第十六章：红黑树模拟实现STL中的map与set

Iterator.h

#pragma once

// 反向迭代器--迭代器适配器
template<class Iterator>
struct ReverseIterator
{
	typedef typename Iterator::reference Ref;
	typedef typename Iterator::pointer Ptr;
	typedef ReverseIterator<Iterator> Self;
	Iterator _it;

	ReverseIterator(Iterator it)
		:_it(it)
	{}

	Ref operator*()
	{
		return *_it;
	}

	Ptr operator->()
	{
		return _it.operator->();
	}

	Self& operator++()
	{
		--_it;
		return *this;
	}

	Self& operator--()
	{
		++_it;
		rteurn *this;
	}

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

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

RBTree.h

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

#include "Iterator.h"

enum Colour
{
	RED,
	BLACK,
};

//red-black
template<class T>
struct RBTreeNode
{
	RBTreeNode<T>* _left;
	RBTreeNode<T>* _right;
	RBTreeNode<T>* _parent;
	T _data;

	Colour _col;

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

template<class T, class Ref, class Ptr>
struct __TreeIterator
{
	typedef Ref reference;
	typedef Ptr pointer;

	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;
	}

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

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

	Self& operator++()
	{
		if (_node->_right)
		{
			// 下一个访问就是右树中，中序的第一个节点
			Node* left = _node->_right;
			while (left->_left)
			{
				left = left->_left;
			}

			_node = left;
		}
		else
		{
			// 找祖先里面还是不是父亲的右的那个
			// 因为 cur 右为空，说明cur所在的子树已经访问完了
			// cur是parent的右的，说明parent也访问完了，继续往上去找
			Node* cur = _node;
			Node* parent = cur->_parent;
			while (parent && cur == parent->_right)
			{
				cur = cur->_parent;
				parent = parent->_parent;
			}

			_node = parent;
		}

		return *this;
	}

	Self& operator--()
	{
		if (_node->_left)
		{
			// 左子树的最右节点
			Node* right = _node->_left;
			while (right->_right)
			{
				right = right->_right;
			}

			_node = right;
		}
		else
		{
			Node* cur = _node;
			Node* parent = cur->_parent;
			while (parent && cur == parent->_left)
			{
				cur = parent;
				parent = parent->_parent;
			}

			_node = parent;
		}

		return *this;
	}
};

//KeyOfT是仿函数
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;
	typedef ReverseIterator<iterator> reverse_iterator;

	reverse_iterator rbegin()
	{
		Node* right = _root;
		while (right && right->_right)
		{
			right = right->_right;
		}
		return reverse_iterator(iterator(right));
	}

	reverse_iterator rend()
	{
		return reverse_iterator(iterator(nullptr));
	}

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

		return iterator(left);
	}

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

	RBTree()
		:_root(nullptr)
	{}

	// 拷贝构造和operator=大家自己去实现一下

	void Destory(Node* root)
	{
		if (root == nullptr)
		{
			return;
		}

		Destory(root->_left);
		Destory(root->_right);
		delete root;
	}

	~RBTree()
	{
		Destory(_root);
		_root = nullptr;
	}

	Node* Find(const K& key)
	{
		KeyOfT kot;
		Node* cur = _root;
		while (cur)
		{
			if (kot(cur->_data) > key)
			{
				cur = cur->_left;
			}
			else if (kot(cur->_data) < key)
			{
				cur = cur->_right;
			}
			else
			{
				return cur;
			}
		}

		return nullptr;
	}

	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);
			}
		}

		Node* newnode = new Node(data);
		newnode->_col = RED;
		if (kot(parent->_data) < kot(data))
		{
			parent->_right = newnode;
			newnode->_parent = parent;
		}
		else
		{
			parent->_left = newnode;
			newnode->_parent = parent;
		}
		cur = newnode;

		// 如果父亲存在，且颜色为红色就需要处理
		while (parent && parent->_col == RED)
		{
			Node* grandfather = parent->_parent;
			// 关键是看叔叔
			if (parent == grandfather->_left)
			{
				Node* uncle = grandfather->_right;
				// 情况1：uncle存在且为红
				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 // 情况2+3：uncle不存在 uncle存在且为黑
				{
					// 情况2：单旋
					if (cur == parent->_left)
					{
						RotateR(grandfather);
						grandfather->_col = RED;
						parent->_col = BLACK;
					}
					else // 情况3：双旋
					{
						RotateL(parent);
						RotateR(grandfather);
						cur->_col = BLACK;
						grandfather->_col = RED;
					}

					break;
				}
			}
			else // parent == grandfather->_right
			{
				Node* uncle = grandfather->_left;
				// 情况1
				if (uncle && uncle->_col == RED)
				{
					uncle->_col = parent->_col = BLACK;
					grandfather->_col = RED;

					cur = grandfather;
					parent = cur->_parent;
				}
				else // 情况2 + 情况3
				{
					if (cur == parent->_right)
					{
						RotateL(grandfather);
						parent->_col = BLACK;
						grandfather->_col = RED;
					}
					else // cur == parent->_left
					{
						RotateR(parent);
						RotateL(grandfather);
						cur->_col = BLACK;
						grandfather->_col = RED;
					}
					// 插入结束
					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* parentParent = parent->_parent;
		parent->_parent = subR;

		if (parent == _root)
		{
			_root = subR;
			_root->_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;

		subL->_right = parent;
		Node* parentParent = parent->_parent;
		parent->_parent = subL;

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

			subL->_parent = parentParent;
		}
	}

	bool _CheckBlance(Node* root, int blackNum, int count)
	{
		if (root == nullptr)
		{
			if (count != blackNum)
			{
				cout << "黑色节点的数量不相等"<<endl;
				return false;
			}

			return true;
		}
		
		if (root->_col == RED && root->_parent->_col == RED)
		{
			cout << "存在连续的红色节点"<<endl;
			return false;
		}

		if (root->_col == BLACK)
		{
			count++;
		}

		return _CheckBlance(root->_left, blackNum, count)
			&& _CheckBlance(root->_right, blackNum, count);
	}

	bool CheckBlance()
	{
		if (_root == nullptr)
		{
			return true;
		}

		if (_root->_col == RED)
		{
			cout << "根节点是红色的" << endl;
			return false;
		}

		// 找最左路径做黑色节点数量参考值
		int blackNum = 0;
		Node* left = _root;
		while (left)
		{
			if (left->_col == BLACK)
			{
				blackNum++;
			}

			left = left->_left;
		}

		int count = 0;
		return _CheckBlance(_root, blackNum, count);
	}

	/*void _InOrder(Node* root)
	{
		if (root == nullptr)
		{
			return;
		}

		_InOrder(root->_left);
		cout << root->_kv.first << ":"<<root->_kv.second<<endl;
		_InOrder(root->_right);
	}*/

	/*void InOrder()
	{
		_InOrder(_root);
		cout << endl;
	}
*/
private:
	Node* _root;
};

Map.h

#pragma once
#include "RBTree.h"

namespace z
{
	template<class K, class V>
	class map
	{
		struct MapKeyOfT
		{
			const K& operator()(const pair<const K, V>& kv)
			{
				return kv.first;
			}
		};
	public:
		typedef typename RBTree<K, pair<const K, V>, MapKeyOfT>::iterator iterator;
		typedef typename RBTree<K, pair<const K, V>, MapKeyOfT>::reverse_iterator reverse_iterator;

		reverse_iterator rbegin()
		{
			return _t.rbegin();
		}

		reverse_iterator rend()
		{
			return _t.rend();
		}

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

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

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

		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;
	};
}

Set.h

#pragma once
#include "RBTree.h"

namespace z
{
	template<class K>
	class set
	{
		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>::reverse_iterator reverse_iterator;

		reverse_iterator rbegin()
		{
			return _t.rbegin();
		}

		reverse_iterator rend()
		{
			return _t.rend();
		}


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

		iterator end()
		{
			return _t.end();
		}
		
		pair<iterator, bool> insert(const K& k)
		{
			return _t.Insert(k);
		}
	private:
		RBTree<K, K, SetKeyOfT> _t;
	};
}