\n| \n map<\/p>\n<\/td>\n | \n Key<\/p>\n<\/td>\n | \n pair<const Key, T><\/p>\n<\/td>\n | \n \u7ed3\u70b9\u91cc\u5b58\u952e\u503c\u5bf9<\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n \u7b2c\u4e8c\u4e2a\u6a21\u677f\u53c2\u6570\u51b3\u5b9a\u4e86\u7ed3\u70b9\u91cc\u5230\u5e95\u5b58\u4ec0\u4e48，\u6240\u4ee5\u540c\u4e00\u4efd\u7ea2\u9ed1\u6811\u4ee3\u7801，\u5582 K \u8fdb\u53bb\u5c31\u53d8\u6210 set，\u5582 pair<const K, V> \u8fdb\u53bb\u5c31\u53d8\u6210 map\u3002<\/p>\n （3）\u90a3\u4e2a"\u591a\u4f59\u7684"\u7b2c\u4e00\u4e2a\u6a21\u677f\u53c2\u6570 K \u662f\u5e72\u561b\u7684？<\/p>\n \u5f88\u591a\u540c\u5b66\u5230\u8fd9\u513f\u90fd\u61f5：\u65e2\u7136\u7b2c\u4e8c\u4e2a\u53c2\u6570\u5df2\u7ecf\u51b3\u5b9a\u5b58\u4ec0\u4e48\u4e86，set \u91cc\u4fe9\u53c2\u6570\u8fd8\u5199\u6210\u4e00\u6837\u7684，\u90a3\u7b2c\u4e00\u4e2a\u53c2\u6570\u662f\u4e0d\u662f\u5e9f\u8bdd？<\/p>\n \u4e0d\u662f\u5e9f\u8bdd\u3002\u56e0\u4e3a find \/ erase \u7684\u5f62\u53c2\u7c7b\u578b\u662f key，\u4e0d\u662f\u7ed3\u70b9\u91cc\u5b58\u7684\u90a3\u4e2a\u6574\u4f53：<\/p>\n \/\/ stl_tree.h
\ntemplate <class Key, class Value, class KeyOfValue, class Compare, class Alloc = alloc>
\nclass rb_tree {
\npublic:
\n\/\/ insert \u7528\u7b2c\u4e8c\u4e2a\u6a21\u677f\u53c2\u6570 Value \u505a\u5f62\u53c2
\npair<iterator, bool> insert_unique(const value_type& x);<\/p>\n \/\/ \u800c erase \/ find \u7528\u7684\u662f\u7b2c\u4e00\u4e2a\u6a21\u677f\u53c2\u6570 Key
\nsize_type erase(const key_type& x);
\niterator find(const key_type& x);
\n};<\/p>\n \u5bf9 set \u6765\u8bf4 key \u548c value \u662f\u540c\u4e00\u4e2a\u4e1c\u897f，\u770b\u8d77\u6765"\u91cd\u590d"；\u4f46\u5bf9 map \u6765\u8bf4\u5c31\u5b8c\u5168\u4e0d\u4e00\u6837\u4e86：\u63d2\u5165\u65f6\u7ed9\u7684\u662f pair，\u67e5\u627e\u65f6\u7ed9\u7684\u662f key\u3002\u6240\u4ee5\u7b2c\u4e00\u4e2a\u53c2\u6570\u5fc5\u987b\u7559\u7740\u3002<\/p>\n （4）\u987a\u624b\u5410\u69fd\u4e00\u4e0b<\/p>\n \u6e90\u7801\u91cc\u547d\u540d\u98ce\u683c\u5176\u5b9e\u5f88\u4e71：set \u7528 Key，map \u7528 Key \u548c T，\u5230\u4e86 rb_tree \u53c8\u53d8\u6210 Key \u548c Value\u3002\u800c\u4e14\u6e90\u7801\u91cc\u7684 value_type \u6307\u7684\u662f\u7ed3\u70b9\u91cc\u771f\u5b9e\u5b58\u50a8\u7684\u7c7b\u578b，\u8ddf\u6211\u4eec\u5e73\u65f6\u8bf4\u7684"key\/value \u91cc\u7684 value"\u5b8c\u5168\u4e0d\u662f\u4e00\u56de\u4e8b\u3002\u5927\u4f6c\u5199\u4ee3\u7801\u4e5f\u4e0d\u4e00\u5b9a\u89c4\u6574，\u6240\u4ee5\u770b\u6e90\u7801\u65f6\u4e00\u5b9a\u8981\u4ee5\u5b9e\u9645\u5b9a\u4e49\u4e3a\u51c6，\u522b\u88ab\u540d\u5b57\u9a97\u4e86\u3002<\/p>\n
\n\u4e8c\u3001KeyOfT \u4eff\u51fd\u6570：\u6574\u4e2a\u5c01\u88c5\u6700\u6838\u5fc3\u7684\u4e00\u6b65<\/h3>\n2.1 \u7b80\u4ecb\u4f5c\u7528<\/h4>\n\u6211\u4eec\u81ea\u5df1\u7684\u7ea2\u9ed1\u6811\u662f\u6cdb\u578b\u7684，\u6a21\u677f\u53c2\u6570 T \u5230\u5e95\u662f K \u8fd8\u662f pair<K, V>，\u7ea2\u9ed1\u6811\u81ea\u5df1\u4e0d\u77e5\u9053\u3002<\/p>\n \u90a3\u4e48\u95ee\u9898\u6765\u4e86：\u63d2\u5165\u7684\u65f6\u5019\u8981\u6bd4\u8f83\u5927\u5c0f，\u5982\u679c T \u662f pair<K, V>，pair \u9ed8\u8ba4\u7684 < \u662f\u628a first \u548c second \u4e00\u8d77\u6bd4\u7684：<\/p>\n template <class T1, class T2>
\nbool operator<(const pair<T1, T2>& lhs, const pair<T1, T2>& rhs)
\n{
\nreturn lhs.first < rhs.first ||
\n (!(rhs.first < lhs.first) && lhs.second < rhs.second);
\n}<\/p>\n \u800c\u6211\u4eec\u5e0c\u671b\u7684\u662f：\u4efb\u4f55\u65f6\u5019\u90fd\u53ea\u6bd4\u8f83 key\u3002<\/p>\n \u89e3\u51b3\u529e\u6cd5\u5c31\u662f\u5927\u540d\u9f0e\u9f0e\u7684 KeyOfT \u4eff\u51fd\u6570：\u8ba9 map \u548c set \u5404\u81ea\u63d0\u4f9b\u4e00\u4e2a"\u4ece T \u91cc\u62a0\u51fa key"\u7684\u5c0f\u5de5\u5177，\u4f20\u7ed9\u7ea2\u9ed1\u6811\u7528\u3002<\/p>\n 2.2 \u4f8b\u5b50\u4e8c：\u7ed9 set \u548c map \u5404\u5199\u4e00\u4e2a KeyOfT<\/h4>\n（1）SetKeyOfT：\u8981\u7684\u5c31\u662f\u5b83\u81ea\u5df1<\/p>\n struct SetKeyOfT
\n{
\nconst K& operator()(const K& key)
\n{
\nreturn key; \/\/ set \u91cc K \u5c31\u662f key，\u76f4\u63a5\u8fd4\u56de
\n}
\n};<\/p>\n （2）MapKeyOfT：\u628a pair \u7684 first \u62a0\u51fa\u6765<\/p>\n struct MapKeyOfT
\n{
\nconst K& operator()(const pair<K, V>& kv)
\n{
\nreturn kv.first; \/\/ map \u91cc\u53d6 pair \u7684\u7b2c\u4e00\u4e2a
\n}
\n};<\/p>\n （3）\u7ea2\u9ed1\u6811\u62ff\u5230\u5b83\u4e4b\u540e\u600e\u4e48\u7528<\/p>\n template<class K, class T, class KeyOfT> \/\/ T \u662f\u7ed3\u70b9\u5b58\u7684\u6570\u636e\u7c7b\u578b
\nclass RBTree
\n{
\npublic:
\nbool Insert(const T& data)
\n{
\n\/\/ …
\nKeyOfT kot; \/\/ \u9020\u4e00\u4e2a\u4eff\u51fd\u6570\u5bf9\u8c61
\nNode* parent = nullptr;
\nNode* cur = _root;<\/p>\n while (cur)
\n{
\nif (kot(cur->_data) < kot(data)) \/\/ \u53ea\u6bd4 key
\n{
\nparent = cur;
\ncur = cur->_right;
\n}
\nelse if (kot(cur->_data) > kot(data)) \/\/ \u53ea\u6bd4 key
\n{
\nparent = cur;
\ncur = cur->_left;
\n}
\nelse
\n{
\nreturn false; \/\/ key \u76f8\u540c，\u4e0d\u5141\u8bb8\u91cd\u590d\u63d2\u5165
\n}
\n}
\n\/\/ …
\n}
\n};<\/p>\n \u770b\u5230\u6ca1？\u7ea2\u9ed1\u6811\u91cc\u6240\u6709\u6bd4\u8f83\u90fd\u53d8\u6210\u4e86 kot(…) < kot(…)，\u5b83\u5f7b\u5e95\u4e0d\u5173\u5fc3 T \u5230\u5e95\u662f\u4ec0\u4e48\u4e86\u3002\u8fd9\u5c31\u662f\u89e3\u8026\u3002<\/p>\n 2.3 \u7ecf\u5178 Bug：\u76f4\u63a5\u6bd4\u8f83 pair \u4f1a\u600e\u6837？<\/h4>\n\u5982\u679c\u4f60\u5077\u61d2\u4e0d\u5199 KeyOfT，\u63d2\u5165\u65f6\u76f4\u63a5 cur->_data < data，\u4f1a\u53d1\u751f\u4e24\u4ef6\u4e8b：<\/p>\n set \u80fd\u7f16\u8bd1\u901a\u8fc7\u4f46\u8bed\u4e49\u9519（\u56e0\u4e3a K \u672c\u8eab\u5c31\u662f key，\u78b0\u5de7\u5bf9）<\/li>\nmap \u76f4\u63a5\u7ffb\u8f66：pair \u7684\u6bd4\u8f83\u89c4\u5219\u53d8\u6210\u4e86"\u5148\u6bd4 key，key \u76f8\u7b49\u518d\u6bd4 value"\u3002\u8fd9\u4e0d\u5149\u8fdd\u53cd\u4e86\u6211\u4eec"\u53ea\u6bd4 key"\u7684\u8bed\u4e49，\u66f4\u4e25\u91cd\u7684\u662f\u2014\u2014V \u8fd9\u4e2a\u7c7b\u578b\u672a\u5fc5\u652f\u6301 < \u8fd0\u7b97！<\/li>\nstruct Date { int y, m, d; }; \/\/ \u6ca1\u6709\u91cd\u8f7d <
\nmap<string, Date> m;
\nm.insert({ "\u751f\u65e5", {2025, 9, 14} });
\n\/\/ \u7f16\u8bd1\u62a5\u9519：no match for 'operator<' (operand types are 'Date' and 'Date')<\/p>\n 🐛 \u907f\u5751\u7ed3\u8bba：KeyOfT \u4e0d\u662f\u4e00\u4e2a\u53ef\u9009\u9879，\u5b83\u662f map \u80fd\u7528\u7684\u524d\u63d0\u3002<\/p>\n
\n\u4e09\u3001\u642d\u6846\u67b6：\u8ba9 mymap \/ myset \u7b2c\u4e00\u6b21\u8dd1\u8d77\u6765<\/h3>\n3.1 \u7b80\u4ecb\u4f5c\u7528<\/h4>\n\u6709\u4e86 KeyOfT，\u6211\u4eec\u5c31\u53ef\u4ee5\u628a set \u548c map \u7684"\u5916\u58f3"\u642d\u8d77\u6765\u4e86\u3002\u8fd9\u4e00\u6b65\u76ee\u6807\u5f88\u7b80\u5355：\u80fd\u63d2\u5165\u3001\u80fd\u6309 key \u67e5\u3002<\/p>\n \u5148\u89c4\u5b9a\u597d\u6211\u4eec\u81ea\u5df1\u7684\u547d\u540d（\u6bd4\u6e90\u7801\u5e72\u51c0\u4e00\u70b9）：<\/p>\n \n- \u7ea2\u9ed1\u6811\u6a21\u677f\u53c2\u6570：K（key \u7c7b\u578b）\u3001T（\u7ed3\u70b9\u771f\u5b9e\u5b58\u50a8\u7c7b\u578b）\u3001KeyOfT（\u53d6 key \u7684\u4eff\u51fd\u6570）；<\/li>\n<\/ul>\n
\n- \u7ed3\u70b9\u7c7b：RBTreeNode<T>；\u5bb9\u5668\u5728 bit \u547d\u540d\u7a7a\u95f4\u91cc\u3002<\/li>\n<\/ul>\n
3.2 \u4f8b\u5b50\u4e09：Myset.h \u7684\u7b2c\u4e00\u7248<\/h4>\n\/\/ Myset.h
\n#pragma once
\n#include "RBTree.h"<\/p>\n namespace bit
\n{
\ntemplate<class K>
\nclass set
\n{
\nstruct SetKeyOfT
\n{
\nconst K& operator()(const K& key)
\n{
\nreturn key;
\n}
\n};<\/p>\n public:
\nbool insert(const K& key)
\n{
\nreturn _t.Insert(key);
\n}<\/p>\n private:
\nRBTree<K, K, SetKeyOfT> _t; \/\/ \u7b2c\u4e8c\u4e2a\u53c2\u6570\u7ed9 K
\n};
\n}<\/p>\n 3.3 \u4f8b\u5b50\u56db：Mymap.h \u7684\u7b2c\u4e00\u7248<\/h4>\n\/\/ Mymap.h
\n#pragma once
\n#include "RBTree.h"<\/p>\n namespace bit
\n{
\ntemplate<class K, class V>
\nclass map
\n{
\nstruct MapKeyOfT
\n{
\nconst K& operator()(const pair<K, V>& kv)
\n{
\nreturn kv.first;
\n}
\n};<\/p>\n public:
\nbool insert(const pair<K, V>& kv)
\n{
\nreturn _t.Insert(kv);
\n}<\/p>\n private:
\nRBTree<K, pair<K, V>, MapKeyOfT> _t; \/\/ \u7b2c\u4e8c\u4e2a\u53c2\u6570\u7ed9 pair
\n};
\n}<\/p>\n 3.4 \u4f8b\u5b50\u4e94：\u914d\u5957\u7684\u7ea2\u9ed1\u6811\u7ed3\u70b9<\/h4>\n\/\/ RBTree.h
\nenum Colour
\n{
\nRED,
\nBLACK
\n};<\/p>\n template<class T>
\nstruct RBTreeNode
\n{
\nT _data;
\nRBTreeNode<T>* _left;
\nRBTreeNode<T>* _right;
\nRBTreeNode<T>* _parent;
\nColour _col;<\/p>\n RBTreeNode(const T& data)
\n: _data(data)
\n, _left(nullptr)
\n, _right(nullptr)
\n, _parent(nullptr)
\n, _col(RED) \/\/ \u65b0\u7ed3\u70b9\u9ed8\u8ba4\u7ed9\u7ea2\u8272，\u63d2\u5165\u903b\u8f91\u624d\u597d\u5904\u7406
\n{}
\n};<\/p>\n 3.5 \u6574\u4ef6\u4e8b\u7684\u5b9e\u73b0\u6b65\u9aa4\u6e05\u5355<\/h4>\n\u2460 \u5b9e\u73b0\u7ea2\u9ed1\u6811（\u524d\u9762\u5df2\u7ecf\u641e\u5b9a）
\n\u2461 \u5c01\u88c5 map \/ set \u6846\u67b6，\u89e3\u51b3 KeyOfT
\n\u2462 \u7ed9\u7ea2\u9ed1\u6811\u52a0 iterator
\n\u2463 \u52a0\u4e0a const_iterator
\n\u2464 \u89e3\u51b3 key \u4e0d\u652f\u6301\u4fee\u6539\u7684\u95ee\u9898
\n\u2465 \u7ed9 map \u52a0 operator[]<\/p>\n
\n\u56db\u3001\u8fed\u4ee3\u5668 iterator：\u8ba9\u5bb9\u5668\u80fd\u88ab for \u5faa\u73af<\/h3>\n4.1 \u7b80\u4ecb\u4f5c\u7528<\/h4>\n\u8981\u80fd\u7528\u8303\u56f4 for，\u5bb9\u5668\u5c31\u5f97\u63d0\u4f9b begin() \u548c end()\u3002\u7ea2\u9ed1\u6811\u8fed\u4ee3\u5668\u7684\u601d\u8def\u548c list \u5b8c\u5168\u4e00\u81f4：\u7528\u4e00\u4e2a\u7c7b\u628a\u7ed3\u70b9\u6307\u9488\u5305\u8d77\u6765，\u518d\u91cd\u8f7d\u8fd0\u7b97\u7b26，\u8ba9\u5b83\u7528\u8d77\u6765\u50cf\u6307\u9488\u3002<\/p>\n \u96be\u70b9\u53ea\u6709\u4e00\u4e2a：++ \u548c –\u3002\u56e0\u4e3a map \/ set \u7684\u904d\u5386\u987a\u5e8f\u662f\u4e2d\u5e8f（\u5de6\u5b50\u6811 \u2192 \u6839 \u2192 \u53f3\u5b50\u6811），\u6240\u4ee5：<\/p>\n \n- begin() \u8fd4\u56de\u7684\u662f\u6574\u68f5\u6811\u7684\u6700\u5de6\u7ed3\u70b9（\u4e2d\u5e8f\u7b2c\u4e00\u4e2a）；<\/li>\n<\/ul>\n
\n- end() \u6211\u4eec\u7528\u4e00\u4e2a\u7279\u6b8a\u503c\u8868\u793a"\u8d70\u5b8c\u4e86"\u3002<\/li>\n<\/ul>\n
4.2 \u4f8b\u5b50\u516d：\u8fed\u4ee3\u5668\u7c7b\u7684\u9aa8\u67b6（Ref \/ Ptr \u5206\u79bb）<\/h4>\ntemplate<class T, class Ref, class Ptr>
\nstruct RBTreeIterator
\n{
\ntypedef RBTreeNode<T> Node;
\ntypedef RBTreeIterator<T, Ref, Ptr> Self;<\/p>\n Node* _node;
\nNode* _root; \/\/ \u989d\u5916\u5b58\u4e00\u4efd\u6839，\u4e3a\u4e86\u652f\u6301 –end()<\/p>\n RBTreeIterator(Node* node, Node* root)
\n: _node(node)
\n, _root(root)
\n{}<\/p>\n Ref operator*()
\n{
\nreturn _node->_data;
\n}<\/p>\n Ptr operator->()
\n{
\nreturn &_node->_data;
\n}<\/p>\n bool operator!=(const Self& s) const { return _node != s._node; }
\nbool operator==(const Self& s) const { return _node == s._node; }
\n};<\/p>\n 💡 \u4e3a\u4ec0\u4e48\u8981 Ref \/ Ptr \u4e24\u4e2a\u989d\u5916\u53c2\u6570？ iterator \u4f20 T& \u548c T*，const_iterator \u4f20 const T& \u548c const T*\u2014\u2014\u540c\u4e00\u4efd\u4ee3\u7801，\u81ea\u52a8\u751f\u6210\u4e24\u4e2a\u7248\u672c\u3002\u8fd9\u5c31\u662f\u6cdb\u578b\u7684\u751c\u5934\u3002<\/p>\n 4.3 \u4f8b\u5b50\u4e03：operator++ \u7684\u4e24\u79cd\u8d70\u6cd5（\u672c\u6587\u6700\u70e7\u8111\u7684\u4e00\u6bb5）<\/h4>\n\u6838\u5fc3\u5fc3\u6cd5\u53ea\u6709\u4e00\u53e5：\u4e0d\u770b\u5168\u5c40，\u53ea\u770b\u5c40\u90e8\u2014\u2014\u53ea\u5173\u5fc3"\u5f53\u524d\u4e2d\u5e8f\u7684\u4e0b\u4e00\u4e2a\u7ed3\u70b9\u662f\u8c01"\u3002<\/p>\n \u60c5\u51b5\u4e00：\u53f3\u5b50\u6811\u4e0d\u4e3a\u7a7a<\/p>\n \u8bf4\u660e\u5f53\u524d\u7ed3\u70b9\u5df2\u7ecf\u8bbf\u95ee\u5b8c\u4e86，\u4e0b\u4e00\u4e2a\u662f\u53f3\u5b50\u6811\u7684\u4e2d\u5e8f\u7b2c\u4e00\u4e2a，\u4e5f\u5c31\u662f\u53f3\u5b50\u6811\u7684\u6700\u5de6\u7ed3\u70b9\u3002<\/p>\n \u60c5\u51b5\u4e8c：\u53f3\u5b50\u6811\u4e3a\u7a7a<\/p>\n \u8bf4\u660e\u5f53\u524d\u7ed3\u70b9\u548c\u5b83\u6240\u5728\u7684\u5b50\u6811\u90fd\u8bbf\u95ee\u5b8c\u4e86，\u5f97\u5f80\u4e0a\u627e\u7956\u5148：<\/p>\n \n- \u5982\u679c\u5f53\u524d\u7ed3\u70b9\u662f\u7236\u4eb2\u7684\u5de6（\u6bd4\u5982 25 \u662f 30 \u7684\u5de6），\u90a3\u4e0b\u4e00\u4e2a\u5c31\u662f\u7236\u4eb2（30）；<\/li>\n<\/ul>\n
\n- \u5982\u679c\u5f53\u524d\u7ed3\u70b9\u662f\u7236\u4eb2\u7684\u53f3（\u6bd4\u5982 15 \u662f 10 \u7684\u53f3），\u8bf4\u660e\u8fde\u7236\u4eb2\u90a3\u68f5\u5b50\u6811\u4e5f\u7ed3\u675f\u4e86，\u7ee7\u7eed\u5f80\u4e0a\u722c，\u76f4\u5230\u627e\u5230"\u5b69\u5b50\u662f\u7236\u4eb2\u5de6"\u7684\u90a3\u4e2a\u7956\u5148（15 \u2192 10 \u2192 18，18 \u5c31\u662f 10 \u7684\u7236\u4eb2\u4e14 10 \u662f\u5de6\u5b69\u5b50，\u6240\u4ee5\u4e0b\u4e00\u4e2a\u662f 18）；<\/li>\n<\/ul>\n
\n- \u5982\u679c\u4e00\u76f4\u722c\u5230\u6839\u90fd\u6ca1\u627e\u5230，\u8bf4\u660e\u6574\u68f5\u6811\u8d70\u5b8c\u4e86，\u628a\u7ed3\u70b9\u6307\u9488\u7f6e\u4e3a nullptr，\u6211\u4eec\u7528 nullptr \u5145\u5f53 end()\u3002<\/li>\n<\/ul>\n
\/\/ ++it \u2014\u2014 \u4e2d\u5e8f\u7684\u4e0b\u4e00\u4e2a\u7ed3\u70b9
\nSelf& operator++()
\n{
\nif (_node->_right)
\n{
\n\/\/ \u60c5\u51b5\u4e00：\u53f3\u5b50\u6811\u4e0d\u4e3a\u7a7a -> \u53f3\u5b50\u6811\u7684\u6700\u5de6\u7ed3\u70b9
\nNode* leftMost = _node->_right;
\nwhile (leftMost->_left)
\n{
\nleftMost = leftMost->_left;
\n}
\n_node = leftMost;
\n}
\nelse
\n{
\n\/\/ \u60c5\u51b5\u4e8c：\u53f3\u5b50\u6811\u4e3a\u7a7a -> \u5f80\u4e0a\u627e"\u5b69\u5b50\u662f\u7236\u4eb2\u5de6"\u7684\u90a3\u4e2a\u7956\u5148
\nNode* cur = _node;
\nNode* parent = cur->_parent;
\nwhile (parent && cur == parent->_right)
\n{
\ncur = parent;
\nparent = cur->_parent;
\n}
\n_node = parent;
\n}
\nreturn *this;
\n}<\/p>\n 💡 \u987a\u5e26\u4e00\u63d0：STL \u6e90\u7801\u91cc\u5e76\u6ca1\u6709\u7528 nullptr \u505a end()，\u800c\u662f\u5728\u7ea2\u9ed1\u6811\u9876\u4e0a\u6302\u4e86\u4e00\u4e2a\u54e8\u5175\u4f4d\u5934\u7ed3\u70b9（\u5b83\u548c\u6839\u4e92\u4e3a\u7236\u4eb2，\u5de6\u6307\u5411\u6700\u5de6\u3001\u53f3\u6307\u5411\u6700\u53f3）\u3002\u4e0d\u8fc7\u5b9e\u529b\u544a\u8bc9\u6211\u4eec：\u5b83\u80fd\u7684\u6211\u4eec\u4e5f\u80fd，\u7528 nullptr \u53ea\u662f –end() \u8981\u7279\u6b8a\u5904\u7406\u4e00\u4e0b\u800c\u5df2\u3002<\/p>\n 4.4 \u4f8b\u5b50\u516b：operator– \u4e0e –end() \u7684\u7279\u6b8a\u5904\u7406<\/h4>\n— \u7684\u903b\u8f91\u548c ++ \u5b8c\u5168\u5bf9\u79f0，\u53cd\u8fc7\u6765\u60f3\u5c31\u884c（\u987a\u5e8f\u53d8\u6210 \u53f3\u5b50\u6811 \u2192 \u6839 \u2192 \u5de6\u5b50\u6811）：<\/p>\n \/\/ –it \u2014\u2014 \u4e2d\u5e8f\u7684\u4e0a\u4e00\u4e2a\u7ed3\u70b9
\nSelf& operator–()
\n{
\nif (_node == nullptr) \/\/ \u5904\u7406 –end()
\n{
\n\/\/ end() \u662f\u7a7a，–end() \u5e94\u8be5\u8d70\u5230\u6574\u68f5\u6811\u7684\u6700\u53f3\u7ed3\u70b9
\nNode* rightMost = _root;
\nwhile (rightMost && rightMost->_right)
\n{
\nrightMost = rightMost->_right;
\n}
\n_node = rightMost;
\n}
\nelse if (_node->_left)
\n{
\n\/\/ \u5de6\u5b50\u6811\u4e0d\u4e3a\u7a7a -> \u5de6\u5b50\u6811\u7684\u6700\u53f3\u7ed3\u70b9
\nNode* rightMost = _node->_left;
\nwhile (rightMost->_right)
\n{
\nrightMost = rightMost->_right;
\n}
\n_node = rightMost;
\n}
\nelse
\n{
\n\/\/ \u5f80\u4e0a\u627e"\u5b69\u5b50\u662f\u7236\u4eb2\u53f3"\u7684\u90a3\u4e2a\u7956\u5148
\nNode* cur = _node;
\nNode* parent = cur->_parent;
\nwhile (parent && cur == parent->_left)
\n{
\ncur = parent;
\nparent = cur->_parent;
\n}
\n_node = parent;
\n}
\nreturn *this;
\n}<\/p>\n 4.5 \u4f8b\u5b50\u4e5d：\u7ea2\u9ed1\u6811\u91cc\u7684 Begin() \/ End()<\/h4>\ntypedef RBTreeIterator<T, T&, T*> Iterator;
\ntypedef RBTreeIterator<T, const T&, const T*> ConstIterator;<\/p>\n Iterator Begin()
\n{
\nNode* leftMost = _root;
\nwhile (leftMost && leftMost->_left) \/\/ \u4e00\u8def\u5411\u5de6，\u5c31\u662f\u4e2d\u5e8f\u7b2c\u4e00\u4e2a
\n{
\nleftMost = leftMost->_left;
\n}
\nreturn Iterator(leftMost, _root); \/\/ \u8bb0\u5f97\u628a _root \u4f20\u8fdb\u53bb
\n}<\/p>\n Iterator End()
\n{
\nreturn Iterator(nullptr, _root); \/\/ \u7528 nullptr \u8868\u793a end
\n}<\/p>\n const \u7248\u672c\u540c\u7406，\u53ea\u662f\u6362\u6210 ConstIterator\u3002<\/p>\n 4.6 \u7ecf\u5178 Bug：\u8fed\u4ee3\u5668\u91cc\u7684\u5751<\/h4>\nBug 1：–end() \u76f4\u63a5\u5d29\u6e83<\/p>\n end() \u91cc\u7ed3\u70b9\u7684\u6307\u9488\u662f nullptr，\u5982\u679c\u4f60\u5728 operator– \u91cc\u4e0d\u52a0 _node == nullptr \u7684\u5224\u65ad，\u7b2c\u4e00\u4ef6\u4e8b\u5c31\u662f\u89e3\u5f15\u7528\u7a7a\u6307\u9488 \u2014\u2014 \u7a0b\u5e8f\u5f53\u573a\u53bb\u4e16\u3002<\/p>\n Bug 2：\u5fd8\u8bb0\u628a _root \u4f20\u7ed9\u8fed\u4ee3\u5668<\/p>\n –end() \u9700\u8981\u9760 _root \u53bb\u627e\u6700\u53f3\u7ed3\u70b9\u3002\u5982\u679c\u4f60\u7684\u8fed\u4ee3\u5668\u6784\u9020\u51fd\u6570\u53ea\u4f20\u4e86\u7ed3\u70b9\u6307\u9488，_root \u5c31\u662f\u91ce\u6307\u9488，\u8fd0\u884c\u8d77\u6765\u65f6\u597d\u65f6\u574f（\u5178\u578b\u7684"\u7384\u5b66 Bug"）\u3002\u8bb0\u4f4f Iterator(node, _root) \u4e24\u4e2a\u53c2\u6570\u90fd\u8981\u4f20\u3002<\/p>\n Bug 3：Begin() \u4e0d\u5224\u7a7a\u6811<\/p>\n \u7a7a\u6811\u65f6 _root \u5c31\u662f nullptr，\u4e0a\u9762\u7684 while (leftMost && leftMost->_left) \u91cc\u7684\u5224\u7a7a\u4e0d\u80fd\u5c11，\u5426\u5219\u7a7a\u6811 begin() \u76f4\u63a5\u5d29\u3002<\/p>\n
\n\u4e94\u3001\u4e0d\u8ba9\u6539 key：const K \u7684\u5999\u7528<\/h3>\n5.1 \u7b80\u4ecb\u4f5c\u7528<\/h4>\n\u7ea2\u9ed1\u6811\u662f\u6392\u5e8f\u7ed3\u6784，\u5b83\u9760 key \u7684\u5927\u5c0f\u5173\u7cfb\u7ef4\u6301\u5e73\u8861\u3002\u5982\u679c\u5141\u8bb8\u7528\u6237\u968f\u624b\u6539 key，\u6574\u68f5\u6811\u7684\u6709\u5e8f\u6027\u77ac\u95f4\u5c31\u4e71\u4e86 \u2014\u2014 \u4e4b\u540e\u518d\u67e5\u627e\u5c31\u4f1a\u627e\u4e0d\u5230\u672c\u6765\u5b58\u5728\u7684\u5143\u7d20\u3002<\/p>\n \u6240\u4ee5\u5728\u8bbe\u8ba1\u4e0a\u5fc5\u987b\u4ece\u7c7b\u578b\u5c42\u9762\u76f4\u63a5\u9501\u6b7b：<\/p>\n \n- set \u7684 key \u5c31\u662f value，\u5168\u90fd\u4e0d\u8bb8\u6539；<\/li>\n<\/ul>\n
\n- map \u7684 key \u662f pair \u7684 first，\u53ea\u9501\u6b7b first，second \u968f\u4fbf\u6539\u3002<\/li>\n<\/ul>\n
5.2 \u4f8b\u5b50\u5341：\u6539\u4e00\u884c\u6a21\u677f\u53c2\u6570\u5c31\u641e\u5b9a\u4e86<\/h4>\n\/\/ Myset.h \u2014\u2014 \u7b2c\u4e8c\u4e2a\u53c2\u6570\u52a0 const
\nRBTree<K, const K, SetKeyOfT> _t;<\/p>\n \/\/ Mymap.h \u2014\u2014 \u628a first \u53d8\u6210 const
\nRBTree<K, pair<const K, V>, MapKeyOfT> _t;<\/p>\n \u5c31\u8fd9\u4e48\u7b80\u5355！ \u52a0\u4e0a const \u4e4b\u540e：<\/p>\n \n- iterator \u7684 Ref \u53d8\u6210 const T&，\u901a\u8fc7 *it \/ it-> \u62ff\u5230\u7684\u4e1c\u897f\u5929\u7136\u5e26 const；<\/li>\n<\/ul>\n
\n- \u60f3\u6539 key？\u7f16\u8bd1\u5668\u7b2c\u4e00\u4e2a\u4e0d\u7b54\u5e94\u3002<\/li>\n<\/ul>\n
5.3 \u4f8b\u5b50\u5341\u4e00：\u540c\u65f6\u63d0\u4f9b iterator \u548c const_iterator<\/h4>\n\/\/ Myset.h
\ntypedef typename RBTree<K, const K, SetKeyOfT>::Iterator iterator;
\ntypedef typename RBTree<K, const K, SetKeyOfT>::ConstIterator const_iterator;<\/p>\n iterator begin() { return _t.Begin(); }
\niterator end() { return _t.End(); }
\nconst_iterator begin() const { return _t.Begin(); }
\nconst_iterator end() const { return _t.End(); }<\/p>\n pair<iterator, bool> insert(const K& key)
\n{
\nreturn _t.Insert(key);
\n}<\/p>\n iterator find(const K& key)
\n{
\nreturn _t.Find(key);
\n}<\/p>\n 5.4 \u4f8b\u5b50\u5341\u4e8c：\u5012\u7740\u6253\u5370\u4e00\u4e2a set<\/h4>\nvoid Print(const set<int>& s)
\n{
\nset<int>::const_iterator it = s.end();
\nwhile (it != s.begin())
\n{
\n–it; \/\/ \u4ece end \u5f80\u524d\u9000，\u6b63\u597d\u662f\u964d\u5e8f
\n\/\/ *it += 2; \/\/ \u274c \u7f16\u8bd1\u62a5\u9519：read-only，\u8bf4\u660e const \u751f\u6548\u4e86
\ncout << *it << " ";
\n}
\ncout << endl;
\n}<\/p>\n void test_set()
\n{
\nset<int> s;
\nint a[] = { 4, 2, 6, 1, 3, 5, 15, 7, 16, 14 };
\nfor (auto e : a)
\n{
\ns.insert(e);
\n}<\/p>\n for (auto e : s) \/\/ \u8303\u56f4 for \u8d70\u4e2d\u5e8f，\u5929\u7136\u5347\u5e8f
\n{
\ncout << e << " ";
\n}
\ncout << endl;<\/p>\n Print(s); \/\/ \u964d\u5e8f\u8f93\u51fa
\n}<\/p>\n \u8fd0\u884c\u7ed3\u679c：<\/p>\n 1 2 3 4 5 6 7 14 15 16
\n16 15 14 7 6 5 4 3 2 1<\/p>\n 5.5 \u7ecf\u5178 Bug：it->first += 'x' \u7f16\u8bd1\u4e0d\u8fc7<\/h4>\nmap<string, string>::iterator it = dict.begin();
\n\/\/ it->first += 'x'; \/\/ \u274c \u62a5\u9519：assignment of read-only member
\nit->second += 'x'; \/\/ \u2705 \u6ca1\u95ee\u9898，value \u53ef\u4ee5\u968f\u4fbf\u6539<\/p>\n 🐛 \u63d0\u793a：\u5982\u679c\u4f60\u53d1\u73b0 it->first \u5c45\u7136\u80fd\u6539，\u8bf4\u660e\u4f60\u5728 Mymap.h \u91cc\u7b2c\u4e8c\u53c2\u6570\u5199\u7684\u662f pair<K, V>，\u6f0f\u4e86 const，\u8d76\u7d27\u8865\u4e0a\u3002<\/p>\n
\n\u516d\u3001map \u7684 operator[]：\u4e00\u884c\u4ee3\u7801\u5e72\u4e24\u4ef6\u4e8b<\/h3>\n6.1 \u7b80\u4ecb\u4f5c\u7528<\/h4>\nmap \u6700\u723d\u7684\u529f\u80fd\u5c31\u662f operator[]，\u5b83\u662f"\u6709\u5219\u8fd4\u56de，\u65e0\u5219\u63d2\u5165"：<\/p>\n dict["left"] = "\u5de6\u8fb9，\u5269\u4f59"; \/\/ left \u5df2\u5b58\u5728 -> \u6539\u5b83\u7684 value
\ndict["insert"] = "\u63d2\u5165"; \/\/ insert \u4e0d\u5b58\u5728 -> \u63d2\u5165\u540e\u518d\u8d4b\u503c
\ndict["string"]; \/\/ \u4e0d\u5b58\u5728 -> \u63d2\u5165\u9ed8\u8ba4\u503c ""<\/p>\n \u8981\u652f\u6301\u5b83，\u524d\u63d0\u662f Insert \u5f97\u628a"\u63d2\u5165\u7ed3\u679c"\u544a\u8bc9\u5916\u9762：\u65e2\u60f3\u77e5\u9053\u6709\u6ca1\u6709\u63d2\u5165\u6210\u529f，\u53c8\u60f3\u62ff\u5230\u90a3\u4e2a\u7ed3\u70b9\u7684\u8fed\u4ee3\u5668\u3002\u6240\u4ee5\u8fd4\u56de\u503c\u8981\u4ece bool \u5347\u7ea7\u6210 pair<iterator, bool>\u3002<\/p>\n 6.2 \u4f8b\u5b50\u5341\u4e09：\u628a Insert \u7684\u8fd4\u56de\u503c\u5347\u7ea7<\/h4>\npair<Iterator, bool> Insert(const T& data)
\n{
\nif (_root == nullptr)
\n{
\n_root = new Node(data);
\n_root->_col = BLACK;
\nreturn make_pair(Iterator(_root, _root), true); \/\/ \u65b0\u6839，\u63d2\u6210\u529f
\n}<\/p>\n KeyOfT kot;
\nNode* parent = nullptr;
\nNode* cur = _root;
\nwhile (cur)
\n{
\nif (kot(cur->_data) < kot(data))
\n{
\nparent = cur;
\ncur = cur->_right;
\n}
\nelse if (kot(cur->_data) > kot(data))
\n{
\nparent = cur;
\ncur = cur->_left;
\n}
\nelse
\n{
\n\/\/ key \u5df2\u5b58\u5728：\u628a"\u5df2\u6709\u7ed3\u70b9"\u7684\u8fed\u4ee3\u5668\u8fd4\u56de\u53bb，bool \u7ed9 false
\nreturn make_pair(Iterator(cur, _root), false);
\n}
\n}<\/p>\n cur = new Node(data); \/\/ \u5230\u8fd9\u513f cur \u624d\u771f\u6b63\u88ab\u63a5\u4e0a
\nNode* newnode = cur;
\ncur->_col = RED;<\/p>\n if (kot(parent->_data) < kot(data))
\nparent->_right = cur;
\nelse
\nparent->_left = cur;<\/p>\n cur->_parent = parent;<\/p>\n \/\/ \u2026\u2026\u4e2d\u95f4\u662f\u7ea2\u9ed1\u6811\u7684\u65cb\u8f6c + \u53d8\u8272\u8c03\u6574（\u524d\u9762\u6587\u7ae0\u5df2\u8be6\u89e3，\u8fd9\u91cc\u7565）<\/p>\n _root->_col = BLACK; \/\/ \u6839\u6c38\u8fdc\u662f\u9ed1\u7684
\nreturn make_pair(Iterator(newnode, _root), true);
\n}<\/p>\n 💡 \u6ce8\u610f\u6700\u540e\u4e00\u884c\u7528\u7684\u662f newnode\u3002\u56e0\u4e3a\u5728\u8c03\u6574\u8fc7\u7a0b\u4e2d cur \u53ef\u80fd\u5df2\u7ecf\u88ab\u6539\u6210\u4e86\u7956\u5148\u7ed3\u70b9，\u800c\u6211\u4eec\u8981\u8fd4\u56de\u7684\u662f\u65b0\u63d2\u5165\u7684\u90a3\u4e2a\u7ed3\u70b9\u7684\u8fed\u4ee3\u5668\u3002<\/p>\n 6.3 \u4f8b\u5b50\u5341\u56db：operator[] \u7684\u5b9e\u73b0<\/h4>\n\u6709\u4e86\u4e0a\u9762\u8fd9\u4e2a\u8fd4\u56de\u503c，operator[] \u53ea\u6709\u4e09\u884c：<\/p>\n V& operator[](const K& key)
\n{
\npair<iterator, bool> ret = insert(make_pair(key, V()));
\nreturn ret.first->second; \/\/ \u76f4\u63a5\u8fd4\u56de value \u7684\u5f15\u7528
\n}<\/p>\n \u62c6\u5f00\u770b\u5c31\u662f：<\/p>\n - \u62ff (key, V()) \u53bb\u63d2\u5165 \u2014\u2014 V() \u662f value \u7c7b\u578b\u7684\u9ed8\u8ba4\u503c（string \u5c31\u662f ""，int \u5c31\u662f 0）；<\/li>\n
- \u5982\u679c key \u5df2\u5b58\u5728，insert \u4f1a\u8fd4\u56de false \u548c\u5df2\u6709\u7ed3\u70b9\u7684\u8fed\u4ee3\u5668，\u63d2\u5165\u52a8\u4f5c\u88ab\u5ffd\u7565；<\/li>\n
- \u5982\u679c key \u4e0d\u5b58\u5728，\u771f\u7684\u63d2\u5165\u6210\u529f，\u8fd4\u56de true \u548c\u65b0\u7ed3\u70b9\u7684\u8fed\u4ee3\u5668；<\/li>\n
- \u65e0\u8bba\u54ea\u79cd\u60c5\u51b5，ret.first \u90fd\u6307\u5411\u90a3\u4e2a key \u5bf9\u5e94\u7684\u7ed3\u70b9，->second \u5c31\u662f\u5b83\u7684 value\u3002<\/li>\n
\u6240\u4ee5 operator[] \u8fd4\u56de\u7684\u662f\u5f15\u7528，\u65e2\u80fd\u8bfb\u4e5f\u80fd\u5199\u3002<\/p>\n 6.4 \u4f8b\u5b50\u5341\u4e94：\u8dd1\u4e00\u904d map<\/h4>\nvoid test_map()
\n{
\nmap<string, string> dict;
\ndict.insert({ "sort", "\u6392\u5e8f" });
\ndict.insert({ "left", "\u5de6\u8fb9" });
\ndict.insert({ "right", "\u53f3\u8fb9" });<\/p>\n dict["left"] = "\u5de6\u8fb9，\u5269\u4f59"; \/\/ \u4fee\u6539\u5df2\u6709
\ndict["insert"] = "\u63d2\u5165"; \/\/ \u63d2\u5165\u65b0\u7684
\ndict["string"]; \/\/ \u63d2\u5165\u9ed8\u8ba4\u503c ""<\/p>\n map<string, string>::iterator it = dict.begin();
\nwhile (it != dict.end())
\n{
\n\/\/ it->first += 'x'; \/\/ \u274c key \u4e0d\u80fd\u6539
\nit->second += 'x'; \/\/ \u2705 value \u53ef\u4ee5\u6539
\ncout << it->first << ":" << it->second << endl;
\n++it;
\n}
\ncout << endl;
\n}<\/p>\n \u8fd0\u884c\u7ed3\u679c（key \u81ea\u52a8\u5347\u5e8f，\u56e0\u4e3a\u4e2d\u5e8f\u904d\u5386）：<\/p>\n insert:\u63d2\u5165x
\nleft:\u5de6\u8fb9，\u5269\u4f59x
\nright:\u53f3\u8fb9x
\nsort:\u6392\u5e8fx
\nstring:x<\/p>\n 6.5 \u7ecf\u5178 Bug：Insert \u53ea\u8fd4\u56de bool<\/h4>\n\u5982\u679c\u4f60\u524d\u9762\u7684 Insert \u5199\u7684\u662f：<\/p>\n bool Insert(const T& data); \/\/ \u274c \u6ca1\u6709\u8fed\u4ee3\u5668<\/p>\n \u90a3 operator[] \u5c31\u5b8c\u5168\u6ca1\u6cd5\u5b9e\u73b0\u4e86 \u2014\u2014 \u4f60\u65e2\u4e0d\u77e5\u9053\u65b0\u7ed3\u70b9\u5728\u54ea，\u4e5f\u4e0d\u77e5\u9053\u5230\u5e95\u63d2\u5165\u6ca1\u6709：<\/p>\n V& operator[](const K& key)
\n{
\nbool ret = insert(make_pair(key, V()));
\n\/\/ ret.first -> \u274c \u7f16\u8bd1\u62a5\u9519，bool \u6ca1\u6709 first
\nreturn ???; \/\/ \u5361\u6b7b\u5728\u8fd9\u91cc
\n}<\/p>\n 🐛 \u907f\u5751\u7ed3\u8bba：map \u60f3\u8981 operator[]，Insert \u5fc5\u987b\u8fd4\u56de pair<iterator, bool>\u3002\u8fd9\u4e5f\u662f\u4e3a\u4ec0\u4e48 STL \u7684 insert \u8981\u8fd4\u56de pair<iterator, bool> \u7684\u771f\u6b63\u539f\u56e0\u3002<\/p>\n
\n\u4e03\u3001\u5b8c\u6574\u4ee3\u7801\u6c47\u603b<\/h3>\n7.1 RBTree.h<\/h4>\n#pragma once
\n#include <iostream>
\n#include <utility>
\nusing namespace std;<\/p>\n enum Colour
\n{
\nRED,
\nBLACK
\n};<\/p>\n template<class T>
\nstruct RBTreeNode
\n{
\nT _data;
\nRBTreeNode<T>* _left;
\nRBTreeNode<T>* _right;
\nRBTreeNode<T>* _parent;
\nColour _col;<\/p>\n RBTreeNode(const T& data)
\n: _data(data)
\n, _left(nullptr)
\n, _right(nullptr)
\n, _parent(nullptr)
\n, _col(RED)
\n{}
\n};<\/p>\n \/\/ \u8fed\u4ee3\u5668
\ntemplate<class T, class Ref, class Ptr>
\nstruct RBTreeIterator
\n{
\ntypedef RBTreeNode<T> Node;
\ntypedef RBTreeIterator<T, Ref, Ptr> Self;<\/p>\n Node* _node;
\nNode* _root;<\/p>\n RBTreeIterator(Node* node, Node* root)
\n: _node(node)
\n, _root(root)
\n{}<\/p>\n Ref operator*() { return _node->_data; }
\nPtr operator->() { return &_node->_data; }<\/p>\n bool operator!=(const Self& s) const { return _node != s._node; }
\nbool operator==(const Self& s) const { return _node == s._node; }<\/p>\n Self& operator++()
\n{
\nif (_node->_right)
\n{
\nNode* leftMost = _node->_right;
\nwhile (leftMost->_left)
\n{
\nleftMost = leftMost->_left;
\n}
\n_node = leftMost;
\n}
\nelse
\n{
\nNode* cur = _node;
\nNode* parent = cur->_parent;
\nwhile (parent && cur == parent->_right)
\n{
\ncur = parent;
\nparent = cur->_parent;
\n}
\n_node = parent;
\n}
\nreturn *this;
\n}<\/p>\n Self& operator–()
\n{
\nif (_node == nullptr) \/\/ –end()
\n{
\nNode* rightMost = _root;
\nwhile (rightMost && rightMost->_right)
\n{
\nrightMost = rightMost->_right;
\n}
\n_node = rightMost;
\n}
\nelse if (_node->_left)
\n{
\nNode* rightMost = _node->_left;
\nwhile (rightMost->_right)
\n{
\nrightMost = rightMost->_right;
\n}
\n_node = rightMost;
\n}
\nelse
\n{
\nNode* cur = _node;
\nNode* parent = cur->_parent;
\nwhile (parent && cur == parent->_left)
\n{
\ncur = parent;
\nparent = cur->_parent;
\n}
\n_node = parent;
\n}
\nreturn *this;
\n}
\n};<\/p>\n template<class K, class T, class KeyOfT>
\nclass RBTree
\n{
\ntypedef RBTreeNode<T> Node;<\/p>\n public:
\ntypedef RBTreeIterator<T, T&, T*> Iterator;
\ntypedef RBTreeIterator<T, const T&, const T*> ConstIterator;<\/p>\n RBTree() = default;<\/p>\n ~RBTree()
\n{
\nDestroy(_root);
\n_root = nullptr;
\n}<\/p>\n Iterator Begin()
\n{
\nNode* leftMost = _root;
\nwhile (leftMost && leftMost->_left)
\n{
\nleftMost = leftMost->_left;
\n}
\nreturn Iterator(leftMost, _root);
\n}<\/p>\n Iterator End()
\n{
\nreturn Iterator(nullptr, _root);
\n}<\/p>\n ConstIterator Begin() const
\n{
\nNode* leftMost = _root;
\nwhile (leftMost && leftMost->_left)
\n{
\nleftMost = leftMost->_left;
\n}
\nreturn ConstIterator(leftMost, _root);
\n}<\/p>\n ConstIterator End() const
\n{
\nreturn ConstIterator(nullptr, _root);
\n}<\/p>\n pair<Iterator, bool> Insert(const T& data)
\n{
\nif (_root == nullptr)
\n{
\n_root = new Node(data);
\n_root->_col = BLACK;
\nreturn make_pair(Iterator(_root, _root), true);
\n}<\/p>\n KeyOfT kot;
\nNode* parent = nullptr;
\nNode* cur = _root;
\nwhile (cur)
\n{
\nif (kot(cur->_data) < kot(data))
\n{
\nparent = cur;
\ncur = cur->_right;
\n}
\nelse if (kot(cur->_data) > kot(data))
\n{
\nparent = cur;
\ncur = cur->_left;
\n}
\nelse
\n{
\nreturn make_pair(Iterator(cur, _root), false);
\n}
\n}<\/p>\n cur = new Node(data);
\nNode* newnode = cur;
\ncur->_col = RED;<\/p>\n if (kot(parent->_data) < kot(data))
\nparent->_right = cur;
\nelse
\nparent->_left = cur;<\/p>\n cur->_parent = parent;<\/p>\n \/\/ \u5e73\u8861\u8c03\u6574
\nwhile (parent && parent->_col == RED)
\n{
\nNode* grandfather = parent->_parent;
\nif (parent == grandfather->_left)
\n{
\nNode* uncle = grandfather->_right;
\nif (uncle && uncle->_col == RED)
\n{
\n\/\/ \u53d4\u53d4\u5b58\u5728\u4e14\u4e3a\u7ea2 -> \u53d8\u8272\u7ee7\u7eed\u5f80\u4e0a\u5904\u7406
\nparent->_col = uncle->_col = BLACK;
\ngrandfather->_col = RED;
\ncur = grandfather;
\nparent = cur->_parent;
\n}
\nelse
\n{
\nif (cur == parent->_left)
\n{
\n\/\/ \u5355\u65cb：g \u5de6，p \u5de6，c \u5de6
\nRotateR(grandfather);
\nparent->_col = BLACK;
\ngrandfather->_col = RED;
\n}
\nelse
\n{
\n\/\/ \u53cc\u65cb：\u5de6\u53f3
\nRotateL(parent);
\nRotateR(grandfather);
\ncur->_col = BLACK;
\ngrandfather->_col = RED;
\n}
\nbreak;
\n}
\n}
\nelse
\n{
\nNode* uncle = grandfather->_left;
\nif (uncle && uncle->_col == RED)
\n{
\nparent->_col = uncle->_col = BLACK;
\ngrandfather->_col = RED;
\ncur = grandfather;
\nparent = cur->_parent;
\n}
\nelse
\n{
\nif (cur == parent->_right)
\n{
\n\/\/ \u5355\u65cb：\u53f3\u53f3
\nRotateL(grandfather);
\nparent->_col = BLACK;
\ngrandfather->_col = RED;
\n}
\nelse
\n{
\n\/\/ \u53cc\u65cb：\u53f3\u5de6
\nRotateR(parent);
\nRotateL(grandfather);
\ncur->_col = BLACK;
\ngrandfather->_col = RED;
\n}
\nbreak;
\n}
\n}
\n}<\/p>\n _root->_col = BLACK;
\nreturn make_pair(Iterator(newnode, _root), true);
\n}<\/p>\n Iterator Find(const K& key)
\n{
\nKeyOfT kot; \/\/ \u7528 KeyOfT \u53d6 key，\u4e0d\u8981\u76f4\u63a5\u5199 _kv.first！
\nNode* cur = _root;
\nwhile (cur)
\n{
\nif (kot(cur->_data) < key)
\n{
\ncur = cur->_right;
\n}
\nelse if (kot(cur->_data) > key)
\n{
\ncur = cur->_left;
\n}
\nelse
\n{
\nreturn Iterator(cur, _root);
\n}
\n}
\nreturn End();
\n}<\/p>\n private:
\nvoid RotateL(Node* parent)
\n{
\nNode* subR = parent->_right;
\nNode* subRL = subR->_left;<\/p>\n parent->_right = subRL;
\nif (subRL)
\nsubRL->_parent = parent;<\/p>\n Node* parentParent = parent->_parent;
\nsubR->_left = parent;
\nparent->_parent = subR;<\/p>\n if (parentParent == nullptr)
\n{
\n_root = subR;
\nsubR->_parent = nullptr;
\n}
\nelse
\n{
\nif (parent == parentParent->_left)
\nparentParent->_left = subR;
\nelse
\nparentParent->_right = subR;<\/p>\n subR->_parent = parentParent;
\n}
\n}<\/p>\n void RotateR(Node* parent)
\n{
\nNode* subL = parent->_left;
\nNode* subLR = subL->_right;<\/p>\n parent->_left = subLR;
\nif (subLR)
\nsubLR->_parent = parent;<\/p>\n Node* parentParent = parent->_parent;
\nsubL->_right = parent;
\nparent->_parent = subL;<\/p>\n if (parentParent == nullptr)
\n{
\n_root = subL;
\nsubL->_parent = nullptr;
\n}
\nelse
\n{
\nif (parent == parentParent->_left)
\nparentParent->_left = subL;
\nelse
\nparentParent->_right = subL;<\/p>\n subL->_parent = parentParent;
\n}
\n}<\/p>\n void Destroy(Node* root)
\n{
\nif (root == nullptr)
\nreturn;
\nDestroy(root->_left);
\nDestroy(root->_right);
\ndelete root;
\n}<\/p>\n private:
\nNode* _root = nullptr;
\n};<\/p>\n 7.2 Myset.h<\/h4>\n#pragma once
\n#include "RBTree.h"<\/p>\n namespace bit
\n{
\ntemplate<class K>
\nclass set
\n{
\nstruct SetKeyOfT
\n{
\nconst K& operator()(const K& key)
\n{
\nreturn key;
\n}
\n};<\/p>\n public:
\ntypedef typename RBTree<K, const K, SetKeyOfT>::Iterator iterator;
\ntypedef typename RBTree<K, const K, SetKeyOfT>::ConstIterator const_iterator;<\/p>\n iterator begin() { return _t.Begin(); }
\niterator end() { return _t.End(); }
\nconst_iterator begin() const { return _t.Begin(); }
\nconst_iterator end() const { return _t.End(); }<\/p>\n pair<iterator, bool> insert(const K& key)
\n{
\nreturn _t.Insert(key);
\n}<\/p>\n iterator find(const K& key)
\n{
\nreturn _t.Find(key);
\n}<\/p>\n private:
\nRBTree<K, const K, SetKeyOfT> _t; \/\/ \u7b2c\u4e8c\u4e2a\u53c2\u6570\u52a0 const，key \u4e0d\u53ef\u6539
\n};
\n}<\/p>\n 7.3 Mymap.h<\/h4>\n#pragma once
\n#include "RBTree.h"<\/p>\n namespace bit
\n{
\ntemplate<class K, class V>
\nclass map
\n{
\nstruct MapKeyOfT
\n{
\nconst K& operator()(const pair<K, V>& kv)
\n{
\nreturn kv.first;
\n}
\n};<\/p>\n public:
\ntypedef typename RBTree<K, pair<const K, V>, MapKeyOfT>::Iterator iterator;
\ntypedef typename RBTree<K, pair<const K, V>, MapKeyOfT>::ConstIterator const_iterator;<\/p>\n iterator begin() { return _t.Begin(); }
\niterator end() { return _t.End(); }
\nconst_iterator begin() const { return _t.Begin(); }
\nconst_iterator end() const { return _t.End(); }<\/p>\n pair<iterator, bool> insert(const pair<K, V>& kv)
\n{
\nreturn _t.Insert(kv);
\n}<\/p>\n iterator find(const K& key)
\n{
\nreturn _t.Find(key);
\n}<\/p>\n V& operator[](const K& key)
\n{
\npair<iterator, bool> ret = insert(make_pair(key, V()));
\nreturn ret.first->second;
\n}<\/p>\n private:
\nRBTree<K, pair<const K, V>, MapKeyOfT> _t; \/\/ \u53ea\u9501\u6b7b first
\n};
\n}<\/p>\n 7.4 test.cpp<\/h4>\n#include "RBTree.h"
\n#include "Myset.h"
\n#include "Mymap.h"<\/p>\n void test_set()
\n{
\nbit::set<int> s;
\nint a[] = { 4, 2, 6, 1, 3, 5, 15, 7, 16, 14 };
\nfor (auto e : a)
\n{
\ns.insert(e);
\n}<\/p>\n for (auto e : s)
\ncout << e << " ";
\ncout << endl;
\n}<\/p>\n void test_map()
\n{
\nbit::map<string, string> dict;
\ndict.insert({ "sort", "\u6392\u5e8f" });
\ndict.insert({ "left", "\u5de6\u8fb9" });
\ndict.insert({ "right", "\u53f3\u8fb9" });<\/p>\n dict["left"] = "\u5de6\u8fb9，\u5269\u4f59";
\ndict["insert"] = "\u63d2\u5165";
\ndict["string"];<\/p>\n bit::map<string, string>::iterator it = dict.begin();
\nwhile (it != dict.end())
\n{
\nit->second += 'x';
\ncout << it->first << ":" << it->second << endl;
\n++it;
\n}
\ncout << endl;
\n}<\/p>\n int main()
\n{
\ntest_set();
\ntest_map();
\nreturn 0;
\n}<\/p>\n
\n\u516b\u3001\u672c\u7bc7\u5c0f\u7ed3<\/h3>\n\u628a\u6574\u4ef6\u4e8b\u634b\u4e00\u904d，\u5176\u5b9e\u5c31\u53ea\u6709 6 \u6b65：<\/p>\n \n\n\n| \n \u6b65\u9aa4<\/p>\n<\/td>\n | \n \u8981\u505a\u7684\u4e8b<\/p>\n<\/td>\n | \n \u5173\u952e\u70b9<\/p>\n<\/td>\n<\/tr>\n | \n| \n \u2460<\/p>\n<\/td>\n | \n \u5b9e\u73b0\u7ea2\u9ed1\u6811<\/p>\n<\/td>\n | \n \u6cdb\u578b\u6a21\u677f RBTree<K, T, KeyOfT><\/p>\n<\/td>\n<\/tr>\n | \n| \n \u2461<\/p>\n<\/td>\n | \n \u5c01\u88c5 map \/ set \u6846\u67b6<\/p>\n<\/td>\n | \n \u7b2c\u4e8c\u4e2a\u6a21\u677f\u53c2\u6570\u51b3\u5b9a\u5b58 K \u8fd8\u662f pair；\u5199 SetKeyOfT \/ MapKeyOfT<\/p>\n<\/td>\n<\/tr>\n | \n| \n \u2462<\/p>\n<\/td>\n | \n \u52a0 iterator<\/p>\n<\/td>\n | \n operator++ \/ operator– \u8d70\u4e2d\u5e8f；end() \u7528 nullptr<\/p>\n<\/td>\n<\/tr>\n | \n| \n \u2463<\/p>\n<\/td>\n | \n \u52a0 const_iterator<\/p>\n<\/td>\n | \n Ref \/ Ptr \u5206\u79bb，\u4e00\u5957\u4ee3\u7801\u4e24\u4e2a\u7248\u672c<\/p>\n<\/td>\n<\/tr>\n | \n| \n \u2464<\/p>\n<\/td>\n | \n \u9501\u6b7b key<\/p>\n<\/td>\n | \n const K \/ pair<const K, V><\/p>\n<\/td>\n<\/tr>\n | \n| \n \u2465<\/p>\n<\/td>\n | \n map \u7684 operator[]<\/p>\n<\/td>\n | \n Insert \u8fd4\u56de pair<iterator, bool><\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n \u6700\u5bb9\u6613\u8e29\u7684\u4e09\u4e2a\u5751，\u518d\u5f3a\u8c03\u4e00\u6b21：<\/p>\n - \u5fd8\u4e86 KeyOfT \u2014\u2014 map \u76f4\u63a5\u7f16\u8bd1\u4e0d\u8fc7（\u56e0\u4e3a V \u4e0d\u652f\u6301 <）；<\/li>\n
- Insert \u53ea\u8fd4\u56de bool \u2014\u2014 operator[] \u65e0\u4ece\u4e0b\u624b；<\/li>\n
- \u8fed\u4ee3\u5668\u4e0d\u4f20 _root \u6216 –end() \u4e0d\u5224\u7a7a \u2014\u2014 \u8fd0\u884c\u671f\u5d29\u6e83，\u800c\u4e14\u5f88\u96be\u67e5\u3002<\/li>\n
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