{"id":1108,"date":"2018-04-17T20:02:36","date_gmt":"2018-04-17T12:02:36","guid":{"rendered":"https:\/\/damogame.cn:15443\/wordpress\/?p=1108"},"modified":"2018-04-17T20:02:36","modified_gmt":"2018-04-17T12:02:36","slug":"%e7%ba%a2%e9%bb%91%e6%a0%91","status":"publish","type":"post","link":"https:\/\/i007.cc\/wordpress\/archives\/1108","title":{"rendered":"\u7ea2\u9ed1\u6811"},"content":{"rendered":"<dl class=\"lemmaWgt-lemmaTitle lemmaWgt-lemmaTitle-\">\n<dd class=\"lemmaWgt-lemmaTitle-title\">\n<h1>\u7ea2\u9ed1\u6811<\/h1>\n<p><a class=\"lock-lemma\" title=\"\u9501\u5b9a\" href=\"https:\/\/baike.baidu.com\/view\/10812319.htm\" target=\"_blank\" rel=\"noopener\">\u9501\u5b9a<\/a><\/dd>\n<\/dl>\n<div class=\"authorityListPrompt\">\n<div class=\"main-content-zj\">\u672c\u8bcd\u6761\u7531<a class=\"nslog:7175\" href=\"http:\/\/www.cast.org.cn\/\" target=\"_blank\" rel=\"noopener\">\u201c\u79d1\u666e\u4e2d\u56fd\u201d\u767e\u79d1\u79d1\u5b66\u8bcd\u6761\u7f16\u5199\u4e0e\u5e94\u7528\u5de5\u4f5c\u9879\u76ee<\/a>\u00a0\u5ba1\u6838 \u3002<\/div>\n<\/div>\n<div class=\"lemma-summary\">\n<div class=\"para\">\u7ea2\u9ed1\u6811\uff08Red Black Tree\uff09 \u662f\u4e00\u79cd\u81ea\u5e73\u8861\u4e8c\u53c9\u67e5\u627e\u6811\uff0c\u662f\u5728<a href=\"https:\/\/baike.baidu.com\/item\/%E8%AE%A1%E7%AE%97%E6%9C%BA\" target=\"_blank\" rel=\"noopener\">\u8ba1\u7b97\u673a<\/a>\u79d1\u5b66\u4e2d\u7528\u5230\u7684\u4e00\u79cd<a href=\"https:\/\/baike.baidu.com\/item\/%E6%95%B0%E6%8D%AE%E7%BB%93%E6%9E%84\" target=\"_blank\" rel=\"noopener\">\u6570\u636e\u7ed3\u6784<\/a>\uff0c\u5178\u578b\u7684\u7528\u9014\u662f\u5b9e\u73b0<a href=\"https:\/\/baike.baidu.com\/item\/%E5%85%B3%E8%81%94%E6%95%B0%E7%BB%84\" target=\"_blank\" rel=\"noopener\">\u5173\u8054\u6570\u7ec4<\/a>\u3002<\/div>\n<div class=\"para\">\u5b83\u662f\u57281972\u5e74\u7531Rudolf Bayer\u53d1\u660e\u7684\uff0c\u5f53\u65f6\u88ab\u79f0\u4e3a\u5e73\u8861\u4e8c\u53c9B\u6811\uff08symmetric binary B-trees\uff09\u3002\u540e\u6765\uff0c\u57281978\u5e74\u88ab Leo J. Guibas \u548c Robert Sedgewick \u4fee\u6539\u4e3a\u5982\u4eca\u7684\u201c\u7ea2\u9ed1\u6811\u201d\u3002<\/div>\n<div class=\"para\">\u7ea2\u9ed1\u6811\u548cAVL\u6811\u7c7b\u4f3c\uff0c\u90fd\u662f\u5728\u8fdb\u884c\u63d2\u5165\u548c\u5220\u9664\u64cd\u4f5c\u65f6\u901a\u8fc7\u7279\u5b9a\u64cd\u4f5c\u4fdd\u6301\u4e8c\u53c9\u67e5\u627e\u6811\u7684\u5e73\u8861\uff0c\u4ece\u800c\u83b7\u5f97\u8f83\u9ad8\u7684\u67e5\u627e\u6027\u80fd\u3002<\/div>\n<div class=\"para\">\u5b83\u867d\u7136\u662f\u590d\u6742\u7684\uff0c\u4f46\u5b83\u7684\u6700\u574f\u60c5\u51b5\u8fd0\u884c\u65f6\u95f4\u4e5f\u662f\u975e\u5e38\u826f\u597d\u7684\uff0c\u5e76\u4e14\u5728\u5b9e\u8df5\u4e2d\u662f\u9ad8\u6548\u7684\uff1a \u5b83\u53ef\u4ee5\u5728O(log n)\u65f6\u95f4\u5185\u505a\u67e5\u627e\uff0c\u63d2\u5165\u548c\u5220\u9664\uff0c\u8fd9\u91cc\u7684n \u662f\u6811\u4e2d\u5143\u7d20\u7684\u6570\u76ee\u3002<\/div>\n<\/div>\n<div class=\"configModuleBanner\"><\/div>\n<div class=\"basic-info cmn-clearfix\">\n<dl class=\"basicInfo-block basicInfo-left\">\n<dt class=\"basicInfo-item name\">\u4e2d\u6587\u540d<\/dt>\n<dd class=\"basicInfo-item value\">\u7ea2\u9ed1\u6811<\/dd>\n<dt class=\"basicInfo-item name\">\u5916\u6587\u540d<\/dt>\n<dd class=\"basicInfo-item value\">RED BLACK TREE<\/dd>\n<dt class=\"basicInfo-item name\">\u6027\u00a0\u00a0\u00a0\u00a0\u8d28<\/dt>\n<dd class=\"basicInfo-item value\">\u81ea\u5e73\u8861\u4e8c\u53c9\u67e5\u627e\u6811<\/dd>\n<\/dl>\n<dl class=\"basicInfo-block basicInfo-right\">\n<dt class=\"basicInfo-item name\">\u7528\u00a0\u00a0\u00a0\u00a0\u9014<\/dt>\n<dd class=\"basicInfo-item value\">\u5b9e\u73b0<a href=\"https:\/\/baike.baidu.com\/item\/%E5%85%B3%E8%81%94%E6%95%B0%E7%BB%84\" target=\"_blank\" rel=\"noopener\">\u5173\u8054\u6570\u7ec4<\/a><\/dd>\n<dt class=\"basicInfo-item name\">\u53d1\u660e\u4eba<\/dt>\n<dd class=\"basicInfo-item value\">\u9c81\u9053\u592b\u00b7\u8d1d\u5c14<\/dd>\n<dt class=\"basicInfo-item name\">\u53d1\u660e\u65f6\u95f4<\/dt>\n<dd class=\"basicInfo-item value\">1972\u5e74<\/dd>\n<dt class=\"basicInfo-item name\">\u522b\u00a0\u00a0\u00a0\u00a0\u540d<\/dt>\n<dd class=\"basicInfo-item value\">\u5bf9\u79f0\u4e8c\u53c9B\u6811<\/dd>\n<\/dl>\n<\/div>\n<div class=\"lemmaWgt-lemmaCatalog\">\n<div class=\"lemma-catalog\">\n<h2 class=\"block-title\">\u76ee\u5f55<\/h2>\n<div class=\"catalog-list column-3\">\n<ol>\n<li class=\"level1\"><span class=\"index\">1<\/span>\u00a0<span class=\"text\"><a href=\"https:\/\/baike.baidu.com\/item\/%E7%BA%A2%E9%BB%91%E6%A0%91\/2413209#1\">\u6570\u636e\u7ed3\u6784<\/a><\/span><\/li>\n<li class=\"level1\"><span class=\"index\">2<\/span>\u00a0<span class=\"text\"><a href=\"https:\/\/baike.baidu.com\/item\/%E7%BA%A2%E9%BB%91%E6%A0%91\/2413209#2\">\u6811\u7684\u65cb\u8f6c<\/a><\/span><\/li>\n<\/ol>\n<ol>\n<li class=\"level1\"><span class=\"index\">3<\/span>\u00a0<span class=\"text\"><a href=\"https:\/\/baike.baidu.com\/item\/%E7%BA%A2%E9%BB%91%E6%A0%91\/2413209#3\">\u6027\u8d28<\/a><\/span><\/li>\n<li class=\"level1\"><span class=\"index\">4<\/span>\u00a0<span class=\"text\"><a href=\"https:\/\/baike.baidu.com\/item\/%E7%BA%A2%E9%BB%91%E6%A0%91\/2413209#4\">\u672f\u8bed<\/a><\/span><\/li>\n<\/ol>\n<ol>\n<li class=\"level1\"><span class=\"index\">5<\/span>\u00a0<span class=\"text\"><a href=\"https:\/\/baike.baidu.com\/item\/%E7%BA%A2%E9%BB%91%E6%A0%91\/2413209#5\">\u7528\u9014<\/a><\/span><\/li>\n<li class=\"level1\"><span class=\"index\">6<\/span>\u00a0<span class=\"text\"><a href=\"https:\/\/baike.baidu.com\/item\/%E7%BA%A2%E9%BB%91%E6%A0%91\/2413209#6\">\u64cd\u4f5c<\/a><\/span><\/li>\n<\/ol>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"anchor-list\"><a class=\"lemma-anchor para-title\" name=\"1\"><\/a><a class=\"lemma-anchor \" name=\"sub133754_1\"><\/a><a class=\"lemma-anchor \" name=\"\u6570\u636e\u7ed3\u6784\"><\/a><\/div>\n<div class=\"para-title level-2\">\n<h2 class=\"title-text\">\u6570\u636e\u7ed3\u6784<\/h2>\n<\/div>\n<div class=\"para\">\u5b83\u7684\u7edf\u8ba1\u6027\u80fd\u8981\u597d\u4e8e<a href=\"https:\/\/baike.baidu.com\/item\/%E5%B9%B3%E8%A1%A1%E4%BA%8C%E5%8F%89%E6%A0%91\" target=\"_blank\" rel=\"noopener\">\u5e73\u8861\u4e8c\u53c9\u6811<\/a>(\u6709\u4e9b\u4e66\u7c4d\u6839<\/p>\n<div class=\"lemma-picture text-pic layout-right\"><a class=\"image-link\" title=\"\u7ea2\u9ed1\u6811\" href=\"https:\/\/baike.baidu.com\/pic\/%E7%BA%A2%E9%BB%91%E6%A0%91\/2413209\/0\/8cf0d513af89ac60dc540106?fr=lemma&amp;ct=single\" target=\"_blank\" rel=\"noopener\"><img decoding=\"async\" class=\"\" src=\"https:\/\/gss2.bdstatic.com\/-fo3dSag_xI4khGkpoWK1HF6hhy\/baike\/s%3D250\/sign=d00e707ab6003af349badb65052bc619\/e4dde71190ef76c641326b589d16fdfaae5167e5.jpg\" alt=\"\u7ea2\u9ed1\u6811\" \/><\/a><span class=\"description\">\u7ea2\u9ed1\u6811<\/span><\/div>\n<p>\u636e\u4f5c\u8005\u59d3\u540d\uff0cAdelson-Velskii\u548cLandis\uff0c\u5c06\u5176\u79f0\u4e3aAVL-\u6811)\uff0c\u56e0\u6b64\uff0c\u7ea2\u9ed1\u6811\u5728\u5f88\u591a\u5730\u65b9\u90fd\u6709\u5e94\u7528\u3002\u5728C++ STL\u4e2d\uff0c\u5f88\u591a\u90e8\u5206(\u5305\u62ecset, multiset, map, multimap)\u5e94\u7528\u4e86\u7ea2\u9ed1\u6811\u7684\u53d8\u4f53(SGI STL\u4e2d\u7684\u7ea2\u9ed1\u6811\u6709\u4e00\u4e9b\u53d8\u5316\uff0c\u8fd9\u4e9b\u4fee\u6539\u63d0\u4f9b\u4e86\u66f4\u597d\u7684\u6027\u80fd\uff0c\u4ee5\u53ca\u5bf9set\u64cd\u4f5c\u7684\u652f\u6301)\u3002\u5176\u4ed6<a href=\"https:\/\/baike.baidu.com\/item\/%E5%B9%B3%E8%A1%A1%E6%A0%91\" target=\"_blank\" rel=\"noopener\">\u5e73\u8861\u6811<\/a>\u8fd8\u6709\uff1a<a href=\"https:\/\/baike.baidu.com\/item\/AVL\" target=\"_blank\" rel=\"noopener\">AVL<\/a>\uff0c<a href=\"https:\/\/baike.baidu.com\/item\/SBT\" target=\"_blank\" rel=\"noopener\">SBT<\/a>\uff0c<a href=\"https:\/\/baike.baidu.com\/item\/%E4%BC%B8%E5%B1%95%E6%A0%91\" target=\"_blank\" rel=\"noopener\">\u4f38\u5c55\u6811<\/a>\uff0c<a href=\"https:\/\/baike.baidu.com\/item\/TREAP\" target=\"_blank\" rel=\"noopener\">TREAP<\/a>\u00a0\u7b49\u7b49\u3002<\/div>\n<div class=\"anchor-list\"><a class=\"lemma-anchor para-title\" name=\"2\"><\/a><a class=\"lemma-anchor \" name=\"sub133754_2\"><\/a><a class=\"lemma-anchor \" name=\"\u6811\u7684\u65cb\u8f6c\"><\/a><\/div>\n<div class=\"para-title level-2\">\n<h2 class=\"title-text\">\u6811\u7684\u65cb\u8f6c<\/h2>\n<\/div>\n<div class=\"para\">\u5f53\u6211\u4eec\u5728\u5bf9\u7ea2\u9ed1\u6811\u8fdb\u884c\u63d2\u5165\u548c\u5220\u9664\u7b49\u64cd\u4f5c\u65f6\uff0c\u5bf9\u6811\u505a\u4e86\u4fee\u6539\uff0c\u90a3\u4e48\u53ef\u80fd\u4f1a\u8fdd\u80cc\u7ea2\u9ed1\u6811\u7684\u6027<\/p>\n<div class=\"album-wrap\"><img decoding=\"async\" class=\"picture\" src=\"https:\/\/gss1.bdstatic.com\/-vo3dSag_xI4khGkpoWK1HF6hhy\/baike\/s%3D220\/sign=ea3c202d46a7d933bba8e3719d4ad194\/86d6277f9e2f0708cdb73039ed24b899a901f25d.jpg\" alt=\"\u6811\u7684\u5de6\u65cb\" \/><\/div>\n<div class=\"description\">\u6811\u7684\u5de6\u65cb<span class=\"number\">(2\u5f20)<\/span><\/div>\n<div class=\"albumBg\">\n<div class=\"albumBgFir\"><\/div>\n<div class=\"albumBgSec\"><\/div>\n<\/div>\n<p>\u8d28\u3002<\/p><\/div>\n<div class=\"para\">\u4e3a\u4e86\u4fdd\u6301\u7ea2\u9ed1\u6811\u7684\u6027\u8d28\uff0c\u6211\u4eec\u53ef\u4ee5\u901a\u8fc7\u5bf9\u6811\u8fdb\u884c\u65cb\u8f6c\uff0c\u5373\u4fee\u6539\u6811\u4e2d\u67d0\u4e9b\u7ed3\u70b9\u7684\u989c\u8272\u53ca\u6307\u9488\u7ed3\u6784\uff0c\u4ee5\u8fbe\u5230\u5bf9\u7ea2\u9ed1\u6811\u8fdb\u884c\u63d2\u5165\u3001\u5220\u9664\u7ed3\u70b9\u7b49\u64cd\u4f5c\u65f6\uff0c\u7ea2\u9ed1\u6811\u4f9d\u7136\u80fd\u4fdd\u6301\u5b83\u7279\u6709\u7684\u6027\u8d28\uff08\u4e94\u70b9\u6027\u8d28\uff09\u3002<\/div>\n<div class=\"para\">\u5982\u53f3\u56fe\u3002<\/div>\n<div class=\"anchor-list\"><a class=\"lemma-anchor para-title\" name=\"3\"><\/a><a class=\"lemma-anchor \" name=\"sub133754_3\"><\/a><a class=\"lemma-anchor \" name=\"\u6027\u8d28\"><\/a><\/div>\n<div class=\"para-title level-2\">\n<h2 class=\"title-text\">\u6027\u8d28<\/h2>\n<\/div>\n<div class=\"para\">\u7ea2\u9ed1\u6811\u662f\u6bcf\u4e2a\u8282\u70b9\u90fd\u5e26\u6709\u989c\u8272\u5c5e\u6027\u7684\u4e8c\u53c9\u67e5\u627e\u6811\uff0c\u989c\u8272\u6216\u7ea2\u8272\u6216\u9ed1\u8272\u3002\u5728\u4e8c\u53c9\u67e5\u627e\u6811\u5f3a\u5236\u4e00\u822c\u8981\u6c42\u4ee5\u5916\uff0c\u5bf9\u4e8e\u4efb\u4f55\u6709\u6548\u7684\u7ea2\u9ed1\u6811\u6211\u4eec\u589e\u52a0\u4e86\u5982\u4e0b\u7684\u989d\u5916\u8981\u6c42:<\/div>\n<div class=\"para\">\u6027\u8d281. \u8282\u70b9\u662f\u7ea2\u8272\u6216\u9ed1\u8272\u3002<\/div>\n<div class=\"para\">\u6027\u8d282. \u6839\u8282\u70b9\u662f\u9ed1\u8272\u3002<\/div>\n<div class=\"para\">\u6027\u8d283 \u6bcf\u4e2a\u53f6\u8282\u70b9\uff08NIL\u8282\u70b9\uff0c\u7a7a\u8282\u70b9\uff09\u662f\u9ed1\u8272\u7684\u3002<\/div>\n<div class=\"para\">\u6027\u8d284 \u6bcf\u4e2a\u7ea2\u8272\u8282\u70b9\u7684\u4e24\u4e2a\u5b50\u8282\u70b9\u90fd\u662f\u9ed1\u8272\u3002(\u4ece\u6bcf\u4e2a\u53f6\u5b50\u5230\u6839\u7684\u6240\u6709\u8def\u5f84\u4e0a\u4e0d\u80fd\u6709\u4e24\u4e2a\u8fde\u7eed\u7684\u7ea2\u8272\u8282\u70b9)<\/div>\n<div class=\"para\">\u6027\u8d285. \u4ece\u4efb\u4e00\u8282\u70b9\u5230\u5176\u6bcf\u4e2a\u53f6\u5b50\u7684\u6240\u6709\u8def\u5f84\u90fd\u5305\u542b\u76f8\u540c\u6570\u76ee\u7684\u9ed1\u8272\u8282\u70b9\u3002<\/div>\n<div class=\"para\">\u8fd9\u4e9b\u7ea6\u675f\u5f3a\u5236\u4e86\u7ea2\u9ed1\u6811\u7684\u5173\u952e\u6027\u8d28: \u4ece\u6839\u5230\u53f6\u5b50\u7684\u6700\u957f\u7684\u53ef\u80fd\u8def\u5f84\u4e0d\u591a\u4e8e\u6700\u77ed\u7684\u53ef\u80fd\u8def\u5f84\u7684\u4e24\u500d\u957f\u3002\u7ed3\u679c\u662f\u8fd9\u4e2a\u6811\u5927\u81f4\u4e0a\u662f\u5e73\u8861\u7684\u3002\u56e0\u4e3a\u64cd\u4f5c\u6bd4\u5982\u63d2\u5165\u3001\u5220\u9664\u548c\u67e5\u627e\u67d0\u4e2a\u503c\u7684\u6700\u574f\u60c5\u51b5\u65f6\u95f4\u90fd\u8981\u6c42\u4e0e\u6811\u7684\u9ad8\u5ea6\u6210\u6bd4\u4f8b\uff0c\u8fd9\u4e2a\u5728\u9ad8\u5ea6\u4e0a\u7684\u7406\u8bba\u4e0a\u9650\u5141\u8bb8\u7ea2\u9ed1\u6811\u5728\u6700\u574f\u60c5\u51b5\u4e0b\u90fd\u662f\u9ad8\u6548\u7684\uff0c\u800c\u4e0d\u540c\u4e8e\u666e\u901a\u7684\u4e8c\u53c9\u67e5\u627e\u6811\u3002<\/div>\n<div class=\"para\">\u8981\u77e5\u9053\u4e3a\u4ec0\u4e48\u8fd9\u4e9b\u7279\u6027\u786e\u4fdd\u4e86\u8fd9\u4e2a\u7ed3\u679c\uff0c\u6ce8\u610f\u5230\u6027\u8d284\u5bfc\u81f4\u4e86\u8def\u5f84\u4e0d\u80fd\u6709\u4e24\u4e2a\u6bd7\u8fde\u7684\u7ea2\u8272\u8282\u70b9\u5c31\u8db3\u591f\u4e86\u3002\u6700\u77ed\u7684\u53ef\u80fd\u8def\u5f84\u90fd\u662f\u9ed1\u8272\u8282\u70b9\uff0c\u6700\u957f\u7684\u53ef\u80fd\u8def\u5f84\u6709\u4ea4\u66ff\u7684\u7ea2\u8272\u548c\u9ed1\u8272\u8282\u70b9\u3002\u56e0\u4e3a\u6839\u636e\u6027\u8d285\u6240\u6709\u6700\u957f\u7684\u8def\u5f84\u90fd\u6709\u76f8\u540c\u6570\u76ee\u7684\u9ed1\u8272\u8282\u70b9\uff0c\u8fd9\u5c31\u8868\u660e\u4e86\u6ca1\u6709\u8def\u5f84\u80fd\u591a\u4e8e\u4efb\u4f55\u5176\u4ed6\u8def\u5f84\u7684\u4e24\u500d\u957f\u3002<\/div>\n<div class=\"para\">\u5728\u5f88\u591a\u6811<a href=\"https:\/\/baike.baidu.com\/item\/%E6%95%B0%E6%8D%AE%E7%BB%93%E6%9E%84\" target=\"_blank\" rel=\"noopener\">\u6570\u636e\u7ed3\u6784<\/a>\u7684\u8868\u793a\u4e2d\uff0c\u4e00\u4e2a\u8282\u70b9\u6709\u53ef\u80fd\u53ea\u6709\u4e00\u4e2a\u5b50\u8282\u70b9\uff0c\u800c<a href=\"https:\/\/baike.baidu.com\/item\/%E5%8F%B6%E5%AD%90%E8%8A%82%E7%82%B9\" target=\"_blank\" rel=\"noopener\">\u53f6\u5b50\u8282\u70b9<\/a>\u4e0d\u5305\u542b\u6570\u636e\u3002\u7528\u8fd9\u79cd\u8303\u4f8b\u8868\u793a\u7ea2\u9ed1\u6811\u662f\u53ef\u80fd\u7684\uff0c\u4f46\u662f\u8fd9\u4f1a\u6539\u53d8\u4e00\u4e9b\u5c5e\u6027\u5e76\u4f7f\u7b97\u6cd5\u590d\u6742\u3002\u4e3a\u6b64\uff0c\u672c\u6587\u4e2d\u6211\u4eec\u4f7f\u7528 &#8220;nil \u53f6\u5b50&#8221; 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class=\"para\">\u7ea2\u9ed1\u6811\u662f\u4e00\u79cd\u7279\u5b9a\u7c7b\u578b\u7684<a href=\"https:\/\/baike.baidu.com\/item\/%E4%BA%8C%E5%8F%89%E6%A0%91\" target=\"_blank\" rel=\"noopener\">\u4e8c\u53c9\u6811<\/a>\uff0c\u5b83\u662f\u5728\u8ba1\u7b97\u673a\u79d1\u5b66\u4e2d\u7528\u6765\u7ec4\u7ec7\u6570\u636e\u6bd4\u5982\u6570\u5b57\u7684\u5757\u7684\u4e00\u79cd\u7ed3\u6784\u3002\u6240\u6709<a href=\"https:\/\/baike.baidu.com\/item\/%E6%95%B0%E6%8D%AE%E5%9D%97\" target=\"_blank\" rel=\"noopener\">\u6570\u636e\u5757<\/a>\u90fd\u5b58\u50a8\u5728<a href=\"https:\/\/baike.baidu.com\/item\/%E8%8A%82%E7%82%B9\" target=\"_blank\" rel=\"noopener\">\u8282\u70b9<\/a>\u4e2d\u3002\u8fd9\u4e9b\u8282\u70b9\u4e2d\u7684\u67d0\u4e00\u4e2a\u8282\u70b9\u603b\u662f\u62c5\u5f53\u8d77\u59cb\u4f4d\u7f6e\u7684\u529f\u80fd\uff0c\u5b83\u4e0d\u662f\u4efb\u4f55\u8282\u70b9\u7684\u513f\u5b50\uff0c\u6211\u4eec\u79f0\u4e4b\u4e3a\u6839\u8282\u70b9\u6216\u6839\u3002\u5b83\u6709\u6700\u591a\u4e24\u4e2a&#8221;\u513f\u5b50&#8221;\uff0c\u90fd\u662f\u5b83\u8fde\u63a5\u5230\u7684\u5176\u4ed6\u8282\u70b9\u3002\u6240\u6709\u8fd9\u4e9b\u513f\u5b50\u90fd\u53ef\u4ee5\u6709\u81ea\u5df1\u7684\u513f\u5b50\uff0c\u4ee5\u6b64\u7c7b\u63a8\u3002\u8fd9\u6837\u6839\u8282\u70b9\u5c31\u6709\u4e86\u628a\u5b83\u8fde\u63a5\u5230\u5728\u6811\u4e2d\u4efb\u4f55\u5176\u4ed6\u8282\u70b9\u7684\u8def\u5f84\u3002<\/div>\n<div class=\"para\">\u5982\u679c\u4e00\u4e2a\u8282\u70b9\u6ca1\u6709\u513f\u5b50\uff0c\u6211\u4eec\u79f0\u4e4b\u4e3a<a href=\"https:\/\/baike.baidu.com\/item\/%E5%8F%B6%E5%AD%90%E8%8A%82%E7%82%B9\" target=\"_blank\" rel=\"noopener\">\u53f6\u5b50\u8282\u70b9<\/a>\uff0c\u56e0\u4e3a\u5728\u76f4\u89c9\u4e0a\u5b83\u662f\u5728\u6811\u7684\u8fb9\u7f18\u4e0a\u3002\u5b50\u6811\u662f\u4ece\u7279\u5b9a<a href=\"https:\/\/baike.baidu.com\/item\/%E8%8A%82%E7%82%B9\" target=\"_blank\" rel=\"noopener\">\u8282\u70b9<\/a>\u53ef\u4ee5\u5ef6\u4f38\u5230\u7684\u6811\u7684\u67d0\u4e00\u90e8\u5206\uff0c\u5176\u81ea\u8eab\u88ab\u5f53\u4f5c\u4e00\u4e2a\u6811\u3002\u5728\u7ea2\u9ed1\u6811\u4e2d\uff0c\u53f6\u5b50\u88ab\u5047\u5b9a\u4e3a null \u6216\u7a7a\u3002<\/div>\n<div class=\"para\">\u7531\u4e8e\u7ea2\u9ed1\u6811\u4e5f\u662f\u4e8c\u53c9\u67e5\u627e\u6811\uff0c\u5b83\u4eec\u5f53\u4e2d\u6bcf\u4e00\u4e2a\u8282\u70b9\u7684\u6bd4\u8f83\u503c\u90fd\u5fc5\u987b\u5927\u4e8e\u6216\u7b49\u4e8e\u5728\u5b83\u7684\u5de6\u5b50\u6811\u4e2d\u7684\u6240\u6709\u8282\u70b9\uff0c\u5e76\u4e14\u5c0f\u4e8e\u6216\u7b49\u4e8e\u5728\u5b83\u7684\u53f3\u5b50\u6811\u4e2d\u7684\u6240\u6709\u8282\u70b9\u3002\u8fd9\u786e\u4fdd\u7ea2\u9ed1\u6811\u8fd0\u4f5c\u65f6\u80fd\u591f\u5feb\u901f\u7684\u5728\u6811\u4e2d\u67e5\u627e\u7ed9\u5b9a\u7684\u503c\u3002<\/div>\n<div class=\"anchor-list\"><a class=\"lemma-anchor para-title\" name=\"5\"><\/a><a class=\"lemma-anchor \" name=\"sub133754_5\"><\/a><a class=\"lemma-anchor \" name=\"\u7528\u9014\"><\/a><\/div>\n<div class=\"para-title level-2\">\n<h2 class=\"title-text\">\u7528\u9014<\/h2>\n<\/div>\n<div class=\"para\">\u7ea2\u9ed1\u6811\u548cAVL\u6811\u4e00\u6837\u90fd\u5bf9\u63d2\u5165\u65f6\u95f4\u3001\u5220\u9664\u65f6\u95f4\u548c\u67e5\u627e\u65f6\u95f4\u63d0\u4f9b\u4e86\u6700\u597d\u53ef\u80fd\u7684\u6700\u574f\u60c5\u51b5\u62c5\u4fdd\u3002\u8fd9\u4e0d\u53ea\u662f\u4f7f\u5b83\u4eec\u5728\u65f6\u95f4\u654f\u611f\u7684\u5e94\u7528\u5982\u5373\u65f6\u5e94\u7528(real time application)\u4e2d\u6709\u4ef7\u503c\uff0c\u800c\u4e14\u4f7f\u5b83\u4eec\u6709\u5728\u63d0\u4f9b\u6700\u574f\u60c5\u51b5\u62c5\u4fdd\u7684\u5176\u4ed6<a href=\"https:\/\/baike.baidu.com\/item\/%E6%95%B0%E6%8D%AE%E7%BB%93%E6%9E%84\" target=\"_blank\" rel=\"noopener\">\u6570\u636e\u7ed3\u6784<\/a>\u4e2d\u4f5c\u4e3a\u5efa\u9020\u677f\u5757\u7684\u4ef7\u503c\uff1b\u4f8b\u5982\uff0c\u5728\u8ba1\u7b97\u51e0\u4f55\u4e2d\u4f7f\u7528\u7684\u5f88\u591a\u6570\u636e\u7ed3\u6784\u90fd\u53ef\u4ee5\u57fa\u4e8e\u7ea2\u9ed1\u6811\u3002<\/div>\n<div class=\"para\">\u7ea2\u9ed1\u6811\u5728<a href=\"https:\/\/baike.baidu.com\/item\/%E5%87%BD%E6%95%B0\" target=\"_blank\" rel=\"noopener\">\u51fd\u6570<\/a>\u5f0f<a href=\"https:\/\/baike.baidu.com\/item\/%E7%BC%96%E7%A8%8B\" target=\"_blank\" rel=\"noopener\">\u7f16\u7a0b<\/a>\u4e2d\u4e5f\u7279\u522b\u6709\u7528\uff0c\u5728\u8fd9\u91cc\u5b83\u4eec\u662f\u6700\u5e38\u7528\u7684\u6301\u4e45<a href=\"https:\/\/baike.baidu.com\/item\/%E6%95%B0%E6%8D%AE%E7%BB%93%E6%9E%84\" target=\"_blank\" rel=\"noopener\">\u6570\u636e\u7ed3\u6784<\/a>\u4e4b\u4e00\uff0c\u5b83\u4eec\u7528\u6765\u6784\u9020<a href=\"https:\/\/baike.baidu.com\/item\/%E5%85%B3%E8%81%94%E6%95%B0%E7%BB%84\" target=\"_blank\" rel=\"noopener\">\u5173\u8054\u6570\u7ec4<\/a>\u548c\u96c6\u5408\uff0c\u5728\u7a81\u53d8\u4e4b\u540e\u5b83\u4eec\u80fd\u4fdd\u6301\u4e3a\u4ee5\u524d\u7684\u7248\u672c\u3002\u9664\u4e86O(log n)\u7684\u65f6\u95f4\u4e4b\u5916\uff0c\u7ea2\u9ed1\u6811\u7684\u6301\u4e45\u7248\u672c\u5bf9\u6bcf\u6b21\u63d2\u5165\u6216\u5220\u9664\u9700\u8981O(log 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