这里相比源码调整⼀下,key参数就用K,value参数就用V,红黑树中的数据类型,我们使用T。(源码中的命名风格实在令人抓狂)

  ③ 其次因为RBTree实现了泛型不知道T参数导致是K,还是pair<K, V>,那么insert内部进行插入逻辑比较时,就没办法进行比较,因为pair的默认支持的是key和value⼀起参与比较,我们需要时的任何时候只比较key,所以我们在map和set层分别实现⼀个MapKeyOfT和SetKeyOfT的仿函数传给RBTree的KeyOfT,然后RBTree中通过KeyOfT仿函数取出T类型对象中的key,再进行比较,具体细节参考如下代码实现。

// 源码中pair⽀持的<重载实现
template <class T1, class T2>
bool operator< (const pair<T1,T2>& lhs, const pair<T1,T2>& rhs)
{ return lhs.first<rhs.first || (!(rhs.first<lhs.first) &&
lhs.second<rhs.second); }
// Mymap.h
namespace bit
{
    template<class K, class V>
    class map
    {
        struct MapKeyOfT
        {
            const K& operator()(const pair<K, V>& kv)
                {
                    return kv.first;
                }
        };
public:
    bool insert(const pair<K, V>& kv)
        {
            return _t.Insert(kv);
        }
private:
        RBTree<K, pair<K, V>, MapKeyOfT> _t;
    };
}
// Myset.h
namespace bit
{
    template<class K>
    class set
    {
        struct SetKeyOfT
        {
            const K& operator()(const K& key)
            return key;
        }
    };
public:
    bool insert(const K& key)
    {
        return _t.Insert(key);
    }
private:
    RBTree<K, K, SetKeyOfT> _t;
};
template<class T>
struct RBTreeNode//红黑树
{
	T _data;
	RBTreeNode<T>* _left;
	RBTreeNode<T>* _right;
	RBTreeNode<T>* _parent;
	Colour _col;
	RBTreeNode(const T& data)
		: _data(data)
		, _left(nullptr)
		, _right(nullptr)
		, _parent(nullptr)
	{}
};

// 实现步骤:
// 1、实现红⿊树
// 2、封装map和set框架,解决KeyOfT
// 3、iterator
// 4、const_iterator
// 5、key不⽀持修改的问题
// 6、operator[]
template<class K, class T, class KeyOfT>
class RBTree
{
	p
		rivate :
	typedef RBTreeNode<T> Node;
	Node* _root = nullptr;
public:
	bool Insert(const T& data)
	{
		if (_root == nullptr)
		{
			_root = new Node(data);
			_root->_col = BLACK;
			return true;
		} K
			eyOfT kot;
		Node* parent = nullptr;
		Node* cur = _root;
		while (cur)
		{
			if (kot(cur->_data) < kot(data))
			{
				parent = cur;
				cur = cur->_right;
			} e
				lse if (kot(cur->_data) > kot(data))
			{
				parent = cur;
				cur = cur->_left;
			} e
				lse
			{
			return false;
			}
		} c
			ur = new Node(data);
			Node* newnode = cur;
			// 新增结点。颜⾊给红⾊
			cur->_col = RED;
			if (kot(parent->_data) < kot(data))
			{
				parent->_right = cur;
			} e
				lse
			{
			parent->_left = cur;
			} c
				ur->_parent = parent;
			//...
			return true;
	}
}
    2.2 支持iterator的实现

  iterator核心源码:

struct __rb_tree_base_iterator
{
	typedef __rb_tree_node_base::base_ptr base_ptr;
	base_ptr node;
	void increment()
	{
		if (node->right != 0) {
			node = node->right;
			while (node->left != 0)
				node = node->left;
		} e
			lse{
			base_ptr y = node->parent;
			while (node == y->right) {
			node = y;
			y = y->parent;
			} i
			f(node->right != y)
			node = y;
		}
	} v
		oid decrement()
		{
			if (node->color == __rb_tree_red &&
				node->parent->parent == node)
				node = node->right;
			else if (node->left != 0) {
				base_ptr y = node->left;
				while (y->right != 0)
					y = y->right;
				node = y;
			} e
				lse{
				base_ptr y = node->parent;
				while (node == y->left) {
				node = y;
				y = y->parent;
				} n
				ode = y;
			}
		}
};
template <class Value, class Ref, class Ptr>
struct __rb_tree_iterator : public __rb_tree_base_iterator
{
	typedef Value value_type;
	typedef Ref reference;
	typedef Ptr pointer;
	typedef __rb_tree_iterator<Value, Value&, Value*> iterator;
	__rb_tree_iterator() {}
	__rb_tree_iterator(link_type x) { node = x; }
	__rb_tree_iterator(const iterator& it) { node = it.node; }
	reference operator*() const { return link_type(node)->value_field; }
#ifndef __SGI_STL_NO_ARROW_OPERATOR
	pointer operator->() const { return &(operator*()); }
#endif /* __SGI_STL_NO_ARROW_OPERATOR */
	self& operator++() { increment(); return *this; }
	self& operator--() { decrement(); return *this; }
	inline bool operator==(const __rb_tree_base_iterator& x,
		const __rb_tree_base_iterator& y) {
		return x.node == y.node;
	} i
		nline bool operator!=(const __rb_tree_base_iterator& x,
			const __rb_tree_base_iterator& y) {
		return x.node != y.node;
	}

iterator实现思路分析:

  ① iterator实现的大框架跟list的iterator思路是一致的,用⼀个类型封装结点的指针,再通过重载运算符实现,迭代器像指针⼀样访问的行为。

  ② 这里的难点是operator++和operator--的实现。之前使用部分,我们分析了,map和set的迭代器走的是中序遍历,左子树->根结点->右子树,那么begin()会返回中序第⼀个结点的iterator也就是10所在结点的迭代器。

  ③ 迭代器++的核心逻辑就是不看全局,只看局部,只考虑当前中序局部要访问的下一个结点。

  ④ 迭代器++时,如果it指向的结点的右子树不为空,代表当前结点已经访问完了,要访问下⼀个结点是右子树的中序第⼀个,一棵树中序第一个是最左结点,所以直接找右子树的最左结点即可。

  ⑤ 迭代器++时,如果it指向的结点的右子树空,代表当前结点已经访问完了且当前结点所在的子树也访问完了,要访问的下一个结点在当前结点的祖先里面,所以要沿着当前结点到根的祖先路径向上找。

  ⑥ 如果当前结点是父亲的左,根据中序左子树->根结点->右子树,那么下一个访问的结点就是当前结点的父亲;如下图:it指向25,25右为空,25是30的左,所以下一个访问的结点就是30。

  ⑦ 如果当前结点是父亲的右,根据中序左子树->根结点->右子树,当前当前结点所在的⼦树访问完了,当前结点所在父亲的子树也访问完了,那么下一个访问的需要继续往根的祖先中去找,直到找到孩⼦是父亲左的那个祖先就是中序要问题的下一个结点。如下图:it指向15,15右为空,15是10的右,15所在⼦树话访问完了,10所在子树也访问完了,继续往上找,10是18的左,那么下⼀个访问的结点就是18。

  ⑧ end()如何表示呢?如下图:当it指向50时,++it时,50是40的右,40是30的右,30是18的右,18到根没有父亲,没有找到孩子是父亲左的那个祖先,这是父亲为空了,那我们就把it中的结点指针置为nullptr,我们用nullptr去充当end。需要注意的是stl源码空,红黑树增加了⼀个哨兵位头结点做为end(),这哨兵位头结点和根互为父亲,左指向最左结点,右指向最右结点。相比我们用nullptr作为end(),差别不大,他能实现的,我们也能实现。只是--end()判断到结点时空,特殊处理一下,让迭代器结点指向最右结点。具体参考迭代器--实现。

  ⑨ 迭代器--的实现跟++的思路完全类似,逻辑正好反过来即可,因为他访问顺序是右子树->根结点->左子树,具体参考下面代码实现。

  ⑩ set的iterator也不支持修改,我们把set的第二个模板参数改成const K即可, RBTree<K,
const K, SetKeyOfT> _t;

  ⑪ map的iterator不支持修改key但是可以修改value,我们把map的第二个模板参数pair的第⼀个参数改成const K即可, RBTree<K, pair<const K, V>, MapKeyOfT> _t;

  实际上支持iterator还有非常多的细节要处理,具体看下面的代码。

    2.3 map支持[]

  ① map要支持[]主要修改insert返回值支持,修改RBTree中的insert返回值为pair<Iterator,bool> Insert(const T& data)

  ② 有了insert支持,[]实现就很简单了,具体实现参考下面代码。

    2.4 Mymap和myset代码实现
//Mymap
#pragma once


#include "RBTree.h"


namespace gjk
{
	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<K, V>, MapKeyOfT>::Iterator iterator;
		typedef typename RBTree<K, pair<K, V>, MapKeyOfT>::ConstIterator const_iterator;


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

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


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

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

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

	private:
		RBTree<K, pair<K, V>, MapKeyOfT> _t;
	};
}
//Myset
#pragma once


#include "RBTree.h"


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

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

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

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

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

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

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

}
//RBTree
#pragma once


#include <iostream>
#include <vector>
#include <utility>
using namespace std;


//枚举存储颜色
enum Color
{
	RED,
	BLACK
};


namespace gjk
{
	template <class T>
	class RBTreeNode
	{
	public:
		T _data;//存储的值
		RBTreeNode<T>* _left;//左孩子
		RBTreeNode<T>* _right;//右孩子
		RBTreeNode<T>* _parent;//父亲
		Color _col;//颜色

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

	template <class T,class Ref,class Ptr>
	struct RBTreeIterator
	{
		typedef RBTreeNode<T> Node;
		typedef RBTreeIterator<T, Ref, Ptr> Self;

		Node* _node;
		Node* _root;
		RBTreeIterator(Node* node,Node* root)
			:_node(node)
			,_root(root)
		{}

		Self& operator++()//前置++
		{
			if (_node->_right)
			{
				Node* min = _node->_right;
				while (min && min->_left) min = min->_left;
				_node = min;
			}
			else
			{
				Node* cur = _node;
				Node* parent = cur->_parent;
				while (parent && parent->_right == cur)
				{
					cur = parent;
					parent = cur->_parent;
				}

				_node = parent;
			}
			return *this;
		}


		Self& operator++(int)//后置++
		{
			if (_node->_right)
			{
				Node* min = _node->_right;
				while (min && min->_left) min = min->_left;
				_node = min;
			}
			else
			{
				Node* cur = _node;
				Node* parent = cur->_parent;
				while (parent && parent->_right == cur)
				{
					cur = parent;
					parent = cur->_parent;
				}

				_node = parent;
			}
			return *this;
		}


		Self& operator--()
		{
			if (!_node)
			{
				Node* cur = _root;
				while (cur && cur->_right) cur = cur->_right;
				_node = cur;
			}
			else if (_node->_left)
			{
				Node* max = _node->_left;
				while (max && max->_right) max = max->_right;
				_node = max;
			}
			else
			{
				Node* cur = _node;
				Node* parent = cur->_parent;
				while (parent && parent->_left == cur)
				{
					cur = parent;
					parent = cur->_parent;
				}
				_node = parent;
			}
		}


		Self& operator--(int)
		{
			if (!_node)
			{
				Node* cur = _root;
				while (cur && cur->_right) cur = cur->_right;
				_node = cur;
			}
			else if (_node->_left)
			{
				Node* max = _node->_left;
				while (max && max->_right) max = max->_right;
				_node = max;
			}
			else
			{
				Node* cur = _node;
				Node* parent = cur->_parent;
				while (parent && parent->_left == cur)
				{
					cur = parent;
					parent = cur->_parent;
				}

				_node = parent;
			}
		}

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

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

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


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


	};


	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;

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

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

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

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

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

			KeyOfT kot;
			Node* cur = _root;
			Node* parent = nullptr;
			while (cur)//插入节点
			{
				if (kot(cur->_data) > kot(data))
				{
					parent = cur;
					cur = cur->_left;
				}
				else if (kot(cur->_data) < kot(data))
				{
					parent = cur;
					cur = cur->_right;
				}
				else return make_pair(Iterator(cur, _root), true);
			}

			cur = new Node(data);
			Node* flag = cur;
			cur->_parent = parent;
			if (kot(parent->_data) > kot(data)) parent->_left = cur;
			else parent->_right = cur;

			//处理两个红连在一起的情况
			while (parent && parent->_col == RED)
			{
				if (parent->_left == cur)//新增节点插入在parent左边的情况
				{
					Node* grandfather = parent->_parent;
					Node* uncle = grandfather->_right;
					if (grandfather->_right == parent) uncle = grandfather->_left;

					if (uncle && uncle->_col == RED)//uncle存在并且颜色为红
					{
						parent->_col = uncle->_col = BLACK;
						grandfather->_col = RED;

						cur = grandfather;
						parent = cur->_parent;
					}
					else//uncle不存在或者颜色为黑
					{
						if (grandfather->_left == parent)
						{
							RotateR(grandfather);
							parent->_col = BLACK;
							grandfather->_col = RED;
						}

						else
						{
							RotateR(parent);
							RotateL(grandfather);
							cur->_col = BLACK;
							grandfather->_col = RED;
						}

						break;
					}
				}
				else//新增节点插入在parent右边的情况
				{
					Node* grandfather = parent->_parent;
					Node* uncle = grandfather->_right;
					if (grandfather->_right == parent) uncle = grandfather->_left;

					if (uncle && uncle->_col == RED)//uncle存在并且颜色为红
					{
						parent->_col = uncle->_col = BLACK;
						grandfather->_col = RED;

						cur = grandfather;
						parent = cur->_parent;
					}

					else
					{
						if (grandfather->_right == parent)
						{
							RotateL(grandfather);
							parent->_col = BLACK;
							grandfather->_col = RED;
						}
						else
						{
							RotateL(parent);
							RotateR(grandfather);
							cur->_col = BLACK;
							grandfather->_col = RED;
						}

						break;
					}
				}
			}
			_root->_col = BLACK;
			return make_pair(Iterator(flag, _root), true);
		}


		void RotateR(Node* parent)//右单旋
		{
			Node* pparent = parent->_parent;
			Node* subL = parent->_left;
			Node* subR = subL->_right;

			parent->_left = subR;
			parent->_parent = subL;
			if (subR) subR->_parent = parent;
			subL->_right = parent;
			subL->_parent = pparent;

			if (pparent)
			{
				if (pparent->_left == parent) pparent->_left = subL;
				else pparent->_right = subL;
			}
			else _root = subL;
		}


		void RotateL(Node* parent)//左单旋
		{
			Node* pparent = parent->_parent;
			Node* subR = parent->_right;
			Node* subL = subR->_left;

			parent->_right = subL;
			parent->_parent = subR;
			if (subL) subL->_parent = parent;
			subR->_left = parent;
			subR->_parent = pparent;

			if (pparent)
			{
				if (pparent->_left == parent) pparent->_left = subR;
				else pparent->_right = subR;
			}
			else _root = subR;
		}


		int leafnodesize()//叶子节点个数
		{
			int sum = 0;
			LeafNodeSize(_root,sum);
			return sum;
		}


		int nodesize()//节点个数
		{
			int sum = 0;
			NodeSize(_root, sum);
			return sum;
		}


		void printf()
		{
			Printf(_root);
			cout << endl;
		}


		void find(const T& data)
		{
			Find(_root,data);
		}


		bool isRBTree()
		{
			return IsRBTree(_root);
		}

		void blacknodenum(vector<int>& arr)
		{
			BlackNodeNum(_root,arr,0);
		}

	private:
			void Printf(Node* cur)
			{
				if (!cur) return;

				Printf(cur->_left);
				cout << cur->_val << " ";
				Printf(cur->_right);
			}


			void Find(Node* cur,const T& data)//查找
			{
				while (cur)
				{
					if (cur->_val > data) cur = cur->_left;
					else if (cur->_val < data) cur = cur->_right;
					else
					{
						cout << data << "->" << cur->_val << endl;
						return;
					}
				}

				cout << "找不到" << endl;
			}


			bool IsRBTree(Node* cur)//验证红黑树
			{
				if (!cur) return true;
				if (cur->_parent && cur->_col == RED && cur->_col == cur->_parent->_col) return false;

				return IsRBTree(cur->_left) && IsRBTree(cur->_right);
			}

			bool IsLeafNode(Node* cur)
			{
				return !cur->_left && !cur->_right;
			}

			void LeafNodeSize(Node* cur,int& sum)
			{
				if (!cur) return;
				if (IsLeafNode(cur))
				{
					sum++;
					return;
				}

				LeafNodeSize(cur->_left, sum);
				LeafNodeSize(cur->_right, sum);
			}


			void NodeSize(Node* cur,int& sum)
			{
				if (!cur) return;

				sum++;
				NodeSize(cur->_left,sum);
				NodeSize(cur->_right,sum);
			}


			void BlackNodeNum(Node* cur,vector<int>& sum,int num)
			{
				if (!cur)
				{
					sum.push_back(num);
					return;
				}

				if (cur->_col == BLACK) num++;

				BlackNodeNum(cur->_left, sum, num);
				BlackNodeNum(cur->_right, sum, num);
			}



	private:
		Node* _root = nullptr;//根节点
	};
}

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