【C++】map & set 底层刨析-Toy模板网

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在 C++ STL 库中，map 与 set 的底层为红黑树，那么在不写冗余代码的情况下使用红黑树同时实现 map 与 set 便是本文的重点。

1. 红黑树的迭代器

迭代器的好处是可以方便遍历，是数据结构的底层实现与用户透明。如果想要给红黑树增加迭代器，需要考虑以下问题：

begin() 与 end()

STL 明确规定，begin() 与 end() 代表的是一段前闭后开的区间，而对红黑树进行中序遍历后，可以得到一个有序的序列，因此：begin() 可以放在红黑树中最小节点（即最左侧节点）的位置，end() 放在最大节点（最右侧节点）的下一个位置。

iterator begin()
{
	Node* subLeft = _root;
	while (subLeft && subLeft->_left)
	{
		subLeft = subLeft->_left;
	}
	return iterator(subLeft);
}

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

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

const_iterator end() const
{
	return const_iterator(nullptr);
}

operator++() 与 operator--()

Self& operator++()
{
	if (_node->_right)
	{
		// 右子树的中序第一个（最左节点）
		Node* subLeft = _node->_right;
		while (subLeft->_left)
		{
			subLeft = subLeft->_left;
		}
		_node = subLeft;
	}
	else
	{
		// 祖先里面孩子是父亲左的那个
		Node* cur = _node;
		Node* parent = cur->_parent;
		while (parent && cur == parent->_right)
		{
			cur = parent;
			parent = cur->_parent;
		}
		_node = parent;
	}
	return *this;
}

Self& operator--()
{
	// 跟++逻辑相反
	return *this;
}

2. 改造红黑树

#pragma once

enum Color
{
	RED,
	BLACK
};

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

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

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

	Node* _node;

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

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

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

	Self& operator++()
	{
		if (_node->_right)
		{
			// 右子树的中序第一个（最左节点）
			Node* subLeft = _node->_right;
			while (subLeft->_left)
			{
				subLeft = subLeft->_left;
			}
			_node = subLeft;
		}
		else
		{
			// 祖先里面孩子是父亲左的那个
			Node* cur = _node;
			Node* parent = cur->_parent;
			while (parent && cur == parent->_right)
			{
				cur = parent;
				parent = cur->_parent;
			}
			_node = parent;
		}
		return *this;
	}

	Self& operator--()
	{
		// 跟++逻辑相反
		return *this;
	}

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

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

// set->RBTree<K, K, SetKeyOfT>
// map->RBTree<K, pair<K, V>, MapKeyOfT>

// 因为关联式容器中存储的是<key, value>的键值对，因此
// K为key的类型
// T：如果是map，则为pair<K, V>；如果是set，则为K
// KeyOfT仿函数，取出T对象中的key
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&> const_iterator;

	iterator begin()
	{
		Node* subLeft = _root;
		while (subLeft && subLeft->_left)
		{
			subLeft = subLeft->_left;
		}
		return iterator(subLeft);
	}

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

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

	const_iterator end() const
	{
		return const_iterator(nullptr);
	}

	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();
	}

	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)
		{
			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);	// 红色的
		Node* newnode = cur;
		if (kot(parent->_data) < kot(data))
		{
			parent->_right = cur;
		}
		else
		{
			parent->_left = cur;
		}
		cur->_parent = parent;

		while (parent && parent->_col == RED)
		{
			Node* grandfather = parent->_parent;
			if (parent == grandfather->_left)
			{
				Node* uncle = grandfather->_right;
				// 情况一：叔叔存在且为红
				if (uncle && uncle->_col == RED)
				{
					// 变色
					parent->_col = uncle->_col = BLACK;
					grandfather->_col = RED;

					// 继续往上处理
					cur = grandfather;
					parent = cur->_parent;
				}
				// 情况二：叔叔不存在或者存在且为黑
				else
				{
					// 旋转+变色
					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;
				// 情况一：叔叔存在且为红
				if (uncle && uncle->_col == RED)
				{
					// 变色
					parent->_col = uncle->_col = BLACK;
					grandfather->_col = RED;

					// 继续往上处理
					cur = grandfather;
					parent = cur->_parent;
				}
				// 情况二：叔叔不存在或者存在且为黑
				else
				{
					// 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 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;
			subR->_parent = nullptr;
		}
		else
		{
			if (ppnode->_left == parent)
			{
				ppnode->_left = subR;
			}
			else
			{
				ppnode->_right = subR;
			}
			subR->_parent = ppnode;
		}
	}

	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;
			subL->_parent = nullptr;
		}
		else
		{
			if (ppnode->_left == parent)
			{
				ppnode->_left = subL;
			}
			else
			{
				ppnode->_right = subL;
			}
			subL->_parent = ppnode;
		}
	}

private:
	Node* _root = nullptr;
};

3. map 的模拟实现

map 的底层结构就是红黑树，因此在 map 中直接封装一棵红黑树，然后将其接口包装下即可。

#pragma once

#include "RBTree.h"

namespace tjq
{
	template<class K, class V>
	class map
	{
		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>::const_iterator 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>& kv)
		{
			return _t.Insert(kv);
		}

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

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

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

4. set 的模拟实现

set 的底层为红黑树，因此只需在 set 内部封装一棵红黑树，即可将该容器实现出来。文章来源地址https://www.toymoban.com/news/detail-848516.html

#pragma once

#include "RBTree.h"

namespace tjq
{
	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>::const_iterator const_iterator;

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

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

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

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

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