{"id":476022,"date":"2023-08-09T07:25:33","date_gmt":"2023-08-09T07:25:33","guid":{"rendered":""},"modified":"2023-09-05T11:11:51","modified_gmt":"2023-09-05T11:11:51","slug":"binary-tree","status":"publish","type":"wiki","link":"https:\/\/oneproxy.pro\/cn\/wiki\/binary-tree\/","title":{"rendered":"\u4e8c\u53c9\u6811"},"content":{"rendered":"<p>\u4e8c\u53c9\u6811\u662f\u8ba1\u7b97\u673a\u79d1\u5b66\u548c\u6570\u5b66\u4e2d\u7528\u4e8e\u8868\u793a\u5143\u7d20\u4e4b\u95f4\u5c42\u6b21\u5173\u7cfb\u7684\u57fa\u672c\u6570\u636e\u7ed3\u6784\u3002\u5b83\u7531\u901a\u8fc7\u8fb9\u8fde\u63a5\u7684\u8282\u70b9\u7ec4\u6210\uff0c\u5f62\u6210\u6811\u72b6\u7ed3\u6784\uff0c\u6bcf\u4e2a\u8282\u70b9\u6700\u591a\u53ef\u4ee5\u6709\u4e24\u4e2a\u5b50\u8282\u70b9\uff0c\u79f0\u4e3a\u5de6\u5b50\u8282\u70b9\u548c\u53f3\u5b50\u8282\u70b9\u3002\u4e8c\u53c9\u6811\u5728\u5404\u79cd\u7b97\u6cd5\u548c\u5e94\u7528\u4e2d\u8d77\u7740\u81f3\u5173\u91cd\u8981\u7684\u4f5c\u7528\uff0c\u5305\u62ec\u6570\u636e\u5e93\u7d22\u5f15\u3001\u641c\u7d22\u3001\u6392\u5e8f\u548c\u8868\u8fbe\u5f0f\u89e3\u6790\u3002<\/p>\n<h2>\u4e8c\u53c9\u6811\u7684\u8d77\u6e90\u5386\u53f2\u4ee5\u53ca\u7b2c\u4e00\u6b21\u63d0\u53ca\u5b83<\/h2>\n<p>\u6811\u7684\u6982\u5ff5\u53ef\u4ee5\u8ffd\u6eaf\u5230 19 \u4e16\u7eaa\u521d\uff0c\u5f53\u65f6\u6570\u5b66\u5bb6\u548c\u8ba1\u7b97\u673a\u79d1\u5b66\u5bb6\u5f00\u59cb\u63a2\u7d22\u5206\u5c42\u6570\u636e\u7ed3\u6784\u3002\u7136\u800c\uff0c\u6211\u4eec\u4eca\u5929\u6240\u77e5\u9053\u7684\u4e8c\u53c9\u6811\u7684\u9996\u6b21\u63d0\u53ca\u53ef\u4ee5\u8ffd\u6eaf\u5230 20 \u4e16\u7eaa\u4e2d\u53f6\u3002\u8457\u540d\u8ba1\u7b97\u673a\u79d1\u5b66\u5bb6\u7ea6\u7ff0\u00b7\u51af\u00b7\u8bfa\u4f9d\u66fc\u5728 1945 \u5e74\u4ece\u4e8b EDVAC \u8ba1\u7b97\u673a\u9879\u76ee\u65f6\u5f15\u5165\u4e86\u4e8c\u53c9\u6811\u7684\u6982\u5ff5\u3002\u540e\u6765\uff0c\u4e8c\u53c9\u6811\u56e0\u5176\u5728\u89e3\u51b3\u5404\u79cd\u8ba1\u7b97\u95ee\u9898\u65b9\u9762\u7684\u6548\u7387\u800c\u5728\u8ba1\u7b97\u673a\u79d1\u5b66\u9886\u57df\u5f15\u8d77\u4e86\u66f4\u591a\u5173\u6ce8\u3002<\/p>\n<h2>\u5173\u4e8e\u4e8c\u53c9\u6811\u7684\u8be6\u7ec6\u4fe1\u606f<\/h2>\n<p>\u4e8c\u53c9\u6811\u662f\u8282\u70b9\u7684\u96c6\u5408\uff0c\u6bcf\u4e2a\u8282\u70b9\u6700\u591a\u6709\u4e24\u4e2a\u5b50\u8282\u70b9\uff0c\u5373\u5de6\u5b50\u8282\u70b9\u548c\u53f3\u5b50\u8282\u70b9\u3002\u6811\u4e2d\u6700\u9876\u7aef\u7684\u8282\u70b9\u79f0\u4e3a\u6839\u8282\u70b9\uff0c\u6ca1\u6709\u5b50\u8282\u70b9\u7684\u8282\u70b9\u79f0\u4e3a\u53f6\u8282\u70b9\u3002\u8282\u70b9\u901a\u8fc7\u8fb9\u76f8\u4e92\u8fde\u63a5\uff0c\u8fb9\u8868\u793a\u5143\u7d20\u4e4b\u95f4\u7684\u5173\u7cfb\u3002<\/p>\n<h3>\u4e8c\u53c9\u6811\u7684\u6027\u8d28\uff1a<\/h3>\n<ol>\n<li>\u4e8c\u53c9\u6811\u4e2d\u7684\u6bcf\u4e2a\u8282\u70b9\u6700\u591a\u6709\u4e24\u4e2a\u5b50\u8282\u70b9\u3002<\/li>\n<li>\u6bcf\u4e2a\u8282\u70b9\u53ef\u4ee5\u6709\u96f6\u4e2a\u3001\u4e00\u4e2a\u6216\u4e24\u4e2a\u5b50\u8282\u70b9\u3002<\/li>\n<li>\u4e8c\u53c9\u6811\u5177\u6709\u5c42\u6b21\u7ed3\u6784\uff0c\u5141\u8bb8\u9ad8\u6548\u7684\u6570\u636e\u8bbf\u95ee\u548c\u64cd\u4f5c\u3002<\/li>\n<li>\u5728\u9002\u5f53\u7684\u4e8c\u53c9\u6811\u4e2d\uff0c\u6bcf\u4e2a\u975e\u53f6\u8282\u70b9\u6070\u597d\u6709\u4e24\u4e2a\u5b50\u8282\u70b9\u3002<\/li>\n<li>\u4e8c\u53c9\u6811\u7684\u6df1\u5ea6\u662f\u6839\u4e0e\u4efb\u4f55\u53f6\u8282\u70b9\u4e4b\u95f4\u7684\u6700\u5927\u8ddd\u79bb\u3002<\/li>\n<li>\u4e8c\u53c9\u6811\u7684\u9ad8\u5ea6\u662f\u6811\u4e2d\u4efb\u4f55\u53f6\u8282\u70b9\u7684\u6700\u5927\u6df1\u5ea6\u3002<\/li>\n<li>\u5177\u6709 N \u4e2a\u8282\u70b9\u7684\u4e8c\u53c9\u6811\u6709 N-1 \u6761\u8fb9\u3002<\/li>\n<\/ol>\n<h2>\u4e8c\u53c9\u6811\u7684\u5185\u90e8\u7ed3\u6784\uff1a\u5b83\u662f\u5982\u4f55\u5de5\u4f5c\u7684<\/h2>\n<p>\u4e8c\u53c9\u6811\u7684\u5185\u90e8\u7ed3\u6784\u57fa\u4e8e\u5176\u8282\u70b9\u53ca\u5176\u8fde\u63a5\u3002\u6bcf\u4e2a\u8282\u70b9\u901a\u5e38\u5305\u542b\u4e00\u4e2a\u6570\u636e\u5143\u7d20\u4ee5\u53ca\u5bf9\u5176\u5de6\u5b50\u8282\u70b9\u548c\u53f3\u5b50\u8282\u70b9\u7684\u5f15\u7528\uff08\u6307\u9488\uff09\u3002\u904d\u5386\u4e8c\u53c9\u6811\u6d89\u53ca\u5404\u79cd\u7b97\u6cd5\uff0c\u4f8b\u5982\u6309\u5e8f\u3001\u524d\u5e8f\u548c\u540e\u5e8f\u904d\u5386\uff0c\u6bcf\u79cd\u7b97\u6cd5\u90fd\u63d0\u4f9b\u4e0d\u540c\u7684\u8bbf\u95ee\u8282\u70b9\u987a\u5e8f\u3002<\/p>\n<h3>\u4e8c\u53c9\u6811\u904d\u5386\u7b97\u6cd5\uff1a<\/h3>\n<ol>\n<li>\u4e2d\u5e8f\u904d\u5386\uff1a\u8bbf\u95ee\u5de6\u5b50\u6811\uff0c\u7136\u540e\u8bbf\u95ee\u6839\uff0c\u6700\u540e\u8bbf\u95ee\u53f3\u5b50\u6811\u3002<\/li>\n<li>\u524d\u5e8f\u904d\u5386\uff1a\u8bbf\u95ee\u6839\uff0c\u7136\u540e\u8bbf\u95ee\u5de6\u5b50\u6811\uff0c\u6700\u540e\u8bbf\u95ee\u53f3\u5b50\u6811\u3002<\/li>\n<li>\u540e\u5e8f\u904d\u5386\uff1a\u8bbf\u95ee\u5de6\u5b50\u6811\uff0c\u7136\u540e\u8bbf\u95ee\u53f3\u5b50\u6811\uff0c\u6700\u540e\u8bbf\u95ee\u6839\u3002<\/li>\n<\/ol>\n<h2>\u4e8c\u53c9\u6811\u4e3b\u8981\u7279\u5f81\u5206\u6790<\/h2>\n<p>\u4e8c\u53c9\u6811\u5177\u6709\u51e0\u4e2a\u57fa\u672c\u7279\u6027\uff0c\u4f7f\u5176\u5728\u8ba1\u7b97\u673a\u79d1\u5b66\u548c\u5404\u79cd\u5e94\u7528\u4e2d\u5177\u6709\u4ef7\u503c\uff1a<\/p>\n<ol>\n<li>\n<p><strong>\u9ad8\u6548\u641c\u7d22<\/strong>\uff1a\u4e8c\u53c9\u6811\u53ef\u4ee5\u5b9e\u73b0\u9ad8\u6548\u7684\u641c\u7d22\u64cd\u4f5c\uff0c\u5c24\u5176\u662f\u5f53\u6811\u662f\u5e73\u8861\u7684\u65f6\u5019\u3002\u5728\u5e73\u8861\u4e8c\u53c9\u6811\u4e2d\u641c\u7d22\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u4e3a O(log N)\uff0c\u8fd9\u6bd4\u5728\u6570\u7ec4\u6216\u94fe\u8868\u4e2d\u8fdb\u884c\u7ebf\u6027\u641c\u7d22\u8981\u5feb\u5f97\u591a\u3002<\/p>\n<\/li>\n<li>\n<p><strong>\u5feb\u901f\u63d2\u5165\u548c\u5220\u9664<\/strong>\uff1a\u4e8c\u53c9\u6811\u5141\u8bb8\u76f8\u5bf9\u8f83\u5feb\u7684\u63d2\u5165\u548c\u5220\u9664\u64cd\u4f5c\u3002\u5f53\u6811\u4fdd\u6301\u5e73\u8861\u65f6\uff0c\u8fd9\u4e9b\u64cd\u4f5c\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u4e3a O(log N)\u3002<\/p>\n<\/li>\n<li>\n<p><strong>\u4e8c\u53c9\u641c\u7d22\u6811 (BST)<\/strong>\uff1a\u4e8c\u53c9\u641c\u7d22\u6811\u662f\u4e00\u79cd\u4e8c\u53c9\u6811\uff0c\u5176\u9075\u5faa\u4ee5\u4e0b\u5c5e\u6027\uff1a\u5bf9\u4e8e\u6bcf\u4e2a\u8282\u70b9\uff0c\u5176\u5de6\u5b50\u6811\u4e2d\u7684\u6240\u6709\u8282\u70b9\u7684\u503c\u90fd\u5c0f\u4e8e\u8be5\u8282\u70b9\uff0c\u800c\u5176\u53f3\u5b50\u6811\u4e2d\u7684\u6240\u6709\u8282\u70b9\u7684\u503c\u90fd\u5927\u4e8e\u8be5\u8282\u70b9\u3002\u6b64\u5c5e\u6027\u6709\u52a9\u4e8e\u9ad8\u6548\u5730\u641c\u7d22\u3001\u63d2\u5165\u548c\u5220\u9664\u5143\u7d20\u3002<\/p>\n<\/li>\n<li>\n<p><strong>\u4f18\u5148\u7ea7\u961f\u5217<\/strong>\uff1a\u4e8c\u53c9\u6811\u53ef\u7528\u4e8e\u5b9e\u73b0\u4f18\u5148\u7ea7\u961f\u5217\uff0c\u5176\u4e2d\u53ef\u4ee5\u5feb\u901f\u8bbf\u95ee\u4f18\u5148\u7ea7\u8f83\u9ad8\u7684\u5143\u7d20\u3002<\/p>\n<\/li>\n<\/ol>\n<h2>\u4e8c\u53c9\u6811\u7684\u7c7b\u578b<\/h2>\n<p>\u4e8c\u53c9\u6811\u6709\u591a\u79cd\u7c7b\u578b\uff0c\u6bcf\u79cd\u7c7b\u578b\u90fd\u6709\u7279\u5b9a\u7684\u7528\u9014\u3002\u4ee5\u4e0b\u662f\u4e00\u4e9b\u5e38\u89c1\u7684\u7c7b\u578b\uff1a<\/p>\n<h3>1. \u6ee1\u4e8c\u53c9\u6811\uff08\u771f\u4e8c\u53c9\u6811\uff09<\/h3>\n<p>\u5728\u4e00\u68f5\u6ee1\u4e8c\u53c9\u6811\u4e2d\uff0c\u6bcf\u4e2a\u975e\u53f6\u8282\u70b9\u6070\u597d\u6709\u4e24\u4e2a\u5b50\u8282\u70b9\uff0c\u5e76\u4e14\u6240\u6709\u53f6\u8282\u70b9\u90fd\u5904\u4e8e\u540c\u4e00\u7ea7\u522b\u3002<\/p>\n<h3>2. \u5b8c\u5168\u4e8c\u53c9\u6811<\/h3>\n<p>\u5b8c\u5168\u4e8c\u53c9\u6811\u662f\u6307\u9664\u6700\u540e\u4e00\u7ea7\u4e4b\u5916\u7684\u6bcf\u4e00\u7ea7\u90fd\u5df2\u586b\u5145\uff0c\u5e76\u4e14\u6240\u6709\u8282\u70b9\u90fd\u5c3d\u53ef\u80fd\u4f4d\u4e8e\u5de6\u8fb9\u7684\u4e8c\u53c9\u6811\u3002<\/p>\n<h3>3.\u5b8c\u7f8e\u4e8c\u53c9\u6811<\/h3>\n<p>\u5b8c\u7f8e\u4e8c\u53c9\u6811\u662f\u4e00\u68f5\u5b8c\u6574\u7684\u4e8c\u53c9\u6811\uff0c\u5176\u4e2d\u6240\u6709\u53f6\u8282\u70b9\u90fd\u5728\u540c\u4e00\u7ea7\u522b\uff0c\u5e76\u4e14\u6240\u6709\u5185\u90e8\u8282\u70b9\u90fd\u6709\u4e24\u4e2a\u5b50\u8282\u70b9\u3002<\/p>\n<h3>4.\u5e73\u8861\u4e8c\u53c9\u6811<\/h3>\n<p>\u5e73\u8861\u4e8c\u53c9\u6811\u662f\u4efb\u610f\u8282\u70b9\u7684\u5de6\u5b50\u6811\u4e0e\u53f3\u5b50\u6811\u7684\u6df1\u5ea6\u5dee\u4e0d\u8d85\u8fc71\u7684\u4e8c\u53c9\u6811\u3002<\/p>\n<h3>5. \u9000\u5316\uff08\u75c5\u6001\uff09\u4e8c\u53c9\u6811<\/h3>\n<p>\u5728\u9000\u5316\u4e8c\u53c9\u6811\u4e2d\uff0c\u6bcf\u4e2a\u8282\u70b9\u53ea\u6709\u4e00\u4e2a\u5b50\u8282\u70b9\u3002\u672c\u8d28\u4e0a\uff0c\u5b83\u7684\u884c\u4e3a\u7c7b\u4f3c\u4e8e\u94fe\u8868\u3002<\/p>\n<h2>\u4e8c\u53c9\u6811\u7684\u4f7f\u7528\u65b9\u6cd5\uff1a\u95ee\u9898\u53ca\u5176\u89e3\u51b3\u65b9\u6848<\/h2>\n<p>\u4e8c\u53c9\u6811\u5728\u8ba1\u7b97\u673a\u79d1\u5b66\u548c\u8f6f\u4ef6\u5de5\u7a0b\u7684\u5404\u4e2a\u9886\u57df\u90fd\u6709\u5e94\u7528\u3002\u4e00\u4e9b\u5e38\u89c1\u7528\u9014\u548c\u76f8\u5173\u95ee\u9898\u5305\u62ec\uff1a<\/p>\n<h3>1.\u7528\u4e8e\u641c\u7d22\u548c\u6392\u5e8f\u7684\u4e8c\u53c9\u641c\u7d22\u6811\uff1a<\/h3>\n<p>\u4e8c\u53c9\u641c\u7d22\u6811 (BST) \u901a\u5e38\u7528\u4e8e\u9ad8\u6548\u5730\u641c\u7d22\u548c\u6392\u5e8f\u6570\u636e\u3002\u7136\u800c\uff0c\u4e0d\u5e73\u8861\u7684 BST \u4f1a\u5bfc\u81f4\u6811\u503e\u659c\uff0c\u4ece\u800c\u5c06\u5176\u641c\u7d22\u548c\u63d2\u5165\u64cd\u4f5c\u7684\u6027\u80fd\u964d\u4f4e\u5230 O(N)\u3002\u4e3a\u4e86\u7f13\u89e3\u8fd9\u79cd\u60c5\u51b5\uff0c\u53ef\u4ee5\u4f7f\u7528 AVL \u6811\u6216\u7ea2\u9ed1\u6811\u7b49\u6280\u672f\u6765\u4fdd\u6301\u5e73\u8861\u3002<\/p>\n<h3>2.\u8868\u8fbe\u5f0f\u89e3\u6790\uff1a<\/h3>\n<p>\u4e8c\u53c9\u6811\u53ef\u7528\u4e8e\u89e3\u6790\u548c\u6c42\u503c\u6570\u5b66\u8868\u8fbe\u5f0f\u3002\u8fd0\u7b97\u7b26\u5b58\u50a8\u5728\u5185\u90e8\u8282\u70b9\uff0c\u64cd\u4f5c\u6570\u5b58\u50a8\u5728\u53f6\u8282\u70b9\uff0c\u4ece\u800c\u53ef\u4ee5\u4f7f\u7528\u904d\u5386\u7b97\u6cd5\u8fdb\u884c\u9ad8\u6548\u6c42\u503c\u3002<\/p>\n<h3>3.\u970d\u592b\u66fc\u7f16\u7801\u7528\u4e8e\u6570\u636e\u538b\u7f29\uff1a<\/h3>\n<p>\u54c8\u592b\u66fc\u7f16\u7801\u662f\u4e00\u79cd\u4e8c\u53c9\u6811\uff0c\u7528\u4e8e\u6570\u636e\u538b\u7f29\uff0c\u5176\u4e2d\u7ecf\u5e38\u51fa\u73b0\u7684\u5b57\u7b26\u88ab\u5206\u914d\u8f83\u77ed\u7684\u4ee3\u7801\u4ee5\u5b9e\u73b0\u538b\u7f29\u3002<\/p>\n<h3>4.\u56fe\u7b97\u6cd5\u7684\u4e8c\u53c9\u6811\u904d\u5386\uff1a<\/h3>\n<p>\u4e8c\u53c9\u6811\u7528\u4e8e\u56fe\u7b97\u6cd5\uff0c\u4f8b\u5982\u6df1\u5ea6\u4f18\u5148\u641c\u7d22 (DFS) \u548c\u5e7f\u5ea6\u4f18\u5148\u641c\u7d22 (BFS)\uff0c\u901a\u8fc7\u6811\u72b6\u904d\u5386\u8868\u793a\u56fe\u7ed3\u6784\u3002<\/p>\n<h3>5.\u4f18\u5148\u7ea7\u961f\u5217\uff1a<\/h3>\n<p>\u4e8c\u53c9\u5806\u662f\u4e8c\u53c9\u6811\u7684\u4e00\u79cd\uff0c\u7528\u4e8e\u5b9e\u73b0\u4f18\u5148\u7ea7\u961f\u5217\uff0c\u53ef\u4ee5\u6709\u6548\u5730\u63d2\u5165\u548c\u63d0\u53d6\u5177\u6709\u6700\u9ad8\u4f18\u5148\u7ea7\u7684\u5143\u7d20\u3002<\/p>\n<h2>\u4e3b\u8981\u7279\u70b9\u53ca\u4e0e\u540c\u7c7b\u672f\u8bed\u7684\u5176\u4ed6\u6bd4\u8f83<\/h2>\n<p>\u4ee5\u4e0b\u662f\u4e8c\u53c9\u6811\u4e0e\u5176\u4ed6\u76f8\u5173\u6570\u636e\u7ed3\u6784\u7684\u6bd4\u8f83\uff1a<\/p>\n<table>\n<thead>\n<tr>\n<th>\u6570\u636e\u7ed3\u6784<\/th>\n<th>\u4e3b\u8981\u7279\u5f81<\/th>\n<th>\u641c\u7d22<\/th>\n<th>\u63d2\u5165<\/th>\n<th>\u5220\u9664<\/th>\n<th>\u7a7a\u95f4\u590d\u6742\u5ea6<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>\u4e8c\u53c9\u6811<\/td>\n<td>\u7b49\u7ea7\u5236\u5ea6\uff0c\u4e24\u4e2a\u5b69\u5b50<\/td>\n<td>O(log N)<\/td>\n<td>O(log 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N)<\/td>\n<td>\u5728\uff09<\/td>\n<\/tr>\n<tr>\n<td>\u94fe\u8868<\/td>\n<td>\u7ebf\u6027\uff0c\u4e0b\u4e00\u4e2a\u8282\u70b9<\/td>\n<td>\u5728\uff09<\/td>\n<td>\u590d\u6742\u5ea6(1)<\/td>\n<td>\u590d\u6742\u5ea6(1)<\/td>\n<td>\u5728\uff09<\/td>\n<\/tr>\n<tr>\n<td>\u5927\u6279<\/td>\n<td>\u7d22\u5f15\uff0c\u56fa\u5b9a\u5927\u5c0f<\/td>\n<td>\u5728\uff09<\/td>\n<td>\u5728\uff09<\/td>\n<td>\u5728\uff09<\/td>\n<td>\u5728\uff09<\/td>\n<\/tr>\n<tr>\n<td>\u54c8\u5e0c\u8868<\/td>\n<td>\u952e\u503c\u6620\u5c04\uff0c\u5feb\u901f\u8bbf\u95ee<\/td>\n<td>\u590d\u6742\u5ea6(1)<\/td>\n<td>\u590d\u6742\u5ea6(1)<\/td>\n<td>\u590d\u6742\u5ea6(1)<\/td>\n<td>\u5728\uff09<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2>\u4e0e\u4e8c\u53c9\u6811\u76f8\u5173\u7684\u672a\u6765\u89c2\u70b9\u548c\u6280\u672f<\/h2>\n<p>\u968f\u7740\u6280\u672f\u7684\u8fdb\u6b65\uff0c\u4e8c\u53c9\u6811\u7684\u91cd\u8981\u6027\u53ef\u80fd\u4f1a\u6301\u7eed\u5b58\u5728\u3002\u968f\u7740\u6570\u636e\u5904\u7406\u548c\u4f18\u5316\u9700\u6c42\u7684\u4e0d\u65ad\u589e\u957f\uff0c\u57fa\u4e8e\u4e8c\u53c9\u6811\u7684\u7b97\u6cd5\u5c06\u7ee7\u7eed\u5728\u5404\u4e2a\u9886\u57df\u53d1\u6325\u5173\u952e\u4f5c\u7528\u3002\u5e73\u8861\u6280\u672f\u548c\u4f18\u5316\u7b56\u7565\u7684\u8fdb\u4e00\u6b65\u53d1\u5c55\u5c06\u63d0\u9ad8\u4e8c\u53c9\u6811\u5728\u5b9e\u9645\u573a\u666f\u4e2d\u7684\u6027\u80fd\u548c\u9002\u7528\u6027\u3002<\/p>\n<h2>\u5982\u4f55\u4f7f\u7528\u4ee3\u7406\u670d\u52a1\u5668\u6216\u5c06\u5176\u4e0e\u4e8c\u53c9\u6811\u5173\u8054<\/h2>\n<p>\u4ee3\u7406\u670d\u52a1\u5668\u53ef\u4ee5\u4ee5\u5404\u79cd\u65b9\u5f0f\u5229\u7528\u4e8c\u53c9\u6811\u6765\u589e\u5f3a\u5176\u6027\u80fd\u5e76\u4f18\u5316\u8def\u7531\u51b3\u7b56\u3002\u4e8c\u53c9\u6811\u53ef\u7528\u4e8e\u5728\u591a\u4e2a\u4ee3\u7406\u670d\u52a1\u5668\u4e4b\u95f4\u8fdb\u884c\u8d1f\u8f7d\u5e73\u8861\uff0c\u4ece\u800c\u9ad8\u6548\u5730\u5206\u914d\u5ba2\u6237\u7aef\u8bf7\u6c42\u3002\u6b64\u5916\uff0c\u4e8c\u53c9\u6811\u8fd8\u53ef\u7528\u4e8e\u7f13\u5b58\u673a\u5236\uff0c\u4ee5\u6709\u6548\u7ba1\u7406\u7f13\u5b58\u6570\u636e\uff0c\u4ece\u800c\u7f29\u77ed\u9891\u7e41\u8bf7\u6c42\u7684\u8d44\u6e90\u7684\u54cd\u5e94\u65f6\u95f4\u3002\u901a\u8fc7\u5c06\u4ee3\u7406\u670d\u52a1\u5668\u57fa\u7840\u8bbe\u65bd\u7ec4\u7ec7\u4e3a\u4e8c\u53c9\u6811\uff0cOneProxy \u7b49\u63d0\u4f9b\u5546\u53ef\u4ee5\u786e\u4fdd\u4e3a\u5176\u5ba2\u6237\u63d0\u4f9b\u987a\u7545\u3001\u5feb\u901f\u7684\u4ee3\u7406\u670d\u52a1\u3002<\/p>\n<h2>\u76f8\u5173\u94fe\u63a5<\/h2>\n<p>\u6709\u5173\u4e8c\u53c9\u6811\u7684\u66f4\u591a\u4fe1\u606f\uff0c\u53ef\u4ee5\u53c2\u8003\u4ee5\u4e0b\u8d44\u6e90\uff1a<\/p>\n<ul>\n<li><a href=\"https:\/\/www.geeksforgeeks.org\/binary-tree-data-structure\/\" target=\"_new\" rel=\"noopener nofollow\">GeeksforGeeks \u2013 \u4e8c\u53c9\u6811<\/a><\/li>\n<li><a href=\"https:\/\/en.wikipedia.org\/wiki\/Binary_tree\" target=\"_new\" rel=\"noopener nofollow\">\u7ef4\u57fa\u767e\u79d1 \u2013 \u4e8c\u53c9\u6811<\/a><\/li>\n<li><a href=\"https:\/\/mitpress.mit.edu\/books\/introduction-algorithms-third-edition\" target=\"_new\" rel=\"noopener nofollow\">\u7b97\u6cd5\u5bfc\u8bba\uff08\u4e66\uff09<\/a> \u4f5c\u8005\uff1aThomas H. Cormen\u3001Charles E. Leiserson\u3001Ronald L. Rivest \u548c Clifford Stein\u3002<\/li>\n<\/ul>","protected":false},"featured_media":467732,"menu_order":0,"template":"","meta":{"_acf_changed":false,"content-type":"","inline_featured_image":false,"footnotes":""},"class_list":["post-476022","wiki","type-wiki","status-publish","has-post-thumbnail","hentry"],"acf":{"faq_title":"Frequently Asked Questions about <mark>Binary Tree: A Comprehensive Overview<\/mark>","faq_items":[{"question":"What is a Binary Tree?","answer":"<p>A Binary Tree is a fundamental data structure used in computer science and mathematics to represent hierarchical relationships between elements. It consists of nodes connected by edges, forming a tree-like structure, where each node can have at most two children, referred to as the left child and the right child.<\/p>"},{"question":"Who introduced the concept of Binary Trees?","answer":"<p>The concept of Binary Trees was introduced by the renowned computer scientist John von Neumann while working on the EDVAC computer project in 1945.<\/p>"},{"question":"What are the key features of Binary Trees?","answer":"<p>Binary Trees offer several key features, including efficient searching, quick insertion and deletion, hierarchical structure, and various traversal algorithms like in-order, pre-order, and post-order traversal.<\/p>"},{"question":"What types of Binary Trees exist?","answer":"<p>Several types of Binary Trees exist, each serving different purposes. Some common types include Full Binary Trees, Complete Binary Trees, Perfect Binary Trees, Balanced Binary Trees, and Degenerate (Pathological) Binary Trees.<\/p>"},{"question":"How are Binary Trees used in computer science?","answer":"<p>Binary Trees find diverse applications, such as searching and sorting using Binary Search Trees, expression parsing, data compression with Huffman coding, graph algorithms like Depth-First Search (DFS) and Breadth-First Search (BFS), and priority queues using Binary Heaps.<\/p>"},{"question":"What is the future outlook for Binary Trees?","answer":"<p>As technology advances, Binary Trees will continue to play a crucial role in various fields. Advancements in balancing techniques and optimization strategies are expected to further improve their performance and applicability.<\/p>"},{"question":"How can proxy servers benefit from using Binary Trees?","answer":"<p>Proxy servers can leverage Binary Trees for load balancing among multiple servers and efficient caching mechanisms. Organizing the proxy infrastructure as a Binary Tree can ensure smooth and fast proxy services for clients.<\/p>"},{"question":"Where can I find more information about Binary Trees?","answer":"<p>For more information about Binary Trees, you can refer to resources like GeeksforGeeks and Wikipedia. Additionally, the book \"Introduction to Algorithms\" provides in-depth coverage of this topic.<\/p>"}]},"_links":{"self":[{"href":"https:\/\/oneproxy.pro\/cn\/wp-json\/wp\/v2\/wiki\/476022","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/oneproxy.pro\/cn\/wp-json\/wp\/v2\/wiki"}],"about":[{"href":"https:\/\/oneproxy.pro\/cn\/wp-json\/wp\/v2\/types\/wiki"}],"version-history":[{"count":0,"href":"https:\/\/oneproxy.pro\/cn\/wp-json\/wp\/v2\/wiki\/476022\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/oneproxy.pro\/cn\/wp-json\/wp\/v2\/media\/467732"}],"wp:attachment":[{"href":"https:\/\/oneproxy.pro\/cn\/wp-json\/wp\/v2\/media?parent=476022"}],"curies":[{"name":"\u53ef\u6e7f\u6027\u7c89\u5242","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}