\u4e00\u3001\u4e8c\u53c9\u6811<\/h3>\n\n\n\n
\u4e00\u79cd\u6811\u5f62\u7ed3\u6784\uff0c\u6bcf\u4e2a\u8282\u70b9\u6700\u591a\u67092\u4e2a\u5b50\u8282\u70b9\uff0c\u5206\u522b\u4e3a\u5de6\u5b50\u7ed3\u70b9\u548c\u53f3\u5b50\u8282\u70b9\uff0c\u662f\u5176\u5b83\u9ad8\u7ea7\u6570\u636e\u7ed3\u6784\u7684\u57fa\u7840\uff08\u5982\u5e73\u8861\u4e8c\u53c9\u6811\u3001\u4e8c\u53c9\u641c\u7d22\u6811\u7b49\uff09\u3002<\/p>\n\n\n\n
\u7279\u6b8a\u7684\u4e8c\u53c9\u6811\u6709\u6ee1\u4e8c\u53c9\u6811\u548c\u5b8c\u5168\u4e8c\u53c9\u6811\u3002<\/p>\n\n\n\n
\u6ee1\u4e8c\u53c9\u6811\uff1a\u975e\u53f6\u5b50\u8282\u70b9\u90fd\u6709\u4e24\u4e2a\u5b50\u8282\u70b9\uff0c\u4e14\u53f6\u5b50\u8282\u70b9\u90fd\u5728\u540c\u4e00\u5c42\u3002\uff08\u5168\u6ee1\uff09<\/p>\n\n\n\n \u5b8c\u5168\u4e8c\u53c9\u6811\uff1a\u9664\u6700\u540e\u4e00\u5c42\u5916\uff0c\u5176\u4f59\u5c42\u7684\u8282\u70b9\u6570\u90fd\u8fbe\u5230\u6700\u5927\u503c\u3002\u4e14\u6700\u540e\u4e00\u5c42\u8282\u70b9\u4ece\u5de6\u5230\u53f3\u8fde\u7eed\u6392\u5217\u3002\uff08\u4e0d\u6ee1\u4f46\u4e0d\u7f3a\u6f0f\uff09<\/p>\n\n\n\n \u4e8c\u53c9\u6811\u7684\u904d\u5386\u65b9\u5f0f\uff08\u5373\u6309\u67d0\u79cd\u89c4\u5219\u8bbf\u95ee\u6811\u4e2d\u6240\u6709\u8282\u70b9\u4e14\u4ec5\u8bbf\u95ee\u4e00\u6b21\uff09\uff1a<\/p>\n\n\n\n \u2460\u524d\u5e8f\u904d\u5386\uff1a\u5148\u8bbf\u95ee\u6839\u8282\u70b9\uff0c\u518d\u904d\u5386\u5de6\u5b50\u6811\uff0c\u6700\u540e\u904d\u5386\u53f3\u5b50\u6811\u3002<\/p>\n\n\n\n \u2461\u4e2d\u5e8f\u904d\u5386\uff1a\u5de6\u2014\u2014>\u6839\u2014\u2014>\u53f3<\/p>\n\n\n\n \u2462\u540e\u5e8f\u904d\u5386\uff1a\u5de6\u2014\u2014>\u53f3\u2014\u2014>\u6839<\/p>\n\n\n\n \u53c8\u79f0\u4e8c\u53c9\u6392\u5e8f\u6811\u3001\u4e8c\u53c9\u67e5\u627e\u6811\uff0c\u662f\u5728\u4e8c\u53c9\u6811\u7684\u57fa\u7840\u4e4b\u4e0a\u884d\u5316\u800c\u6765\uff0c\u5728\u7ee7\u627f\u4e8c\u53c9\u6811\u7684\u6027\u8d28\u540c\u65f6\uff0c\u8fd8\u6709\u81ea\u5df1\u72ec\u7279\u7684\u6027\u8d28\u3002\u76f8\u5173\u6027\u8d28\u6709\uff1a<\/p>\n\n\n\n \u2460\u5de6\u5b50\u6811\u8282\u70b9\u503c\u5c0f\u4e8e\u8be5\u8282\u70b9\u3002<\/p>\n\n\n\n \u2461\u53f3\u5b50\u6811\u8282\u70b9\u503c\u5927\u4e8e\u8be5\u8282\u70b9\u3002<\/p>\n\n\n\n \u2462\u5de6\u53f3\u5b50\u6811\u90fd\u4e3a\u4e8c\u53c9\u641c\u7d22\u6811\u3002\uff08\u5e38\u5047\u8bbe\u6811\u4e2d\u8282\u70b9\u503c\u552f\u4e00\uff09<\/p>\n\n\n\n \u7406\u60f3\u60c5\u51b5\uff1a\u6811\u7684\u9ad8\u5ea6\u5e73\u8861\uff08\u5982\u5b8c\u5168\u4e8c\u53c9\u6811\uff09\uff0c\u67e5\u3001\u63d2\u3001\u5220\u5747\u4e3aO(logn)<\/p>\n\n\n\n \u6700\u574f\u60c5\u51b5\uff1a\u5f53\u8282\u70b9\u6309\u5347\u5e8f\u6216\u964d\u5e8f\u63d2\u5165\u65f6\uff0c\u4f1a\u9000\u5316\u4e3a\u94fe\u8868\uff0c\u6b64\u65f6\u4e3aO(n)<\/p>\n\n\n\n \u5e73\u8861\u4e8c\u53c9\u6811\u662f\u4e00\u79cd\u7279\u6b8a\u7684\u4e8c\u53c9\u641c\u7d22\u6811\uff0c\u7279\u70b9\u662f\u901a\u8fc7\u7ef4\u6301\u6811\u7684 \u201c\u5e73\u8861\u6027\u201d\uff0c\u907f\u514d\u666e\u901a\u4e8c\u53c9\u641c\u7d22\u6811\u5728\u6781\u7aef\u60c5\u51b5\u4e0b\u9000\u5316\u4e3a\u7ebf\u6027\u7ed3\u6784\uff08O(n)\uff09\uff0c\u4ece\u800c\u4fdd\u8bc1\u67e5\u627e\u3001\u63d2\u5165\u3001\u5220\u9664\u7b49\u64cd\u4f5c\u7684\u9ad8\u6548\u6027\uff08O(log n)\uff09\u3002<\/p>\n\n\n\n AVL\u6811\u662f\u6700\u65e9\u7684\u5e73\u8861\u4e8c\u53c9\u6811\uff0c\u662f \u201c\u4e25\u683c\u5e73\u8861\u201d \u7684\u4e8c\u53c9\u641c\u7d22\u6811\uff08\u5e73\u8861\u56e0\u5b50\u4e25\u683c\u9650\u5236\u4e3a – 1\u30010\u30011\uff09\u3002\u6bcf\u4e2a\u8282\u70b9\u7684\u5de6\u53f3\u5b50\u6811\u9ad8\u5ea6\u5dee\u4e0d\u80fd\u8d85\u8fc71\u3002<\/strong><\/p>\n\n\n\n AVL \u6811\u7684\u63d2\u5165\u3001\u5220\u9664\u53ef\u80fd\u7834\u574f\u5e73\u8861\u6027\uff0c\u9700\u901a\u8fc7\u65cb\u8f6c\u64cd\u4f5c<\/strong>\u8c03\u6574\u7ed3\u6784\u4ee5\u6062\u590d\u5e73\u8861\uff0c\u800c\u65cb\u8f6c\u7684\u76ee\u6807\u662f\u964d\u4f4e\u6811\u7684\u9ad8\u5ea6\u3002<\/p>\n\n\n\n \u5de6\u65cb\uff1a\u4ee5\u67d0\u4e2a\u8282\u70b9\u4e3a\u65cb\u8f6c\u8282\u70b9\uff0c\u5176\u53f3\u5b50\u8282\u70b9\u53d8\u4e3a\u7236\u8282\u70b9\uff0c\u539f\u6765\u7684\u7236\u8282\u70b9\u53d8\u4e3a\u5de6\u5b50\u7ed3\u70b9\u3002<\/p>\n\n\n\n \u53f3\u65cb\uff1a\u540c\u7406\uff0c\u5de6\u5b50\u7ed3\u70b9\u53d8\u4e3a\u7236\u8282\u70b9\uff0c\u539f\u7236\u8282\u70b9\u53d8\u4e3a\u53f3\u5b50\u8282\u70b9\u3002<\/p>\n\n\n\n \u7f3a\u70b9\uff1a\u76f8\u6bd4\u8f83\u7ea2\u9ed1\u6811\uff0cAVL\u6811\u5728\u63d2\u5165\/\u5220\u9664\u65f6\u4f1a\u9891\u7e41\u89e6\u53d1\u65cb\u8f6c\u64cd\u4f5c\uff0c\u4ece\u800c\u6765\u8fbe\u5230\u6811\u7684\u9ad8\u5ea6\u5e73\u8861\uff0c\u8fd9\u4f1a\u5bfc\u81f4\u8017\u65f6\u6bd4\u7ea2\u9ed1\u6811\u9ad8\u3002<\/p>\n\n\n\n \u4e00\u79cd \u201c\u5f31\u5e73\u8861\u201d \u4e8c\u53c9\u641c\u7d22\u6811\uff08\u901a\u8fc7\u989c\u8272\u89c4\u5219\u7ef4\u6301\u5e73\u8861\uff0c\u5e73\u8861\u56e0\u5b50\u53ef\u5927\u4e8e 1(\u5373\u5de6\u53f3\u5b50\u6811\u7684\u9ad8\u5ea6\u5dee\u53ef\u5927\u4e8e1)\uff09\uff0c\u63d2\u5165 \/ \u5220\u9664\u7684\u65cb\u8f6c\u64cd\u4f5c\u66f4\u5c11\uff0c\u9002\u5408\u9891\u7e41\u4fee\u6539\u7684\u573a\u666f\uff08\u5982 Java \u7684TreeMap\u3001HashMap\uff08JDK8+\uff09\u3002\u76f8\u5173\u6027\u8d28\uff1a<\/p>\n\n\n\n \u2460\u6bcf\u4e2a\u8282\u70b9\u8981\u4e48\u662f\u7ea2\u8272\uff0c\u8981\u4e48\u662f\u9ed1\u8272\u3002<\/p>\n\n\n\n \u2461\u6839\u8282\u70b9\u662f\u9ed1\u8272\u7684\u3002<\/p>\n\n\n\n \u2462\u53f6\u5b50\u7ed3\u70b9\u90fd\u662f\u9ed1\u8272\u7684NULL\u8282\u70b9\u3002<\/p>\n\n\n\n \u2463\u82e5\u4e00\u4e2a\u8282\u70b9\u4e3a\u7ea2\u8272\uff0c\u5176\u4e24\u4e2a\u5b50\u8282\u70b9\u4e00\u5b9a\u4e3a\u9ed1\u8272\u3002<\/p>\n\n\n\n \u2464\u4efb\u610f\u8282\u70b9\u5230\u5176\u53ef\u5230\u8fbe\u7684\u53f6\u5b50\u7ed3\u70b9\u4e4b\u95f4\u6709\u76f8\u540c\u6570\u91cf\u7684\u9ed1\u8272\u8282\u70b9\u3002<\/p>\n\n\n\n \u5b9e\u73b0\u81ea\u5e73\u8861\u7684\u65b9\u5f0f\u2014\u2014>\u53d8\u8272+\u65cb\u8f6c\u3002<\/p>\n\n\n\n \u63a8\u8bba\uff1a\u4ece\u6839\u5230\u53f6\u5b50\u7ed3\u70b9\u7684\u6700\u957f\u8def\u5f84\u4e0d\u5927\u4e8e\u6700\u77ed\u8def\u5f84\u76842\u500d\u3002<\/p>\n\n\n\n \u5373\u6811\u9ad8\u63a7\u5236\u5728 2log (n+1) \u4ee5\u5185\uff0c\u786e\u4fdd\u64cd\u4f5c\u6548\u7387\u7a33\u5b9a\u5728 O (log n)\u3002<\/p>\n\n\n\n \u4e00\u79cd\u591a\u8def\u5e73\u8861\u641c\u7d22\u6811\uff0c\u6bcf\u4e2a\u8282\u70b9\u53ef\u4ee5\u5b58\u50a8\u591a\u4e2a\u6570\u636e\u5143\u7d20\uff0c\u5e76\u62e5\u6709\u591a\u4e2a\u5b50\u8282\u70b9\uff08\u4e8c\u53c9\u6811\u7684\u6bcf\u4e2a\u8282\u70b9\u6700\u591a\u5b58\u50a81\u4e2a\u5143\u7d20\u4e14\u6700\u591a\u67092\u4e2a\u5b50\u8282\u70b9\uff09\u3002\u4f18\u52bf\u662f\u964d\u4f4e\u6811\u7684\u9ad8\u5ea6\uff0c\u51cf\u5c11\u8bbf\u95ee\u6570\u636e\u65f6\u7684\u78c1\u76d8\u8bfb\u5199\u6b21\u6570\u3002<\/p>\n\n\n\n B \u6811\u7684\u9636\uff08\u901a\u5e38\u7528m\u8868\u793a\uff09\u662f\u5176\u6838\u5fc3\u53c2\u6570\uff0c\u6307\u7684\u662f\u4e00\u4e2a\u8282\u70b9\u6700\u591a\u80fd\u62e5\u6709\u7684\u5b50\u8282\u70b9\u6570\u3002\u4e00\u68f5m\u9636 B \u6811\u9700\u6ee1\u8db3\u4ee5\u4e0b\u6761\u4ef6\uff1a<\/p>\n\n\n\n \u2460\u6bcf\u4e2a\u8282\u70b9\u6700\u591a\u5305\u542bm-1\u4e2a\u5173\u952e\u5b57\uff08\u6570\u636e\u5143\u7d20\uff09\uff0c\u4ee5\u53cam\u4e2a\u5b50\u8282\u70b9\u3002<\/p>\n\n\n\n \u2461\u82e5\u4e00\u4e2a\u8282\u70b9\u5b58\u50a8\u7684\u5143\u7d20\u8d85\u8fc7\u6700\u5927\u503c\uff0c\u5219\u4e2d\u95f4\u5143\u7d20\u5411\u4e0a\u5206\u88c2\u6210\u7236\u8282\u70b9\uff0c\u5de6\u53f3\u4e24\u8fb9\u5143\u7d20\u5206\u88c2\u6210\u5de6\u53f3\u5b50\u8282\u70b9\u3002<\/p>\n\n\n\n \u2462\u975e\u6839\u975e\u53f6\u5b50\u8282\u70b9\u81f3\u5c11\u5b58\u5728\u5411\u4e0a\u53d6\u6574\uff08m\/2\uff09\u4e2a\u5b50\u8282\u70b9\u3002<\/p>\n\n\n\n \u2463\u6811\u4e2d\u6240\u6709\u53f6\u5b50\u8282\u70b9\u5230\u6839\u8282\u70b9\u7684\u8def\u5f84\u957f\u5ea6\u76f8\u7b49\u3002<\/p>\n\n\n\n \u4f18\u52bf\uff1a<\/p>\n\n\n\n 1\u3001\u4f4e\u9ad8\u5ea6\uff1a\u591a\u8def\u8282\u70b9\u7ed3\u6784\u4f7f\u6811\u7684\u9ad8\u5ea6\u8fdc\u4f4e\u4e8e\u4e8c\u53c9\u6811\uff0c\u51cf\u5c11\u78c1\u76d8 I\/O \u6b21\u6570\u3002\uff08\u6811\u7684\u9ad8\u5ea6\u51b3\u5b9a\u68c0\u7d22\u7684\u6b21\u6570\uff09<\/p>\n\n\n\n 2\u3001\u6240\u6709\u53f6\u5b50\u8282\u70b9\u5728\u540c\u4e00\u5c42\uff0c\u4fdd\u8bc1\u67e5\u8be2\u3001\u63d2\u5165\u3001\u5220\u9664\u64cd\u4f5c\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u5747\u4e3aO(log n)<\/p>\n\n\n\n \u662f B \u6811\u7684\u53d8\u79cd\uff0c\u4e24\u8005\u6838\u5fc3\u533a\u522b\u5728\u4e8e\uff1a<\/p>\n\n\n\n \u2460B+\u6811\u7684\u975e\u53f6\u5b50\u8282\u70b9\u4ec5\u4f5c\u4e3a\u7d22\u5f15\uff0c\u4e0d\u5b58\u50a8\u5b9e\u9645\u6570\u636e\uff0c\u6240\u6709\u5173\u952e\u5b57\u548c\u6570\u636e\u90fd\u5b58\u50a8\u5728\u53f6\u5b50\u8282\u70b9\u4e2d\u3002<\/p>\n\n\n\n \u2461B+\u6811\u7684\u53f6\u5b50\u8282\u70b9\u901a\u8fc7\u94fe\u8868\u8fde\u63a5\uff0c\u652f\u6301\u8303\u56f4\u67e5\u8be2\uff0c\u800cB\u6811\u53ef\u80fd\u9700\u8981\u904d\u5386\u591a\u4e2a\u5c42\u6b21\u7684\u8282\u70b9\u624d\u80fd\u5b8c\u6210\u8303\u56f4\u67e5\u8be2\u3002<\/p>\n\n\n\n \u4e3a\u4ec0\u4e48\u6570\u636e\u5e93\u7d22\u5f15\u7528B+\u6811\uff0c\u800c\u4e0d\u7528B\u6811\uff1f<\/p>\n\n\n\n 1\u3001\u8fdb\u884c\u8303\u56f4\u67e5\u8be2\u65f6\uff0cB+\u6811\u53ea\u9700\u4ece\u6839\u8282\u70b9\u5b9a\u4f4d\u5230\u53f6\u5b50\u7ed3\u70b9\u7684\u8303\u56f4\u8d77\u70b9\uff0c\u7136\u540e\u987a\u5e8f\u626b\u63cf\u94fe\u8868\u5c31\u80fd\u904d\u5386\u540e\u7eed\u6570\u636e\uff0c\u975e\u5e38\u9ad8\u6548\u3002\u800cB\u6811\u53ef\u80fd\u8981\u5728\u4e0d\u540c\u5c42\u6b21\u7684\u8282\u70b9\u95f4\u591a\u6b21\u8df3\u8f6c\u67e5\u627e\uff0c\u65e0\u7591\u589e\u52a0\u4e86\u67e5\u8be2\u7684\u65f6\u95f4\u548c\u590d\u6742\u5ea6\u3002<\/p>\n\n\n\n 2\u3001\u66f4\u9002\u5408\u987a\u5e8f\u8bbf\u95ee\uff0cB+\u6811\u53ef\u901a\u8fc7\u94fe\u8868\u5feb\u901f\u5b9a\u4f4d\u548c\u8bbf\u95ee\u76f8\u90bb\u6570\u636e\uff0c\u800cB\u6811\u6ca1\u8fd9\u4f18\u52bf\u3002<\/p>\n\n\n\n 3\u3001\u51cf\u5c11\u975e\u53f6\u5b50\u7ed3\u70b9\u7684\u5b58\u50a8\u5f00\u9500\uff0cB+\u6811\u7684\u975e\u53f6\u5b50\u8282\u70b9\u4ec5\u5305\u542b\u952e\u4fe1\u606f\uff0c\u4e0d\u5305\u542b\u6570\u636e\uff0c\u4f7f\u5f97\u975e\u53f6\u5b50\u8282\u70b9\u53ef\u4ee5\u5b58\u50a8\u66f4\u591a\u7684\u952e\uff0c\u4ece\u800c\u51cf\u5c11\u6811\u7684\u9ad8\u5ea6\u3002B\u6811\u7684\u975e\u53f6\u5b50\u8282\u70b9\u65e2\u5305\u542b\u952e\u53c8\u5305\u542b\u6570\u636e\uff0c\u76f8\u6bd4\u4e4b\u4e0b\uff0c\u6bcf\u4e2a\u8282\u70b9\u80fd\u5b58\u50a8\u7684\u952e\u7684\u6570\u91cf\u76f8\u5bf9\u8f83\u5c11\uff0c\u5bfc\u81f4\u6811\u7684\u9ad8\u5ea6\u53ef\u80fd\u66f4\u9ad8\u3002<\/p>\n\n\n\n <\/p>\n","protected":false},"excerpt":{"rendered":" 1\u3001\u4e8c\u53c9\u6811 2\u3001\u4e8c\u53c9\u641c\u7d22\u6811 3\u3001\u5e73\u8861\u4e8c\u53c9\u6811\u4e4bAVL\u6811 4\u3001\u5e73\u8861\u4e8c\u53c9\u6811\u4e4b\u7ea2\u9ed1\u6811 5\u3001BTree 6\u3001B+Tree […]<\/p>\n","protected":false},"author":1,"featured_media":857,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[4],"tags":[],"class_list":["post-919","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-java"],"_links":{"self":[{"href":"http:\/\/luohuayu.top\/index.php?rest_route=\/wp\/v2\/posts\/919","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/luohuayu.top\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/luohuayu.top\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/luohuayu.top\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/luohuayu.top\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=919"}],"version-history":[{"count":6,"href":"http:\/\/luohuayu.top\/index.php?rest_route=\/wp\/v2\/posts\/919\/revisions"}],"predecessor-version":[{"id":929,"href":"http:\/\/luohuayu.top\/index.php?rest_route=\/wp\/v2\/posts\/919\/revisions\/929"}],"wp:featuredmedia":[{"embeddable":true,"href":"http:\/\/luohuayu.top\/index.php?rest_route=\/wp\/v2\/media\/857"}],"wp:attachment":[{"href":"http:\/\/luohuayu.top\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=919"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/luohuayu.top\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=919"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/luohuayu.top\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=919"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}![\"\"](\"http:\/\/luohuayu.top\/wp-content\/uploads\/2025\/07\/\u5fae\u4fe1\u56fe\u7247_20250716105322-1024x902.jpg\")
<\/div>\u4e8c\u3001\u4e8c\u53c9\u641c\u7d22\u6811<\/h3>\n\n\n\n
![\"\"](\"http:\/\/luohuayu.top\/wp-content\/uploads\/2025\/07\/\u5fae\u4fe1\u56fe\u7247_20250716111602-1024x986.jpg\")
<\/div><\/figure>\n\n\n\n\u4e09\u3001\u5e73\u8861\u4e8c\u53c9\u6811\u4e4bAVL\u6811<\/h3>\n\n\n\n
![\"\"](\"http:\/\/luohuayu.top\/wp-content\/uploads\/2025\/07\/\u5fae\u4fe1\u56fe\u7247_20250716123809-1024x918.jpg\")
<\/div><\/figure>\n\n\n\n\u56db\u3001\u5e73\u8861\u4e8c\u53c9\u6811\u4e4b\u7ea2\u9ed1\u6811<\/h3>\n\n\n\n
\u4e94\u3001BTree<\/h3>\n\n\n\n
\u516d\u3001B+\u6811<\/h3>\n\n\n\n