C++ 模拟实现 map 和 set：掌握核心数据结构

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一、set 和 map 的结构

STL中set和map底层是一颗红黑树，模拟set和map需要一颗红黑树作为我们的成员变量
点击这里了解红黑树

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1.1 set的结构

set结构就是 K模型，所以set容器对红黑树的封装如下：

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1.2 map的结构

map结构就是 KV模型，所以map容器对红黑树的封装如下

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二、对红黑树的改造

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2.1 改造红黑树的节点

其中红黑树的节点类型就是模版参数T

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2.2 改造红黑树

2.2.1 仿函数的使用

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然后我们将所有需要比较key的函数利用仿函数进行替换，我们以Find为例

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2.2.2 插入函数的改造

代码如下（示例）：

pair<iterator, bool> Insert(const T& data)
{//情况一：如果是根节点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->_value) < kot(data)){parent = cur;cur = cur->_right;}else if (kot(cur->_value) > kot(data)){parent = cur;cur = cur->_left;}else{return make_pair(iterator(cur), false);}}//找到插入位置cur = new Node(data);Node* newnode = cur;if (kot(parent->_value) < 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;//情况三：如果叔叔存在且为红if (uncle && uncle->_col == RED){parent->_col = uncle->_col = BLACK;grandfather->_col = RED;cur = grandfather;parent = cur->_parent;}else{//情况四：叔叔不存在/存在且为黑，且cur在parent的左侧if (cur == parent->_left){//     g  //   p   u// c RotateR(grandfather);parent->_col = BLACK;grandfather->_col = RED;}else//情况五：叔叔不存在 / 存在且为黑，cur在parent的右侧{//     g//   p   u//     cRotateLR(grandfather);cur->_col = BLACK;grandfather->_col = RED;}//这时该子树的根节点变为黑色，不需要继续调整break;}}else{Node* uncle = grandfather->_left;//情况三：如果叔叔存在且为红if (uncle && uncle->_col == RED){parent->_col = uncle->_col = BLACK;grandfather->_col = RED;//继续调整cur = grandfather;parent = cur->_parent;}else{//情况四：叔叔不存在/存在且为黑，且cur在parent的左侧if (cur == parent->_right){//    g//  u   p//        cRotateL(grandfather);parent->_col = BLACK;grandfather->_col = RED;}else // 情况五：叔叔不存在 / 存在且为黑，cur在parent的右侧{//    g//  u   p//    cRotateRL(grandfather);cur->_col = BLACK;grandfather->_col = RED;}//这时该子树的根节点变为黑色，不需要继续调整break;}}}//防止情况三改到根节点变为红色_root->_col = BLACK;return make_pair(iterator(newnode), true);
}

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2.2.3 删除函数的改造

代码如下（示例）：

else //待删除结点的左右子树均不为空
{//替换法删除//寻找待删除结点右子树当中key值最小的结点作为实际删除结点Node* minParent = cur;Node* minRight = cur->_right;while (minRight->_left){minParent = minRight;minRight = minRight->_left;}// 原本直接可以赋值// cur->_value = minRight->_value //将待删除结点的键值改为minRight的键值Node* newnode = new Node(minRight->_value,cur->_col);Node* parent = cur->_parent;//重新链接祖父孙三代节点关系cur->_left->_parent = newnode;cur->_right->_parent = newnode;if (parent){if (parent->_left == cur){parent->_left = newnode;}else{parent->_right = newnode;}}else{//如果是根节点_root = newnode;}newnode->_parent = parent;newnode->_left = cur->_left;newnode->_right = cur->_right;//如果minParent是curif (minParent == cur){minParent = newnode;}delete cur;delParent = minParent; //标记实际删除的父节点delCur = minRight; //标记实际删除的结点
}

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三、对迭代器的改造

3.1 *、->、！=、==

代码如下（示例）：

template<class T, class Ref, class Ptr>
struct __RBTreeIterator
{typedef RBNode<T> Node;typedef __RBTreeIterator<T, Ref, Ptr> Self;Node* _node;//构造__RBTreeIterator(Node* node):_node(node){}Ref operator*(){return _node->_value;}Ptr operator->(){return &_node->_value;}//判断两个正向迭代器是否不同bool operator!=(const Self& s) const{return _node != s._node;}//判断两个正向迭代器是否相同bool operator==(const Self& s) const{return _node == s._node;}Node* getNode(){return _node;}
};

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3.2 begin和end

代码如下（示例）：

typedef __RBTreeIterator<T, T&, T*> iterator;//普通迭代器
typedef __RBTreeIterator<T, const T&, const T*> const_iterator;//const迭代器
//最左节点
iterator begin()
{Node* cur = _root;while (cur && cur->_left){cur = cur->_left;}return iterator(cur);
}
iterator end()
{return iterator(nullptr);
}
//const版本begin和end
const_iterator begin()const
{Node* cur = _root;while (cur && cur->_left){cur = cur->_left;}return const_iterator(cur);
}const_iterator end()const
{return const_iterator(nullptr);
}

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3.3 ++ 和 –

代码如下（示例）：

 //前置++Self& operator++(){//如果右子树不为空if (_node->_right){//寻找该结点右子树当中的最左结点Node* left = _node->_right;while (left->_left){left = left->_left;}_node = left;}else{Node* cur = _node;Node* parent = cur->_parent;//寻找孩子不在右的祖先while (parent && cur == parent->_right){cur = parent;parent = cur->_parent;}_node = parent;}return *this;}//前置--Self& operator--(){if (_node->_left) //结点的左子树不为空{//寻找该结点左子树当中的最右结点Node* right = _node->_left;while (right->_right){right = right->_right;}_node = right;}else{//寻找孩子不在父亲左的祖先Node* cur = _node;Node* parent = cur->_parent;while (parent && cur == parent->_left){cur = parent;parent = parent->_parent;}_node = parent;}return *this;}

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3.4 const迭代器

代码如下（示例）：

//普通迭代器构造const迭代器
__RBTreeIterator(const __RBTreeIterator<T,T&,T*>& it):_node(it._node)
{}

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3.5 复用红黑树接口实现set/map中的成员函数

3.5.1 set成员函数

代码如下（示例）：

template<class K>
class set
{struct SetKeyOfT{const K& operator()(const K& key){return key;}};
public://typename声明是一个类型而不是静态变量typedef typename RBTree<K, K, SetKeyOfT>::const_iterator iterator;typedef typename RBTree<K, K, SetKeyOfT>::const_iterator const_iterator;//成员函数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& key){return _t.Insert(key);}//删除函数void erase(const K& key){_t.Erase(key);}//查找函数iterator find(const K& key){return _t.Find(key);}
private:RBTree<K, K, SetKeyOfT> _t;
};

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3.5.2 map成员函数

代码如下（示例）：

template<class K, class V>
class map
{//仿函数struct MapKeyOfT{const K& operator()(const pair<K, V>& kv){return kv.first;}};
public://typename声明是一个类型而不是静态变量typedef typename RBTree<K, pair<const K, V>, MapKeyOfT>::iterator iterator; typedef typename RBTree<K, pair<const K, V>, MapKeyOfT>::const_iterator const_iterator;//成员函数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>& key){return _t.Insert(key);}//删除函数void erase(const K& key){_t.Erase(key);}//查找函数iterator find(const K& key){return _t.Find(key);}//[]运算符重载V& operator[](const K& key){pair<iterator, bool> ret = _t.Insert(make_pair(key, V()));return ret.first->second;}
private:RBTree<K, pair<const K, V>, MapKeyOfT> _t;
};

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四、源代码总结

4.1 Myset.h

代码如下（示例）：

#pragma once
// Myset.h
#include"RBTree.h"
namespace bit
{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>::ConstIteratorconst_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& key){return _t.Insert(key);}iterator find(const K& key){return _t.Find(key);}private:RBTree<K, const K, SetKeyOfT> _t;};void Print(const set<int>& s){set<int>::const_iterator it = s.end();while (it != s.begin()){--it;// 不⽀持修改//*it += 2;cout << *it << " ";}cout << endl;}void test_set(){set<int> s;int a[] = { 4, 2, 6, 1, 3, 5, 15, 7, 16, 14 };for (auto e : a){s.insert(e);}for (auto e : s){cout << e << " ";}cout << endl;Print(s);}
}

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4.2 Mymap.h

代码如下（示例）：

#pragma once
#include"RBTree.h"
namespace bit
{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>::Iteratoriterator;typedef typename RBTree<K, pair<const K, V>, MapKeyOfT>::ConstIteratorconst_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;};void test_map(){map<string, string> dict;dict.insert({ "sort", "排序" });dict.insert({ "left", "左边" });dict.insert({ "right", "右边" });dict["left"] = "左边，剩余";dict["insert"] = "插⼊";dict["string"];map<string, string>::iterator it = dict.begin();while (it != dict.end()){// 不能修改first，可以修改second//it->first += 'x';it->second += 'x';cout << it->first << ":" << it->second << endl;++it;}cout << endl;}
}

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4.3 RBTree.h

代码如下（示例）：

#pragma once
#include<iostream>
using namespace std;// RBtree.h
enum Colour
{RED,BLACK
};
template<class T>
struct RBTreeNode
{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){}
};
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++(){if (_node->_right){// 右不为空，右⼦树最左结点就是中序第⼀个Node* leftMost = _node->_right;while (leftMost->_left){leftMost = leftMost->_left;}_node = leftMost;}else{// 孩⼦是⽗亲左的那个祖先Node* cur = _node;Node* parent = cur->_parent;while (parent && cur == parent->_right){cur = parent;parent = cur->_parent;}_node = parent;}return *this;}Self& operator--(){if (_node == nullptr) // end(){// --end()，特殊处理，⾛到中序最后⼀个结点，整棵树的最右结点Node* rightMost = _root;while (rightMost && rightMost->_right){rightMost = rightMost->_right;}_node = rightMost;}else if (_node->_left){// 左⼦树不为空，中序左⼦树最后⼀个Node* rightMost = _node->_left;while (rightMost->_right){rightMost = rightMost->_right;}_node = rightMost;}else{// 孩⼦是⽗亲右的那个祖先Node* cur = _node;Node* parent = cur->_parent;while (parent && cur == parent->_left){cur = parent;parent = cur->_parent;}_node = parent;}return *this;}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;}
};
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* leftMost = _root;while (leftMost && leftMost->_left){leftMost = leftMost->_left;}return Iterator(leftMost, _root);}Iterator End(){return Iterator(nullptr, _root);}ConstIterator Begin() const{Node* leftMost = _root;while (leftMost && leftMost->_left){leftMost = leftMost->_left;}return ConstIterator(leftMost, _root);}ConstIterator End() const{return ConstIterator(nullptr, _root);}RBTree() = default;~RBTree(){Destroy(_root);_root = nullptr;}pair<Iterator, bool> Insert(const T & data){if (_root == nullptr){_root = new Node(data);_root->_col = BLACK;return make_pair(Iterator(_root, _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, _root), false);}}cur = new Node(data);Node* newnode = cur;// 新增结点。颜⾊红⾊给红⾊cur->_col = RED;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;// g// p uif (parent == grandfather->_left){Node* uncle = grandfather->_right;if (uncle && uncle->_col == RED){// u存在且为红 -》变⾊再继续往上处理parent->_col = uncle->_col = BLACK;grandfather->_col = RED;cur = grandfather;parent = cur->_parent;}else{// u存在且为⿊或不存在 -》旋转+变⾊if (cur == parent->_left){// g// p u//c//单旋RotateR(grandfather);parent->_col = BLACK;grandfather->_col = RED;}else{// g// p u// c//双旋RotateL(parent);RotateR(grandfather);cur->_col = BLACK;grandfather->_col = RED;}break;}}else{// g// u pNode* uncle = grandfather->_left;// 叔叔存在且为红，-》变⾊即可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 // 叔叔不存在，或者存在且为⿊{// 情况⼆：叔叔不存在或者存在且为⿊// 旋转+变⾊// g// u p// cif (cur == parent->_right){RotateL(grandfather);parent->_col = BLACK;grandfather->_col = RED;}else{// g// u p// cRotateR(parent);RotateL(grandfather);cur->_col = BLACK;grandfather->_col = RED;}break;}}}_root->_col = BLACK;return make_pair(Iterator(newnode, _root), true);
}
Iterator Find(const K& key)
{Node* cur = _root;while (cur){if (cur->_kv.first < key){cur = cur->_right;}else if (cur->_kv.first > key){cur = cur->_left;}else{return Iterator(cur, _root);}}return End();
}
private:void RotateL(Node* parent){Node* subR = parent->_right;Node* subRL = subR->_left;parent->_right = subRL;if (subRL)subRL->_parent = parent;Node* parentParent = parent->_parent;subR->_left = parent;parent->_parent = subR;if (parentParent == nullptr){_root = subR;subR->_parent = nullptr;}else{if (parent == parentParent->_left){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;Node* parentParent = parent->_parent;subL->_right = parent;parent->_parent = subL;if (parentParent == nullptr){_root = subL;subL->_parent = nullptr;}else{if (parent == parentParent->_left){parentParent->_left = subL;}else{parentParent->_right = subL;}subL->_parent = parentParent;}}void Destroy(Node* root){if (root == nullptr)return;Destroy(root->_left);Destroy(root->_right);delete root;}
private:Node* _root = nullptr;
};

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