【C++笔记】红黑树封装map和set深度剖析

【C++笔记】红黑树封装map和set深度剖析

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🔥专栏：C++笔记

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前言

哈喽，各位小伙伴大家好!上期我们讲了红黑树。今天我们来讲一下用红黑树封装map和set。话不多说，我们进入正题！向大厂冲锋

一. 源码及框架分析

我们看一下源码是如何实现红黑树封装map和set。

参考SGI-STL30版本源代码，map和set的源代码在map/set/stl_map.h/stl_set.h/stl_tree.h等几个头文件中。

// set
#ifndef __SGI_STL_INTERNAL_TREE_H
#include <stl_tree.h>
#endif
#include <stl_set.h>
#include <stl_multiset.h>
// map
#ifndef __SGI_STL_INTERNAL_TREE_H
#include <stl_tree.h>
#endif
#include <stl_map.h>
#include <stl_multimap.h>
// stl_set.h
template <class Key, class Compare = less<Key>, class Alloc = alloc>
class set {
public:// typedefs:typedef Key key_type;typedef Key value_type;
private:typedef rb_tree<key_type, value_type,identity<value_type>, key_compare, Alloc> rep_type;rep_type t; // red-black tree representing set
};
// stl_map.h
template <class Key, class T, class Compare = less<Key>, class Alloc = alloc>
class map {
public:// typedefs:typedef Key key_type;typedef T mapped_type;typedef pair<const Key, T> value_type;
private:
typedef rb_tree<key_type, value_type,
select1st<value_type>, key_compare, Alloc> rep_type;
rep_type t; // red-black tree representing map
};
// stl_tree.h
struct __rb_tree_node_base
{
typedef __rb_tree_color_type color_type;
typedef __rb_tree_node_base* base_ptr;
color_type color;
base_ptr parent;
base_ptr left;
base_ptr right;
};
// stl_tree.h
template <class Key, class Value, class KeyOfValue, class Compare, class Alloc= alloc>
class rb_tree {
protected:typedef void* void_pointer;typedef __rb_tree_node_base* base_ptr;typedef __rb_tree_node<Value> rb_tree_node;typedef rb_tree_node* link_type;typedef Key key_type;typedef Value value_type;
public:// insert⽤的是第⼆个模板参数左形参pair<iterator, bool> insert_unique(const value_type& x);// erase和find⽤第⼀个模板参数做形参size_type erase(const key_type& x);iterator find(const key_type& x);
protected:size_type node_count; // keeps track of size of treelink_type header;
};
template <class Value>
struct __rb_tree_node : public __rb_tree_node_base
{
typedef __rb_tree_node<Value>* link_type;
Value value_field;
};

1.1 源码框架分析

• 通过下图对框架的分析，我们可以看到源码中rb_tree用了⼀个巧妙的泛型思想实现，rb_tree是实现key的搜索场景，还是key/value的搜索场景不是直接写死的，而是由第⼆个模板参数Value决定_rb_tree_node中存储的数据类型。
• set实例化rb_tree时第二个模板参数给的是key，map实例化rb_tree时第二个模板参数给的是pair<const key, T>，这样⼀颗红黑树既可以实现key搜索场景的set，也可以实现key/value搜索场景的map。
• 要注意一下，源码里面模板参数是用T代表value，而内部写的value_type不是我们我们日常key/value场景中说的value，源码中的value_type反而是红黑树结点中存储的真实的数据的类型。
• rb_tree第二个模板参数Value已经控制了红黑树结点中存储的数据类型，为什么还要传第一个模板参数Key呢？尤其是set，两个模板参数是⼀样的，这是很多同学这时的⼀个疑问。要注意的是对于map和set，find/erase时的函数参数都是Key，所以第⼀个模板参数是传给find/erase等函数做形参的类型的。对于set而言两个参数是⼀样的，但是对于map而言就完全不一样了，map insert的是pair对象，但是find和ease的是Key对象。

所以我们可以通过模版参数来控制红黑树底层的结构。
所以不用实现两颗红黑树，但是本质还是编译器根据模版参数生成两颗不同的红黑树。

二. 模拟实现map和set

这里借鉴源码的底层实现。
我们也自己模拟实现出我们的mymap和myset.

2.1封装map和set

• 参考源码框架，map和set复用之前我们实现的红黑树。
• 我们这里相比源码调整⼀下，key参数就用K，value参数就用V，红黑树中的数据类型，我们使用T。
• 其次因为RBTree实现了泛型不知道T参数导致是K，还是pair<K, V>，那么insert内部进行插入逻辑比较时，就没办法进行比较，因为pair的默认支持的是key和value⼀起参与比较，我们需要时的任何时候只比较key，所以我们在map和set层分别实现⼀个MapKeyOfT和SetKeyOfT的仿函数传给RBTree的KeyOfT，然后RBTree中通过KeyOfT仿函数取出T类型对象中的key，再进行比较，具体细节参考如下代码实现。

set.h:

template<class k>
class set
{
public:struct SetKeyofT{const k& operator()(const k& key){return key;}};bool insert(const k& kv){return _t.Insert(kv);}
private:qcj::RBTree<k,  const k, SetKeyofT> _t;
};

map.h:

template<class k,class v>
class map
{
public:struct MapKeyofT{const k& operator()(const pair<k, v>& key){return key.first;}};bool insert(const pair<k, v>& kv) {return _t.Insert(kv);}
private:qcj::RBTree<k, pair< const k, v>, MapKeyofT> _t;
};

insert:

bool Insert(const T& x) 
{if (_root == nullptr)//插入根节点{_root = new node(x);_root->col = BLACK;return true;};node* cur = _root;node* parent = nullptr;//保留父亲节点KeyofT kot;while (cur){/*介质不冗余*/if (kot(x) < kot(cur->_date)){parent = cur;cur = cur->left;}else if (kot(x) > kot(cur->_date)){parent = cur;cur = cur->right;}else{return false;}}cur = new node(x);cur->col = RED;if (kot(x) > kot(parent->_date)){parent->right = cur;}else//相等插入左子树{parent->left = cur;}cur->parent = parent;while (parent&&parent->parent&&parent->col == RED){node* grandfather = parent->parent;if (parent == grandfather->left){node* uncle = grandfather->right;//         g//       p    u//     c  c//u存在且为红if (uncle&&uncle->col==RED){parent->col = uncle->col=BLACK;grandfather->col = RED;cur = grandfather;parent = cur->parent;}//u不存在或存在为黑else{//         g//       p    //     cif (cur == parent->left){RoRateR(grandfather);parent->col = BLACK;grandfather->col = RED;}//         g//       p    //         celse{RoRateL(parent);RoRateR(grandfather);cur->col = BLACK;grandfather->col = RED;}break;}}else{node* uncle = grandfather->left;//         g//       u   p    //          c  c//u存在且为红if (uncle && uncle->col == RED){parent->col = uncle->col = BLACK;grandfather->col = RED;cur = grandfather;parent = cur->parent;}//u不存在或存在为黑else{//         g//            p    //              cif (cur == parent->right){RoRateL(grandfather);parent->col = BLACK;grandfather->col = RED;}//         g//            p    //          celse{RoRateR(parent);RoRateL(grandfather);cur->col = BLACK;grandfather->col = RED;}break;}}}_root->col = BLACK;//循环结束把根变黑return true;
}

find：

node* Find(const k& x)
{node* ret = nullptr;node* cur = _root;while (cur){if (x < kot(cur)){cur = cur->left;}else if (x > kot(cur)){cur = cur->right;}else{ret = cur;//保留当前节点cur = cur->left;//继续向左子树查找中序的第一个}}return ret;
}

这里通过仿函数就取出key控制了比较逻辑。

三.迭代器

3.1思路分析

• operator++
  
• operator- -
  
• 迭代器的key修改问题
  
  如果我们这样实现的迭代器是可以修改的key的。
  但是红黑树的key是不能被修改的。那怎么办呢？
  我们只需要把红黑树的第二个模版参数的key改为
  const key即可这样迭代器的模版参数T的key也是const的了
  set的iterator也不支持修改，我们把set的第⼆个模板参数改成const K即可，

qcj::RBTree<k, pair< const k, v>, MapKeyofT> _t;
qcj::RBTree<k,  const k, SetKeyofT> _t;

• 对比库里的迭代器
  为了实现反向迭代器我们可以在operator- -多加一个判断。
  同时还需要在迭代器里面加一个_root节点
  

• 运算符重载
  运算符重载比较简单具体参考下面的代码

3.2 代码实现

template<class T,class Ref,class Ptr>
struct RBTreeIteraor
{using node= RBNode<T>;using self= RBTreeIteraor< T, Ref, Ptr >;node* _node;node* _root;RBTreeIteraor(node* Node,node* root):_node(Node),_root(root){}self& operator++(){if (_node == nullptr){node* cur = _root;while (cur->right){cur = cur->right;}}else if (_node->right!=nullptr){node* cur = _node->right;while (cur->left){cur = cur->left;}_node = cur;}else{node* parent = _node->parent;while (parent&&_node != parent->left){_node = parent;parent = _node->parent;}_node = parent;}return *this;}self& operator--(){if (_node == nullptr){node* cur = _root;while (cur->right){cur = cur->right;}_node = cur;}else if (_node->left != nullptr){node* cur = _node->left;while (cur->right){cur = cur->right;}_node = cur;}else{node* parent = _node->parent;while (parent && _node != parent->right){_node = parent;parent = _node->parent;}_node = parent;}return *this;}Ref operator*(){return _node->_date;}Ptr operator->(){return &_node->_date;}bool operator==(const self& tmp) const{return _node==tmp._node;}bool operator!=(const self& tmp) const{return _node != tmp._node;}
};

四.operator[]

4.1思路分析

对于map我们还需要支持operator[]。
对于operator[]我们前面已经讲过底层实现了。
参考博文：map的operator[]底层剖析
主要就是insert来支持的。改一下返回值即可。
让insert返回迭代器和bool的pair即可。
返回insert迭代器的second也就是value即可。

v& operator[](const k& key)
{pair<iterator, bool> ret = _t.Insert(make_pair(key, v()));return ret.first->second;
}

五.源码

• set.h

#pragma once
#include"RBTree.h"
namespace qcj
{template<class k>class set{public:struct SetKeyofT{const k& operator()(const k& key){return key;}};public:typedef typename RBTree<k,  const k, SetKeyofT>::Iteratoriterator;typedef typename RBTree<k, const k, SetKeyofT>::Const_Iteratorconst_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& kv){return _t.Insert(kv);}iterator find(const k& key){return _t.find(key);}private:qcj::RBTree<k,  const k, SetKeyofT> _t;};void Print(const set<int>& s){set<int>::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){e += 1;cout << e << " ";}cout << endl;}}

• map.h

#pragma once
#include"RBTree.h"
namespace qcj 
{template<class k,class v>class map{public:struct MapKeyofT{const k& operator()(const pair<k, v>& key){return key.first;}};public:typedef typename RBTree<k, pair<const  k, v>, MapKeyofT>::Iteratoriterator;typedef typename RBTree<k, pair<const  k, v>, MapKeyofT>::Const_Iteratorconst_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 = _t.Insert(make_pair(key, v()));return ret.first->second;}private:qcj::RBTree<k, pair< const k, v>, MapKeyofT> _t;};void test_map(){map<int,int> dict;dict.insert({1,1});dict.insert({2,2 });dict.insert({3,3 });dict.insert({ 4,4 });dict.insert({ 5,5 });dict.insert({ 6,6 });map<int,int>::iterator it = dict.end();while (it != dict.begin()){--it;// 不能修改first，可以修改second//it->first += 'x';it->second += 1;cout << it->first << ":" << it->second << endl;}cout << endl;}
}

• RBTree.h

#pragma once
#include<iostream>
#include<assert.h>
using namespace std;
namespace qcj
{enum coloros{RED,BLACK};template<class T>struct RBNode{using node= RBNode<T>;T _date;node* left;//左节点node* right;//右节点node* parent;//父亲节点coloros col;//颜色RBNode(const T& date):_date(date), left(nullptr), right(nullptr), parent(nullptr){}};template<class T,class Ref,class Ptr>struct RBTreeIteraor{using node= RBNode<T>;using self= RBTreeIteraor< T, Ref, Ptr >;node* _node;node* _root;RBTreeIteraor(node* Node,node* root):_node(Node),_root(root){}self& operator++(){if (_node == nullptr){node* cur = _root;while (cur->right){cur = cur->right;}}else if (_node->right!=nullptr){node* cur = _node->right;while (cur->left){cur = cur->left;}_node = cur;}else{node* parent = _node->parent;while (parent&&_node != parent->left){_node = parent;parent = _node->parent;}_node = parent;}return *this;}self& operator--(){if (_node == nullptr){node* cur = _root;while (cur->right){cur = cur->right;}_node = cur;}else if (_node->left != nullptr){node* cur = _node->left;while (cur->right){cur = cur->right;}_node = cur;}else{node* parent = _node->parent;while (parent && _node != parent->right){_node = parent;parent = _node->parent;}_node = parent;}return *this;}Ref operator*(){return _node->_date;}Ptr operator->(){return &_node->_date;}bool operator==(const self& tmp) const{return _node==tmp._node;}bool operator!=(const self& tmp) const{return _node != tmp._node;}};template<class k, class T, class KeyofT>class RBTree{using node = RBNode<T>;public:RBTree() = default;using Iterator = RBTreeIteraor<T, T&, T*>;using Const_Iterator = RBTreeIteraor<T, const T&, const T*>;Iterator Begin(){node* cur = _root;while (cur&&cur->left){cur = cur->left;}return Iterator(cur,_root );}Iterator End(){return Iterator(nullptr,_root);}Const_Iterator Begin() const{node* cur = _root;while (cur&&cur->left){cur = cur->left;}return { cur,_root };}Const_Iterator End() const{return { nullptr,_root };}void Destory(const node* root){if (root == nullptr){return;}Destory(root->left);Destory(root->right);delete root;}~RBTree(){Destory(_root);_root = nullptr;}RBTree<k,T,KeyofT>& operator = (RBTree<k, T, KeyofT> tmp){swap(_root, tmp._root);return *this;}RBTree(const RBTree<k, T, KeyofT>& x){_root = Copy(x._root,nullptr);}node* Copy(node* x,node* parent){if (x == nullptr){return x;}node* root = new node(x->_date);root->parent = parent;root->left = Copy(x->left,root);root->right = Copy(x->right,root);return root;}void RoRateR(node* parent)//右单旋{node* subL = parent->left;node* subLR = subL->right;node* pparnet = parent->parent;parent->left = subLR;if (subLR){subLR->parent = parent;//修改父节点}subL->right = parent;parent->parent = subL;if (pparnet == nullptr)//parent就是根节点{_root = subL;subL->parent = nullptr;}else{if (pparnet->left == parent)//确定parent节点是左还是右{pparnet->left = subL;}else{pparnet->right = subL;}subL->parent = pparnet;//修改父节点}}void RoRateL(node* parent)//左单旋{node* subR = parent->right;node* subRL = subR->left;node* pparnet = parent->parent;parent->right = subRL;if (subRL)//防止subRL为空{subRL->parent = parent;//修改父节点}subR->left = parent;parent->parent = subR;if (pparnet == nullptr)//parent就是根节点{_root = subR;subR->parent = nullptr;}else{if (pparnet->left == parent)//确定parent节点是左还是右{pparnet->left = subR;}else{pparnet->right = subR;}subR->parent = pparnet;//修改父节点}}pair<Iterator,bool> Insert(const T& x) {if (_root == nullptr)//插入根节点{_root = new node(x);_root->col = BLACK;return make_pair(Iterator(_root, _root), true);};node* cur = _root;node* parent = nullptr;//保留父亲节点KeyofT kot;while (cur){/*介质不冗余*/if (kot(x) < kot(cur->_date)){parent = cur;cur = cur->left;}else if (kot(x) > kot(cur->_date)){parent = cur;cur = cur->right;}else{return make_pair(Iterator(cur, _root), true);}}cur = new node(x);cur->col = RED;if (kot(x) > kot(parent->_date)){parent->right = cur;}else//相等插入左子树{parent->left = cur;}cur->parent = parent;while (parent&&parent->parent&&parent->col == RED){node* grandfather = parent->parent;if (parent == grandfather->left){node* uncle = grandfather->right;//         g//       p    u//     c  c//u存在且为红if (uncle&&uncle->col==RED){parent->col = uncle->col=BLACK;grandfather->col = RED;cur = grandfather;parent = cur->parent;}//u不存在或存在为黑else{//         g//       p    //     cif (cur == parent->left){RoRateR(grandfather);parent->col = BLACK;grandfather->col = RED;}//         g//       p    //         celse{RoRateL(parent);RoRateR(grandfather);cur->col = BLACK;grandfather->col = RED;}break;}}else{node* uncle = grandfather->left;//         g//       u   p    //          c  c//u存在且为红if (uncle && uncle->col == RED){parent->col = uncle->col = BLACK;grandfather->col = RED;cur = grandfather;parent = cur->parent;}//u不存在或存在为黑else{//         g//            p    //              cif (cur == parent->right){RoRateL(grandfather);parent->col = BLACK;grandfather->col = RED;}//         g//            p    //          celse{RoRateR(parent);RoRateL(grandfather);cur->col = BLACK;grandfather->col = RED;}break;}}}_root->col = BLACK;//循环结束把根变黑return make_pair(Iterator(cur, _root), true);}bool check(node* cur,size_t tmp,size_t sum){if (cur == nullptr){if (tmp != sum){cout << "存在黑色结点的数量不相等的路径" << endl;return false;}return true;}if (cur->col == RED){if (cur->parent->col == RED){cout << cur->_key << ":" << "存在连续红节点" << endl;return false;}}else{sum++;}return check(cur->left, tmp, sum) && check(cur->right, tmp, sum);}bool ISRBTree(){return _ISRBTree(_root);}bool _ISRBTree(node* cur){if (cur == nullptr){return true;}if (cur->col == RED){return false;}size_t t = 0;while (cur){if (cur->col == BLACK){t++;}cur = cur->left;}return check(_root,t,0);}node* Find(const k& x){node* ret = nullptr;node* cur = _root;while (cur){if (x < kot(cur)){cur = cur->left;}else if (x > kot(cur)){cur = cur->right;}else{ret = cur;//保留当前节点cur = cur->left;//继续向左子树查找中序的第一个}}return ret;}void Inorder(){_Inorder(_root);cout << endl;}bool IsBalanceTree(){return _IsBalanceTree(_root);}void _Inorder(const node* root){if (root == nullptr){return;}_Inorder(root->left);cout << root->_key << ":" << root->_value << endl;_Inorder(root->right);}size_t Size(){return _Size(_root);}size_t _Size(const node* parent){if (parent){return 1 + _Size(parent->left) + _Size(parent->right);}else{return 0;}}size_t Height(){return _Height(_root);}size_t _Height(const node* parent){if (parent){return 1 + max(_Height(parent->left), _Height(parent->right));}else{return 0;}}bool Empty(){return _root == nullptr;}private:node* _root = nullptr;};
}

后言

这就是红黑树封装map和set深度剖析。大家自己好好消化！今天就分享到这！感谢各位的耐心垂阅！咱们下期见！拜拜~