【C++进阶】封装红黑树实现map和set
【C++进阶】封装红黑树实现map和set
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🌼文章目录🌼
1. 源码及框架分析
2. 模拟实现map和set
2.1 实现出复用红黑树的框架，并支持insert
2.2 支持iterator的实现
2.3 map支持[]
2.4 Mymap和myset代码实现
1. 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等几个头文件中。
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 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。
② 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。
③ 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。
④ 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。
2. 模拟实现map和set
2.1 实现出复用红黑树的框架，并支持insert
① 参考源码框架，map和set复用之前我们实现的红黑树。
② 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。（源码中的命名风格实在令人抓狂）
③ 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。
// 源码中pair⽀持的<重载实现
template <class T1, class T2>
bool operator< (const pair<T1,T2>& lhs, const pair<T1,T2>& rhs)
{ return lhs.first<rhs.first || (!(rhs.first<lhs.first) &&
lhs.second<rhs.second); }
// Mymap.h
namespace bit
{template<class K, class V>class map{struct MapKeyOfT{const K& operator()(const pair<K, V>& kv){return kv.first;}};
public:bool insert(const pair<K, V>& kv){return _t.Insert(kv);}
private:RBTree<K, pair<K, V>, MapKeyOfT> _t;};
}// Myset.h
namespace bit
{template<class K>class set{struct SetKeyOfT{const K& operator()(const K& key)return key;}};
public:bool insert(const K& key){return _t.Insert(key);}
private:RBTree<K, K, SetKeyOfT> _t;
};template<class T>
struct RBTreeNode//红黑树
{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){}
};// 实现步骤：
// 1、实现红⿊树
// 2、封装map和set框架，解决KeyOfT
// 3、iterator
// 4、const_iterator
// 5、key不⽀持修改的问题
// 6、operator[]
template<class K, class T, class KeyOfT>
class RBTree
{private :typedef RBTreeNode<T> Node;Node* _root = nullptr;
public:bool Insert(const T& data){if (_root == nullptr){_root = new Node(data);_root->_col = BLACK;return 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 false;}} cur = new Node(data);Node* newnode = cur;// 新增结点。颜⾊给红⾊cur->_col = RED;if (kot(parent->_data) < kot(data)){parent->_right = cur;} else{parent->_left = cur;} cur->_parent = parent;//...return true;}
}2.2 支持iterator的实现
iterator核心源码：
struct __rb_tree_base_iterator
{typedef __rb_tree_node_base::base_ptr base_ptr;base_ptr node;void increment(){if (node->right != 0) {node = node->right;while (node->left != 0)node = node->left;} else{base_ptr y = node->parent;while (node == y->right) {node = y;y = y->parent;} if(node->right != y)node = y;}} void decrement(){if (node->color == __rb_tree_red &&node->parent->parent == node)node = node->right;else if (node->left != 0) {base_ptr y = node->left;while (y->right != 0)y = y->right;node = y;} else{base_ptr y = node->parent;while (node == y->left) {node = y;y = y->parent;} node = y;}}
};
template <class Value, class Ref, class Ptr>
struct __rb_tree_iterator : public __rb_tree_base_iterator
{typedef Value value_type;typedef Ref reference;typedef Ptr pointer;typedef __rb_tree_iterator<Value, Value&, Value*> iterator;__rb_tree_iterator() {}__rb_tree_iterator(link_type x) { node = x; }__rb_tree_iterator(const iterator& it) { node = it.node; }reference operator*() const { return link_type(node)->value_field; }
#ifndef __SGI_STL_NO_ARROW_OPERATORpointer operator->() const { return &(operator*()); }
#endif /* __SGI_STL_NO_ARROW_OPERATOR */self& operator++() { increment(); return *this; }self& operator--() { decrement(); return *this; }inline bool operator==(const __rb_tree_base_iterator& x,const __rb_tree_base_iterator& y) {return x.node == y.node;} inline bool operator!=(const __rb_tree_base_iterator& x,const __rb_tree_base_iterator& y) {return x.node != y.node;}iterator实现思路分析：
① 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。
② 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10所在结点的迭代器。
③ 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。
④ 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。
⑤ 迭代器++时，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。
⑥ 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；如下图：it指向25，25右为空，25是30的左，所以下一个访问的结点就是30。
⑦ 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问题的下一个结点。如下图：it指向15，15右为空，15是10的右，15所在⼦树话访问完了，10所在子树也访问完了，继续往上找，10是18的左，那么下⼀个访问的结点就是18。
⑧ end()如何表示呢？如下图：当it指向50时，++it时，50是40的右，40是30的右，30是18的右，18到根没有父亲，没有找到孩子是父亲左的那个祖先，这是父亲为空了，那我们就把it中的结点指针置为nullptr，我们用nullptr去充当end。需要注意的是stl源码空，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。相比我们用nullptr作为end()，差别不大，他能实现的，我们也能实现。只是--end()判断到结点时空，特殊处理一下，让迭代器结点指向最右结点。具体参考迭代器--实现。
⑨ 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，具体参考下面代码实现。
⑩ 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;
⑪ 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;
实际上支持iterator还有非常多的细节要处理，具体看下面的代码。
2.3 map支持[]
① map要支持[]主要修改insert返回值支持，修改RBTree中的insert返回值为pair<Iterator,bool> Insert(const T& data)
② 有了insert支持，[]实现就很简单了，具体实现参考下面代码。
2.4 Mymap和myset代码实现
//Mymap
#pragma once#include "RBTree.h"namespace gjk
{template <class K,class V>class Mymap{struct MapKeyOfT{const K& operator()(const pair<K,V>& kv){return kv.first;}};public:typedef typename RBTree<K, pair<K, V>, MapKeyOfT>::Iterator iterator;typedef typename RBTree<K, pair<K, V>, MapKeyOfT>::ConstIterator 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<K, V>& data){return _t.Insert(data);}private:RBTree<K, pair<K, V>, MapKeyOfT> _t;};
}//Myset
#pragma once#include "RBTree.h"namespace gjk
{template <class K>class Myset{struct SetKeyOfT{const K& operator()(const K& key){return key;}};public:typedef typename RBTree<K, K, SetKeyOfT>::Iterator iterator;typedef typename RBTree<K, K, SetKeyOfT>::ConstIterator 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 K& data){return _t.Insert(data);}private:RBTree<K, K, SetKeyOfT> _t;};}//RBTree
#pragma once#include <iostream>
#include <vector>
#include <utility>
using namespace std;//枚举存储颜色
enum Color
{RED,BLACK
};namespace gjk
{template <class T>class RBTreeNode{public:T _data;//存储的值RBTreeNode<T>* _left;//左孩子RBTreeNode<T>* _right;//右孩子RBTreeNode<T>* _parent;//父亲Color _col;//颜色RBTreeNode(const T& data,Color col = RED):_left(nullptr),_right(nullptr),_parent(nullptr),_data(data),_col(col){}};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++()//前置++{if (_node->_right){Node* min = _node->_right;while (min && min->_left) min = min->_left;_node = min;}else{Node* cur = _node;Node* parent = cur->_parent;while (parent && parent->_right == cur){cur = parent;parent = cur->_parent;}_node = parent;}return *this;}Self& operator++(int)//后置++{if (_node->_right){Node* min = _node->_right;while (min && min->_left) min = min->_left;_node = min;}else{Node* cur = _node;Node* parent = cur->_parent;while (parent && parent->_right == cur){cur = parent;parent = cur->_parent;}_node = parent;}return *this;}Self& operator--(){if (!_node){Node* cur = _root;while (cur && cur->_right) cur = cur->_right;_node = cur;}else if (_node->_left){Node* max = _node->_left;while (max && max->_right) max = max->_right;_node = max;}else{Node* cur = _node;Node* parent = cur->_parent;while (parent && parent->_left == cur){cur = parent;parent = cur->_parent;}_node = parent;}}Self& operator--(int){if (!_node){Node* cur = _root;while (cur && cur->_right) cur = cur->_right;_node = cur;}else if (_node->_left){Node* max = _node->_left;while (max && max->_right) max = max->_right;_node = max;}else{Node* cur = _node;Node* parent = cur->_parent;while (parent && parent->_left == cur){cur = parent;parent = cur->_parent;}_node = parent;}}Ref operator*(){return _node->_data;}Ptr operator->(){return &_node->_data;}bool operator!=(const Self& s){return _node != s._node;}bool operator==(const Self& s){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* cur = _root;while (cur && cur->_left) cur = cur->_left;return Iterator(cur, _root);}Iterator End(){return Iterator(nullptr, _root);}ConstIterator Begin() const{Node* cur = _root;while (cur && cur->_left) cur = cur->_left;return ConstIterator(cur, _root);}ConstIterator End() const{return ConstIterator(nullptr, _root);}pair<Iterator,bool> Insert(const T& data){if (!_root){_root = new Node(data,BLACK);return make_pair(Iterator(_root, _root), true);}KeyOfT kot;Node* cur = _root;Node* parent = nullptr;while (cur)//插入节点{if (kot(cur->_data) > kot(data)){parent = cur;cur = cur->_left;}else if (kot(cur->_data) < kot(data)){parent = cur;cur = cur->_right;}else return make_pair(Iterator(cur, _root), true);}cur = new Node(data);Node* flag = cur;cur->_parent = parent;if (kot(parent->_data) > kot(data)) parent->_left = cur;else parent->_right = cur;//处理两个红连在一起的情况while (parent && parent->_col == RED){if (parent->_left == cur)//新增节点插入在parent左边的情况{Node* grandfather = parent->_parent;Node* uncle = grandfather->_right;if (grandfather->_right == parent) uncle = grandfather->_left;if (uncle && uncle->_col == RED)//uncle存在并且颜色为红{parent->_col = uncle->_col = BLACK;grandfather->_col = RED;cur = grandfather;parent = cur->_parent;}else//uncle不存在或者颜色为黑{if (grandfather->_left == parent){RotateR(grandfather);parent->_col = BLACK;grandfather->_col = RED;}else{RotateR(parent);RotateL(grandfather);cur->_col = BLACK;grandfather->_col = RED;}break;}}else//新增节点插入在parent右边的情况{Node* grandfather = parent->_parent;Node* uncle = grandfather->_right;if (grandfather->_right == parent) uncle = grandfather->_left;if (uncle && uncle->_col == RED)//uncle存在并且颜色为红{parent->_col = uncle->_col = BLACK;grandfather->_col = RED;cur = grandfather;parent = cur->_parent;}else{if (grandfather->_right == parent){RotateL(grandfather);parent->_col = BLACK;grandfather->_col = RED;}else{RotateL(parent);RotateR(grandfather);cur->_col = BLACK;grandfather->_col = RED;}break;}}}_root->_col = BLACK;return make_pair(Iterator(flag, _root), true);}void RotateR(Node* parent)//右单旋{Node* pparent = parent->_parent;Node* subL = parent->_left;Node* subR = subL->_right;parent->_left = subR;parent->_parent = subL;if (subR) subR->_parent = parent;subL->_right = parent;subL->_parent = pparent;if (pparent){if (pparent->_left == parent) pparent->_left = subL;else pparent->_right = subL;}else _root = subL;}void RotateL(Node* parent)//左单旋{Node* pparent = parent->_parent;Node* subR = parent->_right;Node* subL = subR->_left;parent->_right = subL;parent->_parent = subR;if (subL) subL->_parent = parent;subR->_left = parent;subR->_parent = pparent;if (pparent){if (pparent->_left == parent) pparent->_left = subR;else pparent->_right = subR;}else _root = subR;}int leafnodesize()//叶子节点个数{int sum = 0;LeafNodeSize(_root,sum);return sum;}int nodesize()//节点个数{int sum = 0;NodeSize(_root, sum);return sum;}void printf(){Printf(_root);cout << endl;}void find(const T& data){Find(_root,data);}bool isRBTree(){return IsRBTree(_root);}void blacknodenum(vector<int>& arr){BlackNodeNum(_root,arr,0);}private:void Printf(Node* cur){if (!cur) return;Printf(cur->_left);cout << cur->_val << " ";Printf(cur->_right);}void Find(Node* cur,const T& data)//查找{while (cur){if (cur->_val > data) cur = cur->_left;else if (cur->_val < data) cur = cur->_right;else{cout << data << "->" << cur->_val << endl;return;}}cout << "找不到" << endl;}bool IsRBTree(Node* cur)//验证红黑树{if (!cur) return true;if (cur->_parent && cur->_col == RED && cur->_col == cur->_parent->_col) return false;return IsRBTree(cur->_left) && IsRBTree(cur->_right);}bool IsLeafNode(Node* cur){return !cur->_left && !cur->_right;}void LeafNodeSize(Node* cur,int& sum){if (!cur) return;if (IsLeafNode(cur)){sum++;return;}LeafNodeSize(cur->_left, sum);LeafNodeSize(cur->_right, sum);}void NodeSize(Node* cur,int& sum){if (!cur) return;sum++;NodeSize(cur->_left,sum);NodeSize(cur->_right,sum);}void BlackNodeNum(Node* cur,vector<int>& sum,int num){if (!cur){sum.push_back(num);return;}if (cur->_col == BLACK) num++;BlackNodeNum(cur->_left, sum, num);BlackNodeNum(cur->_right, sum, num);}private:Node* _root = nullptr;//根节点};
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