map、set底层封装模拟实现（红黑树）

微风拂柳絮2024-05-07 12:17

文章目录

一、红黑树

相较于前面的AVL树，红黑树的优势是：旋转次数减少，效率提高了，同时还保留了AVL树的查找优势

1.1红黑树的规则：

1.每个节点不是红色就是黑色
2.红色节点的孩子一定是黑色节点
3.不能有连续的红色节点
4.每条路径（走到空为止）上的黑色节点数量相同
5.最短路径<=最长路径<=2最短路径（当某条路径只有黑色节点，而另一条路径红色节点数量和黑色节点相同，那么最长路径就是最短路路径的两倍）

1.2红黑树的插入操作

1.2.1不需要旋转（如果叔叔存在且为红,这里的C表示孩子，P表示父亲，U表示叔叔，G表示祖父），包含四种情况，无论孩子在哪里，都是只需要改变叔叔和父亲的颜色为黑，祖父为红，然后向上继续走，C = G
1.2.2需要旋转（左旋，右旋，左右双旋，右左双旋），叔叔不存在或者为黑

右旋的情况(这里省略了C,P,U所连的节点）


左右双旋的情况(这里省略了C,P,U所连的节点）

下面两种情况省略

1.2红黑树的插入代码

cpp 复制代码 
	bool Insert(const pair<K, V>& data)
	{
		if (_root == nullptr)
		{
			_root = new Node(data);
			_root->_col = BLACK;
			return true;
		}

		Node* cur = _root;
		Node* parent = nullptr;
		while (cur)
		{
			if (data.first > cur->_data.first)
			{
				parent = cur;
				cur = cur->_right;
			}
			else if (data.first < cur->_data.first)
			{
				parent = cur;
				cur = cur->_left;
			}
			else
				return false;
		}

		cur = new Node(data);
		if (parent->_data.first > cur->_data.first)
			parent->_left = cur;
		else
			parent->_right = cur;

		cur->_parent = parent;

		//判断父亲是否为红，为黑就不管
		while (parent && parent->_col == RED)
		{
			Node* grandfather = parent->_parent;
			if (parent == grandfather->_left)
			{
				Node* uncle = grandfather->_right;
				if (uncle && uncle->_col == RED)//叔叔存在且为红
				{
					uncle->_col = parent->_col = BLACK;
					grandfather->_col = RED;
					cur = grandfather;//继续向上处理
					parent = cur->_parent;
				}
				else
				{
					if (cur == parent->_left)
					{
						//叔叔为黑或者叔叔不存在
						RotateR(grandfather);
						parent->_col = BLACK;
						grandfather->_col = RED;
					}
					else
					{
						RotateL(parent);
						RotateR(grandfather);
						cur->_col = BLACK;
						parent->_col = RED;
					}
					break;
				}
			}
			else
			{
				Node* uncle = grandfather->_left;
				if (uncle && uncle->_col == RED)
				{
					uncle->_col = parent->_col = BLACK;
					grandfather->_col = RED;
					cur = grandfather;//继续向上处理
					parent = cur->_parent;
				}
				else
				{
					if (cur == parent->_right)
					{
						RotateL(grandfather);
						parent->_col = BLACK;
						grandfather->_col = RED;
					}
					else
					{
						RotateR(parent);
						RotateL(grandfather);
						cur->_col = BLACK;
						grandfather->_col = RED;
					}
					break;
				}
			}
		}
		_root->_col = BLACK;
		return true;
	}
	void RotateL(Node* parent)
{
	Node* subR = parent->_right;
	Node* subRL = subR->_left;

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

	Node* ppnode = parent->_parent;

	subR->_left = parent;
	parent->_parent = subR;

	if (ppnode == nullptr)
	{
		_root = subR;
		_root->_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;

	Node* ppnode = parent->_parent;

	subL->_right = parent;
	parent->_parent = subL;

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

1.3红黑树的整体框架

cpp 复制代码 
#pragma once
#include<iostream>
#include<assert.h>
using namespace std;

//颜色定义
enum color
{
	RED,
	BLACK
};

template<class K,class V>
struct RBTreeNode
{
	typedef RBTreeNode<K, V> Node;
	pair<K, V> _data;
	Node* _left;
	Node* _right;
	Node* _parent;
	color _col;

	//构造函数
	RBTreeNode(const pair<K, V>& data)
		:_left(nullptr)
		, _right(nullptr)
		, _parent(nullptr)
		, _col(RED)
		, _data(data)
	{}
};


template<class K,class V>
class RBTree
{
public:
	typedef RBTreeNode<K, V> Node;
	bool Insert(const pair<K, V>& data)
	{
		if (_root == nullptr)
		{
			_root = new Node(data);
			_root->_col = BLACK;
			return true;
		}

		Node* cur = _root;
		Node* parent = nullptr;
		while (cur)
		{
			if (data.first > cur->_data.first)
			{
				parent = cur;
				cur = cur->_right;
			}
			else if (data.first < cur->_data.first)
			{
				parent = cur;
				cur = cur->_left;
			}
			else
				return false;
		}

		cur = new Node(data);
		if (parent->_data.first > cur->_data.first)
			parent->_left = cur;
		else
			parent->_right = cur;

		cur->_parent = parent;

		//判断父亲是否为红，为黑就不管
		while (parent && parent->_col == RED)
		{
			Node* grandfather = parent->_parent;
			if (parent == grandfather->_left)
			{
				Node* uncle = grandfather->_right;
				if (uncle && uncle->_col == RED)//叔叔存在且为红
				{
					uncle->_col = parent->_col = BLACK;
					grandfather->_col = RED;
					cur = grandfather;//继续向上处理
					parent = cur->_parent;
				}
				else
				{
					if (cur == parent->_left)
					{
						//叔叔为黑或者叔叔不存在
						RotateR(grandfather);
						parent->_col = BLACK;
						grandfather->_col = RED;
					}
					else
					{
						RotateL(parent);
						RotateR(grandfather);
						cur->_col = BLACK;
						parent->_col = RED;
					}
					break;
				}
			}
			else
			{
				Node* uncle = grandfather->_left;
				if (uncle && uncle->_col == RED)
				{
					uncle->_col = parent->_col = BLACK;
					grandfather->_col = RED;
					cur = grandfather;//继续向上处理
					parent = cur->_parent;
				}
				else
				{
					if (cur == parent->_right)
					{
						RotateL(grandfather);
						parent->_col = BLACK;
						grandfather->_col = RED;
					}
					else
					{
						RotateR(parent);
						RotateL(grandfather);
						cur->_col = BLACK;
						grandfather->_col = RED;
					}
					break;
				}
			}
		}
		_root->_col = BLACK;
		return true;
	}

	void Inorder()
	{
		_Inorder(_root);
	}

private:
	void _Inorder(Node* root)
	{
		if (root == nullptr)
			return;
		_Inorder(root->_left);
		cout << root->_data.first << endl;
		_Inorder(root->_right);
	}
	void RotateL(Node* parent)
	{
		Node* subR = parent->_right;
		Node* subRL = subR->_left;

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

		Node* ppnode = parent->_parent;

		subR->_left = parent;
		parent->_parent = subR;

		if (ppnode == nullptr)
		{
			_root = subR;
			_root->_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;

		Node* ppnode = parent->_parent;

		subL->_right = parent;
		parent->_parent = subL;

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

	Node* _root = nullptr;
};

二、map、set的底层封装

这里我们需要加上迭代器和仿函数（为了套用同一个红黑树的模版）
map有两个模版参数、set只有一个模版参数，因此我们需要加一个仿函数来确定是map还是set

2.1set的底层封装

cpp 复制代码 
namespace SF
{
	//仿函数
	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;
		iterator begin()
		{
			return _t.begin();
		}

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

		bool insert(const K& key)
		{
			return _t.Insert(key);
		}

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

	};
}

2.2map的底层封装

cpp 复制代码 
namespace SF
{
	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;

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

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

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

2.3红黑树的底层封装

cpp 复制代码 
#pragma once
#include<vector>

enum Colour
{
	RED,
	BLACK
};

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

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


template<class T>
struct RBTreeIterator
{
	typedef RBTreeNode<T> Node;
	typedef RBTreeIterator<T> 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--()
	{
		// 
		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>

// 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> iterator;

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

		return iterator(subLeft);
	}

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

	bool Insert(const T& data)
	{
		if (_root == nullptr)
		{
			_root = new Node(data);
			_root->_col = BLACK;
			return 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 false;
			}
		}

		cur = new Node(data); // 红色的
		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;
				}
				else
				{
					// 情况二：叔叔不存在或者存在且为黑
					// 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;
				}
				else
				{
					// 情况二：叔叔不存在或者存在且为黑
					// 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 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;
};
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