一、基础铺垫

在前面的博客中我们了解了map和set的基本使用，以及对二叉搜索树、AVL树和红黑树的概念和简单实现有了一定的了解后，对于map和set来说，他们的底层实现都是基于红黑树的。我们知道set是key的模型、map是key/value的模型，那么一棵红黑树是如何实现出map和set的呢？

二、基本结构分析

1. 节点结构分析

以上是截取的部分源码结构，我们可以看到set的模板参数是Key，map的模板参数是Key和T；set将Key这个模板参数typedef成了key_type和value_type，map将Key这个模板参数typedef成了key_type、将T这个模板参数typedef成了data_type；

他们同时调用红黑树时，都是用的value_type，对应set的value_type是Key，对应map的value_type是pair<const key，T>；这意味着红黑树只看传过来的value_type是什么类型的，当上层容器是set的时候，结点当中存储的是键值Key；当上层容器是map的时候，结点当中存储的就是<Key, Value>键值对。

结点结构：

enum Colour
{RED,BLACK
};template<class T>
struct RBTreeNode
{RBTreeNode<T>* _left;RBTreeNode<T>* _right;RBTreeNode<T>* _parent;T _data;//存储的数据类型：如果是set，T对应的就是K；如果是map，T对应的就是pairColour _col;RBTreeNode(const T& data):_left(nullptr), _right(nullptr), _parent(nullptr), _col(RED), _data(data){}
};

红黑树基本结构：

template<class k, class T>
class RBTree
{typedef RBTreeNode<T> Node;
private:Node* _root;
};

map的基本结构：

namespace mlg
{template<class k, class v>class map{private:RBTree<k, pair<k, v>> _t;};
}

set的基本结构：

namespace mlg
{template<class k>class set{private:RBTree<k, k> _t;};
}

2. 模板参数中仿函数分析

        因为红黑树中存储的是T类型，有可能是Key，也有可能是<Key, Value>键值对；那么当我们需要进行结点的键值比较时，应该如何获取结点的键值呢？

        当上层容器是set的时候T就是键值Key，直接用T进行比较即可，但当上层容器是map的时候就不行了，此时我们需要从<Key, Value>键值对当中取出键值Key后，再用Key值进行比较。

        因此，上层容器map需要向底层红黑树提供一个仿函数，用于获取T当中的键值Key，这样一来，当底层红黑树当中需要比较两个结点的键值时，就可以通过这个仿函数来获取T当中的键值了。

map的仿函数：

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

set的仿函数：

namespace mlg
{template<class k>class set{public:struct SetKeyOfT{const k& operator()(const k& k){return k;}};private:RBTree<k, k, SetKeyOfT> _t;};
}

三、正向迭代器

红黑树的正向迭代器实际上就是对结点指针进行了封装，因此在正向迭代器当中实际上就只有一个成员变量，那就是正向迭代器所封装结点的指针。

template<class T, class Ref, class Ptr>
struct RBTreeIterator
{typedef RBTreeNode<T> Node;//结点的类型typedef RBTreeIterator<T, Ref, Ptr> Self;//正向迭代器的类型Node* _node;//正向迭代器所封装结点的指针RBTreeIterator(Node* node)//根据所给结点指针构造一个正向迭代器:_node(node){}Ref operator*(){return _node->_data;//返回结点数据的引用}Ptr operator->(){return &_node->_data;//返回结点数据的指针}//前置++/*如果当前结点的右子树不为空，则++操作后应该找到其右子树当中的最左结点。如果当前结点的右子树为空，则++操作后应该在该结点的祖先结点中，找到孩子不在父亲右的祖先。*/Self& operator++(){if (_node->_right)//结点的右子树不为空{Node* min = _node->_right;while (min->_left){min = min->_left;}_node = min;}else  //结点的右子树为空{Node* cur = _node;Node* parent = cur->_parent;while (parent && cur == parent->_right){cur = cur->_parent;parent = parent->_parent;}_node = parent;}return *this;}//前置--/*如果当前结点的左子树不为空，则--操作后应该找到其左子树当中的最右结点。如果当前结点的左子树为空，则--操作后应该在该结点的祖先结点中，找到孩子不在父亲左的祖先。*/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 = parent;parent = parent->_parent;}_node = parent;}return *this;}//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;}
};

四、封装完成的红黑树

#pragma once
#include <iostream>
#include <algorithm>
using namespace std;enum Colour
{RED,BLACK
};template<class T>
struct RBTreeNode
{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 Ref, class Ptr>
struct RBTreeIterator
{typedef RBTreeNode<T> Node;typedef RBTreeIterator<T, Ref, Ptr> Self;Node* _node;RBTreeIterator(Node* node):_node(node){}Ref operator*(){return _node->_data;}Ptr operator->(){return &_node->_data;}//前置++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;}//前置--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 = 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;}
};//set RBTree<k, k>
//map RBTree<k, pair<k, v>>
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;iterator begin(){Node* min = _root;while (min && min->_left){min = min->_left;}return iterator(min);}iterator end(){return iterator(nullptr);}RBTree():_root(nullptr){}RBTree(const RBTree<k, T, keyofT>& t){_root = Copy(t._root);}Node* Copy(Node* root){if (root == nullptr){return nullptr;}Node* newRoot = new Node(root->_data);newRoot->_col = root->_col;newRoot->_left = Copy(root->_left);newRoot->_right = Copy(root->_right);if (newRoot->_left){newRoot->_left->_parent = newRoot;}if (newRoot->_right){newRoot->_right->_parent = newRoot;}return newRoot;}RBTree<k, T, keyofT>& operator=(RBTree<k, T, keyofT> t){swap(_root, t._root);return *this;}~RBTree(){Destroy(_root);_root = nullptr;}void Destroy(Node* root){if (root == nullptr){return;}Destroy(root->_left);Destroy(root->_right);delete root;}iterator Find(const k& key){Node* cur = _root;keyofT kot;while (cur){if (kot(cur->_data) < key){cur = cur->_right;}else if (kot(cur->_data) > key){cur = cur->_left;}else{return iterator(cur);}}return end();}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; // 新增节点if (kot(parent->_data) < kot(data)){parent->_right = cur;cur->_parent = parent;}else{parent->_left = cur;cur->_parent = parent;}// 控制平衡while (parent && parent->_col == RED){Node* grandfather = parent->_parent;if (parent == grandfather->_left){Node* uncle = grandfather->_right;// 1、uncle存在且为红if (uncle && uncle->_col == RED){// 变色+继续向上处理parent->_col = uncle->_col = BLACK;grandfather->_col = RED;cur = grandfather;parent = cur->_parent;}else // 2 + 3、uncle不存在/ 存在且为黑{if (cur == parent->_left){// 单旋RotateR(grandfather);parent->_col = BLACK;grandfather->_col = RED;}else{// 双旋RotateL(parent);RotateR(grandfather);cur->_col = BLACK;grandfather->_col = RED;}break;}}else // parent == grandfather->_right{Node* uncle = grandfather->_left;if (uncle && uncle->_col == RED){// 变色+继续向上处理parent->_col = uncle->_col = BLACK;grandfather->_col = RED;cur = grandfather;parent = cur->_parent;}else // 2 + 3、uncle不存在/ 存在且为黑{if (cur == parent->_right){RotateL(grandfather);parent->_col = BLACK;grandfather->_col = RED;}else{RotateR(parent);RotateL(grandfather);cur->_col = BLACK;grandfather->_col = RED;}break;}}}_root->_col = BLACK;return make_pair(iterator(newnode), true);}//左单选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 (parent == _root)//这里表明原来是根{_root = subR;subR->_parent = nullptr;}else{if (parentParent->_left == parent){parentParent->_left = subR;}else{parentParent->_right = subR;}subR->_parent = parentParent;}}//由单旋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 (parent == _root)//这里表明原来是根{_root = subL;_root->_parent = nullptr;}else{if (parentParent->_left == parent){parentParent->_left = subL;}else{parentParent->_right = subL;}subL->_parent = parentParent;}}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);}
private:Node* _root;
};

五、map的模拟实现

#include "RBTree.h"
namespace mlg
{template<class k, class v>class map{public:struct MapKeyOfT{const k& operator()(const pair<k, v>& kv){return kv.first;}};typedef typename RBTree<k, pair<k, v>, MapKeyOfT>::iterator iterator;iterator begin(){return _t.begin();}iterator end(){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){auto ret = _t.Insert(make_pair(key, v()));return ret.first->second;}private:RBTree<k, pair<k, v>, MapKeyOfT> _t;};
}

六、set的模拟实现

#include "RBTree.h"
namespace mlg
{template<class k>class set{public:struct SetKeyOfT{const k& operator()(const k& k){return k;}};typedef typename RBTree<k, k, SetKeyOfT>::iterator iterator;iterator begin(){return _t.begin();}iterator end(){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, k, SetKeyOfT> _t;};
}