一、源码及框架分析
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等及个头文件中。
map和set的实现结构框架核心部分截取出来如下：
// 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做形参 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;}；
• 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。
二、模拟实现 set 和 map
2.1 实现出符合要求的红黑树
2.1.1 iterator 与 reverse_iterator
iterator实现思路分析
• iterator实现的大框架跟list的iterator思路是一致的，用一个类型封装结点的指针，再通过重载运算符实现迭代器像指针一样访问的行为。
• 这里的难点是operator++和operator–的实现。之前使用部分，我们分析了，map和set的迭代器走的是中序遍历，左子树->根结点->右子树，那么begin()会返回中序第一个结点的iterator也就是最左节点的迭代器。
• 迭代器++的核心逻辑就是不看全局，只看局部，只考虑当前中序局部要访问的下一个结点。迭代器++时，如果it指向的结点的右子树不为空，代表当前结点已经访问完了，要访问下一个结点是右子树的中序第一个，一棵树中序第一个是最左结点，所以直接找右子树的最左结点即可；如果it指向的结点的右子树空，代表当前结点已经访问完了且当前结点所在的子树也访问完了，要访问的下一个结点在当前结点的祖先里面，所以要沿着当前结点到根的祖先路径向上找。如果当前结点是父亲的左，根据中序左子树->根结点->右子树，那么下一个访问的结点就是当前结点的父亲；如果当前结点是父亲的右，根据中序左子树->根结点->右子树，当前当前结点所在的子树访问完了，当前结点所在父亲的子树也访问完了，那么下一个访问的需要继续往根的祖先中去找，直到找到孩子是父亲左的那个祖先就是中序要遍历的下一个结点。
• end()如何表示呢？stl源码中，红黑树增加了一个哨兵位头结点做为end()，这哨兵位头结点和根互为父亲，左指向最左结点，右指向最右结点。
• 迭代器–的实现跟++的思路完全类似，逻辑正好反过来即可，因为他访问顺序是右子树->根结点->左子树。
• 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， RBTree<K, const K, SetKeyOfT> _t;
• map的iterator不支持修改key但是可以修改value，我们把map的第二个模板参数pair的第一个参数改成const K即可， RBTree<K, pair<const K, V>, MapKeyOfT> _t;
• 至于reverse_iterator的实现和iterator类似，就不多赘述，具体实现看下面的代码。
通过上面的叙述我们了解到整体需要从结点的定义开始改造，即定义哨兵结点。
2.1.2 改造红黑树的代码
#pragma once#include<iostream>
#include<assert.h>
using namespace std;
//节点颜色
enum Colour
{RED,BLACK
};//红黑树的节点
//K是用来查找的，T是用来插入的
//set中T是key，map中T是pair<key,value>
template<class T>
struct RBTreeNode
{T _t;//dataRBTreeNode* _left;RBTreeNode* _right;RBTreeNode* _parent;Colour _col;RBTreeNode(const T& t = T(), Colour col = RED):_t(t),_left(nullptr),_right(nullptr),_parent(nullptr),_col(col){}
};
//红黑树的迭代器
template<class T, class Ref, class Ptr>
struct RBTreeIterator
{typedef RBTreeNode<T> Node;Node* _node;//要操作的节点RBTreeIterator(Node* node) :_node(node) {}typedef RBTreeIterator Self;//++itSelf& operator++(){Node* cur = _node;if (cur->_right){Node* LeftMost = cur->_right;while (LeftMost->_left){LeftMost = LeftMost->_left;}_node = LeftMost;}else{Node* parent = cur->_parent;while (parent->_right == cur){cur = parent;parent = cur->_parent;}_node = parent;}return *this;}//it++Self operator++(int){Self temp(*this);++*this;return temp;}//--itSelf& operator--(){Node* cur = _node;//end()时if (_node->_parent->_parent == _node && _node->_col == RED){_node = _node->_right;}else if (cur->_left){Node* RightMost = cur->_left;while (RightMost->_right){RightMost = RightMost->_right;}_node = RightMost;}else{Node* parent = cur->_parent;while (parent->_left == cur){cur = parent;parent = cur->_parent;}_node = parent;}return *this;}//it--Self operator--(int){Self temp(*this);--*this;return temp;}Ref operator*(){return _node->_t;}Ptr operator->(){return &_node->_t;}bool operator!=(const Self& it){return _node != it._node;}bool operator==(const Self& it){return _node == it._node;}
};
//红黑树的反向迭代器
template<class T, class Ref, class Ptr>
struct RBTreeReverseIterator
{typedef RBTreeNode<T> Node;Node* _node;//要操作的节点RBTreeReverseIterator(Node* node) :_node(node) {}typedef RBTreeReverseIterator Self;//++itSelf& operator--(){Node* cur = _node;if (cur->_right){Node* LeftMost = cur->_right;while (LeftMost->_left){LeftMost = LeftMost->_left;}_node = LeftMost;}else{Node* parent = cur->_parent;while (parent->_right == cur){cur = parent;parent = cur->_parent;}_node = parent;}return *this;}//it++Self operator++(int){Self temp(*this);++*this;return temp;}//--itSelf& operator++(){Node* cur = _node;//end()时if (_node->_parent->_parent == _node && _node->_col == RED){_node = _node->_right;}else if (cur->_left){Node* RightMost = cur->_left;while (RightMost->_right){RightMost = RightMost->_right;}_node = RightMost;}else{Node* parent = cur->_parent;while (parent->_left == cur){cur = parent;parent = cur->_parent;}_node = parent;}return *this;}//it--Self operator--(int){Self temp(*this);--*this;return temp;}Ref operator*(){return _node->_t;}Ptr operator->(){return &_node->_t;}bool operator!=(const Self& it){return _node != it._node;}bool operator==(const Self& it){return _node == it._node;}
};//红黑树
template<class K, class T, class KeyOfT>
class RBTree
{typedef RBTreeNode< T> Node;void destory(Node* root){if (root == nullptr)return;//必须后续销毁节点destory(root->_left);root->_left = nullptr;destory(root->_right);root->_right = nullptr;delete root;root = nullptr;}
public:RBTree(){_header = new Node(T());}//拷贝构造RBTree(const RBTree& rbt){_header = new Node(T());for (const auto e : rbt){insert(e);}}RBTree(initializer_list<T> il){_header = new Node(T());for (const auto& e : il)insert(e);}//赋值重载RBTree& operator=(const RBTree& bst){//现代写法RBTree temp(bst);std::swap(_header, temp._header);return *this;}// 析构~RBTree(){destory(_header->_parent);delete _header;_header = nullptr;}typedef RBTreeIterator<T, T&, T*> iterator;typedef RBTreeIterator<T, const T&, const T*> const_iterator;typedef RBTreeReverseIterator<T, T&, T*> reverse_iterator;typedef RBTreeReverseIterator<T, const T&, const T*> const_reverse_iterator;//迭代器iterator begin(){return iterator(_header->_left);}const_iterator begin() const{return const_iterator(_header->_left);}iterator end(){return iterator(_header);}const_iterator end() const{return const_iterator(_header);}//反向迭代器reverse_iterator rbegin(){return reverse_iterator(_header->_right);}const_reverse_iterator rbegin()const{return const_reverse_iterator(_header->_right);}reverse_iterator rend(){return reverse_iterator(_header);}const_reverse_iterator rend()const{return const_reverse_iterator(_header);}//此时需要注意key是set中的key，是map中pair<key,value>中的key，// 因此我们需要取出想要的keyiterator find(const K& key) const{Node* cur = _header->_parent;//指向根节点while (cur){if (key < KeyOfT()(cur->_t)){cur = cur->_left;}else if (key > KeyOfT()(cur->_t)){cur = cur->_right;}else{return iterator(cur);}}return iterator(_header);}pair<iterator, bool> insert(const T& t){if (_header->_parent == nullptr){_header->_parent = new Node(t);_header->_parent->_col = BLACK;_header->_parent->_parent = _header;return { iterator(_header->_parent),true };}//查找结点Node* parent = _header;Node* cur = _header->_parent;while (cur){if (KeyOfT()(t) < KeyOfT()(cur->_t)){parent = cur;cur = cur->_left;}else if (KeyOfT()(t) > KeyOfT()(cur->_t)){parent = cur;cur = cur->_right;}else{return { iterator(cur), false };}}//插入节点cur = new Node(t);cur->_parent = parent;if (KeyOfT()(t) < KeyOfT()(parent->_t))parent->_left = cur;elseparent->_right = cur;//保存cur，留待返回Node* ret = cur;//调整颜色//情况一：parent存在且为黑，不需要调整//情况二：parent存在且为红，需要调整while (parent != _header && parent->_col == RED){//确定 g 和 u 节点Node* grandfather = parent->_parent;Node* uncle = nullptr;if (parent == grandfather->_left)uncle = grandfather->_right;elseuncle = grandfather->_left;//在情况二下又有如下情况：//情况1：unclude存在且为红if (uncle && uncle->_col == RED){parent->_col = uncle->_col = BLACK;grandfather->_col = RED;//继续向上调整cur = grandfather;parent = cur->_parent;}//情况2：uncle不存在或uncle为黑else if (!uncle || uncle->_col == BLACK){//parent 是 grandfather 的左孩子if (parent == grandfather->_left){//cur 是 parent 的左孩子if (cur == parent->_left){//旋转加变色RotateRight(grandfather);parent->_col = BLACK;grandfather->_col = RED;}//cur 是 parent 的右孩子else{//旋转加变色RotateLeftThenRight(grandfather);cur->_col = BLACK;grandfather->_col = RED;}}//parent 是 grandfather 的右孩子else{//cur 是 parent 的左孩子if (cur == parent->_left){//旋转加变色RotateRightThenLeft(grandfather);cur->_col = BLACK;grandfather->_col = RED;}//cur 是 parent 的右孩子else{//旋转加变色RotateLeft(grandfather);parent->_col = BLACK;grandfather->_col = RED;}}break;//调整好能退出了}else{assert(false);//逻辑错误，理论上不可能走到}}//保证根节点必须是黑色的_header->_parent->_col = BLACK;_header->_left = LeftMost();_header->_right = RightMost();return { iterator(ret), true };}bool empty(){return _header->_parent == nullptr;}size_t size(){size_t count = 0;auto it = begin();while (it != end()){count++;++it;}return count;}void clear(){destory(_header->_parent);_header->_parent = nullptr;}
private:Node* LeftMost(){Node* MostLeftChild = _header->_parent;while (MostLeftChild->_left){MostLeftChild = MostLeftChild->_left;}return MostLeftChild;}Node* RightMost(){Node* MostRightChild = _header->_parent;while (MostRightChild->_right){MostRightChild = MostRightChild->_right;}return MostRightChild;}void RotateLeft(Node* parent){//保存节点，后面链接Node* parentparent = parent->_parent;Node* sub = parent->_right;Node* subleft = sub->_left;//重新链接parent->_right = subleft;if (subleft)subleft->_parent = parent;sub->_left = parent;parent->_parent = sub;//和上面的节点链接if (parentparent == _header){//说明parent原来是根节点_header->_parent = sub;sub->_parent = _header;}else{if (parentparent->_left == parent){//原来是上面节点的左子树parentparent->_left = sub;}else{parentparent->_right = sub;}sub->_parent = parentparent;}}void RotateRight(Node* parent){//保存节点，后面链接Node* parentparent = parent->_parent;Node* sub = parent->_left;Node* subright = sub->_right;//重新链接parent->_left = subright;if (subright)subright->_parent = parent;sub->_right = parent;parent->_parent = sub;//和上面的节点链接if (parentparent == _header){//说明parent原来是根节点_header->_parent = sub;sub->_parent = _header;}else{if (parentparent->_left == parent){//原来是上面节点的左子树parentparent->_left = sub;}else{parentparent->_right = sub;}sub->_parent = parentparent;}}void RotateLeftThenRight(Node* parent){RotateLeft(parent->_left);RotateRight(parent);}void RotateRightThenLeft(Node* parent){RotateRight(parent->_right);RotateLeft(parent);}
private:Node* _header;
};
2.2 复用红黑树实现 set
#pragma once#include"RBTree.h"template<class K>
class set
{typedef const K T;//用以插入struct KeyOfT{const K& operator()(const T& key){return key;}};typedef typename RBTree<K, T, KeyOfT>::iterator iterator;typedef typename RBTree<K, T, KeyOfT>::const_iterator const_iterator;typedef typename RBTree<K, T, KeyOfT>::reverse_iterator reverse_iterator;typedef typename RBTree<K, T, KeyOfT>::const_reverse_iterator const_reverse_iterator;
public:set() = default;set(initializer_list<T> il){_rbt = { il };}//迭代器iterator begin(){return _rbt.begin();}const_iterator begin()const{return _rbt.begin();}iterator end(){return _rbt.end();}const_iterator end() const{return _rbt.end();}//反向迭代器reverse_iterator rbegin(){return _rbt.rbegin();}const_reverse_iterator rbegin()const{return _rbt.rbegin();}reverse_iterator rend(){return _rbt.rend();}const_reverse_iterator rend() const{return _rbt.rend();}bool empty(){return _rbt.empty();}size_t size(){return _rbt.size();}void clear(){_rbt.clear();}iterator find(const K& key)const{return _rbt.find(key);}pair<iterator, bool> insert(const T& t){return _rbt.insert(t);}private:RBTree<K, T, KeyOfT> _rbt;
};
2.3 复用红黑树实现 map
#pragma once#include"RBTree.h"template<class K, class V>
class map
{typedef pair<const K, V> T;struct KeyOfT{const K& operator()(const T& data){return data.first;}};typedef typename RBTree<K, T, KeyOfT>::iterator iterator;typedef typename RBTree<K, T, KeyOfT>::const_iterator const_iterator;typedef typename RBTree<K, T, KeyOfT>::reverse_iterator reverse_iterator;typedef typename RBTree<K, T, KeyOfT>::const_reverse_iterator const_reverse_iterator;
public:map() = default;map(initializer_list<T> il){_rbt = { il };}//迭代器iterator begin(){return _rbt.begin();}const_iterator begin()const{return _rbt.begin();}iterator end(){return _rbt.end();}const_iterator end() const{return _rbt.end();}//反向迭代器reverse_iterator rbegin(){return _rbt.rbegin();}const_reverse_iterator rbegin()const{return _rbt.rbegin();}reverse_iterator rend(){return _rbt.rend();}const_reverse_iterator rend() const{return _rbt.rend();}bool empty(){return _rbt.empty();}size_t size(){return _rbt.size();}void clear(){_rbt.clear();}iterator find(const K& key)const{return _rbt.find(key);}pair<iterator, bool> insert(const pair<const K, V>& kv){return _rbt.insert(kv);}V& operator[](const K& key){pair<iterator, bool> ret = insert({ key, V() });iterator it = ret.first;return it->second;}
private:RBTree < K, pair<const K, V>, KeyOfT> _rbt;//key 不能修改
};