{"id":124,"date":"2025-07-06T12:23:37","date_gmt":"2025-07-06T04:23:37","guid":{"rendered":"http:\/\/120.76.99.214\/?p=124"},"modified":"2025-11-24T16:42:18","modified_gmt":"2025-11-24T08:42:18","slug":"%e7%ba%a2%e9%bb%91%e6%a0%91%e7%9a%84%e5%ae%9e%e7%8e%b0","status":"publish","type":"post","link":"https:\/\/www.tgwttt.xyz\/?p=124","title":{"rendered":"\u7ea2\u9ed1\u6811\u7684\u5b9e\u73b0"},"content":{"rendered":"\n<p>\u7ea2\u9ed1\u6811\u662f\u641c\u7d22\u4e8c\u53c9\u6811\u7684\u4e00\u79cd\uff0c\u4e0e\u5e73\u8861\u4e8c\u53c9\u6811\u76f8\u8fd1\uff0c\u641c\u7d22\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u53ef\u4e3alogn,\u6548\u7387\u5f88\u9ad8\uff0c\u4e0e\u7ea2\u9ed1\u6811\u4e0d\u540c\u7684\u662f\u4ed6\u989c\u8272\uff08\u7ea2 \u9ed1\uff09\u7684\u89c4\u5219\uff0c\u901a\u8fc7\u8fd9\u4e2a\u89c4\u5219\u53bb\u63a7\u5236\u4e8c\u53c9\u6811\u7684 \u9ad8\u5ea6\u3002<\/p>\n\n\n\n<p>\u7ea2\u9ed1\u6811\u7684\u89c4\u5219\uff1a                                                                                                                                                             1.\u6bcf\u4e2a\u8282\u70b9\u4e0d\u662f\u7ea2\u8272\u5c31\u662f\u9ed1\u8272<br>2.\u6839\u8282\u70b9\u662f\u9ed1\u8272<br>3.\u4efb\u610f\u4e00\u6761\u8def\u5f84\u4e0d\u4f1a\u6709\u8fde\u7eed\u7684\u7ea2\u8272\u8282\u70b9<br>4.\u6bcf\u6761\u8def\u5f84\u90fd\u6709\u76f8\u540c\u7684\u9ed1\u8272\u8282\u70b9\u6570\u91cf<br>5.\u7a7a\u8282\u70b9\u90fd\u4e3a\u9ed1\u8272<br>\u7ea2\u9ed1\u6811\u8282\u70b9\u7684\u989c\u8272\u679a\u4e3e<\/p>\n\n\n\n<p>\u4e0b\u9762\u662f\u4e00\u68f5\u7b26\u5408\u89c4\u5219\u7684\u7ea2\u9ed1\u6811<\/p>\n\n\n\n<figure class=\"wp-block-image size-full is-resized\"><img loading=\"lazy\" decoding=\"async\" width=\"446\" height=\"240\" src=\"http:\/\/120.76.99.214\/wp-content\/uploads\/2025\/07\/image-11.png\" alt=\"\" class=\"wp-image-125\" style=\"width:446px;height:auto\" srcset=\"https:\/\/www.tgwttt.xyz\/wp-content\/uploads\/2025\/07\/image-11.png 446w, https:\/\/www.tgwttt.xyz\/wp-content\/uploads\/2025\/07\/image-11-300x161.png 300w\" sizes=\"auto, (max-width: 446px) 100vw, 446px\" \/><\/figure>\n\n\n\n<p>\u4ed6\u7684\u6839\u8282\u70b9\u4e3a\u7a7a\uff0c\u6ce8\u610f\u7a7a\u8282\u70b9\u4e5f\u7b97\u4e00\u4e2a\u9ed1\u8272\u8282\u70b9<\/p>\n\n\n\n<p>\u4e0b\u9762\u662f\u7ea2\u9ed1\u6811\u7684\u4ee3\u7801\u5b9e\u73b0<\/p>\n\n\n\n<p>\u9996\u5148\u662f\u8282\u70b9\u7684\u5b9a\u4e49\uff0c\u4e0e\u524d\u9762\u7684\u5e73\u8861\u4e8c\u53c9\u6811\uff08\u89c1\u535a\u4e3b\u524d\u9762\u7684\u6587\u7ae0\u4ecb\u7ecd\uff09\u76f8\u540c<\/p>\n\n\n\n<p>enum Colour<br>{<br>RED,<br>BLACK<br>};<\/p>\n\n\n\n<p>template<br>struct RBTreeNode<br>{<br>\/\/ \u8fd9\u91cc\u66f4\u65b0\u63a7\u5236\u5e73\u8861\u4e5f\u8981\u52a0\u5165parent\u6307\u9488<br>pair _kv;<br>RBTreeNode* _left;<br>RBTreeNode* _right;<br>RBTreeNode* _parent;<br>Colour _col;<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>RBTreeNode(const pair<K, V>& kv)\n    :_kv(kv)\n    , _left(nullptr)\n    , _right(nullptr)\n    , _parent(nullptr)\n{\n}<\/code><\/pre>\n\n\n\n<p>};                                                                                                                                                                                    \u6b64\u5904\u552f\u4e00\u4e0d\u540c\u7684\u5c31\u662f\u5b9a\u4e49\u4e86\u4e00\u4e2acolor\u53bb\u5b9a\u4e49\u7ea2\u9ed1\u6811\u989c\u8272<\/p>\n\n\n\n<p>\u4e0b\u9762\u662f\u63d2\u5165\u64cd\u4f5c\uff0c\u63d2\u5165\u64cd\u4f5c\u662f\u4e8c\u53c9\u641c\u7d22\u6811\uff0c\u5e73\u8861\u4e8c\u53c9\u6811\uff0c\u7ea2\u9ed1\u6811\u6700\u5927\u7684\u4e0d\u540c\uff0c\u4e8c\u53c9\u641c\u7d20\u6811\u65e0\u9700\u53bb\u63a7\u5236\u6811\u7684\u9ad8\u5ea6\uff0c\u5e73\u8861\u4e8c\u53c9\u6811\u5219\u901a\u8fc7\u5e73\u8861\u56e0\u5b50\u63a7\u5236\u6811\u7684\u9ad8\u5ea6\uff0c\u800c\u6211\u4eec\u7684\u7ea2\u9ed1\u6811\u5219\u901a\u8fc7\u4e0a\u9762\u56db\u6761\u89c4\u5219\u63a7\u5236\u4e8c\u53c9\u6811\u7684\u9ad8\u5ea6\uff0c\u4ed6\u5206\u51e0\u79cd\u60c5\u51b5                                                                                                                                                           case1:\u5f53\u63d2\u5165\u7684\u7236\u8282\u70b9\u4e3a\u9ed1\u8272\u65f6\u76f4\u63a5\u63d2\u5165\u8fd4\u56de                                                                                                               case2:\u5f53\u63d2\u5165\u8282\u70b9\u7684uncle\u8282\u70b9\u5b58\u5728\u4e14\u4e3a\u7a7a\uff08\u5982\u56fe\uff09g\u8282\u70b9\u4e3agranderfater\u8282\u70b9\uff0cu\u8282\u70b9\u4e3auncle\u8282\u70b9\uff0cc\u8282\u70b9\u4e3acurrent\u8282\u70b9\uff0cp\u8282\u70b9\u4e3aparent\u8282\u70b9\u3002\u5f53\u4ed6\u5b58\u5728\u4e14\u4e3a\u7ea2\u8272\u65f6\u53ea\u9700\u8981\u5faa\u73af\u53d8\u8272\u5373\u53ef\uff0c\u5c06p\u8282\u70b9\u7f6e\u4e3a\u7ea2\u8272\uff0cp,u\u8282\u70b9\u7f6e\u4e3a\u9ed1\u8272\uff0c\u4e00\u76f4\u5faa\u73af\u5230p\u8282\u70b9\u4e3a\u7a7a<\/p>\n\n\n\n<p>                                                             <\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"824\" height=\"232\" src=\"http:\/\/120.76.99.214\/wp-content\/uploads\/2025\/07\/image-13.png\" alt=\"\" class=\"wp-image-127\" srcset=\"https:\/\/www.tgwttt.xyz\/wp-content\/uploads\/2025\/07\/image-13.png 824w, https:\/\/www.tgwttt.xyz\/wp-content\/uploads\/2025\/07\/image-13-300x84.png 300w, https:\/\/www.tgwttt.xyz\/wp-content\/uploads\/2025\/07\/image-13-768x216.png 768w\" sizes=\"auto, (max-width: 824px) 100vw, 824px\" \/><\/figure>\n\n\n\n<p>                                      <\/p>\n\n\n\n<p>case3:\u5f53u\u7ed3\u70b9\u4e3a\u7a7a\u65f6\u6216\u8005u\u8282\u70b9\u4e3a\u9ed1\u8272\uff0c\u5c31\u9700\u8981\u5229\u7528\u4e0a\u4e00\u7bc7\u6587\u7ae0\u7684\u65b9\u6cd5\u8fdb\u884c\u65cb\u8f6c\uff0c\u5982\u4e0b\u56fe\uff1a<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"874\" height=\"198\" src=\"http:\/\/120.76.99.214\/wp-content\/uploads\/2025\/07\/image-14.png\" alt=\"\" class=\"wp-image-128\" srcset=\"https:\/\/www.tgwttt.xyz\/wp-content\/uploads\/2025\/07\/image-14.png 874w, https:\/\/www.tgwttt.xyz\/wp-content\/uploads\/2025\/07\/image-14-300x68.png 300w, https:\/\/www.tgwttt.xyz\/wp-content\/uploads\/2025\/07\/image-14-768x174.png 768w\" sizes=\"auto, (max-width: 874px) 100vw, 874px\" \/><\/figure>\n\n\n\n<p>\u5c06g\u8282\u70b9\u8fdb\u884c\u53f3\u65cb\u518d\u5c06\u989c\u8272\u53d8\u5316<\/p>\n\n\n\n<p>case4\uff1acase3\u7684\u60c5\u51b5\u5e76\u4e14\u63d2\u5165\u5728p\u8282\u70b9\u7684\u53f3\u8fb9\u5982\u56fe\uff1a<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"674\" height=\"169\" src=\"http:\/\/120.76.99.214\/wp-content\/uploads\/2025\/07\/image-16.png\" alt=\"\" class=\"wp-image-130\" srcset=\"https:\/\/www.tgwttt.xyz\/wp-content\/uploads\/2025\/07\/image-16.png 674w, https:\/\/www.tgwttt.xyz\/wp-content\/uploads\/2025\/07\/image-16-300x75.png 300w\" sizes=\"auto, (max-width: 674px) 100vw, 674px\" \/><\/figure>\n\n\n\n<p>\u8fd9\u65f6\u5019\u5c31\u9700\u8981\u53bb\u53cc\u65cb\u5148\u5bf9p\u8282\u70b9\u8fdb\u884c\u65cb\u8f6c\uff0c\u540e\u5bf9g\u8282\u70b9\u8fdb\u884c\u65cb\u8f6c<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"384\" height=\"192\" src=\"http:\/\/120.76.99.214\/wp-content\/uploads\/2025\/07\/image-17.png\" alt=\"\" class=\"wp-image-131\" srcset=\"https:\/\/www.tgwttt.xyz\/wp-content\/uploads\/2025\/07\/image-17.png 384w, https:\/\/www.tgwttt.xyz\/wp-content\/uploads\/2025\/07\/image-17-300x150.png 300w\" sizes=\"auto, (max-width: 384px) 100vw, 384px\" \/><\/figure>\n\n\n\n<p>\u8fd9\u662f\u4e2d\u95f4\u8fc7\u7a0b<\/p>\n\n\n\n<p>\u4e0b\u9762\u662f\u5b9e\u73b0\u4ee3\u7801\uff1a\u3001<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>bool Insert(const pair<K, V>& kv)\n{\n\tif (_root == nullptr)\n\t{\n\t\t_root = new Node(kv);\n\t\t_root->_col = BLACK;\n\n\t\treturn true;\n\t}\n\n\tNode* parent = nullptr;\n\tNode* cur = _root;\n\twhile (cur)\n\t{\n\t\tif (cur->_kv.first < kv.first)\n\t\t{\n\t\t\tparent = cur;\n\t\t\tcur = cur->_right;\n\t\t}\n\t\telse if (cur->_kv.first > kv.first)\n\t\t{\n\t\t\tparent = cur;\n\t\t\tcur = cur->_left;\n\t\t}\n\t\telse\n\t\t{\n\t\t\treturn false;\n\t\t}\n\t}\n\n\tcur = new Node(kv);\n\tcur->_col = RED;\n\tif (parent->_kv.first < kv.first)\n\t{\n\t\tparent->_right = cur;\n\t}\n\telse\n\t{\n\t\tparent->_left = cur;\n\t}\n\t\/\/ \u94fe\u63a5\u7236\u4eb2\n\tcur->_parent = parent;\n\n\t\/\/ \u7236\u4eb2\u662f\u7ea2\u8272\uff0c\u51fa\u73b0\u8fde\u7eed\u7684\u7ea2\u8272\u8282\u70b9\uff0c\u9700\u8981\u5904\u7406\n\twhile (parent && parent->_col == RED)\n\t{\n\t\tNode* grandfather = parent->_parent;\n\t\tif (parent == grandfather->_left)\n\t\t{\n\t\t\t\/\/   g\n\t\t\t\/\/ p   u\n\t\t\tNode* uncle = grandfather->_right;\n\t\t\tif (uncle && uncle->_col == RED)\n\t\t\t{\n\t\t\t\t\/\/ \u53d8\u8272\n\t\t\t\tparent->_col = uncle->_col = BLACK;\n\t\t\t\tgrandfather->_col = RED;\n\n\t\t\t\t\/\/ \u7ee7\u7eed\u5f80\u4e0a\u5904\u7406\n\t\t\t\tcur = grandfather;\n\t\t\t\tparent = cur->_parent;\n\t\t\t}\n\t\t\telse\n\t\t\t{\n\t\t\t\tif (cur == parent->_left)\n\t\t\t\t{\n\t\t\t\t\t\/\/     g\n\t\t\t\t\t\/\/   p    u\n\t\t\t\t\t\/\/ c\n\t\t\t\t\tRotateR(grandfather);\n\t\t\t\t\tparent->_col = BLACK;\n\t\t\t\t\tgrandfather->_col = RED;\n\t\t\t\t}\n\t\t\t\telse\n\t\t\t\t{\n\t\t\t\t\t\/\/      g\n\t\t\t\t\t\/\/   p    u\n\t\t\t\t\t\/\/     c\n\t\t\t\t\tRotateL(parent);\n\t\t\t\t\tRotateR(grandfather);\n\t\t\t\t\tcur->_col = BLACK;\n\t\t\t\t\tgrandfather->_col = RED;\n\t\t\t\t}\n\n\t\t\t\tbreak;\n\t\t\t}\n\t\t}\n\t\telse\n\t\t{\n\t\t\t\/\/   g\n\t\t\t\/\/ u   p\n\t\t\tNode* uncle = grandfather->_left;\n\t\t\t\/\/ \u53d4\u53d4\u5b58\u5728\u4e14\u4e3a\u7ea2\uff0c-\u300b\u53d8\u8272\u5373\u53ef\n\t\t\tif (uncle && uncle->_col == RED)\n\t\t\t{\n\t\t\t\tparent->_col = uncle->_col = BLACK;\n\t\t\t\tgrandfather->_col = RED;\n\n\t\t\t\t\/\/ \u7ee7\u7eed\u5f80\u4e0a\u5904\u7406\n\t\t\t\tcur = grandfather;\n\t\t\t\tparent = cur->_parent;\n\t\t\t}\n\t\t\telse \/\/ \u53d4\u53d4\u4e0d\u5b58\u5728\uff0c\u6216\u8005\u5b58\u5728\u4e14\u4e3a\u9ed1\n\t\t\t{\n\t\t\t\t\/\/ \u60c5\u51b5\u4e8c\uff1a\u53d4\u53d4\u4e0d\u5b58\u5728\u6216\u8005\u5b58\u5728\u4e14\u4e3a\u9ed1\n\t\t\t\t\/\/ \u65cb\u8f6c+\u53d8\u8272\n\t\t\t\t\/\/   g\n\t\t\t\t\/\/ u   p\n\t\t\t\t\/\/       c\n\t\t\t\tif (cur == parent->_right)\n\t\t\t\t{\n\t\t\t\t\tRotateL(grandfather);\n\t\t\t\t\tparent->_col = BLACK;\n\t\t\t\t\tgrandfather->_col = RED;\n\t\t\t\t}\n\t\t\t\telse\n\t\t\t\t{\n\t\t\t\t\tRotateR(parent);\n\t\t\t\t\tRotateL(grandfather);\n\t\t\t\t\tcur->_col = BLACK;\n\t\t\t\t\tgrandfather->_col = RED;\n\t\t\t\t}\n\n\t\t\t\tbreak;\n\t\t\t}\n\t\t}\n\t}\n\n\t_root->_col = BLACK;\n\n\treturn true;\n}<\/code><\/pre>\n\n\n\n<p>\u5176\u4f59\u4ee3\u7801\u4e0e\u535a\u4e3b\u4ee5\u524d\u7684\u6587\u7ae0AVL\u6811\u7684\u63d2\u5165\u4e00\u6837\u89c1<a href=\"http:\/\/120.76.99.214\/index.php\/2025\/07\/01\/%e5%b9%b3%e8%a1%a1%e4%ba%8c%e5%8f%89%e6%90%9c%e7%b4%a2%e6%a0%91%ef%bc%88avl%ef%bc%89\/\">http:\/\/120.76.99.214\/index.php\/2025\/07\/01\/%e5%b9%b3%e8%a1%a1%e4%ba%8c%e5%8f%89%e6%90%9c%e7%b4%a2%e6%a0%91%ef%bc%88avl%ef%bc%89\/<\/a><\/p>\n\n\n\n<p>\u6700\u540e\u662f\u6d4b\u8bd5\u4ee3\u7801\uff1a<\/p>\n\n\n\n<pre class=\"wp-block-code\"><code>define _CRT_SECURE_NO_WARNINGS 1\n\ninclude\n\ninclude\"RBTree.h\"\n\ninclude\"AVLTree.h\"\n\ninclude\n\ninclude \/\/ for rand() and srand()\n\ninclude \/\/ for time()\n\ninclude \/\/ for high_resolution_clock\n\nvector GenerateRandomData(int N) {\nvector v;\nv.reserve(N);\nfor (size_t i = 0; i < N; i++) { v.push_back(rand() + i); } return v; } using namespace std::chrono; void TestRBTree(const vector&#038; data) {\nRBTree t;\nauto start = high_resolution_clock::now();\nfor (int e : data) {\nt.Insert({ e, e });\n}\nauto stop = high_resolution_clock::now();\nauto duration = duration_cast(stop - start);\ncout << \"RBTree \u63d2\u5165 \" << data.size() << \" \u4e2a\u5143\u7d20\u7684\u65f6\u95f4: \" << duration.count() << \" \u6beb\u79d2\" << endl;\n}\n\nvoid TestAVLTree(const vector&#038; data) {\nAVLTree t;\nauto start = high_resolution_clock::now();\nfor (int e : data) {\nt.Insert({ e, e });\n}\nauto stop = high_resolution_clock::now();\nauto duration = duration_cast(stop - start);\ncout << \"AVLTree \u63d2\u5165 \" << data.size() << \" \u4e2a\u5143\u7d20\u7684\u65f6\u95f4: \" << duration.count() << \" \u6beb\u79d2\" << endl; } \/\/\/\/ \u63d2\u5165\u4e00\u5806\u968f\u673a\u503c\uff0c\u6d4b\u8bd5\u5e73\u8861\uff0c\u987a\u4fbf\u6d4b\u8bd5\u4e00\u4e0b\u9ad8\u5ea6\u548c\u6027\u80fd\u7b49 \/\/void TestAVLTree2() \/\/{ \/\/ size_t begin2 = clock(); \/\/ AVLTree t;\n\/\/ for (auto e : v)\n\/\/ {\n\/\/ t.Insert(make_pair(e, e));\n\/\/ }\n\/\/ size_t end2 = clock();\n\/\/\n\/\/ cout << \"Insert:\" << end2 - begin2 << endl; \/\/ cout << t.IsBalanceTree() << endl; \/\/ \/\/ cout << \"Height:\" << t.Height() << endl; \/\/ cout << \"Size:\" << t.Size() << endl; \/\/ \/\/ size_t begin1 = clock(); \/\/ \/\/ \u786e\u5b9a\u5728\u7684\u503c \/\/ for (auto e : v) \/\/ { \/\/ t.Find(e); \/\/ } \/\/ \/\/ \u968f\u673a\u503c \/\/ \/for (size_t i = 0; i < N; i++) \/\/ { \/\/ t.Find((rand() + i)); \/\/ }\/ \/\/ size_t end1 = clock(); \/\/ cout << \"Find:\" << end1 - begin1 << endl; \/\/} int main() { \/\/ \u521d\u59cb\u5316\u968f\u673a\u6570\u79cd\u5b50 srand(static_cast(time(0)));\n\n\/\/ \u751f\u6210\u968f\u673a\u6570\u636e\nconst int N = 1000000; \/\/ \u63d2\u5165\u6570\u91cf\nvector<int> data = GenerateRandomData(N);\nTestAVLTree(data);\nTestRBTree(data);\nreturn 0;\n\n}<\/code><\/pre>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"446\" height=\"47\" src=\"http:\/\/120.76.99.214\/wp-content\/uploads\/2025\/07\/image-18.png\" alt=\"\" class=\"wp-image-132\" srcset=\"https:\/\/www.tgwttt.xyz\/wp-content\/uploads\/2025\/07\/image-18.png 446w, https:\/\/www.tgwttt.xyz\/wp-content\/uploads\/2025\/07\/image-18-300x32.png 300w\" sizes=\"auto, (max-width: 446px) 100vw, 446px\" \/><\/figure>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"463\" height=\"56\" src=\"http:\/\/120.76.99.214\/wp-content\/uploads\/2025\/07\/image-19.png\" alt=\"\" class=\"wp-image-133\" srcset=\"https:\/\/www.tgwttt.xyz\/wp-content\/uploads\/2025\/07\/image-19.png 463w, https:\/\/www.tgwttt.xyz\/wp-content\/uploads\/2025\/07\/image-19-300x36.png 300w\" sizes=\"auto, (max-width: 463px) 100vw, 463px\" 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