文章目录
1. 红黑树的迭代器2. 改造红黑树3. map 的模拟实现4. set 的模拟实现
在 C++ STL 库中，map 与 set 的底层为红黑树，那么在不写冗余代码的情况下使用红黑树同时实现 map 与 set 便是本文的重点。
1. 红黑树的迭代器
迭代器的好处是可以方便遍历，是数据结构的底层实现与用户透明。如果想要给红黑树增加迭代器，需要考虑以下问题：
begin() 与 end()
STL 明确规定，begin() 与 end() 代表的是一段前闭后开的区间，而对红黑树进行中序遍历后，可以得到一个有序的序列，因此：begin() 可以放在红黑树中最小节点（即最左侧节点）的位置，end() 放在最大节点（最右侧节点）的下一个位置。
iterator begin(){Node* subLeft = _root;while (subLeft && subLeft->_left){subLeft = subLeft->_left;}return iterator(subLeft);}const_iterator begin() const{Node* subLeft = _root;while (subLeft && subLeft->_left){subLeft = subLeft->_left;}return const_iterator(subLeft);}iterator end(){return iterator(nullptr);}const_iterator end() const{return const_iterator(nullptr);}operator++() 与 operator--()
Self& operator++(){if (_node->_right){// 右子树的中序第一个（最左节点）Node* subLeft = _node->_right;while (subLeft->_left){subLeft = subLeft->_left;}_node = subLeft;}else{// 祖先里面孩子是父亲左的那个Node* cur = _node;Node* parent = cur->_parent;while (parent && cur == parent->_right){cur = parent;parent = cur->_parent;}_node = parent;}return *this;}Self& operator--(){// 跟++逻辑相反return *this;}2. 改造红黑树
#pragma onceenum Color{RED,BLACK};template<class T>struct RBTreeNode{RBTreeNode<T>* _left;RBTreeNode<T>* _right;RBTreeNode<T>* _parent;Color _col;T _data;RBTreeNode(const T& data): _left(nullptr), _right(nullptr), _parent(nullptr), _data(data), _col(RED){}};template<class T, class Ptr, class Ref>struct RBTreeIterator{typedef RBTreeNode<T> Node;typedef RBTreeIterator<T, Ptr, Ref> Self;Node* _node;RBTreeIterator(Node* node): _node(node){}T& operator*(){return _node->_data;}T* operator->(){return &_node->_data;}Self& operator++(){if (_node->_right){// 右子树的中序第一个（最左节点）Node* subLeft = _node->_right;while (subLeft->_left){subLeft = subLeft->_left;}_node = subLeft;}else{// 祖先里面孩子是父亲左的那个Node* cur = _node;Node* parent = cur->_parent;while (parent && cur == parent->_right){cur = parent;parent = cur->_parent;}_node = parent;}return *this;}Self& operator--(){// 跟++逻辑相反return *this;}bool operator!=(const Self& s){return _node != s._node;}bool operator==(const Self& s){return _node == s._node;}};// set->RBTree<K, K, SetKeyOfT>// map->RBTree<K, pair<K, V>, MapKeyOfT>// 因为关联式容器中存储的是<key, value>的键值对，因此// K为key的类型// T：如果是map，则为pair<K, V>；如果是set，则为K// KeyOfT仿函数，取出T对象中的keytemplate<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* subLeft = _root;while (subLeft && subLeft->_left){subLeft = subLeft->_left;}return iterator(subLeft);}const_iterator begin() const{Node* subLeft = _root;while (subLeft && subLeft->_left){subLeft = subLeft->_left;}return const_iterator(subLeft);}iterator end(){return iterator(nullptr);}const_iterator end() const{return const_iterator(nullptr);}iterator Find(const K& key){KeyOfT kot;Node* cur = _root;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);// 红色的Node* newnode = cur;if (kot(parent->_data) < kot(data)){parent->_right = cur;}else{parent->_left = cur;}cur->_parent = parent;while (parent && parent->_col == RED){Node* grandfather = parent->_parent;if (parent == grandfather->_left){Node* uncle = grandfather->_right;// 情况一：叔叔存在且为红if (uncle && uncle->_col == RED){// 变色parent->_col = uncle->_col = BLACK;grandfather->_col = RED;// 继续往上处理cur = grandfather;parent = cur->_parent;}// 情况二：叔叔不存在或者存在且为黑else{// 旋转+变色if (cur == parent->_left){// g// p u// cRotateR(grandfather);parent->_col = BLACK;grandfather->_col = RED;}else{// g// p u// cRotateL(parent);RotateR(grandfather);cur->_col = BLACK;grandfather->_col = RED;}break;}}else{Node* uncle = grandfather->_left;// 情况一：叔叔存在且为红if (uncle && uncle->_col == RED){// 变色parent->_col = uncle->_col = BLACK;grandfather->_col = RED;// 继续往上处理cur = grandfather;parent = cur->_parent;}// 情况二：叔叔不存在或者存在且为黑else{// 旋转+变色// g// u p// cif (cur == parent->_right){RotateL(grandfather);parent->_col = BLACK;grandfather->_col = RED;}else{// g// u p// cRotateR(parent);RotateL(grandfather);cur->_col = BLACK;grandfather->_col = RED;}break;}}}_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;subR->_left = parent;Node* ppnode = parent->_parent;parent->_parent = subR;if (parent == _root){_root = subR;subR->_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;subL->_right = parent;Node* ppnode = parent->_parent;parent->_parent = subL;if (parent == _root){_root = subL;subL->_parent = nullptr;}else{if (ppnode->_left == parent){ppnode->_left = subL;}else{ppnode->_right = subL;}subL->_parent = ppnode;}}private:Node* _root = nullptr;};3. map 的模拟实现
map 的底层结构就是红黑树，因此在 map 中直接封装一棵红黑树，然后将其接口包装下即可。
#pragma once#include "RBTree.h"namespace tjq{template<class K, class V>class map{struct MapKeyOfT{const K& operator()(const pair<K, V>& kv){return kv.first;}};public:typedef typename RBTree<K, pair<const K, V>, MapKeyOfT>::iterator iterator;typedef typename RBTree<K, const K, 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<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 = insert(make_pair(key, V()));return ret.first->second;}private:RBTree<K, pair<const K, V>, MapKeyOfT> _t;};}4. set 的模拟实现
set 的底层为红黑树，因此只需在 set 内部封装一棵红黑树，即可将该容器实现出来。
#pragma once#include "RBTree.h"namespace tjq{template<class K>class set{struct SetKeyOfT{const K& operator()(const K& key){return key;}};public:typedef typename RBTree<K, const K, SetKeyOfT>::iterator iterator;typedef typename RBTree<K, const K, SetKeyOfT>::const_iterator const_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, const K, SetKeyOfT> _t;};}
