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1<\/strong> <\/strong><\/a>\u4e8c\u53c9\u6392\u5e8f\u6811\uff08BST\uff09<\/strong><\/p>\n\n\n\n1.1 <\/strong>\u5b9a\u4e49<\/strong><\/strong><\/p>\n\n\n\n\u4e8c\u53c9\u6392\u5e8f\u6811\uff08Binary Sort 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>\n<\/figure><\/noscript>\n\n\n\n1.4 <\/strong>\u4e8c\u53c9\u6392\u5e8f\u6811\u7684\u67e5\u627e\u6548\u7387<\/strong><\/strong><\/p>\n\n\n\n\u4e8c\u53c9\u6392\u5e8f\u6811\u7684\u67e5\u627e\u6548\u7387\u4e3b\u8981\u53d6\u51b3\u4e8e\u6811\u7684\u9ad8\u5ea6\u3002\u82e5\u6784\u9020\u4e8c\u53c9\u6392\u5e8f\u6811\u7684\u8f93\u5165\u5e8f\u5217\u8d8a\u63a5\u8fd1\u6709\u5e8f\uff0c\u5219\u4e8c\u53c9\u6392\u5e8f\u6811\u7684\u67e5\u627e\u6548\u7387\u8d8a\u5dee\uff08\u56e0\u4e3a\u6784\u9020\u51fa\u7684\u4e8c\u53c9\u6392\u5e8f\u6811\u7684\u9ad8\u5ea6\u8d8a\u9ad8\uff09\u3002<\/p>\n\n\n\n\u6781\u7aef\u60c5\u51b5\u4e0b\uff0c\u4e8c\u53c9\u6392\u5e8f\u6811\u662f\u4e00\u4e2a\u53ea\u6709\u5de6\u5b69\u5b50\u6216\u53f3\u5b69\u5b50\u7684\u5355\u652f\u6811\uff0c\u6b64\u65f6\u6811\u7684\u9ad8\u5ea6\u6700\u9ad8\u4e14\u7b49\u4e8e\u603b\u7ed3\u70b9\u6570\uff0c\u67e5\u627e\u6027\u80fd\u6700\u5dee\u3002<\/p>\n\n\n\n<\/figure >\n<\/figure><\/noscript>\n\n\n\n\u5982\u4e0a\u56fe\u6240\u793a\uff0c\u4e24\u68f5\u6811\u7684\u5e73\u5747\u67e5\u627e\u957f\u5ea6\u4e3a\uff1a<\/p>\n\n\n\n<\/figure >\n<\/figure><\/noscript>\n\n\n\n\u56e0\u6b64\uff0c\u4e3a\u907f\u514d\u6811\u7684\u9ad8\u5ea6\u589e\u957f\u8fc7\u5feb\uff0c\u964d\u4f4e\u4e8c\u53c9\u6392\u5e8f\u6811\u7684\u6027\u80fd\uff0c\u4fbf\u63d0\u51fa\u4e86\u5e73\u8861\u4e8c\u53c9\u6811<\/strong>\uff0c\u5e73\u8861\u4e8c\u53c9\u6811\u7684\u5e73\u5747\u67e5\u627e\u957f\u5ea6\u4e3aO<\/em>(log<\/em>2\u200bn<\/em>)\uff0c\u5176\u4e2dn\u4e3a\u8282\u70b9\u6570\u3002<\/p>\n\n\n\n2 <\/strong>\u5e73\u8861\u4e8c\u53c9\u6811\uff08AVL\uff09<\/strong><\/strong><\/p>\n\n\n\n\u5e73\u8861\u4e8c\u53c9\u6811<\/strong>\uff08Balanced Binary Tree\uff09\uff0c\u4e3a\u907f\u514d\u6811\u7684\u9ad8\u5ea6\u589e\u957f\u8fc7\u5feb\uff0c\u964d\u4f4e\u4e8c\u53c9\u6392\u5e8f\u6811\u7684\u6027\u80fd\uff0c\u89c4\u5b9a\u5728\u63d2\u5165\u548c\u5220\u9664\u4e8c\u53c9\u6811\u8282\u70b9\u65f6\uff0c\u4fdd\u8bc1\u8282\u70b9\u5de6\u3001\u53f3\u5b50\u6811\u9ad8\u5ea6\u5dee\u7684\u7edd\u5bf9\u503c\u4e0d\u8d85\u8fc71\uff08-1\u30010\u30011\uff09\uff0c\u5c06\u8fd9\u6837\u7684\u4e8c\u53c9\u6811\u6210\u4e3a\u5e73\u8861\u4e8c\u53c9\u6811\u3002\u53c8\u79f0AVL<\/strong>\u6811<\/strong>\uff0cAVL\u6811\u5f97\u540d\u4e8e\u5b83\u7684\u53d1\u660e\u8005G. M. Adelson-Velsky<\/strong>\u548cE. M. Landis<\/strong>\uff0c\u4ed6\u4eec\u57281962\u5e74\u7684\u8bba\u6587\u300aAn algorithm for the organization of information\u300b\u4e2d\u53d1\u8868\u4e86\u5b83\u3002<\/p>\n\n\n\n\u5e73\u8861\u56e0\u5b50\uff1a\u8282\u70b9\u5de6\u5b50\u6811\u548c\u53f3\u5b50\u6811\u7684\u9ad8\u5ea6\u5dee\uff0c\u5373\u5e73\u8861\u56e0\u5b50 = \u5de6\u5b50\u6811\u9ad8\u5ea6 - \u53f3\u5b50\u6811\u9ad8\u5ea6\uff0c\u5219\u7531\u5e73\u8861\u4e8c\u53c9\u6811\u5b9a\u4e49\u53ef\u77e5\uff0c\u8282\u70b9\u7684\u5e73\u8861\u56e0\u5b50\u53d6\u503c\u53ea\u80fd\u4e3a-1\u30010\u30011\u3002<\/p>\n\n\n\n2.1 <\/strong>\u5e73\u8861\u4e8c\u53c9\u6811\u7684\u63d2\u5165<\/strong><\/strong><\/p>\n\n\n\n1 LL<\/strong>\u5e73\u8861\u65cb\u8f6c\uff08\u53f3\u5355\u65cb\u8f6c\uff09<\/strong><\/strong><\/p>\n\n\n\n\u6b64\u79cd\u65b9\u5f0f\u5728\u67d0\u8282\u70b9\u5de6\u5b69\u5b50\uff08L\uff09\u7684\u5de6\u5b50\u6811\uff08L\uff09\u4e0a\u63d2\u5165\u65b0\u8282\u70b9\uff0c\u6545\u540d\u4e3aLL\u578b\u3002<\/p>\n\n\n\n\u5982\u56fe\u6240\u793a\uff0c\u5728\u8282\u70b94\u7684\u5de6\u5b69\u5b502\u7684\u5de6\u5b50\u68111\uff0c\u63d2\u5165\u65b0\u8282\u70b90\u3002\u8282\u70b94\u7684\u5e73\u8861\u56e0\u5b50\u75311\u53d8\u4e3a2\uff08\u5de6\u5b50\u6811\u9ad8\u5ea6\u589e\u52a0\uff09\uff0c\u6545\u8981\u53f3\u65cb\uff08\u9ad8\u5ea6\u4f4e\u7684\u5411\u4e0b\u53bb\uff09\u4ee5\u5e73\u8861\u5b50\u6811\u3002<\/p>\n\n\n\n\u89e3\u51b3\u65b9\u6cd5\uff1a<\/p>\n\n\n\n\n\u8282\u70b94\u53f3\u4e0b\u65cb\u8f6c\u6210\u4e3a2\u7684\u53f3\u5b50\u6811\uff082\u7684\u53f3\u5b50\u6811\u88ab\u66ff\u4ee3\uff0c4\u7684\u5de6\u5b50\u6811\u53d8\u7a7a\uff09\u3002<\/li>\n\n\n\n\u8282\u70b92\u7684\u539f\u53f3\u5b50\u6811\u6210\u4e3a4\u7684\u5de6\u5b50\u6811\uff082\u7684\u539f\u53f3\u5b50\u6811\u8865\u4e0a4\u7684\u7a7a\u5de6\u5b50\u6811\uff09\u3002<\/li>\n<\/ul>\n\n\n\n<\/figure >\n<\/figure><\/noscript>\n\n\n\nQ\uff1a\u82e5\u662f\u5728\u4e0a\u56fe\u4e2d1\u7684\u53f3\u4fa7\u63d2\u5165\u4e00\u4e2a\u7ed3\u70b9\u53c8\u8be5\u600e\u6837\u64cd\u4f5c\u5462\uff1fA\uff1a\u63d2\u5165\u57281\u53f3\u4fa7\u7684\u8282\u70b9\uff0c\u540c\u65f6\u53c8\u57282\u7684\u5de6\u4fa7\uff081<\u65b0\u8282\u70b9\u503c<2\uff09\uff0c\u7531\u4e8e\u662f\u987a\u5e8f\u6811\uff0c\u52194\u7ecf\u8fc7\u65cb\u8f6c\u540e\u65b0\u8282\u70b9\u6700\u7ec8\u4f4d\u7f6e\u4ecd\u5e94\u57281\u53f3\u4fa7\u30012\u5de6\u4fa7\uff0c\u65cb\u8f6c\u540e\u8282\u70b9\u987a\u5e8f\u4e0d\u53d8\uff08\u65b0\u8282\u70b9\u4ecd\u57281\u53f3\u4fa7\u30012\u5de6\u4fa7\uff09\uff0c\u6240\u4ee5\u65e0\u8bba\u5728\u5de6\u4fa7\u548c\u53f3\u4fa7\u63d2\u5165\uff0c\u64cd\u4f5c\u6b65\u9aa4\u4e0d\u53d8\u3002<\/p>\n\n\n\n2 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Tree\uff09\uff0c\u4e3a\u907f\u514d\u6811\u7684\u9ad8\u5ea6\u589e\u957f\u8fc7\u5feb\uff0c\u964d\u4f4e\u4e8c\u53c9\u6392\u5e8f\u6811\u7684\u6027\u80fd\uff0c\u89c4\u5b9a\u5728\u63d2\u5165\u548c\u5220\u9664\u4e8c\u53c9\u6811\u8282\u70b9\u65f6\uff0c\u4fdd\u8bc1\u8282\u70b9\u5de6\u3001\u53f3\u5b50\u6811\u9ad8\u5ea6\u5dee\u7684\u7edd\u5bf9\u503c\u4e0d\u8d85\u8fc71\uff08-1\u30010\u30011\uff09\uff0c\u5c06\u8fd9\u6837\u7684\u4e8c\u53c9\u6811\u6210\u4e3a\u5e73\u8861\u4e8c\u53c9\u6811\u3002\u53c8\u79f0AVL<\/strong>\u6811<\/strong>\uff0cAVL\u6811\u5f97\u540d\u4e8e\u5b83\u7684\u53d1\u660e\u8005G. M. Adelson-Velsky<\/strong>\u548cE. M. Landis<\/strong>\uff0c\u4ed6\u4eec\u57281962\u5e74\u7684\u8bba\u6587\u300aAn algorithm for the organization of information\u300b\u4e2d\u53d1\u8868\u4e86\u5b83\u3002<\/p>\n\n\n\n\u5e73\u8861\u56e0\u5b50\uff1a\u8282\u70b9\u5de6\u5b50\u6811\u548c\u53f3\u5b50\u6811\u7684\u9ad8\u5ea6\u5dee\uff0c\u5373\u5e73\u8861\u56e0\u5b50 = \u5de6\u5b50\u6811\u9ad8\u5ea6 - \u53f3\u5b50\u6811\u9ad8\u5ea6\uff0c\u5219\u7531\u5e73\u8861\u4e8c\u53c9\u6811\u5b9a\u4e49\u53ef\u77e5\uff0c\u8282\u70b9\u7684\u5e73\u8861\u56e0\u5b50\u53d6\u503c\u53ea\u80fd\u4e3a-1\u30010\u30011\u3002<\/p>\n\n\n\n2.1 <\/strong>\u5e73\u8861\u4e8c\u53c9\u6811\u7684\u63d2\u5165<\/strong><\/strong><\/p>\n\n\n\n1 LL<\/strong>\u5e73\u8861\u65cb\u8f6c\uff08\u53f3\u5355\u65cb\u8f6c\uff09<\/strong><\/strong><\/p>\n\n\n\n\u6b64\u79cd\u65b9\u5f0f\u5728\u67d0\u8282\u70b9\u5de6\u5b69\u5b50\uff08L\uff09\u7684\u5de6\u5b50\u6811\uff08L\uff09\u4e0a\u63d2\u5165\u65b0\u8282\u70b9\uff0c\u6545\u540d\u4e3aLL\u578b\u3002<\/p>\n\n\n\n\u5982\u56fe\u6240\u793a\uff0c\u5728\u8282\u70b94\u7684\u5de6\u5b69\u5b502\u7684\u5de6\u5b50\u68111\uff0c\u63d2\u5165\u65b0\u8282\u70b90\u3002\u8282\u70b94\u7684\u5e73\u8861\u56e0\u5b50\u75311\u53d8\u4e3a2\uff08\u5de6\u5b50\u6811\u9ad8\u5ea6\u589e\u52a0\uff09\uff0c\u6545\u8981\u53f3\u65cb\uff08\u9ad8\u5ea6\u4f4e\u7684\u5411\u4e0b\u53bb\uff09\u4ee5\u5e73\u8861\u5b50\u6811\u3002<\/p>\n\n\n\n\u89e3\u51b3\u65b9\u6cd5\uff1a<\/p>\n\n\n\n\n\u8282\u70b94\u53f3\u4e0b\u65cb\u8f6c\u6210\u4e3a2\u7684\u53f3\u5b50\u6811\uff082\u7684\u53f3\u5b50\u6811\u88ab\u66ff\u4ee3\uff0c4\u7684\u5de6\u5b50\u6811\u53d8\u7a7a\uff09\u3002<\/li>\n\n\n\n\u8282\u70b92\u7684\u539f\u53f3\u5b50\u6811\u6210\u4e3a4\u7684\u5de6\u5b50\u6811\uff082\u7684\u539f\u53f3\u5b50\u6811\u8865\u4e0a4\u7684\u7a7a\u5de6\u5b50\u6811\uff09\u3002<\/li>\n<\/ul>\n\n\n\n<\/figure >\n<\/figure><\/noscript>\n\n\n\nQ\uff1a\u82e5\u662f\u5728\u4e0a\u56fe\u4e2d1\u7684\u53f3\u4fa7\u63d2\u5165\u4e00\u4e2a\u7ed3\u70b9\u53c8\u8be5\u600e\u6837\u64cd\u4f5c\u5462\uff1fA\uff1a\u63d2\u5165\u57281\u53f3\u4fa7\u7684\u8282\u70b9\uff0c\u540c\u65f6\u53c8\u57282\u7684\u5de6\u4fa7\uff081<\u65b0\u8282\u70b9\u503c<2\uff09\uff0c\u7531\u4e8e\u662f\u987a\u5e8f\u6811\uff0c\u52194\u7ecf\u8fc7\u65cb\u8f6c\u540e\u65b0\u8282\u70b9\u6700\u7ec8\u4f4d\u7f6e\u4ecd\u5e94\u57281\u53f3\u4fa7\u30012\u5de6\u4fa7\uff0c\u65cb\u8f6c\u540e\u8282\u70b9\u987a\u5e8f\u4e0d\u53d8\uff08\u65b0\u8282\u70b9\u4ecd\u57281\u53f3\u4fa7\u30012\u5de6\u4fa7\uff09\uff0c\u6240\u4ee5\u65e0\u8bba\u5728\u5de6\u4fa7\u548c\u53f3\u4fa7\u63d2\u5165\uff0c\u64cd\u4f5c\u6b65\u9aa4\u4e0d\u53d8\u3002<\/p>\n\n\n\n2 RR<\/strong>\u5e73\u8861\u65cb\u8f6c\uff08\u5de6\u5355\u65cb\u8f6c\uff09<\/strong><\/strong><\/p>\n\n\n\n\u6b64\u79cd\u65b9\u5f0f\u5728\u67d0\u8282\u70b9\u53f3\u5b69\u5b50\uff08R\uff09\u7684\u53f3\u5b50\u6811\uff08R\uff09\u4e0a\u63d2\u5165\u65b0\u8282\u70b9\uff0c\u6545\u540d\u4e3aRR\u578b\u3002<\/p>\n\n\n\n\u5982\u56fe\u6240\u793a\uff0c\u5728\u8282\u70b93\u7684\u53f3\u5b69\u5b505\u7684\u53f3\u5b50\u68116\uff0c\u63d2\u5165\u65b0\u8282\u70b97\u3002\u8282\u70b93\u7684\u5e73\u8861\u56e0\u5b50\u7531-1\u53d8\u4e3a-2\uff08\u53f3\u5b50\u6811\u9ad8\u5ea6\u589e\u52a0\uff09\uff0c\u6545\u8981\u5de6\u65cb\uff08\u9ad8\u5ea6\u4f4e\u7684\u5411\u4e0b\u53bb\uff09\u4ee5\u5e73\u8861\u5b50\u6811\u3002<\/p>\n\n\n\n\u89e3\u51b3\u65b9\u6cd5\uff1a<\/p>\n\n\n\n\n\u8282\u70b93\u5de6\u4e0b\u65cb\u8f6c\u6210\u4e3a5\u7684\u5de6\u5b50\u6811\uff085\u7684\u5de6\u5b50\u6811\u88ab\u66ff\u4ee3\uff0c3\u7684\u53f3\u5b50\u6811\u53d8\u7a7a\uff09<\/li>\n\n\n\n\u8282\u70b95\u7684\u539f\u5de6\u5b50\u6811\u6210\u4e3a3\u7684\u53f3\u5b50\u6811\uff085\u7684\u539f\u5de6\u5b50\u6811\u8865\u4e0a3\u7684\u7a7a\u53f3\u5b50\u6811\uff09<\/li>\n<\/ul>\n\n\n\n<\/figure 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Tree\uff09\uff0c\u4e3a\u907f\u514d\u6811\u7684\u9ad8\u5ea6\u589e\u957f\u8fc7\u5feb\uff0c\u964d\u4f4e\u4e8c\u53c9\u6392\u5e8f\u6811\u7684\u6027\u80fd\uff0c\u89c4\u5b9a\u5728\u63d2\u5165\u548c\u5220\u9664\u4e8c\u53c9\u6811\u8282\u70b9\u65f6\uff0c\u4fdd\u8bc1\u8282\u70b9\u5de6\u3001\u53f3\u5b50\u6811\u9ad8\u5ea6\u5dee\u7684\u7edd\u5bf9\u503c\u4e0d\u8d85\u8fc71\uff08-1\u30010\u30011\uff09\uff0c\u5c06\u8fd9\u6837\u7684\u4e8c\u53c9\u6811\u6210\u4e3a\u5e73\u8861\u4e8c\u53c9\u6811\u3002\u53c8\u79f0AVL<\/strong>\u6811<\/strong>\uff0cAVL\u6811\u5f97\u540d\u4e8e\u5b83\u7684\u53d1\u660e\u8005G. M. Adelson-Velsky<\/strong>\u548cE. M. Landis<\/strong>\uff0c\u4ed6\u4eec\u57281962\u5e74\u7684\u8bba\u6587\u300aAn algorithm for the organization of information\u300b\u4e2d\u53d1\u8868\u4e86\u5b83\u3002<\/p>\n\n\n\n\u5e73\u8861\u56e0\u5b50\uff1a\u8282\u70b9\u5de6\u5b50\u6811\u548c\u53f3\u5b50\u6811\u7684\u9ad8\u5ea6\u5dee\uff0c\u5373\u5e73\u8861\u56e0\u5b50 = \u5de6\u5b50\u6811\u9ad8\u5ea6 - \u53f3\u5b50\u6811\u9ad8\u5ea6\uff0c\u5219\u7531\u5e73\u8861\u4e8c\u53c9\u6811\u5b9a\u4e49\u53ef\u77e5\uff0c\u8282\u70b9\u7684\u5e73\u8861\u56e0\u5b50\u53d6\u503c\u53ea\u80fd\u4e3a-1\u30010\u30011\u3002<\/p>\n\n\n\n2.1 <\/strong>\u5e73\u8861\u4e8c\u53c9\u6811\u7684\u63d2\u5165<\/strong><\/strong><\/p>\n\n\n\n1 LL<\/strong>\u5e73\u8861\u65cb\u8f6c\uff08\u53f3\u5355\u65cb\u8f6c\uff09<\/strong><\/strong><\/p>\n\n\n\n\u6b64\u79cd\u65b9\u5f0f\u5728\u67d0\u8282\u70b9\u5de6\u5b69\u5b50\uff08L\uff09\u7684\u5de6\u5b50\u6811\uff08L\uff09\u4e0a\u63d2\u5165\u65b0\u8282\u70b9\uff0c\u6545\u540d\u4e3aLL\u578b\u3002<\/p>\n\n\n\n\u5982\u56fe\u6240\u793a\uff0c\u5728\u8282\u70b94\u7684\u5de6\u5b69\u5b502\u7684\u5de6\u5b50\u68111\uff0c\u63d2\u5165\u65b0\u8282\u70b90\u3002\u8282\u70b94\u7684\u5e73\u8861\u56e0\u5b50\u75311\u53d8\u4e3a2\uff08\u5de6\u5b50\u6811\u9ad8\u5ea6\u589e\u52a0\uff09\uff0c\u6545\u8981\u53f3\u65cb\uff08\u9ad8\u5ea6\u4f4e\u7684\u5411\u4e0b\u53bb\uff09\u4ee5\u5e73\u8861\u5b50\u6811\u3002<\/p>\n\n\n\n\u89e3\u51b3\u65b9\u6cd5\uff1a<\/p>\n\n\n\n\n\u8282\u70b94\u53f3\u4e0b\u65cb\u8f6c\u6210\u4e3a2\u7684\u53f3\u5b50\u6811\uff082\u7684\u53f3\u5b50\u6811\u88ab\u66ff\u4ee3\uff0c4\u7684\u5de6\u5b50\u6811\u53d8\u7a7a\uff09\u3002<\/li>\n\n\n\n\u8282\u70b92\u7684\u539f\u53f3\u5b50\u6811\u6210\u4e3a4\u7684\u5de6\u5b50\u6811\uff082\u7684\u539f\u53f3\u5b50\u6811\u8865\u4e0a4\u7684\u7a7a\u5de6\u5b50\u6811\uff09\u3002<\/li>\n<\/ul>\n\n\n\n<\/figure >\n<\/figure><\/noscript>\n\n\n\nQ\uff1a\u82e5\u662f\u5728\u4e0a\u56fe\u4e2d1\u7684\u53f3\u4fa7\u63d2\u5165\u4e00\u4e2a\u7ed3\u70b9\u53c8\u8be5\u600e\u6837\u64cd\u4f5c\u5462\uff1fA\uff1a\u63d2\u5165\u57281\u53f3\u4fa7\u7684\u8282\u70b9\uff0c\u540c\u65f6\u53c8\u57282\u7684\u5de6\u4fa7\uff081<\u65b0\u8282\u70b9\u503c<2\uff09\uff0c\u7531\u4e8e\u662f\u987a\u5e8f\u6811\uff0c\u52194\u7ecf\u8fc7\u65cb\u8f6c\u540e\u65b0\u8282\u70b9\u6700\u7ec8\u4f4d\u7f6e\u4ecd\u5e94\u57281\u53f3\u4fa7\u30012\u5de6\u4fa7\uff0c\u65cb\u8f6c\u540e\u8282\u70b9\u987a\u5e8f\u4e0d\u53d8\uff08\u65b0\u8282\u70b9\u4ecd\u57281\u53f3\u4fa7\u30012\u5de6\u4fa7\uff09\uff0c\u6240\u4ee5\u65e0\u8bba\u5728\u5de6\u4fa7\u548c\u53f3\u4fa7\u63d2\u5165\uff0c\u64cd\u4f5c\u6b65\u9aa4\u4e0d\u53d8\u3002<\/p>\n\n\n\n2 RR<\/strong>\u5e73\u8861\u65cb\u8f6c\uff08\u5de6\u5355\u65cb\u8f6c\uff09<\/strong><\/strong><\/p>\n\n\n\n\u6b64\u79cd\u65b9\u5f0f\u5728\u67d0\u8282\u70b9\u53f3\u5b69\u5b50\uff08R\uff09\u7684\u53f3\u5b50\u6811\uff08R\uff09\u4e0a\u63d2\u5165\u65b0\u8282\u70b9\uff0c\u6545\u540d\u4e3aRR\u578b\u3002<\/p>\n\n\n\n\u5982\u56fe\u6240\u793a\uff0c\u5728\u8282\u70b93\u7684\u53f3\u5b69\u5b505\u7684\u53f3\u5b50\u68116\uff0c\u63d2\u5165\u65b0\u8282\u70b97\u3002\u8282\u70b93\u7684\u5e73\u8861\u56e0\u5b50\u7531-1\u53d8\u4e3a-2\uff08\u53f3\u5b50\u6811\u9ad8\u5ea6\u589e\u52a0\uff09\uff0c\u6545\u8981\u5de6\u65cb\uff08\u9ad8\u5ea6\u4f4e\u7684\u5411\u4e0b\u53bb\uff09\u4ee5\u5e73\u8861\u5b50\u6811\u3002<\/p>\n\n\n\n\u89e3\u51b3\u65b9\u6cd5\uff1a<\/p>\n\n\n\n\n\u8282\u70b93\u5de6\u4e0b\u65cb\u8f6c\u6210\u4e3a5\u7684\u5de6\u5b50\u6811\uff085\u7684\u5de6\u5b50\u6811\u88ab\u66ff\u4ee3\uff0c3\u7684\u53f3\u5b50\u6811\u53d8\u7a7a\uff09<\/li>\n\n\n\n\u8282\u70b95\u7684\u539f\u5de6\u5b50\u6811\u6210\u4e3a3\u7684\u53f3\u5b50\u6811\uff085\u7684\u539f\u5de6\u5b50\u6811\u8865\u4e0a3\u7684\u7a7a\u53f3\u5b50\u6811\uff09<\/li>\n<\/ul>\n\n\n\n<\/figure >\n<\/figure><\/noscript>\n\n\n\nQ\uff1a\u82e5\u662f\u5728\u4e0a\u56fe\u4e2d6\u7684\u5de6\u4fa7\u63d2\u5165\u4e00\u4e2a\u7ed3\u70b9\u53c8\u8be5\u600e\u6837\u64cd\u4f5c\u5462\uff1f<\/p>\n\n\n\nA\uff1a\u63d2\u5165\u57286\u5de6\u4fa7\u7684\u8282\u70b9\uff0c\u540c\u65f6\u53c8\u57285\u7684\u53f3\u4fa7\uff085<\u65b0\u8282\u70b9\u503c<6\uff09\uff0c\u7531\u4e8e\u662f\u987a\u5e8f\u6811\uff0c\u52193\u7ecf\u8fc7\u65cb\u8f6c\u540e\u65b0\u8282\u70b9\u6700\u7ec8\u4f4d\u7f6e\u4ecd\u5e94\u57286\u5de6\u4fa7\u30015\u53f3\u4fa7\uff0c\u65cb\u8f6c\u540e\u8282\u70b9\u987a\u5e8f\u4e0d\u53d8\uff08\u65b0\u8282\u70b9\u4ecd\u57286\u5de6\u4fa7\u30015\u53f3\u4fa7\uff09\uff0c\u6240\u4ee5\u65e0\u8bba\u5728\u5de6\u4fa7\u548c\u53f3\u4fa7\u63d2\u5165\uff0c\u64cd\u4f5c\u6b65\u9aa4\u4e0d\u53d8\u3002<\/p>\n\n\n\n3 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M. Adelson-Velsky<\/strong>\u548cE. M. Landis<\/strong>\uff0c\u4ed6\u4eec\u57281962\u5e74\u7684\u8bba\u6587\u300aAn algorithm for the organization of information\u300b\u4e2d\u53d1\u8868\u4e86\u5b83\u3002<\/p>\n\n\n\n\u5e73\u8861\u56e0\u5b50\uff1a\u8282\u70b9\u5de6\u5b50\u6811\u548c\u53f3\u5b50\u6811\u7684\u9ad8\u5ea6\u5dee\uff0c\u5373\u5e73\u8861\u56e0\u5b50 = \u5de6\u5b50\u6811\u9ad8\u5ea6 - \u53f3\u5b50\u6811\u9ad8\u5ea6\uff0c\u5219\u7531\u5e73\u8861\u4e8c\u53c9\u6811\u5b9a\u4e49\u53ef\u77e5\uff0c\u8282\u70b9\u7684\u5e73\u8861\u56e0\u5b50\u53d6\u503c\u53ea\u80fd\u4e3a-1\u30010\u30011\u3002<\/p>\n\n\n\n2.1 <\/strong>\u5e73\u8861\u4e8c\u53c9\u6811\u7684\u63d2\u5165<\/strong><\/strong><\/p>\n\n\n\n1 LL<\/strong>\u5e73\u8861\u65cb\u8f6c\uff08\u53f3\u5355\u65cb\u8f6c\uff09<\/strong><\/strong><\/p>\n\n\n\n\u6b64\u79cd\u65b9\u5f0f\u5728\u67d0\u8282\u70b9\u5de6\u5b69\u5b50\uff08L\uff09\u7684\u5de6\u5b50\u6811\uff08L\uff09\u4e0a\u63d2\u5165\u65b0\u8282\u70b9\uff0c\u6545\u540d\u4e3aLL\u578b\u3002<\/p>\n\n\n\n\u5982\u56fe\u6240\u793a\uff0c\u5728\u8282\u70b94\u7684\u5de6\u5b69\u5b502\u7684\u5de6\u5b50\u68111\uff0c\u63d2\u5165\u65b0\u8282\u70b90\u3002\u8282\u70b94\u7684\u5e73\u8861\u56e0\u5b50\u75311\u53d8\u4e3a2\uff08\u5de6\u5b50\u6811\u9ad8\u5ea6\u589e\u52a0\uff09\uff0c\u6545\u8981\u53f3\u65cb\uff08\u9ad8\u5ea6\u4f4e\u7684\u5411\u4e0b\u53bb\uff09\u4ee5\u5e73\u8861\u5b50\u6811\u3002<\/p>\n\n\n\n\u89e3\u51b3\u65b9\u6cd5\uff1a<\/p>\n\n\n\n\n\u8282\u70b94\u53f3\u4e0b\u65cb\u8f6c\u6210\u4e3a2\u7684\u53f3\u5b50\u6811\uff082\u7684\u53f3\u5b50\u6811\u88ab\u66ff\u4ee3\uff0c4\u7684\u5de6\u5b50\u6811\u53d8\u7a7a\uff09\u3002<\/li>\n\n\n\n\u8282\u70b92\u7684\u539f\u53f3\u5b50\u6811\u6210\u4e3a4\u7684\u5de6\u5b50\u6811\uff082\u7684\u539f\u53f3\u5b50\u6811\u8865\u4e0a4\u7684\u7a7a\u5de6\u5b50\u6811\uff09\u3002<\/li>\n<\/ul>\n\n\n\n<\/figure >\n<\/figure><\/noscript>\n\n\n\nQ\uff1a\u82e5\u662f\u5728\u4e0a\u56fe\u4e2d1\u7684\u53f3\u4fa7\u63d2\u5165\u4e00\u4e2a\u7ed3\u70b9\u53c8\u8be5\u600e\u6837\u64cd\u4f5c\u5462\uff1fA\uff1a\u63d2\u5165\u57281\u53f3\u4fa7\u7684\u8282\u70b9\uff0c\u540c\u65f6\u53c8\u57282\u7684\u5de6\u4fa7\uff081<\u65b0\u8282\u70b9\u503c<2\uff09\uff0c\u7531\u4e8e\u662f\u987a\u5e8f\u6811\uff0c\u52194\u7ecf\u8fc7\u65cb\u8f6c\u540e\u65b0\u8282\u70b9\u6700\u7ec8\u4f4d\u7f6e\u4ecd\u5e94\u57281\u53f3\u4fa7\u30012\u5de6\u4fa7\uff0c\u65cb\u8f6c\u540e\u8282\u70b9\u987a\u5e8f\u4e0d\u53d8\uff08\u65b0\u8282\u70b9\u4ecd\u57281\u53f3\u4fa7\u30012\u5de6\u4fa7\uff09\uff0c\u6240\u4ee5\u65e0\u8bba\u5728\u5de6\u4fa7\u548c\u53f3\u4fa7\u63d2\u5165\uff0c\u64cd\u4f5c\u6b65\u9aa4\u4e0d\u53d8\u3002<\/p>\n\n\n\n2 RR<\/strong>\u5e73\u8861\u65cb\u8f6c\uff08\u5de6\u5355\u65cb\u8f6c\uff09<\/strong><\/strong><\/p>\n\n\n\n\u6b64\u79cd\u65b9\u5f0f\u5728\u67d0\u8282\u70b9\u53f3\u5b69\u5b50\uff08R\uff09\u7684\u53f3\u5b50\u6811\uff08R\uff09\u4e0a\u63d2\u5165\u65b0\u8282\u70b9\uff0c\u6545\u540d\u4e3aRR\u578b\u3002<\/p>\n\n\n\n\u5982\u56fe\u6240\u793a\uff0c\u5728\u8282\u70b93\u7684\u53f3\u5b69\u5b505\u7684\u53f3\u5b50\u68116\uff0c\u63d2\u5165\u65b0\u8282\u70b97\u3002\u8282\u70b93\u7684\u5e73\u8861\u56e0\u5b50\u7531-1\u53d8\u4e3a-2\uff08\u53f3\u5b50\u6811\u9ad8\u5ea6\u589e\u52a0\uff09\uff0c\u6545\u8981\u5de6\u65cb\uff08\u9ad8\u5ea6\u4f4e\u7684\u5411\u4e0b\u53bb\uff09\u4ee5\u5e73\u8861\u5b50\u6811\u3002<\/p>\n\n\n\n\u89e3\u51b3\u65b9\u6cd5\uff1a<\/p>\n\n\n\n\n\u8282\u70b93\u5de6\u4e0b\u65cb\u8f6c\u6210\u4e3a5\u7684\u5de6\u5b50\u6811\uff085\u7684\u5de6\u5b50\u6811\u88ab\u66ff\u4ee3\uff0c3\u7684\u53f3\u5b50\u6811\u53d8\u7a7a\uff09<\/li>\n\n\n\n\u8282\u70b95\u7684\u539f\u5de6\u5b50\u6811\u6210\u4e3a3\u7684\u53f3\u5b50\u6811\uff085\u7684\u539f\u5de6\u5b50\u6811\u8865\u4e0a3\u7684\u7a7a\u53f3\u5b50\u6811\uff09<\/li>\n<\/ul>\n\n\n\n<\/figure >\n<\/figure><\/noscript>\n\n\n\nQ\uff1a\u82e5\u662f\u5728\u4e0a\u56fe\u4e2d6\u7684\u5de6\u4fa7\u63d2\u5165\u4e00\u4e2a\u7ed3\u70b9\u53c8\u8be5\u600e\u6837\u64cd\u4f5c\u5462\uff1f<\/p>\n\n\n\nA\uff1a\u63d2\u5165\u57286\u5de6\u4fa7\u7684\u8282\u70b9\uff0c\u540c\u65f6\u53c8\u57285\u7684\u53f3\u4fa7\uff085<\u65b0\u8282\u70b9\u503c<6\uff09\uff0c\u7531\u4e8e\u662f\u987a\u5e8f\u6811\uff0c\u52193\u7ecf\u8fc7\u65cb\u8f6c\u540e\u65b0\u8282\u70b9\u6700\u7ec8\u4f4d\u7f6e\u4ecd\u5e94\u57286\u5de6\u4fa7\u30015\u53f3\u4fa7\uff0c\u65cb\u8f6c\u540e\u8282\u70b9\u987a\u5e8f\u4e0d\u53d8\uff08\u65b0\u8282\u70b9\u4ecd\u57286\u5de6\u4fa7\u30015\u53f3\u4fa7\uff09\uff0c\u6240\u4ee5\u65e0\u8bba\u5728\u5de6\u4fa7\u548c\u53f3\u4fa7\u63d2\u5165\uff0c\u64cd\u4f5c\u6b65\u9aa4\u4e0d\u53d8\u3002<\/p>\n\n\n\n3 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1.3 \u4e8c\u53c9\u6392\u5e8f\u6811\u7684\u5220\u9664<\/strong><\/p>\n\n\n\n\u5728\u4e8c\u53c9\u6392\u5e8f\u6811\u4e2d\u5220\u9664\u4e00\u4e2a\u7ed3\u70b9\u65f6\uff0c\u4e0d\u80fd\u628a\u4ee5\u8be5\u7ed3\u70b9\u4e3a\u6839\u7684\u5b50\u6811\u4e0a\u7684\u7ed3\u70b9\u90fd\u5220\u9664\uff0c\u5fc5\u987b\u5148\u628a\u88ab\u5220\u9664\u7ed3\u70b9\u4ece\u5b58\u50a8\u4e8c\u53c9\u6392\u5e8f\u6811\u7684\u94fe\u8868\u4e0a\u6458\u4e0b\uff0c\u5c06\u56e0\u5220\u9664\u7ed3\u70b9\u800c\u65ad\u5f00\u7684\u4e8c\u53c9\u94fe\u8868\u91cd\u65b0\u94fe\u63a5\u8d77\u6765\uff0c\u540c\u65f6\u786e\u4fdd\u4e8c\u53c9\u6392\u5e8f\u6811\u7684\u6027\u8d28\u4e0d\u4f1a\u4e22\u5931\u3002<\/p>\n\n\n\n\u5220\u9664\u65f6\u5171\u52063\u79cd\u60c5\u51b5\uff1a<\/p>\n\n\n\n\n\u82e5\u88ab\u5220\u9664\u7ed3\u70b9z\u662f\u53f6\u7ed3\u70b9\uff0c\u5219\u76f4\u63a5\u5220\u9664\uff0c\u4e0d\u4f1a\u7834\u574f\u4e8c\u53c9\u6392\u5e8f\u6811\u7684\u6027\u8d28\u3002<\/li>\n\n\n\n\u82e5\u7ed3\u70b9\u53ea\u6709\u4e00\u68f5\u5de6\u5b50\u6811\u6216\u53f3\u5b50\u6811\uff0c\u5219\u8ba9z\u7684\u5b50\u6811\u76f4\u63a5\u66ff\u4ee3z\uff0c\u6210\u4e3az\u7236\u7ed3\u70b9\u7684\u5b50\u6811\u3002<\/li>\n\n\n\n\u82e5\u7ed3\u70b9\u6709\u5de6\u3001\u53f3\u4e24\u68f5\u5b50\u6811\uff0c\u5219\u4ee4z\u7684\u76f4\u63a5\u540e\u7ee7\uff08\u6216\u76f4\u63a5\u524d\u9a71\uff09\u66ff\u4ee3z\uff0c\u7136\u540e\u4ece\u4e8c\u53c9\u6392\u5e8f\u6811\u4e2d\u5220\u53bb\u8fd9\u4e2a\u76f4\u63a5\u540e\u7ee7\uff08\u6216\u76f4\u63a5\u524d\u9a71\uff09\uff0c\u8fd9\u6837\u5c31\u8f6c\u6362\u6210\u4e86\u7b2c1\u6216\u7b2c2\u79cd\u60c5\u51b5\u3002<\/li>\n<\/ol>\n\n\n\n<\/figure >\n<\/figure><\/noscript>\n\n\n\n1.4 <\/strong>\u4e8c\u53c9\u6392\u5e8f\u6811\u7684\u67e5\u627e\u6548\u7387<\/strong><\/strong><\/p>\n\n\n\n\u4e8c\u53c9\u6392\u5e8f\u6811\u7684\u67e5\u627e\u6548\u7387\u4e3b\u8981\u53d6\u51b3\u4e8e\u6811\u7684\u9ad8\u5ea6\u3002\u82e5\u6784\u9020\u4e8c\u53c9\u6392\u5e8f\u6811\u7684\u8f93\u5165\u5e8f\u5217\u8d8a\u63a5\u8fd1\u6709\u5e8f\uff0c\u5219\u4e8c\u53c9\u6392\u5e8f\u6811\u7684\u67e5\u627e\u6548\u7387\u8d8a\u5dee\uff08\u56e0\u4e3a\u6784\u9020\u51fa\u7684\u4e8c\u53c9\u6392\u5e8f\u6811\u7684\u9ad8\u5ea6\u8d8a\u9ad8\uff09\u3002<\/p>\n\n\n\n\u6781\u7aef\u60c5\u51b5\u4e0b\uff0c\u4e8c\u53c9\u6392\u5e8f\u6811\u662f\u4e00\u4e2a\u53ea\u6709\u5de6\u5b69\u5b50\u6216\u53f3\u5b69\u5b50\u7684\u5355\u652f\u6811\uff0c\u6b64\u65f6\u6811\u7684\u9ad8\u5ea6\u6700\u9ad8\u4e14\u7b49\u4e8e\u603b\u7ed3\u70b9\u6570\uff0c\u67e5\u627e\u6027\u80fd\u6700\u5dee\u3002<\/p>\n\n\n\n<\/figure >\n<\/figure><\/noscript>\n\n\n\n\u5982\u4e0a\u56fe\u6240\u793a\uff0c\u4e24\u68f5\u6811\u7684\u5e73\u5747\u67e5\u627e\u957f\u5ea6\u4e3a\uff1a<\/p>\n\n\n\n<\/figure >\n<\/figure><\/noscript>\n\n\n\n\u56e0\u6b64\uff0c\u4e3a\u907f\u514d\u6811\u7684\u9ad8\u5ea6\u589e\u957f\u8fc7\u5feb\uff0c\u964d\u4f4e\u4e8c\u53c9\u6392\u5e8f\u6811\u7684\u6027\u80fd\uff0c\u4fbf\u63d0\u51fa\u4e86\u5e73\u8861\u4e8c\u53c9\u6811<\/strong>\uff0c\u5e73\u8861\u4e8c\u53c9\u6811\u7684\u5e73\u5747\u67e5\u627e\u957f\u5ea6\u4e3aO<\/em>(log<\/em>2\u200bn<\/em>)\uff0c\u5176\u4e2dn\u4e3a\u8282\u70b9\u6570\u3002<\/p>\n\n\n\n2 <\/strong>\u5e73\u8861\u4e8c\u53c9\u6811\uff08AVL\uff09<\/strong><\/strong><\/p>\n\n\n\n\u5e73\u8861\u4e8c\u53c9\u6811<\/strong>\uff08Balanced Binary Tree\uff09\uff0c\u4e3a\u907f\u514d\u6811\u7684\u9ad8\u5ea6\u589e\u957f\u8fc7\u5feb\uff0c\u964d\u4f4e\u4e8c\u53c9\u6392\u5e8f\u6811\u7684\u6027\u80fd\uff0c\u89c4\u5b9a\u5728\u63d2\u5165\u548c\u5220\u9664\u4e8c\u53c9\u6811\u8282\u70b9\u65f6\uff0c\u4fdd\u8bc1\u8282\u70b9\u5de6\u3001\u53f3\u5b50\u6811\u9ad8\u5ea6\u5dee\u7684\u7edd\u5bf9\u503c\u4e0d\u8d85\u8fc71\uff08-1\u30010\u30011\uff09\uff0c\u5c06\u8fd9\u6837\u7684\u4e8c\u53c9\u6811\u6210\u4e3a\u5e73\u8861\u4e8c\u53c9\u6811\u3002\u53c8\u79f0AVL<\/strong>\u6811<\/strong>\uff0cAVL\u6811\u5f97\u540d\u4e8e\u5b83\u7684\u53d1\u660e\u8005G. 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1.4 <\/strong>\u4e8c\u53c9\u6392\u5e8f\u6811\u7684\u67e5\u627e\u6548\u7387<\/strong><\/strong><\/p>\n\n\n\n\u4e8c\u53c9\u6392\u5e8f\u6811\u7684\u67e5\u627e\u6548\u7387\u4e3b\u8981\u53d6\u51b3\u4e8e\u6811\u7684\u9ad8\u5ea6\u3002\u82e5\u6784\u9020\u4e8c\u53c9\u6392\u5e8f\u6811\u7684\u8f93\u5165\u5e8f\u5217\u8d8a\u63a5\u8fd1\u6709\u5e8f\uff0c\u5219\u4e8c\u53c9\u6392\u5e8f\u6811\u7684\u67e5\u627e\u6548\u7387\u8d8a\u5dee\uff08\u56e0\u4e3a\u6784\u9020\u51fa\u7684\u4e8c\u53c9\u6392\u5e8f\u6811\u7684\u9ad8\u5ea6\u8d8a\u9ad8\uff09\u3002<\/p>\n\n\n\n\u6781\u7aef\u60c5\u51b5\u4e0b\uff0c\u4e8c\u53c9\u6392\u5e8f\u6811\u662f\u4e00\u4e2a\u53ea\u6709\u5de6\u5b69\u5b50\u6216\u53f3\u5b69\u5b50\u7684\u5355\u652f\u6811\uff0c\u6b64\u65f6\u6811\u7684\u9ad8\u5ea6\u6700\u9ad8\u4e14\u7b49\u4e8e\u603b\u7ed3\u70b9\u6570\uff0c\u67e5\u627e\u6027\u80fd\u6700\u5dee\u3002<\/p>\n\n\n\n<\/figure >\n<\/figure><\/noscript>\n\n\n\n\u5982\u4e0a\u56fe\u6240\u793a\uff0c\u4e24\u68f5\u6811\u7684\u5e73\u5747\u67e5\u627e\u957f\u5ea6\u4e3a\uff1a<\/p>\n\n\n\n<\/figure >\n<\/figure><\/noscript>\n\n\n\n\u56e0\u6b64\uff0c\u4e3a\u907f\u514d\u6811\u7684\u9ad8\u5ea6\u589e\u957f\u8fc7\u5feb\uff0c\u964d\u4f4e\u4e8c\u53c9\u6392\u5e8f\u6811\u7684\u6027\u80fd\uff0c\u4fbf\u63d0\u51fa\u4e86\u5e73\u8861\u4e8c\u53c9\u6811<\/strong>\uff0c\u5e73\u8861\u4e8c\u53c9\u6811\u7684\u5e73\u5747\u67e5\u627e\u957f\u5ea6\u4e3aO<\/em>(log<\/em>2\u200bn<\/em>)\uff0c\u5176\u4e2dn\u4e3a\u8282\u70b9\u6570\u3002<\/p>\n\n\n\n2 <\/strong>\u5e73\u8861\u4e8c\u53c9\u6811\uff08AVL\uff09<\/strong><\/strong><\/p>\n\n\n\n\u5e73\u8861\u4e8c\u53c9\u6811<\/strong>\uff08Balanced Binary Tree\uff09\uff0c\u4e3a\u907f\u514d\u6811\u7684\u9ad8\u5ea6\u589e\u957f\u8fc7\u5feb\uff0c\u964d\u4f4e\u4e8c\u53c9\u6392\u5e8f\u6811\u7684\u6027\u80fd\uff0c\u89c4\u5b9a\u5728\u63d2\u5165\u548c\u5220\u9664\u4e8c\u53c9\u6811\u8282\u70b9\u65f6\uff0c\u4fdd\u8bc1\u8282\u70b9\u5de6\u3001\u53f3\u5b50\u6811\u9ad8\u5ea6\u5dee\u7684\u7edd\u5bf9\u503c\u4e0d\u8d85\u8fc71\uff08-1\u30010\u30011\uff09\uff0c\u5c06\u8fd9\u6837\u7684\u4e8c\u53c9\u6811\u6210\u4e3a\u5e73\u8861\u4e8c\u53c9\u6811\u3002\u53c8\u79f0AVL<\/strong>\u6811<\/strong>\uff0cAVL\u6811\u5f97\u540d\u4e8e\u5b83\u7684\u53d1\u660e\u8005G. M. Adelson-Velsky<\/strong>\u548cE. M. Landis<\/strong>\uff0c\u4ed6\u4eec\u57281962\u5e74\u7684\u8bba\u6587\u300aAn algorithm for the organization of information\u300b\u4e2d\u53d1\u8868\u4e86\u5b83\u3002<\/p>\n\n\n\n\u5e73\u8861\u56e0\u5b50\uff1a\u8282\u70b9\u5de6\u5b50\u6811\u548c\u53f3\u5b50\u6811\u7684\u9ad8\u5ea6\u5dee\uff0c\u5373\u5e73\u8861\u56e0\u5b50 = \u5de6\u5b50\u6811\u9ad8\u5ea6 - \u53f3\u5b50\u6811\u9ad8\u5ea6\uff0c\u5219\u7531\u5e73\u8861\u4e8c\u53c9\u6811\u5b9a\u4e49\u53ef\u77e5\uff0c\u8282\u70b9\u7684\u5e73\u8861\u56e0\u5b50\u53d6\u503c\u53ea\u80fd\u4e3a-1\u30010\u30011\u3002<\/p>\n\n\n\n2.1 <\/strong>\u5e73\u8861\u4e8c\u53c9\u6811\u7684\u63d2\u5165<\/strong><\/strong><\/p>\n\n\n\n1 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>\n<\/figure><\/noscript>\n\n\n\nQ\uff1a\u82e5\u662f\u5728\u4e0a\u56fe\u4e2d1\u7684\u53f3\u4fa7\u63d2\u5165\u4e00\u4e2a\u7ed3\u70b9\u53c8\u8be5\u600e\u6837\u64cd\u4f5c\u5462\uff1fA\uff1a\u63d2\u5165\u57281\u53f3\u4fa7\u7684\u8282\u70b9\uff0c\u540c\u65f6\u53c8\u57282\u7684\u5de6\u4fa7\uff081<\u65b0\u8282\u70b9\u503c<2\uff09\uff0c\u7531\u4e8e\u662f\u987a\u5e8f\u6811\uff0c\u52194\u7ecf\u8fc7\u65cb\u8f6c\u540e\u65b0\u8282\u70b9\u6700\u7ec8\u4f4d\u7f6e\u4ecd\u5e94\u57281\u53f3\u4fa7\u30012\u5de6\u4fa7\uff0c\u65cb\u8f6c\u540e\u8282\u70b9\u987a\u5e8f\u4e0d\u53d8\uff08\u65b0\u8282\u70b9\u4ecd\u57281\u53f3\u4fa7\u30012\u5de6\u4fa7\uff09\uff0c\u6240\u4ee5\u65e0\u8bba\u5728\u5de6\u4fa7\u548c\u53f3\u4fa7\u63d2\u5165\uff0c\u64cd\u4f5c\u6b65\u9aa4\u4e0d\u53d8\u3002<\/p>\n\n\n\n2 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>\n<\/figure><\/noscript>\n\n\n\nQ\uff1a\u82e5\u662f\u5728\u4e0a\u56fe\u4e2d6\u7684\u5de6\u4fa7\u63d2\u5165\u4e00\u4e2a\u7ed3\u70b9\u53c8\u8be5\u600e\u6837\u64cd\u4f5c\u5462\uff1f<\/p>\n\n\n\nA\uff1a\u63d2\u5165\u57286\u5de6\u4fa7\u7684\u8282\u70b9\uff0c\u540c\u65f6\u53c8\u57285\u7684\u53f3\u4fa7\uff085<\u65b0\u8282\u70b9\u503c<6\uff09\uff0c\u7531\u4e8e\u662f\u987a\u5e8f\u6811\uff0c\u52193\u7ecf\u8fc7\u65cb\u8f6c\u540e\u65b0\u8282\u70b9\u6700\u7ec8\u4f4d\u7f6e\u4ecd\u5e94\u57286\u5de6\u4fa7\u30015\u53f3\u4fa7\uff0c\u65cb\u8f6c\u540e\u8282\u70b9\u987a\u5e8f\u4e0d\u53d8\uff08\u65b0\u8282\u70b9\u4ecd\u57286\u5de6\u4fa7\u30015\u53f3\u4fa7\uff09\uff0c\u6240\u4ee5\u65e0\u8bba\u5728\u5de6\u4fa7\u548c\u53f3\u4fa7\u63d2\u5165\uff0c\u64cd\u4f5c\u6b65\u9aa4\u4e0d\u53d8\u3002<\/p>\n\n\n\n3 LR<\/strong>\u5e73\u8861\u65cb\u8f6c\uff08\u5148\u5de6\u65cb\u3001\u540e\u53f3\u65cb\uff09<\/strong><\/strong><\/p>\n\n\n\n\u6b64\u79cd\u65b9\u5f0f\u5728\u67d0\u8282\u70b9\u5de6\u5b69\u5b50\uff08L\uff09\u7684\u53f3\u5b50\u6811\uff08R\uff09\u4e0a\u63d2\u5165\u65b0\u8282\u70b9\uff0c\u6545\u540d\u4e3aLR\u578b\u3002<\/p>\n\n\n\n\u5982\u56fe\u6240\u793a\uff0c\u5728\u8282\u70b96\u7684\u5de6\u5b69\u5b502\u7684\u53f3\u5b50\u68113\uff0c\u63d2\u5165\u65b0\u8282\u70b94\u3002\u8282\u70b96\u7684\u5e73\u8861\u56e0\u5b50\u75311\u53d8\u4e3a2\uff08\u5de6\u5b50\u6811\u9ad8\u5ea6\u589e\u52a0\uff09\uff0c\u6b64\u65f6\u9700\u8981\u8fdb\u884c\u5148\u5de6\u540e\u53f3\u4e24\u6b21\u65cb\u8f6c\u64cd\u4f5c\u3002<\/p>\n\n\n\n\u89e3\u51b3\u65b9\u6cd5\uff1a<\/p>\n\n\n\n\n\u8282\u70b96\u7684\u5de6\u5b69\u5b502\u7684\u53f3\u5b50\u6811\u6839\u8282\u70b93\u5148\u5de6\u4e0a\u65cb\u8f6c\uff0c\u66ff\u4ee32\u6210\u4e3a6\u7684\u5de6\u5b50\u6811\uff0c2\u6210\u4e3a3\u7684\u5de6\u5b50\u6811\u3002<\/li>\n\n\n\n\u8282\u70b96\u540e\u53f3\u4e0b\u65cb\u8f6c\uff0c\u6210\u4e3a3\u7684\u53f3\u5b50\u6811\uff083\u7684\u53f3\u5b50\u6811\u88ab\u66ff\u4ee3\uff0c6\u7684\u5de6\u5b50\u6811\u53d8\u7a7a\uff09\uff0c\u518d\u5c06\u8282\u70b93\u7684\u539f\u53f3\u5b50\u6811\u6210\u4e3a6\u7684\u5de6\u5b50\u6811\uff083\u7684\u539f\u53f3\u5b50\u6811\u8865\u4e0a6\u7684\u7a7a\u5de6\u5b50\u6811\uff09\u3002<\/li>\n<\/ul>\n\n\n\n<\/p>\n\n\n\n<\/figure 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2 <\/strong>\u5e73\u8861\u4e8c\u53c9\u6811\uff08AVL\uff09<\/strong><\/strong><\/p>\n\n\n\n\u5e73\u8861\u4e8c\u53c9\u6811<\/strong>\uff08Balanced Binary Tree\uff09\uff0c\u4e3a\u907f\u514d\u6811\u7684\u9ad8\u5ea6\u589e\u957f\u8fc7\u5feb\uff0c\u964d\u4f4e\u4e8c\u53c9\u6392\u5e8f\u6811\u7684\u6027\u80fd\uff0c\u89c4\u5b9a\u5728\u63d2\u5165\u548c\u5220\u9664\u4e8c\u53c9\u6811\u8282\u70b9\u65f6\uff0c\u4fdd\u8bc1\u8282\u70b9\u5de6\u3001\u53f3\u5b50\u6811\u9ad8\u5ea6\u5dee\u7684\u7edd\u5bf9\u503c\u4e0d\u8d85\u8fc71\uff08-1\u30010\u30011\uff09\uff0c\u5c06\u8fd9\u6837\u7684\u4e8c\u53c9\u6811\u6210\u4e3a\u5e73\u8861\u4e8c\u53c9\u6811\u3002\u53c8\u79f0AVL<\/strong>\u6811<\/strong>\uff0cAVL\u6811\u5f97\u540d\u4e8e\u5b83\u7684\u53d1\u660e\u8005G. M. Adelson-Velsky<\/strong>\u548cE. M. 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