【C++】map和set的封装

一、前情回顾

set 参数只有 key，但是map除了key还有value。我们还是需要KV模型的红黑树的：

#pragma once
#include <iostream>
#include <assert.h>
#include <time.h>
using namespace std;
enum Color
{RED,BLACK,
};
template<class K, class V >
struct RBTreeNode
{pair<K, V> _kv;RBTreeNode<K, V>* _left;RBTreeNode<K, V>* _right;RBTreeNode<K, V>* _parent;Color _col;RBTreeNode(const pair<K,V>& kv):_kv(kv),_left(nullptr),_right(nullptr),_parent(nullptr),_col(RED){}
};template<class K,class V>
class RBTree
{typedef RBTreeNode<K, V> Node;
public:bool Insert(const pair<K, V>& kv){if (_root == nullptr){_root = new Node(kv);_root->_col = BLACK;return true;}Node* parent = nullptr;Node* cur = _root;while (cur){if (cur->_kv.first < kv.first){parent = cur;cur = cur->_right;}else if (cur->_kv.first > kv.first){parent = cur;cur = cur->_left;}else{return false;}}cur = new Node(kv);cur->_col = RED;if (parent->_kv.first < kv.first){parent->_right = cur;cur->_parent = parent;}else{parent->_left = cur;cur->_parent = parent;}while (parent && parent->_col == RED){Node* grandfater = parent->_parent;if (parent == grandfater->_left){Node* uncle = grandfater->_right;//情况一：u存在且为红if (uncle && uncle->_col == RED){parent->_col = uncle->_col = BLACK;grandfater->_col = RED;//向上调整cur = grandfater;parent = cur->_parent;}else{//情况2if (cur == parent->_left){RotateR(grandfater);parent->_col = BLACK;grandfater->_col = RED;}//情况3else{//       g//  p//    c RotateL(parent);RotateR(grandfater);cur->_col = BLACK;grandfater->_col = RED;}break;}}else//parent==grandfater->_right{Node* uncle = grandfater->_left;//情况1：u存在且为红色if (uncle && uncle->_col == RED){uncle->_col = parent->_col = BLACK;grandfater->_col = RED;//向上调整cur = grandfater;parent = cur->_parent;}else{//情况2：u不存在/u存在为黑色//g//    p//        cif (cur == parent->_right){RotateL(grandfater);grandfater->_col = RED;parent->_col = BLACK;}//情况3//     g//         p//      celse{RotateR(parent);RotateL(grandfater);cur->_col = BLACK;grandfater->_col = RED;}break;}}}//根变黑_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;parent->_parent = subL;subL->_right = parent;if (ppNode == nullptr){_root = subL;_root->_parent = nullptr;}else{if (ppNode->_left == parent){ppNode->_left = subL;}else{ppNode->_right = subL;}subL->_parent = ppNode;}}void InOrder(){_InOrder(_root);}void _InOrder(Node* root){if (root == nullptr)return;_InOrder(root->_left);cout << root->_kv.first << ":" << root->_kv.second << endl;_InOrder(root->_right);}bool Check(Node*root,int blackNum,int ref){if (root == nullptr){//cout << blackNum << endl;if (blackNum != ref){cout << "违反规则：本条路径的黑色结点的数量根最左路径不相等" << endl;return false;}return true;}if (root->_col == RED && root->_parent->_col == RED){cout << "违反规则：出现连续的红色结点" << endl;return false;}if (root->_col == BLACK){++blackNum;}return Check(root->_left,blackNum,ref)&& Check(root->_right,blackNum,ref);}bool IsBalance(){if (_root == nullptr){return true;}if (_root->_col != BLACK){return false;}int ref = 0;Node* left = _root;while (left){if (left->_col == BLACK){++ref;}left = left->_left;}return Check(_root,0,ref);}
private:Node* _root = nullptr;
};

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二、简化源码

翻开源码一看📕

RBTree的结构源码：是KV结构的红黑树

RBTree是通过传入的Value的值来判断类型，也就是一棵泛型的RBTree，通过不同的实例化，实现出了Map和Set：

对于map:传key，对于set:传pair

map的结构简化源码：

set的结构简化源码：

为了让我们的红黑树能够识别set与map我们增加一个模板参数T：

template<class K, class T>
class RBTree

对于T模板参数可能是键值Key，也可能是由Key和Value共同构成的键值对。

如果是set容器，那么它传入底层红黑树的模板参数就是Key和Key：

template<class K>
class set
{private:RBTree<K,K> _t;
};

如果是map容器，传入底层红黑树的模板参数就是Key和Key和value的键值对：

class map
{
private:RBTree<K, pair<const K,V>> _t;
};

通过上面，我们可以知道，对于set和map的区别：我们只要通过第二个模板参数就能进行区分，那是不是第一个模板参数就没有意义了呢？

对于insert(const Value&v)来说，需要放入存入的值，确实是这个样子的，插入的值是value，对于set就是key，对于map就是pair。

但是对于find(const Key&key)来说，查找的参数不是value，找的不是pair而是Key，对于map容器来说就不行了。

**红黑树的节点**：set容器：K和T都是键值Key; map容器：K是键值Key，T由Key和Value构成的键值对；但是底层红黑树并不知道上层容器到底是map还是set，因此红黑树的结点当中直接存储T就行了，如果是set的时候，结点当中存储的是键值Key；如果是map的时候，结点当中存储的就是键值对,所以红黑树的结点定义如下,由T类型来决定红黑树存的是key还是pair：

template<class T>//三叉链结构
struct RBTreeNode
{T _data;RBTreeNode<T>* _left;RBTreeNode<T>* _right;RBTreeNode<T>* _parent;Color _col;RBTreeNode(const T& data):_data(data), _left(nullptr), _right(nullptr), _parent(nullptr), _col(RED){}
};

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三、仿函数

这里存在一个问题📝：插入的时候data的大小如何去进行比较：我们并不知道是什么类型是key，还是pair的比较，而我们刚开始kv结构就直接用kv.first去比较了。

对于set是Key，可以比较

对于map是pair，那我们要取其中的first来比较，但是pair的大小并不是直接按照first去进行比较的，而我们只需要按照first去进行比较

由于底层的红黑树不知道传的是map还是set容器，当需要进行两个结点键值的比较时，底层红黑树传入的仿函数来获取键值Key，进行两个结点键值的比较：这个时候我们就需要仿函数了，如果是set那就是用于返回T当中的键值Key,如果是map那就是用于返回pair的first：

仿函数/函数对象也是类，是一个类对象。仿函数要重载operator()。

namespace HWC
{template<class K,class V>class map{struct  MapKeyOfT{const K& operator()(const pair<const K, V>& kv){return kv.first;}};public:private:RBTree<K, pair<const K,V>,MapKeyOfT> _t;};

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

博主画了个图更加容易进行比对👇

查找过程，此时就可以套上我们所写的仿函数对象去进行数据的大小比较了：

        KeyOfT kot;//仿函数对象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;}}

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四、迭代器

红黑树的正向迭代器是对结点指针进行了封装，所以这里的正向迭代器就只有一个成员变量：结点的指针，并没有什么其他的地方，迭代器的定义：

template<class T,class Ref,class Ptr>
struct __RBTreeIterator
{typedef RBTreeNode<T> Node;typedef __RBTreeIterator<T,Ref,Ptr> Self;typedef __RBTreeIterator<T, T&, T*> iterator;Node* _node;__RBTreeIterator(Node*node):_node(node){}//普通迭代器的时候，它是拷贝构造//const迭代器的时候，它是构造，支持用普通迭代器构造const迭代器__RBTreeIterator(const iterator& s):_node(s._node){}
}

*:解引用操作，返回对应结点数据的引用:

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

->:成员访问操作符,返回结点数据的引用：

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

!=、==:比较简单

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

这里的迭代器重点是迭代器的++:

一个结点的正向迭代器进行++操作后，根据红黑树中序(左、根、右)找到当前结点的下一个结点，中序的第一个节点是最左，迭代器的++怎么去找：

如果节点的右子树不为空，++就是找右子树的最左节点

如果节点的右子树为空，++就是找祖先（孩子是父亲的左的那个祖先）

代码实现✍：

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

迭代器的--

对于–，如果是根，–就是左子树，找到左子树最大的那一个（最右节点）

如果节点的左子树不为空，--找左子树最右的节点

如果节点的左子树为空，--找祖先（孩子是父亲的右的祖先）

代码实现✍：

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

不要忘记迭代器的两个核心成员：begin()与end()

begin()：返回中序（左、根、右）第一个结点的正向迭代器，即最左节点，返回的是最左节点,直接找最左节点即可

end()：返回中序（左、根、右）最后一个结点下一个位置的正向迭代器，这里直接用空指针

template<class K, class T,class KeyOfT>
class RBTree
{typedef RBTreeNode<T> Node;
public:typedef __RBTreeIterator<T> iterator;iterator begin(){Node* left = _root;while (left && left->_left){left = left->_left;}return iterator(left);}iterator end(){return iterator(nullptr);}
}

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五、set的实现

通过前面底层红黑树的接口进行套用即可实现set的实现：

值得注意的是🔴：typename:没有实例化的模板，区分不了是静态变量还是类型，typename告诉编译器是类型

#pragma once
#include "RBTree.h"namespace hwc
{template <class K>class set{struct SetKeyOfT{const K& operator()(const K& key){return key;}};public://typename:没有实例化的模板，区分不了是静态变量还是类型，typename告诉编译器是类型typedef typename RBTree<K, K, SetKeyOfT>::const_iterator iterator;//key不可以修改typedef typename RBTree<K, K, SetKeyOfT>::const_iterator const_iterator;iterator begin() const {return _t.begin();}iterator end() const {return _t.end();}pair<iterator,bool> insert(const K& key){//底层红黑树的iterator是普通迭代器pair<typename RBTree<K, K, SetKeyOfT>::iterator, bool> ret =  _t.Insert(key);return pair<iterator, bool>(ret.first, ret.second);//用普通迭代器构造const迭代器}private:RBTree<K, K,SetKeyOfT> _t;};void test_set(){int a[] = { 4, 2, 6, 1, 3, 5, 15, 7, 16, 14 };set<int> s;for (auto e : a){s.insert(e);}set<int>::iterator it = s.begin();while (it != s.end()){cout << *it << " ";++it;}cout << endl;for (auto e : s){cout << e << " ";}cout << endl;}
}

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六、map的实现

同样是套用上底层红黑树的接口，不过map的实现有一个很重要的地方，那就是[]的实现

#pragma once
#include "RBTree.h"
namespace hwc
{template<class K,class V>class map{struct MapkeyOfT{const K& operator()(const pair<const K, V>& kv){return kv.first;}};public://typename:没有实例化的模板，区分不了是静态变量还是类型，typename告诉编译器是类型typedef typename RBTree<K, pair<const K, V>, MapkeyOfT>::iterator iterator;typedef typename RBTree<K, pair<const K, V>, 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<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;};void test_map(){int a[] = { 4, 2, 6, 1, 3, 5, 15, 7, 16, 14 };map<int, int> m;for (auto e : a){m.insert(make_pair(e, e));}map<int, int>::iterator it = m.begin();while(it!=m.end()){it->second++;cout << it->first << ":" << it->second << endl;++it;}cout << endl;map<string, int> countMap;string arr[] = { "苹果","西瓜","香蕉","苹果"};for (auto& e : arr){countMap[e]++;}for (auto& kv : countMap){cout << kv.first << ":" << kv.second << endl;}}
}

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七、红黑树代码

最后，在这里送上源码：

#pragma once#pragma once
#include <iostream>
#include <assert.h>
#include <time.h>
using namespace std;
enum Color
{RED,BLACK,
};
template<class T>
struct RBTreeNode
{T _data;RBTreeNode<T>* _left;RBTreeNode<T>* _right;RBTreeNode<T>* _parent;Color _col;RBTreeNode(const T& data):_data(data), _left(nullptr), _right(nullptr), _parent(nullptr), _col(RED){}
};template<class T,class Ref,class Ptr>
struct __RBTreeIterator
{typedef RBTreeNode<T> Node;typedef __RBTreeIterator<T,Ref,Ptr> Self;typedef __RBTreeIterator<T, T&, T*> iterator;Node* _node;__RBTreeIterator(Node*node):_node(node){}//普通迭代器的时候，它是拷贝构造//const迭代器的时候，它是构造，支持用普通迭代器构造const迭代器__RBTreeIterator(const iterator& s):_node(s._node){}Ref operator*(){return _node->_data;}Ptr operator->(){return &_node->_data;}Self& operator++(){if (_node->_right){Node* min = _node->_right;while (min->_left){min = min->_left;}_node = min;}else{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){Node* max = _node->_left;while (max->_right){max = max->_right;}_node = max;}else{Node* cur = _node;Node* parent = cur->_parent;while (parent&&cur==parent->_left){cur = cur->_parent;parent = parent->_parent;}_node = parent;}return *this;}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*> const_iterator;const_iterator begin() const {Node* left = _root;while (left && left->_left){left = left->_left;}return const_iterator(left);}const_iterator end() const {return const_iterator(nullptr);}iterator begin(){Node* left = _root;while (left && left->_left){left = left->_left;}return iterator(left);}iterator end(){return iterator(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);}}cur = new Node(data);Node* newnode = cur;cur->_col = RED;if (kot(parent->_data) < kot(data)){parent->_right = cur;cur->_parent = parent;}else{parent->_left = cur;cur->_parent = parent;}while (parent && parent->_col == RED){Node* grandfater = parent->_parent;if (parent == grandfater->_left){Node* uncle = grandfater->_right;//情况一：u存在且为红if (uncle && uncle->_col == RED){parent->_col = uncle->_col = BLACK;grandfater->_col = RED;//向上调整cur = grandfater;parent = cur->_parent;}else{//情况2if (cur == parent->_left){RotateR(grandfater);parent->_col = BLACK;grandfater->_col = RED;}//情况3else{//       g//  p//    c RotateL(parent);RotateR(grandfater);cur->_col = BLACK;grandfater->_col = RED;}break;}}else//parent==grandfater->_right{Node* uncle = grandfater->_left;//情况1：u存在且为红色if (uncle && uncle->_col == RED){uncle->_col = parent->_col = BLACK;grandfater->_col = RED;//向上调整cur = grandfater;parent = cur->_parent;}else{//情况2：u不存在/u存在为黑色//g//    p//        cif (cur == parent->_right){RotateL(grandfater);grandfater->_col = RED;parent->_col = BLACK;}//情况3//     g//         p//      celse{RotateR(parent);RotateL(grandfater);cur->_col = BLACK;grandfater->_col = RED;}break;}}}//根变黑_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;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;parent->_parent = subL;subL->_right = parent;if (ppNode == nullptr){_root = subL;_root->_parent = nullptr;}else{if (ppNode->_left == parent){ppNode->_left = subL;}else{ppNode->_right = subL;}subL->_parent = ppNode;}}void InOrder(){_InOrder(_root);}void _InOrder(Node* root){if (root == nullptr)return;_InOrder(root->_left);cout << root->_kv.first << ":" << root->_kv.second << endl;_InOrder(root->_right);}bool Check(Node* root, int blackNum, int ref){if (root == nullptr){//cout << blackNum << endl;if (blackNum != ref){cout << "违反规则：本条路径的黑色结点的数量根最左路径不相等" << endl;return false;}return true;}if (root->_col == RED && root->_parent->_col == RED){cout << "违反规则：出现连续的红色结点" << endl;return false;}if (root->_col == BLACK){++blackNum;}return Check(root->_left, blackNum, ref)&& Check(root->_right, blackNum, ref);}bool IsBalance(){if (_root == nullptr){return true;}if (_root->_col != BLACK){return false;}int ref = 0;Node* left = _root;while (left){if (left->_col == BLACK){++ref;}left = left->_left;}return Check(_root, 0, ref);}
private:Node* _root = nullptr;
};

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