【C++】set模拟实现

前言：

C++中的set是标准模板库（STL）中的一种关联容器，它存储了一组唯一的元素，并且这些元素是按照特定的顺序（默认是升序）进行排序的

set的介绍

C++中的set是标准模板库（STL）中的一种关联容器，它存储了一组唯一的元素，并且这些元素是按照特定顺序（默认是升序）排序的。set内部使用红黑树这种平衡二叉搜索树来组织元素，这使得set能够提供对数时间复杂度的查找、插入和删除操作。

set的特点

• 唯一性：set中的元素是唯一的，插入重复元素时，新元素不会被添加到容器中。
• 自动排序：set会自动对元素进行排序，不需要用户手动维护元素的顺序。
• 高效的查找、插入和删除操作：由于set内部通常使用红黑树实现，这些操作的时间复杂度为对数级别（O(log n)）。
• 迭代器稳定性：在set中插入或删除元素不会使现有的迭代器失效，除了指向被删除元素的迭代器

set的实现（set的底层是红黑树）红黑树

set的结构

• 由于set和map是公用一棵树，set是K 、map是KV的结构，为了适应map的结构，set做出一定的改变
• 内部类是为了取到set内所存储的数据
• 在set的map中 set所存储的是key而map是pair

template<class K>class set{struct setofkey{const K& operator()(const K& key){return key;}};public:private:RBTree <K, K, setofkey> _t;};

set的插入

这是红黑树的底层插入，大体上和红黑树是一样的

• 寻找插入位置，进行插入。

• 调整红黑树，保持红黑树的结构

• 第一行的iterator是普通迭代器，而return返回的是const迭代器。在迭代器的封装的时候就要写iterator的构造函数

• pair<iterator,bool> insert(const K& key)
  {pair<typename RBTree <K, K, setofkey>::iterator, bool> ret = _t.insert(key);return pair<iterator, bool>(ret.first, ret.second);
  }
  

pair<iterator,bool> insert(const T& data)
{if (_root == nullptr){_root = new Node(data);_root->_col = BLACK;return make_pair(iterator(_root),true);}Node* parent = nullptr;Node* cur = _root;keyofT kot;while (cur){if (kot(data) > kot(cur->_data)){parent = cur;cur = cur->_right;}else if (kot(data) < kot(cur->_data)){parent = cur;cur = cur->_left;}else{return make_pair(iterator(cur), false);}}cur = new Node(data);Node* newnode = cur;cur->_col = RED;if (kot(data) < kot(parent->_data)){parent->_left = cur;}else{parent->_right = cur;}cur->_parent = parent;while (parent && parent->_col == RED){Node* grandparent = parent->_parent;if (parent == grandparent->_left){Node* uncle = grandparent->_right;if (uncle && uncle->_col == RED){parent->_col = uncle->_col = BLACK;grandparent->_col = RED;cur = grandparent;parent = cur->_parent;}else//uncle is not or black{if (cur == parent->_left){RotateR(grandparent);grandparent->_col = RED;parent->_col = BLACK;}else{RotateL(parent);RotateR(grandparent);grandparent->_col = RED;cur->_col = BLACK;}break;}}else//parent == grandparent->_right{Node* uncle = grandparent->_left;if (uncle && uncle->_col == RED){grandparent->_col = RED;parent->_col = uncle->_col = BLACK;cur = grandparent;parent = cur->_parent;}else{if (cur == parent->_right){RotateL(grandparent);parent->_col = BLACK;grandparent->_col = RED;}else{RotateR(parent);RotateL(grandparent);cur->_col = BLACK;grandparent->_col = RED;}}break;}}_root->_col = BLACK;return make_pair(iterator(newnode),true );
}

set的查找

• 红黑树的查找类似于，AVL的查找。本质上是一样的。

Node* find(const T& data)
{keyofT kot;Node* cur = _root;while (cur){if (kot(data) > kot(cur->_data)){cur = cur->_right;}else if (kot(data) < kot(cur->_data)){cur = cur->_left;}else{return cur;}}return nullptr;
}

set的迭代器

迭代器的概念

迭代器是一种抽象数据类型，它提供了一种方法来遍历容器中的元素，就像指针遍历数组一样。C++中的迭代器分为五种：输入迭代器、输出迭代器、前向迭代器、双向迭代器和随机访问迭代器。set的迭代器是双向迭代器，这意味着它们可以向前和向后遍历元素

迭代器的封装

• set迭代器类似于list的迭代器
• 主要区别在于++和--
• Ptr是T*，Ref是T&，设置这么多的模板参数是为适配出const的迭代器
• 注意的是需要Iterator的构造函数，因为set的迭代器都是const的迭代器。

template<class T,class Ptr,class Ref>
struct TreeIterator
{typedef RBTreeNode<T> Node;typedef TreeIterator<T,Ptr,Ref> self;typedef TreeIterator<T, T*, T&> Iterator;Node* _node;TreeIterator(Node* node):_node(node){}TreeIterator(const Iterator& it):_node(it._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;}};

迭代器的核心

set的迭代器在内部维护了指向树中节点的指针。由于set是有序的，迭代器在递增或递减时会沿着树的左子树或右子树进行遍历。迭代器的operator++（递增）和operator–（递减）操作会更新迭代器所指向的节点，移动到下一个或上一个有序元素。

前置++

• 前置++ 的本质上就是中序的遍历，左子树-根-右子树
• 如果右子树存在就去右子树的最左节点
• _node 不是右节点那么，证明子树的左右节点均访问完成，需要访问祖父的节点

self& operator++()
{if (_node->_right){Node* cur = _node->_right;while (cur->_left){cur = cur->_left;}_node = cur;}else{Node* cur = _node;Node* parent = _node->_parent;while (parent){if (cur == parent->_left){break;}else{cur = cur->_parent;parent = parent->_parent;}}_node = parent;}return *this;
}

前置- -

• 前置-- 是前置++的镜像的一个顺序的访问，右子树-根-左子树
• 方法是类似于前置++

self& operator--()
{if (_node->_left){Node* cur = _node->_right;while (cur->_left){cur = cur->_right;}_node = cur;}else{Node* cur = _node;Node* parent = _node->_parent;while (parent && parent->_left){cur = cur->_parent;parent = parent->_parent;}_node = parent;}return *this;
}

迭代器

• 前面是将迭代器封装，因为正常的++或者–已不可以支持自定义类型的加减
• 在红黑树的类中实现，在实现set时候只需要调用，在这里面可以认为红黑树是容器的适配器

typedef TreeIterator<T, T*, T&> iterator;typedef TreeIterator<T,const T*,const T&> const_iterator;iterator begin()
{Node* leftmin = _root;while (leftmin->_left){leftmin = leftmin->_left;}return iterator(leftmin);
}iterator end()
{return iterator(nullptr);
}const_iterator begin()const 
{Node* leftmin = _root;while (leftmin->_left){leftmin = leftmin->_left;}return const_iterator(leftmin);
}const_iterator end()const 
{return const_iterator(nullptr);
}

源码

set

#pragma once
#include"RBTree.h"
#include<iostream>
using namespace std;namespace Set
{template<class K>class set{struct setofkey{const K& operator()(const K& key){return key;}};public:typedef typename RBTree<K, K, setofkey>::const_iterator iterator;typedef typename RBTree<K, K, setofkey>::const_iterator const_iterator;iterator begin()const {return _t.begin();}iterator end()const {return _t.end();}pair<iterator,bool> insert(const K& key){pair<typename RBTree <K, K, setofkey>::iterator, bool> ret = _t.insert(key);return pair<iterator, bool>(ret.first, ret.second);}private:RBTree <K, K, setofkey> _t;};
}

红黑树

enum Colour
{RED,BLACK
};
template< class T>
class RBTreeNode
{
public:RBTreeNode<T>* _left;RBTreeNode<T>* _right;RBTreeNode<T>* _parent;T _data;Colour _col;RBTreeNode(const T& data):_left(nullptr), _right(nullptr), _parent(nullptr), _col(RED), _data(data){}
};template<class T,class Ptr,class Ref>
struct TreeIterator
{typedef RBTreeNode<T> Node;typedef TreeIterator<T,Ptr,Ref> self;typedef TreeIterator<T, T*, T&> Iterator;Node* _node;TreeIterator(Node* node):_node(node){}TreeIterator(const Iterator& it):_node(it._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->_left){Node* cur = _node->_right;while (cur->_left){cur = cur->_right;}_node = cur;}else{Node* cur = _node;Node* parent = _node->_parent;while (parent && parent->_left){cur = cur->_parent;parent = parent->_parent;}_node = parent;}return *this;}self& operator++(){if (_node->_right){Node* cur = _node->_right;while (cur->_left){cur = cur->_left;}_node = cur;}else{Node* cur = _node;Node* parent = _node->_parent;while (parent){if (cur == parent->_left){break;}else{cur = cur->_parent;parent = parent->_parent;}}_node = parent;}return *this;}
};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;iterator begin(){Node* leftmin = _root;while (leftmin->_left){leftmin = leftmin->_left;}return iterator(leftmin);}iterator end(){return iterator(nullptr);}const_iterator begin()const {Node* leftmin = _root;while (leftmin->_left){leftmin = leftmin->_left;}return const_iterator(leftmin);}const_iterator end()const {return const_iterator(nullptr);}Node* find(const T& data){keyofT kot;Node* cur = _root;while (cur){if (kot(data) > kot(cur->_data)){cur = cur->_right;}else if (kot(data) < kot(cur->_data)){cur = cur->_left;}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);}Node* parent = nullptr;Node* cur = _root;keyofT kot;while (cur){if (kot(data) > kot(cur->_data)){parent = cur;cur = cur->_right;}else if (kot(data) < kot(cur->_data)){parent = cur;cur = cur->_left;}else{return make_pair(iterator(cur), false);}}cur = new Node(data);Node* newnode = cur;cur->_col = RED;if (kot(data) < kot(parent->_data)){parent->_left = cur;}else{parent->_right = cur;}cur->_parent = parent;while (parent && parent->_col == RED){Node* grandparent = parent->_parent;if (parent == grandparent->_left){Node* uncle = grandparent->_right;if (uncle && uncle->_col == RED){parent->_col = uncle->_col = BLACK;grandparent->_col = RED;cur = grandparent;parent = cur->_parent;}else//uncle is not or black{if (cur == parent->_left){RotateR(grandparent);grandparent->_col = RED;parent->_col = BLACK;}else{RotateL(parent);RotateR(grandparent);grandparent->_col = RED;cur->_col = BLACK;}break;}}else//parent == grandparent->_right{Node* uncle = grandparent->_left;if (uncle && uncle->_col == RED){grandparent->_col = RED;parent->_col = uncle->_col = BLACK;cur = grandparent;parent = cur->_parent;}else{if (cur == parent->_right){RotateL(grandparent);parent->_col = BLACK;grandparent->_col = RED;}else{RotateR(parent);RotateL(grandparent);cur->_col = BLACK;grandparent->_col = RED;}}break;}}_root->_col = BLACK;return make_pair(iterator(newnode),true );}void RotateR(Node* parent){Node* cur = parent->_left;Node* curright = cur->_right;parent->_left = curright;if (curright){curright->_parent = parent;}cur->_right = parent;Node* ppnode = parent->_parent;parent->_parent = cur;if (ppnode == nullptr){_root = cur;cur->_parent = nullptr;}else{if (ppnode->_left == parent){ppnode->_left = cur;}else{ppnode->_right = cur;}cur->_parent = ppnode;}}void RotateL(Node* parent){Node* cur = parent->_right;Node* curleft = cur->_left;parent->_right = curleft;if (curleft){curleft->_parent = parent;}cur->_left = parent;Node* ppnode = parent->_parent;parent->_parent = cur;if (parent == _root){_root = cur;cur->_parent = nullptr;}else{if (ppnode->_left == parent){ppnode->_left = cur;}else{ppnode->_right = cur;}cur->_parent = ppnode;}}private:Node* _root = nullptr;
};