{"id":5533,"date":"2024-07-18T16:12:52","date_gmt":"2024-07-18T08:12:52","guid":{"rendered":"https:\/\/www.xinyixx.com\/?p=5533"},"modified":"2024-07-18T16:15:23","modified_gmt":"2024-07-18T08:15:23","slug":"math","status":"publish","type":"post","link":"https:\/\/www.xinyixx.com\/index.php\/2024\/07\/18\/math\/","title":{"rendered":"\u51e0\u4f55\u4e0e\u6570\u8bba\u4e0a\u7684\u6709\u8da3\u73b0\u8c61"},"content":{"rendered":"\n<p><strong>\u600e\u4e48\u7b80\u5355\u7684\u8bc1\u660e\u56db\u8272\u5b9a\u7406\uff1a \u5373\u4efb\u4f55\u5e73\u9762\u5730\u56fe\u90fd\u53ef\u4ee5\u7528\u56db\u79cd\u989c\u8272\u7740\u8272\uff0c\u4f7f\u5f97\u76f8\u90bb\u7684\u533a\u57df\u989c\u8272\u4e0d\u540c\u3002<\/strong><\/p>\n\n\n\n<p>\u56db\u8272\u5b9a\u7406\u7684\u4e25\u683c\u8bc1\u660e\u975e\u5e38\u590d\u6742\uff0c\u751a\u81f3\u9700\u8981\u8ba1\u7b97\u673a\u8f85\u52a9\u3002\u7136\u800c\uff0c\u6211\u53ef\u4ee5\u63d0\u4f9b\u4e00\u4e9b\u7406\u89e3\u8fd9\u4e2a\u5b9a\u7406\u7684\u601d\u8def\u548c\u4e00\u4e2a\u7b80\u5316\u7684&#8221;\u8bc1\u660e\u6982\u5ff5&#8221;\uff1a<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>\u7b80\u5316\u95ee\u9898\uff1a \u9996\u5148\uff0c\u6211\u4eec\u53ef\u4ee5\u5c06\u5730\u56fe\u7b80\u5316\u4e3a\u56fe\uff0c\u5176\u4e2d\u6bcf\u4e2a\u533a\u57df\u53d8\u6210\u4e00\u4e2a\u9876\u70b9\uff0c\u76f8\u90bb\u533a\u57df\u4e4b\u95f4\u7528\u8fb9\u8fde\u63a5\u3002<\/li>\n\n\n\n<li>\u5f52\u7eb3\u6cd5\u601d\u8def\uff1a\n<ul class=\"wp-block-list\">\n<li>\u5bf9\u4e8e1\u30012\u30013\u4e2a\u533a\u57df\u7684\u5730\u56fe\uff0c\u663e\u7136\u53ef\u4ee5\u75284\u79cd\u989c\u8272\u7740\u8272\u3002<\/li>\n\n\n\n<li>\u5047\u8bbe\u5bf9\u4e8en\u4e2a\u533a\u57df\u7684\u5730\u56fe\uff0c\u56db\u8272\u5b9a\u7406\u6210\u7acb\u3002<\/li>\n\n\n\n<li>\u8003\u8651n+1\u4e2a\u533a\u57df\u7684\u5730\u56fe\u3002<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li>\u5173\u952e\u89c2\u5bdf\uff1a \u5728\u5e73\u9762\u56fe\u4e2d\uff0c\u603b\u5b58\u5728\u4e00\u4e2a\u533a\u57df\u4e0e\u4e0d\u8d85\u8fc75\u4e2a\u5176\u4ed6\u533a\u57df\u76f8\u90bb\u3002\uff08\u8fd9\u4e2a\u6027\u8d28\u53eb\u505a&#8221;\u4e94\u8272\u5b9a\u7406&#8221;\uff0c\u76f8\u5bf9\u5bb9\u6613\u8bc1\u660e\uff09<\/li>\n\n\n\n<li>\u79fb\u9664\u4e00\u4e2a\u9876\u70b9\uff1a\n<ul class=\"wp-block-list\">\n<li>\u627e\u5230\u4e00\u4e2a\u6700\u591a\u4e0e5\u4e2a\u533a\u57df\u76f8\u90bb\u7684\u533a\u57df\uff0c\u6682\u65f6\u79fb\u9664\u5b83\u3002<\/li>\n\n\n\n<li>\u5269\u4e0b\u7684n\u4e2a\u533a\u57df\u6839\u636e\u5f52\u7eb3\u5047\u8bbe\u53ef\u4ee5\u75284\u79cd\u989c\u8272\u7740\u8272\u3002<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li>\u91cd\u65b0\u6dfb\u52a0\u9876\u70b9\uff1a\n<ul class=\"wp-block-list\">\n<li>\u73b0\u5728\u91cd\u65b0\u6dfb\u52a0\u521a\u624d\u79fb\u9664\u7684\u533a\u57df\u3002<\/li>\n\n\n\n<li>\u5b83\u6700\u591a\u4e0e5\u4e2a\u533a\u57df\u76f8\u90bb\uff0c\u8fd95\u4e2a\u533a\u57df\u6700\u591a\u4f7f\u7528\u4e864\u79cd\u989c\u8272\uff08\u56e0\u4e3a\u5b83\u4eec\u4e92\u76f8\u76f8\u90bb\uff09\u3002<\/li>\n\n\n\n<li>\u57284\u79cd\u989c\u8272\u4e2d\uff0c\u5fc5\u5b9a\u6709\u4e00\u79cd\u6ca1\u6709\u88ab\u8fd95\u4e2a\u76f8\u90bb\u533a\u57df\u4f7f\u7528\u3002<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li>\u5b8c\u6210\u7740\u8272\uff1a \u4f7f\u7528\u90a3\u4e2a\u672a\u88ab\u76f8\u90bb\u533a\u57df\u4f7f\u7528\u7684\u989c\u8272\u7ed9\u65b0\u6dfb\u52a0\u7684\u533a\u57df\u7740\u8272\u3002<\/li>\n\n\n\n<li>\u7ed3\u8bba\uff1a \u56e0\u6b64\uff0cn+1\u4e2a\u533a\u57df\u7684\u5730\u56fe\u4e5f\u53ef\u4ee5\u75284\u79cd\u989c\u8272\u7740\u8272\u3002<\/li>\n<\/ol>\n\n\n\n<p>\u6ce8\u610f\u4e8b\u9879\uff1a<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u8fd9\u4e2a&#8221;\u8bc1\u660e&#8221;\u5ffd\u7565\u4e86\u5f88\u591a\u590d\u6742\u7684\u60c5\u51b5\u548c\u7ec6\u8282\u3002<\/li>\n\n\n\n<li>\u5b9e\u9645\u7684\u56db\u8272\u5b9a\u7406\u8bc1\u660e\u6d89\u53ca\u5927\u91cf\u7684\u6848\u4f8b\u5206\u6790\u548c\u8ba1\u7b97\u673a\u9a8c\u8bc1\u3002<\/li>\n\n\n\n<li>1976\u5e74\u7531Appel\u548cHaken\u9996\u6b21\u7ed9\u51fa\u7684\u8bc1\u660e\u5305\u542b\u4e861936\u79cd\u4e0d\u540c\u7684\u60c5\u51b5\uff0c\u9700\u8981\u8ba1\u7b97\u673a\u9a8c\u8bc1\u3002<\/li>\n\n\n\n<li>1997\u5e74\uff0cRobertson\u3001Sanders\u3001Seymour\u548cThomas\u7ed9\u51fa\u4e86\u4e00\u4e2a\u66f4\u7b80\u5316\u7684\u8bc1\u660e\uff0c\u4f46\u4ecd\u7136\u9700\u8981\u8ba1\u7b97\u673a\u8f85\u52a9\u3002<\/li>\n<\/ul>\n\n\n\n<p>\u867d\u7136\u8fd9\u4e2a\u7b80\u5316\u7684\u8bf4\u660e\u4e0d\u662f\u4e25\u683c\u7684\u8bc1\u660e\uff0c\u4f46\u5b83\u63d0\u4f9b\u4e86\u7406\u89e3\u56db\u8272\u5b9a\u7406\u7684\u4e00\u4e2a\u76f4\u89c2\u65b9\u6cd5\u3002\u56db\u8272\u5b9a\u7406\u7684\u590d\u6742\u6027\u6b63\u662f\u5b83\u5438\u5f15\u4eba\u7684\u5730\u65b9\uff0c\u5b83\u5c55\u793a\u4e86\u770b\u4f3c\u7b80\u5355\u7684\u51e0\u4f55\u95ee\u9898\u53ef\u80fd\u9690\u85cf\u7740\u6df1\u523b\u7684\u6570\u5b66\u590d\u6742\u6027\u3002<\/p>\n\n\n\n<p><strong>\u4e3a\u4ec0\u4e48\u67cf\u62c9\u56fe\u7acb\u4f53\u53ea\u67095\u79cd\uff0c\u600e\u4e48\u8bc1\u660e\uff1f<\/strong><\/p>\n\n\n\n<p>\u67cf\u62c9\u56fe\u7acb\u4f53\uff08\u6b63\u591a\u9762\u4f53\uff09\u786e\u5b9e\u53ea\u67095\u79cd\uff0c\u8fd9\u662f\u4e00\u4e2a\u975e\u5e38\u6709\u8da3\u7684\u51e0\u4f55\u4e8b\u5b9e\u3002\u8ba9\u6211\u4eec\u6765\u770b\u770b\u5982\u4f55\u8bc1\u660e\u8fd9\u4e00\u70b9\uff1a<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>\u5b9a\u4e49\u6b63\u591a\u9762\u4f53\uff1a\n<ul class=\"wp-block-list\">\n<li>\u6240\u6709\u9762\u90fd\u662f\u5168\u7b49\u7684\u6b63\u591a\u8fb9\u5f62<\/li>\n\n\n\n<li>\u6bcf\u4e2a\u9876\u70b9\u5904\u6c47\u805a\u7684\u9762\u7684\u6570\u91cf\u76f8\u7b49<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li>\u5173\u952e\u89c2\u5bdf\uff1a \u5728\u6bcf\u4e2a\u9876\u70b9\u5904\uff0c\u81f3\u5c11\u9700\u89813\u4e2a\u9762\u624d\u80fd\u5f62\u6210\u4e00\u4e2a\u7acb\u4f53\u89d2\u3002<\/li>\n\n\n\n<li>\u6b27\u62c9\u516c\u5f0f\uff1a \u5bf9\u4e8e\u4efb\u4f55\u51f8\u591a\u9762\u4f53\uff0c\u90fd\u6ee1\u8db3 V &#8211; E + F = 2 \u5176\u4e2d V \u662f\u9876\u70b9\u6570\uff0cE \u662f\u8fb9\u6570\uff0cF \u662f\u9762\u6570<\/li>\n\n\n\n<li>\u8bbe\u7acb\u53c2\u6570\uff1a\n<ul class=\"wp-block-list\">\n<li>\u5047\u8bbe\u6bcf\u4e2a\u9762\u662f n \u8fb9\u5f62<\/li>\n\n\n\n<li>\u6bcf\u4e2a\u9876\u70b9\u6c47\u805a m \u4e2a\u9762<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li>\u5efa\u7acb\u5173\u7cfb\uff1a\n<ul class=\"wp-block-list\">\n<li>\u6bcf\u4e2a\u9762\u6709 n \u6761\u8fb9\uff0c\u6bcf\u6761\u8fb9\u88ab\u4e24\u4e2a\u9762\u5171\u4eab\uff1anF = 2E<\/li>\n\n\n\n<li>\u6bcf\u4e2a\u9876\u70b9\u6c47\u805a m \u6761\u8fb9\uff0c\u6bcf\u6761\u8fb9\u8fde\u63a5\u4e24\u4e2a\u9876\u70b9\uff1amV = 2E<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li>\u4ee3\u5165\u6b27\u62c9\u516c\u5f0f\uff1a V &#8211; E + F = 2 2E\/m &#8211; E + 2E\/n = 2 2E(1\/m + 1\/n &#8211; 1\/2) = 2<\/li>\n\n\n\n<li>\u6c42\u89e3\u4e0d\u7b49\u5f0f\uff1a 1\/m + 1\/n > 1\/2 \u8fd9\u4e2a\u4e0d\u7b49\u5f0f\u53ea\u67095\u79cd\u6574\u6570\u89e3\uff1a\n<ul class=\"wp-block-list\">\n<li>(3,3)\uff1a\u6b63\u56db\u9762\u4f53<\/li>\n\n\n\n<li>(3,4)\uff1a\u6b63\u516b\u9762\u4f53<\/li>\n\n\n\n<li>(3,5)\uff1a\u6b63\u4e8c\u5341\u9762\u4f53<\/li>\n\n\n\n<li>(4,3)\uff1a\u6b63\u516d\u9762\u4f53\uff08\u7acb\u65b9\u4f53\uff09<\/li>\n\n\n\n<li>(5,3)\uff1a\u6b63\u5341\u4e8c\u9762\u4f53<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li>\u9a8c\u8bc1\uff1a\n<ul class=\"wp-block-list\">\n<li>\u5bf9\u4e8e\u6bcf\u79cd\u60c5\u51b5\uff0c\u6211\u4eec\u53ef\u4ee5\u9a8c\u8bc1\u5b83\u786e\u5b9e\u6ee1\u8db3\u6b63\u591a\u9762\u4f53\u7684\u6240\u6709\u6761\u4ef6\u3002<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li>\u7ed3\u8bba\uff1a \u56e0\u6b64\uff0c\u53ea\u5b58\u5728\u8fd95\u79cd\u6b63\u591a\u9762\u4f53\u3002<\/li>\n<\/ol>\n\n\n\n<p>\u8fd9\u4e2a\u8bc1\u660e\u7684\u5173\u952e\u5728\u4e8e\u5c06\u51e0\u4f55\u95ee\u9898\u8f6c\u5316\u4e3a\u4ee3\u6570\u95ee\u9898\uff0c\u7136\u540e\u5229\u7528\u6b27\u62c9\u516c\u5f0f\u548c\u7b80\u5355\u7684\u4e0d\u7b49\u5f0f\u6c42\u89e3\u3002\u8fd9\u79cd\u65b9\u6cd5\u4e0d\u4ec5\u8bc1\u660e\u4e86\u53ea\u67095\u79cd\u6b63\u591a\u9762\u4f53\uff0c\u8fd8\u51c6\u786e\u5730\u544a\u8bc9\u6211\u4eec\u8fd95\u79cd\u662f\u4ec0\u4e48\u3002<\/p>\n\n\n\n<p>\u8fd9\u4e2a\u7ed3\u679c\u6709\u51e0\u4e2a\u6709\u8da3\u7684\u542b\u4e49\uff1a<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u5b83\u5c55\u793a\u4e86\u4e09\u7ef4\u7a7a\u95f4\u7684\u4e00\u4e9b\u6df1\u523b\u9650\u5236\u3002<\/li>\n\n\n\n<li>\u8fd95\u79cd\u7acb\u4f53\u4e0e\u8bb8\u591a\u81ea\u7136\u73b0\u8c61\u548c\u4eba\u9020\u7ed3\u6784\u76f8\u5173\u3002<\/li>\n\n\n\n<li>\u5728\u66f4\u9ad8\u7ef4\u5ea6\u4e2d\uff0c\u89c4\u5219\u591a\u80de\u4f53\uff08\u6b63\u591a\u9762\u4f53\u7684\u9ad8\u7ef4\u7c7b\u6bd4\uff09\u7684\u6570\u91cf\u4e5f\u662f\u6709\u9650\u7684\uff0c\u4f46\u89c4\u5f8b\u4e0d\u540c\u3002<\/li>\n<\/ul>\n\n\n\n<p>\u67cf\u62c9\u56fe\u7acb\u4f53\u7684\u8fd9\u4e2a\u6027\u8d28\u4e0d\u4ec5\u5728\u6570\u5b66\u4e0a\u5f88\u91cd\u8981\uff0c\u5728\u5316\u5b66\u3001\u7269\u7406\u3001\u5efa\u7b51\u7b49\u9886\u57df\u4e5f\u6709\u5e7f\u6cdb\u5e94\u7528\u3002<\/p>\n\n\n\n<p><strong>\u83ab\u6bd4\u4e4c\u65af\u73af\u6709\u4ec0\u4e48\u7279\u70b9\uff0c\u5b83\u795e\u5947\u5728\u54ea\uff1f\u8fd8\u6709\u4ec0\u4e48\u7c7b\u4f3c\u7684\u51e0\u4f55\u56fe\u5f62\uff1f<\/strong><\/p>\n\n\n\n<p>\u83ab\u6bd4\u4e4c\u65af\u73af\uff08M\u00f6bius strip\uff09\u786e\u5b9e\u662f\u4e00\u4e2a\u975e\u5e38\u6709\u8da3\u548c\u795e\u5947\u7684\u51e0\u4f55\u56fe\u5f62\u3002\u8ba9\u6211\u4eec\u6765\u63a2\u8ba8\u5b83\u7684\u7279\u70b9\u3001\u795e\u5947\u4e4b\u5904\uff0c\u4ee5\u53ca\u7c7b\u4f3c\u7684\u51e0\u4f55\u56fe\u5f62\uff1a<\/p>\n\n\n\n<p>\u83ab\u6bd4\u4e4c\u65af\u73af\u7684\u7279\u70b9\uff1a<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>\u5355\u9762\u6027\uff1a\u5c3d\u7ba1\u770b\u8d77\u6765\u6709\u4e24\u4e2a\u8868\u9762\uff0c\u5b9e\u9645\u4e0a\u53ea\u6709\u4e00\u4e2a\u8fde\u7eed\u7684\u9762\u3002<\/li>\n\n\n\n<li>\u5355\u8fb9\u6027\uff1a\u53ea\u6709\u4e00\u4e2a\u8fde\u7eed\u7684\u8fb9\u7f18\u3002<\/li>\n\n\n\n<li>\u975e\u5b9a\u5411\u6027\uff1a\u65e0\u6cd5\u5728\u8868\u9762\u5b9a\u4e49&#8221;\u5185side&#8221;\u548c&#8221;\u5916side&#8221;\u3002<\/li>\n\n\n\n<li>\u8fde\u7eed\u6027\uff1a\u6cbf\u7740\u8868\u9762\u884c\u8d70\uff0c\u53ef\u4ee5\u5230\u8fbe\u8d77\u70b9\u7684&#8221;opposite side&#8221;\u3002<\/li>\n<\/ol>\n\n\n\n<p>\u83ab\u6bd4\u4e4c\u65af\u73af\u7684\u795e\u5947\u4e4b\u5904\uff1a<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>\u62d3\u6251\u7279\u6027\uff1a\u5207\u5f00\u83ab\u6bd4\u4e4c\u65af\u73af\u4f1a\u4ea7\u751f\u610f\u60f3\u4e0d\u5230\u7684\u7ed3\u679c\u3002\u4f8b\u5982\uff0c\u6cbf\u4e2d\u5fc3\u7ebf\u5207\u5272\u4f1a\u5f97\u5230\u4e00\u4e2a\u66f4\u957f\u7684\u3001\u6709\u4e24\u4e2a\u626d\u8f6c\u7684\u73af\uff0c\u800c\u4e0d\u662f\u4e24\u4e2a\u5206\u79bb\u7684\u73af\u3002<\/li>\n\n\n\n<li>\u6096\u8bba\u6027\uff1a\u5b83\u6311\u6218\u4e86\u6211\u4eec\u5bf9\u4e8c\u7ef4\u8868\u9762\u5728\u4e09\u7ef4\u7a7a\u95f4\u4e2d\u5b58\u5728\u65b9\u5f0f\u7684\u76f4\u89c9\u7406\u89e3\u3002<\/li>\n\n\n\n<li>\u5e94\u7528\u5e7f\u6cdb\uff1a\u4ece\u673a\u68b0\u5de5\u7a0b\uff08\u5982\u4f20\u9001\u5e26\uff09\u5230\u6570\u5b66\u548c\u827a\u672f\uff0c\u83ab\u6bd4\u4e4c\u65af\u73af\u90fd\u6709\u5e7f\u6cdb\u5e94\u7528\u3002<\/li>\n\n\n\n<li>\u6982\u5ff5\u542f\u53d1\uff1a\u5b83\u542f\u53d1\u4e86\u8bb8\u591a\u6570\u5b66\u6982\u5ff5\uff0c\u5982\u62d3\u6251\u5b66\u4e2d\u7684\u975e\u5b9a\u5411\u66f2\u9762\u3002<\/li>\n<\/ol>\n\n\n\n<p>\u7c7b\u4f3c\u7684\u51e0\u4f55\u56fe\u5f62\uff1a<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>\u514b\u83b1\u56e0\u74f6\uff08Klein bottle\uff09\uff1a\n<ul class=\"wp-block-list\">\n<li>\u4e00\u4e2a\u6ca1\u6709\u5185\u5916\u4e4b\u5206\u7684\u975e\u5b9a\u5411\u66f2\u9762\uff0c\u4f46\u5728\u4e09\u7ef4\u7a7a\u95f4\u4e2d\u65e0\u6cd5\u4e0d\u81ea\u4ea4\u5730\u5b9e\u73b0\u3002<\/li>\n\n\n\n<li>\u53ef\u4ee5\u770b\u4f5c\u4e24\u4e2a\u83ab\u6bd4\u4e4c\u65af\u73af\u8fde\u63a5\u5728\u4e00\u8d77\u3002<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li>\u5b9e\u5c04\u5f71\u5e73\u9762\uff08Real projective plane\uff09\uff1a\n<ul class=\"wp-block-list\">\n<li>\u53e6\u4e00\u79cd\u975e\u5b9a\u5411\u66f2\u9762\uff0c\u53ef\u4ee5\u901a\u8fc7\u5c06\u4e00\u4e2a\u5706\u76d8\u7684\u5bf9\u5f84\u70b9\u8bc6\u522b\u5f97\u5230\u3002<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li>\u73af\u9762\uff08Torus\uff09\uff1a\n<ul class=\"wp-block-list\">\n<li>\u867d\u7136\u662f\u5b9a\u5411\u7684\uff0c\u4f46\u4e5f\u662f\u4e00\u4e2a\u95ed\u5408\u7684\u4e8c\u7ef4\u66f2\u9762\u5d4c\u5165\u4e09\u7ef4\u7a7a\u95f4\u3002<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li>\u535a\u4f0a\u5b9a\u7406\u66f2\u9762\uff08Boy&#8217;s surface\uff09\uff1a\n<ul class=\"wp-block-list\">\n<li>\u5b9e\u5c04\u5f71\u5e73\u9762\u5728\u4e09\u7ef4\u7a7a\u95f4\u4e2d\u7684\u6d78\u5165\uff0c\u6ca1\u6709\u5947\u70b9\u3002<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li>\u7f57\u9a6c\u66f2\u9762\uff08Roman surface\uff09\uff1a\n<ul class=\"wp-block-list\">\n<li>\u4e5f\u79f0\u4e3a\u65bd\u6cf0\u7eb3\u66f2\u9762\uff0c\u662f\u4e00\u79cd\u81ea\u4ea4\u7684\u66f2\u9762\u3002<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li>\u5706\u73af\u7ed3\uff08Trefoil knot\uff09\uff1a\n<ul class=\"wp-block-list\">\n<li>\u6700\u7b80\u5355\u7684\u975e\u5e73\u51e1\u7ed3\uff0c\u5c55\u793a\u4e86\u4e00\u7ef4\u7269\u4f53\u5728\u4e09\u7ef4\u7a7a\u95f4\u4e2d\u7684\u590d\u6742\u884c\u4e3a\u3002<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li>\u56db\u7ef4\u8d85\u7acb\u65b9\u4f53\u7684\u4e09\u7ef4\u6295\u5f71\uff08Tesseract projection\uff09\uff1a\n<ul class=\"wp-block-list\">\n<li>\u5c55\u793a\u4e86\u9ad8\u7ef4\u7a7a\u95f4\u51e0\u4f55\u4f53\u5728\u4f4e\u7ef4\u7a7a\u95f4\u7684\u8868\u73b0\u3002<\/li>\n<\/ul>\n<\/li>\n<\/ol>\n\n\n\n<p>\u8fd9\u4e9b\u51e0\u4f55\u56fe\u5f62\u90fd\u6311\u6218\u4e86\u6211\u4eec\u5bf9\u7a7a\u95f4\u548c\u7ef4\u5ea6\u7684\u76f4\u89c2\u7406\u89e3\uff0c\u5c55\u793a\u4e86\u51e0\u4f55\u5b66\u548c\u62d3\u6251\u5b66\u7684\u6df1\u5ea6\u548c\u590d\u6742\u6027\u3002\u5b83\u4eec\u4e0d\u4ec5\u5728\u6570\u5b66\u4e0a\u5f88\u6709\u8da3\uff0c\u4e5f\u5728\u7269\u7406\u5b66\u3001\u827a\u672f\u548c\u54f2\u5b66\u7b49\u9886\u57df\u6709\u91cd\u8981\u5f71\u54cd\u3002\u8fd9\u4e9b\u56fe\u5f62\u5e2e\u52a9\u6211\u4eec\u7406\u89e3\u7a7a\u95f4\u7684\u672c\u8d28\uff0c\u4ee5\u53ca\u7ef4\u5ea6\u4e4b\u95f4\u7684\u5173\u7cfb\uff0c\u63ed\u793a\u4e86\u770b\u4f3c\u7b80\u5355\u7684\u7a7a\u95f4\u5b9e\u9645\u4e0a\u53ef\u80fd\u5177\u6709\u975e\u5e38\u590d\u6742\u548c\u53cd\u76f4\u89c9\u7684\u6027\u8d28\u3002<\/p>\n\n\n\n<p><strong>\u600e\u4e48\u8bc1\u660e\u5728\u4efb\u610f\u4e09\u89d2\u5f62\u7684\u6bcf\u6761\u8fb9\u4e0a\u5411\u5916\u4f5c\u7b49\u8fb9\u4e09\u89d2\u5f62\uff0c\u8fd9\u4e09\u4e2a\u7b49\u8fb9\u4e09\u89d2\u5f62\u7684\u4e2d\u5fc3\u6784\u6210\u4e00\u4e2a\u7b49\u8fb9\u4e09\u89d2\u5f62<\/strong><\/p>\n\n\n\n<p>\u8fd9\u4e2a\u5b9a\u7406\u88ab\u79f0\u4e3a\u62ff\u7834\u4ed1\u5b9a\u7406\uff08Napoleon&#8217;s theorem\uff09\u3002\u6211\u4eec\u53ef\u4ee5\u901a\u8fc7\u4ee5\u4e0b\u6b65\u9aa4\u6765\u8bc1\u660e\u5b83\uff1a<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>\u8bbe\u5b9a\uff1a \u5047\u8bbe\u539f\u4e09\u89d2\u5f62\u4e3a ABC\uff0c\u5728\u5176\u4e09\u8fb9\u4e0a\u5411\u5916\u4f5c\u7684\u7b49\u8fb9\u4e09\u89d2\u5f62\u5206\u522b\u4e3a BCX, CAY, ABZ\u3002 \u6211\u4eec\u9700\u8981\u8bc1\u660e XYZ \u662f\u7b49\u8fb9\u4e09\u89d2\u5f62\u3002<\/li>\n\n\n\n<li>\u5f15\u5165\u8f85\u52a9\u7ebf\uff1a \u8fde\u63a5 AX, BY, CZ\u3002<\/li>\n\n\n\n<li>\u5173\u952e\u89c2\u5bdf\uff1a \u4e09\u89d2\u5f62 BCX \u662f\u7b49\u8fb9\u4e09\u89d2\u5f62\uff0c\u6240\u4ee5 \u2220CBX = 60\u00b0\u3002 \u540c\u7406\uff0c\u2220ACY = 60\u00b0, \u2220BAZ = 60\u00b0\u3002<\/li>\n\n\n\n<li>\u8bc1\u660e AX = AY\uff1a\n<ul class=\"wp-block-list\">\n<li>\u5728\u4e09\u89d2\u5f62 AXY \u4e2d\uff1a \u2220XAY = \u2220BAC + 60\u00b0 + 60\u00b0 = \u2220BAC + 120\u00b0<\/li>\n\n\n\n<li>\u2220AXY = 30\u00b0 (\u7b49\u8fb9\u4e09\u89d2\u5f62 BCX \u7684\u5916\u89d2\u5e73\u5206\u7ebf\u6027\u8d28)<\/li>\n\n\n\n<li>\u2220AYX = 30\u00b0 (\u540c\u7406)<\/li>\n\n\n\n<li>\u6240\u4ee5\u4e09\u89d2\u5f62 AXY \u662f\u7b49\u8170\u4e09\u89d2\u5f62\uff0cAX = AY<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li>\u540c\u7406\u53ef\u8bc1\uff1a BY = BZ \u548c CZ = CX<\/li>\n\n\n\n<li>\u8bc1\u660e XY = YZ = ZX\uff1a<ul><li>\u5728\u4e09\u89d2\u5f62 AXY \u4e2d\uff1a \u2220XAY = \u2220BAC + 120\u00b0<\/li><li>\u5728\u4e09\u89d2\u5f62 BYZ \u4e2d\uff1a \u2220YBZ = \u2220ABC + 120\u00b0<\/li><li>\u5728\u4e09\u89d2\u5f62 CZX \u4e2d\uff1a \u2220ZCX = \u2220BCA + 120\u00b0<\/li><\/ul>\u7531\u4e8e \u2220BAC + \u2220ABC + \u2220BCA = 180\u00b0\uff08\u4e09\u89d2\u5f62\u5185\u89d2\u548c\uff09\uff0c \u6240\u4ee5 \u2220XAY + \u2220YBZ + \u2220ZCX = 180\u00b0 + 360\u00b0 = 540\u00b0<\/li>\n\n\n\n<li>\u6700\u540e\u4e00\u6b65\uff1a\n<ul class=\"wp-block-list\">\n<li>XYZ \u662f\u4e00\u4e2a\u4e09\u89d2\u5f62\uff0c\u5176\u5185\u89d2\u548c\u4e3a 180\u00b0\u3002<\/li>\n\n\n\n<li>\u4ece\u4e0a\u4e00\u6b65\u6211\u4eec\u77e5\u9053\uff0c\u2220XYA + \u2220YZB + \u2220ZXC = 540\u00b0 &#8211; 180\u00b0 = 360\u00b0<\/li>\n\n\n\n<li>\u8fd9\u610f\u5473\u7740 \u2220XYA = \u2220YZB = \u2220ZXC = 120\u00b0<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li>\u7ed3\u8bba\uff1a \u7531\u4e8e XYZ \u4e09\u89d2\u5f62\u7684\u4e09\u4e2a\u89d2\u90fd\u662f 60\u00b0\uff0c\u6240\u4ee5\u5b83\u662f\u7b49\u8fb9\u4e09\u89d2\u5f62\u3002<\/li>\n<\/ol>\n\n\n\n<p>\u8fd9\u4e2a\u8bc1\u660e\u5229\u7528\u4e86\u51e0\u4f55\u5b66\u7684\u591a\u4e2a\u6027\u8d28\uff0c\u5305\u62ec\u7b49\u8fb9\u4e09\u89d2\u5f62\u7684\u6027\u8d28\u3001\u4e09\u89d2\u5f62\u7684\u5185\u89d2\u548c\u5b9a\u7406\u3001\u4ee5\u53ca\u7b49\u8170\u4e09\u89d2\u5f62\u7684\u6027\u8d28\u3002\u62ff\u7834\u4ed1\u5b9a\u7406\u4e0d\u4ec5\u7f8e\u4e3d\uff0c\u800c\u4e14\u63ed\u793a\u4e86\u4e09\u89d2\u5f62\u51e0\u4f55\u4e2d\u7684\u6df1\u523b\u8054\u7cfb\u3002<\/p>\n\n\n\n<p>\u8fd9\u4e2a\u5b9a\u7406\u6709\u4e00\u4e9b\u6709\u8da3\u7684\u6269\u5c55\u548c\u5e94\u7528\uff1a<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u5b83\u9002\u7528\u4e8e\u4efb\u610f\u4e09\u89d2\u5f62\uff0c\u4e0d\u8bba\u5176\u5f62\u72b6\u5982\u4f55\u3002<\/li>\n\n\n\n<li>\u5982\u679c\u5411\u5185\u4f5c\u7b49\u8fb9\u4e09\u89d2\u5f62\uff0c\u5f97\u5230\u7684\u4e5f\u662f\u7b49\u8fb9\u4e09\u89d2\u5f62\u3002<\/li>\n\n\n\n<li>\u8fd9\u4e2a\u5b9a\u7406\u5728\u590d\u5e73\u9762\u4e2d\u6709\u4f18\u96c5\u7684\u4ee3\u6570\u8868\u8fbe\u3002<\/li>\n<\/ul>\n\n\n\n<p>\u62ff\u7834\u4ed1\u5b9a\u7406\u662f\u51e0\u4f55\u5b66\u4e2d\u4f17\u591a\u4f18\u96c5\u5b9a\u7406\u4e4b\u4e00\uff0c\u5c55\u793a\u4e86\u770b\u4f3c\u7b80\u5355\u7684\u56fe\u5f62\u4e2d\u9690\u85cf\u7684\u590d\u6742\u548c\u7f8e\u4e3d\u5173\u7cfb\u3002<\/p>\n\n\n\n<p><strong>\u751f\u6210\u6811\u6709\u54ea\u4e9b\u6709\u8da3\u7684\u5b9a\u7406\u548c\u73b0\u8c61\uff1f<\/strong><\/p>\n\n\n\n<p>\u751f\u6210\u6811\uff08Spanning Tree\uff09\u662f\u56fe\u8bba\u4e2d\u7684\u4e00\u4e2a\u57fa\u672c\u6982\u5ff5\uff0c\u6d89\u53ca\u5230\u4ece\u4e00\u4e2a\u56fe\u4e2d\u9009\u62e9\u51fa\u7684\u4e00\u68f5\u6811\uff0c\u5305\u542b\u6240\u6709\u7684\u9876\u70b9\u4f46\u4e0d\u5305\u542b\u73af\u3002\u4ee5\u4e0b\u662f\u4e00\u4e9b\u4e0e\u751f\u6210\u6811\u76f8\u5173\u7684\u6709\u8da3\u5b9a\u7406\u548c\u73b0\u8c61\uff1a<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">1. \u514b\u9c81\u65af\u5361\u5c14\u7b97\u6cd5\u548c\u666e\u91cc\u59c6\u7b97\u6cd5<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>\u514b\u9c81\u65af\u5361\u5c14\u7b97\u6cd5\uff08Kruskal&#8217;s Algorithm\uff09<\/strong>\uff1a\u4e00\u79cd\u8d2a\u5fc3\u7b97\u6cd5\uff0c\u7528\u4e8e\u627e\u5230\u52a0\u6743\u65e0\u5411\u56fe\u7684\u6700\u5c0f\u751f\u6210\u6811\u3002\u8be5\u7b97\u6cd5\u6309\u7167\u8fb9\u7684\u6743\u91cd\u4ece\u5c0f\u5230\u5927\u6392\u5e8f\uff0c\u7136\u540e\u9010\u4e00\u6dfb\u52a0\u8fb9\uff0c\u5982\u679c\u6dfb\u52a0\u8fb9\u540e\u4e0d\u5f62\u6210\u73af\uff0c\u5c31\u4fdd\u7559\u8be5\u8fb9\uff0c\u76f4\u5230\u751f\u6210\u6811\u5305\u542b\u6240\u6709\u9876\u70b9\u3002<\/li>\n\n\n\n<li><strong>\u666e\u91cc\u59c6\u7b97\u6cd5\uff08Prim&#8217;s Algorithm\uff09<\/strong>\uff1a\u4e5f\u662f\u4e00\u79cd\u8d2a\u5fc3\u7b97\u6cd5\uff0c\u4f46\u5b83\u4ece\u67d0\u4e2a\u9876\u70b9\u5f00\u59cb\uff0c\u9010\u6e10\u6269\u5c55\u6811\u7684\u8fb9\u754c\uff0c\u6bcf\u6b21\u9009\u62e9\u6743\u91cd\u6700\u5c0f\u7684\u8fb9\u6765\u6dfb\u52a0\u3002<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">2. \u6700\u5c0f\u751f\u6210\u6811\u7684\u552f\u4e00\u6027<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u5bf9\u4e8e\u6743\u91cd\u4e0d\u540c\u7684\u8fb9\u7ec4\u6210\u7684\u56fe\uff0c\u6700\u5c0f\u751f\u6210\u6811\u662f\u552f\u4e00\u7684\u3002<\/li>\n\n\n\n<li>\u5982\u679c\u56fe\u4e2d\u5b58\u5728\u591a\u6761\u6743\u91cd\u76f8\u540c\u7684\u8fb9\uff0c\u5219\u53ef\u80fd\u5b58\u5728\u591a\u68f5\u6700\u5c0f\u751f\u6210\u6811\u3002<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">3. \u624b\u6447\u6cd5\uff08Bor\u016fvka&#8217;s Algorithm\uff09<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u7531Otakar Bor\u016fvka\u63d0\u51fa\u7684\u4e00\u79cd\u7b97\u6cd5\uff0c\u662f\u6700\u65e9\u63d0\u51fa\u7684\u7528\u4e8e\u5bfb\u627e\u6700\u5c0f\u751f\u6210\u6811\u7684\u7b97\u6cd5\u4e4b\u4e00\u3002\u5b83\u901a\u8fc7\u53cd\u590d\u5408\u5e76\u6700\u5c0f\u8fb9\u7684\u6b65\u9aa4\u6765\u6784\u5efa\u6700\u5c0f\u751f\u6210\u6811\u3002<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">4. Cayley&#8217;s \u516c\u5f0f<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u5bf9\u4e8e\u4e00\u4e2a\u6709 nnn \u4e2a\u9876\u70b9\u7684\u5b8c\u5168\u56fe\uff0c\u5171\u6709 nn\u22122n^{n-2}nn\u22122 \u68f5\u4e0d\u540c\u7684\u751f\u6210\u6811\u3002\u8fd9\u662f\u4e00\u4e2a\u7ecf\u5178\u7684\u7ec4\u5408\u6570\u5b66\u7ed3\u679c\uff0c\u7531Arthur Cayley\u572819\u4e16\u7eaa\u63d0\u51fa\u3002<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">5. \u77e9\u9635\u6811\u5b9a\u7406\uff08Matrix-Tree Theorem\uff09<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u7ed9\u5b9a\u56fe\u7684\u62c9\u666e\u62c9\u65af\u77e9\u9635\uff0c\u5220\u9664\u5176\u4e2d\u4efb\u610f\u4e00\u884c\u548c\u4e00\u5217\uff0c\u6c42\u5176\u884c\u5217\u5f0f\u7684\u503c\uff0c\u8fd9\u4e2a\u503c\u5373\u4e3a\u56fe\u4e2d\u751f\u6210\u6811\u7684\u6570\u91cf\u3002\u8fd9\u4e00\u5b9a\u7406\u4e3a\u8ba1\u7b97\u751f\u6210\u6811\u6570\u91cf\u63d0\u4f9b\u4e86\u4e00\u79cd\u4ee3\u6570\u65b9\u6cd5\u3002<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">6. Karger\u968f\u673a\u6536\u7f29\u7b97\u6cd5<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u8fd9\u662f\u4e00\u4e2a\u57fa\u4e8e\u968f\u673a\u5316\u7684\u7b97\u6cd5\uff0c\u7528\u4e8e\u5bfb\u627e\u56fe\u7684\u6700\u5c0f\u5272\uff0c\u4f46\u4e5f\u53ef\u4ee5\u7528\u4e8e\u751f\u6210\u6811\u95ee\u9898\u3002\u5b83\u901a\u8fc7\u968f\u673a\u9009\u62e9\u8fb9\u8fdb\u884c\u6536\u7f29\u64cd\u4f5c\uff0c\u6700\u7ec8\u7559\u4e0b\u7684\u8fb9\u6784\u6210\u751f\u6210\u6811\u3002<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">7. \u56fe\u7684\u76f4\u5f84\u548c\u751f\u6210\u6811<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u751f\u6210\u6811\u7684\u76f4\u5f84\uff0c\u5373\u751f\u6210\u6811\u4e2d\u6700\u8fdc\u7684\u4e24\u4e2a\u9876\u70b9\u4e4b\u95f4\u7684\u8ddd\u79bb\uff0c\u4e0e\u539f\u56fe\u7684\u76f4\u5f84\u6709\u5bc6\u5207\u5173\u7cfb\u3002\u67d0\u4e9b\u56fe\u7684\u6700\u5c0f\u751f\u6210\u6811\u7684\u76f4\u5f84\u53ef\u4ee5\u663e\u8457\u5c0f\u4e8e\u539f\u56fe\u7684\u76f4\u5f84\u3002<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">8. Steiner\u6811\u95ee\u9898<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u8fd9\u662f\u751f\u6210\u6811\u95ee\u9898\u7684\u4e00\u4e2a\u6269\u5c55\u3002\u7ed9\u5b9a\u56fe\u7684\u4e00\u90e8\u5206\u9876\u70b9\uff0c\u8981\u6c42\u627e\u5230\u4e00\u68f5\u8fde\u63a5\u8fd9\u4e9b\u9876\u70b9\u4e14\u6743\u91cd\u6700\u5c0f\u7684\u6811\u3002Steiner\u6811\u95ee\u9898\u5728\u4e00\u822c\u60c5\u51b5\u4e0b\u662fNP\u5b8c\u5168\u7684\u3002<\/li>\n<\/ul>\n\n\n\n<p>\u8fd9\u4e9b\u5b9a\u7406\u548c\u73b0\u8c61\u5c55\u793a\u4e86\u751f\u6210\u6811\u5728\u56fe\u8bba\u4e2d\u7684\u4e30\u5bcc\u6027\u548c\u6df1\u5ea6\uff0c\u63d0\u4f9b\u4e86\u8bb8\u591a\u6709\u8da3\u7684\u7814\u7a76\u65b9\u5411\u548c\u5e94\u7528\u573a\u666f\u3002<\/p>\n\n\n\n<p><strong>\u8be6\u7ec6\u8bf4\u8bf4Tree3\u662f\u4ec0\u4e48\uff1f\u5b83\u5230\u5e95\u6709\u591a\u5927\uff1f<\/strong><\/p>\n\n\n\n<p>Tree3\uff08\u901a\u5e38\u5199\u4f5c TREE(3)\uff09\u662f\u4e00\u4e2a\u5728\u6570\u7406\u903b\u8f91\u548c\u7ec4\u5408\u6570\u5b66\u4e2d\u7684\u5927\u6570\uff0c\u7531\u7ea6\u745f\u592b\u00b7\u514b\u9c81\u65af\u5361\u5c14\uff08Joseph Kruskal\uff09\u5728\u7814\u7a76\u6781\u7aef\u7ec4\u5408\u95ee\u9898\u65f6\u5f15\u5165\u3002\u5b83\u662f\u514b\u9c81\u65af\u5361\u5c14\u5b9a\u7406\uff08Kruskal&#8217;s Theorem\uff09\u4e2d\u7684\u4e00\u4e2a\u7279\u6b8a\u503c\u3002\u8be5\u5b9a\u7406\u6d89\u53ca\u65e0\u7a77\u5e8f\u5217\u7684\u201c\u4e0d\u53ef\u907f\u514d\u6027\u201d\u95ee\u9898\uff0c\u7279\u522b\u662f\u5728\u6811\u7684\u5d4c\u5165\uff08embedding\uff09\u7406\u8bba\u4e2d\u3002\u5c3d\u7ba1 TREE(3)\u7684\u5177\u4f53\u6570\u503c\u65e0\u6cd5\u5177\u4f53\u8ba1\u7b97\uff0c\u4f46\u6211\u4eec\u53ef\u4ee5\u4e86\u89e3\u5b83\u7684\u4e00\u4e9b\u7279\u6027\u548c\u89c4\u6a21\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">1. TREE(3)\u7684\u5b9a\u4e49<\/h3>\n\n\n\n<p>TREE(3)\u662f\u4e00\u4e2a\u5173\u4e8e\u65e0\u6807\u8bb0\u6811\uff08unlabeled trees\uff09\u7684\u5e8f\u5217\u7684\u95ee\u9898\u3002\u5b9a\u4e49\u5982\u4e0b\uff1a<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>TREE(1)\u662f\u53ef\u4ee5\u5728\u4e00\u884c\u4e2d\u5d4c\u5165\u7684\u4e0d\u540c\u65e0\u6807\u8bb0\u6811\u7684\u6700\u5927\u6570\u91cf\u3002<\/li>\n\n\n\n<li>TREE(2)\u662f\u53ef\u4ee5\u5728\u4e00\u884c\u4e2d\u5d4c\u5165\u7684\u4e0d\u540c\u65e0\u6807\u8bb0\u6811\u7684\u6700\u5927\u6570\u91cf\uff0c\u5176\u4e2d\u8fd9\u4e9b\u6811\u7684\u5d4c\u5165\u5173\u7cfb\u6ee1\u8db3\u4e00\u5b9a\u7684\u6761\u4ef6\u3002<\/li>\n\n\n\n<li>TREE(3)\u662f\u53ef\u4ee5\u5728\u4e00\u884c\u4e2d\u5d4c\u5165\u7684\u4e0d\u540c\u65e0\u6807\u8bb0\u6811\u7684\u6700\u5927\u6570\u91cf\uff0c\u5176\u4e2d\u8fd9\u4e9b\u6811\u7684\u5d4c\u5165\u5173\u7cfb\u6ee1\u8db3\u66f4\u590d\u6742\u7684\u6761\u4ef6\u3002<\/li>\n<\/ul>\n\n\n\n<p>\u514b\u9c81\u65af\u5361\u5c14\u5b9a\u7406\u8bc1\u660e\u4e86\u5bf9\u4e8e\u4efb\u610f\u81ea\u7136\u6570 nnn\uff0cTREE(n)\u90fd\u662f\u6709\u9650\u7684\uff0c\u4f46\u5177\u4f53\u7684\u6570\u503c\u4f1a\u968f\u7740 nnn \u7684\u589e\u52a0\u800c\u8fc5\u901f\u53d8\u5927\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">2. TREE(3)\u7684\u89c4\u6a21<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>TREE(1) \u548c TREE(2) \u867d\u7136\u975e\u5e38\u5927\uff0c\u4f46\u8fd8\u662f\u53ef\u4ee5\u8ba1\u7b97\u548c\u7406\u89e3\u7684\u3002<\/li>\n\n\n\n<li>\u7136\u800c\uff0cTREE(3) \u7684\u89c4\u6a21\u6781\u5176\u5e9e\u5927\uff0c\u8d85\u51fa\u4e86\u6211\u4eec\u65e5\u5e38\u6240\u80fd\u7406\u89e3\u548c\u60f3\u8c61\u7684\u4efb\u4f55\u5927\u6570\u7684\u8303\u56f4\u3002\u5b9e\u9645\u4e0a\uff0cTREE(3) \u88ab\u8ba4\u4e3a\u662f\u6bd4\u5927\u591a\u6570\u6211\u4eec\u80fd\u60f3\u5230\u7684\u5de8\u5927\u6570\u503c\uff08\u5982\u845b\u7acb\u6052\u6570\uff09\u8fd8\u8981\u5927\u7684\u591a\u3002<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">3. \u845b\u7acb\u6052\u6570\uff08Graham&#8217;s Number\uff09\u5bf9\u6bd4<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u845b\u7acb\u6052\u6570\u662f\u53e6\u4e00\u4e2a\u5728\u7ec4\u5408\u6570\u5b66\u4e2d\u51fa\u73b0\u7684\u5de8\u5927\u6570\uff0c\u5176\u5b9a\u4e49\u6d89\u53ca\u5230\u975e\u5e38\u5927\u7684\u6307\u6570\u5854\u548c\u8d85\u5927\u5e42\u6b21\u8fd0\u7b97\u3002<\/li>\n\n\n\n<li>\u5c3d\u7ba1\u845b\u7acb\u6052\u6570\u975e\u5e38\u5e9e\u5927\uff0c\u4f46TREE(3)\u8fdc\u8fdc\u8d85\u51fa\u5b83\u7684\u89c4\u6a21\u3002\u53ef\u4ee5\u8ba4\u4e3a\uff0c\u845b\u7acb\u6052\u6570\u4e0eTREE(3)\u76f8\u6bd4\uff0c\u51e0\u4e4e\u53ef\u4ee5\u5ffd\u7565\u4e0d\u8ba1\u3002<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">4. \u4e0d\u53ef\u8ba1\u7b97\u6027<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u867d\u7136TREE(3)\u662f\u4e00\u4e2a\u5177\u4f53\u7684\u81ea\u7136\u6570\uff0c\u4f46\u5b83\u7684\u5177\u4f53\u503c\u65e0\u6cd5\u901a\u8fc7\u4efb\u4f55\u5df2\u77e5\u7684\u8ba1\u7b97\u65b9\u6cd5\u6765\u8868\u793a\u6216\u8ba1\u7b97\u3002\u8fd9\u662f\u56e0\u4e3a\u5176\u5b9a\u4e49\u6d89\u53ca\u5230\u590d\u6742\u7684\u5d4c\u5165\u5173\u7cfb\u548c\u65e0\u9650\u9012\u5f52\u7684\u7ec4\u5408\u7ed3\u6784\u3002<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">5. \u5728\u5b9e\u9645\u4e2d\u7684\u5e94\u7528<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u867d\u7136TREE(3)\u8fd9\u6837\u7684\u6570\u5728\u5b9e\u9645\u5e94\u7528\u4e2d\u5e76\u4e0d\u76f4\u63a5\u6709\u7528\uff0c\u4f46\u5b83\u5728\u7406\u8bba\u8ba1\u7b97\u673a\u79d1\u5b66\u548c\u6570\u7406\u903b\u8f91\u4e2d\u6709\u91cd\u8981\u610f\u4e49\u3002\u5b83\u5c55\u793a\u4e86\u67d0\u4e9b\u6570\u5b66\u95ee\u9898\u4e2d\u7684\u6781\u7aef\u590d\u6742\u6027\u548c\u4e0d\u53ef\u907f\u514d\u7684\u65e0\u7a77\u589e\u957f\u3002<\/li>\n<\/ul>\n\n\n\n<p>\u603b\u4e4b\uff0cTREE(3)\u662f\u4e00\u4e2a\u5c55\u793a\u7ec4\u5408\u6570\u5b66\u548c\u6570\u7406\u903b\u8f91\u4e2d\u6781\u7aef\u89c4\u6a21\u7684\u6570\u503c\u3002\u867d\u7136\u6211\u4eec\u65e0\u6cd5\u5177\u4f53\u8ba1\u7b97\u51fa\u5b83\u7684\u6570\u503c\uff0c\u4f46\u5b83\u4e3a\u6211\u4eec\u63d0\u4f9b\u4e86\u7406\u89e3\u6781\u7aef\u5927\u6570\u548c\u590d\u6742\u6570\u5b66\u7ed3\u6784\u7684\u673a\u4f1a\u3002<\/p>\n\n\n\n<p><strong>TREE(3)\u662f\u53ef\u4ee5\u5728\u4e00\u884c\u4e2d\u5d4c\u5165\u7684\u4e0d\u540c\u65e0\u6807\u8bb0\u6811\u7684\u6700\u5927\u6570\u91cf\uff0c\u5176\u4e2d\u8fd9\u4e9b\u6811\u7684\u5d4c\u5165\u5173\u7cfb\u6ee1\u8db3\u66f4\u590d\u6742\u7684\u6761\u4ef6\u3002\u600e\u4e48\u7406\u89e3\u8fd9\u53e5\u8bdd\uff1f<\/strong><\/p>\n\n\n\n<p>\u7406\u89e3 TREE(3) \u4ee5\u53ca\u5b83\u5728\u6570\u5b66\u4e2d\u7684\u542b\u4e49\uff0c\u9996\u5148\u9700\u8981\u4e86\u89e3\u4e00\u4e9b\u5173\u4e8e\u65e0\u6807\u8bb0\u6811\uff08unlabeled trees\uff09\u548c\u5d4c\u5165\u5173\u7cfb\uff08embedding\uff09\u7684\u57fa\u7840\u77e5\u8bc6\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">1. \u65e0\u6807\u8bb0\u6811<\/h3>\n\n\n\n<p>\u65e0\u6807\u8bb0\u6811\u662f\u6307\u6ca1\u6709\u7279\u5b9a\u6807\u7b7e\u6216\u6807\u8bb0\u7684\u6811\u5f62\u7ed3\u6784\u3002\u5728\u8fd9\u79cd\u6811\u4e2d\uff0c\u53ea\u6709\u6811\u7684\u7ed3\u6784\u672c\u8eab\u88ab\u8003\u8651\uff0c\u800c\u4e0d\u6d89\u53ca\u9876\u70b9\u7684\u5177\u4f53\u6807\u8bb0\u6216\u540d\u79f0\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">2. \u5d4c\u5165\u5173\u7cfb<\/h3>\n\n\n\n<p>\u6811\u7684\u5d4c\u5165\u5173\u7cfb\u662f\u6307\u4e00\u4e2a\u6811\u53ef\u4ee5\u901a\u8fc7\u9002\u5f53\u7684\u53d8\u6362\u5d4c\u5165\u5230\u53e6\u4e00\u4e2a\u6811\u4e2d\u3002\u4e00\u4e2a\u6811 T1 \u53ef\u4ee5\u5d4c\u5165\u5230\u53e6\u4e00\u4e2a\u6811 T2 \u4e2d\uff0c\u610f\u5473\u7740\u53ef\u4ee5\u901a\u8fc7\u67d0\u79cd\u65b9\u5f0f\u5c06 T1 \u7684\u7ed3\u6784\u6620\u5c04\u5230 T2 \u4e2d\uff0c\u4fdd\u6301 T1 \u7684\u7236\u5b50\u5173\u7cfb\u3002<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">3. TREE(n) \u7684\u5b9a\u4e49<\/h3>\n\n\n\n<p>TREE(n) \u662f\u4e00\u7cfb\u5217\u5173\u4e8e\u65e0\u6807\u8bb0\u6811\u7684\u5d4c\u5165\u5173\u7cfb\u7684\u590d\u6742\u6027\u5ea6\u91cf\u3002\u5177\u4f53\u6765\u8bf4\uff1a<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>TREE(1) \u662f\u53ef\u4ee5\u5728\u4e00\u884c\u4e2d\u5d4c\u5165\u7684\u4e0d\u540c\u65e0\u6807\u8bb0\u6811\u7684\u6700\u5927\u6570\u91cf\uff0c\u5176\u4e2d\u8fd9\u4e9b\u6811\u7684\u5d4c\u5165\u5173\u7cfb\u662f\u76f8\u5bf9\u7b80\u5355\u7684\u3002<\/li>\n\n\n\n<li>TREE(2) \u662f\u5728\u66f4\u590d\u6742\u7684\u5d4c\u5165\u5173\u7cfb\u4e0b\uff0c\u53ef\u4ee5\u5728\u4e00\u884c\u4e2d\u5d4c\u5165\u7684\u4e0d\u540c\u65e0\u6807\u8bb0\u6811\u7684\u6700\u5927\u6570\u91cf\u3002<\/li>\n\n\n\n<li>TREE(3) \u662f\u5728\u8fdb\u4e00\u6b65\u590d\u6742\u7684\u5d4c\u5165\u5173\u7cfb\u4e0b\uff0c\u53ef\u4ee5\u5728\u4e00\u884c\u4e2d\u5d4c\u5165\u7684\u4e0d\u540c\u65e0\u6807\u8bb0\u6811\u7684\u6700\u5927\u6570\u91cf\u3002<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">\u7406\u89e3 TREE(3) \u7684\u5177\u4f53\u542b\u4e49<\/h3>\n\n\n\n<p>TREE(3) \u662f\u5728\u7279\u5b9a\u5d4c\u5165\u6761\u4ef6\u4e0b\uff0c\u80fd\u591f\u5728\u4e00\u884c\u4e2d\u5d4c\u5165\u7684\u4e0d\u540c\u65e0\u6807\u8bb0\u6811\u7684\u6700\u5927\u6570\u91cf\u3002\u8981\u7406\u89e3\u8fd9\u4e00\u70b9\uff0c\u53ef\u4ee5\u8003\u8651\u4ee5\u4e0b\u51e0\u4e2a\u65b9\u9762\uff1a<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>\u5d4c\u5165\u6761\u4ef6\u7684\u590d\u6742\u6027<\/strong>\uff1aTREE(3) \u6d89\u53ca\u7684\u5d4c\u5165\u6761\u4ef6\u6bd4 TREE(1) \u548c TREE(2) \u66f4\u590d\u6742\u3002\u8fd9\u610f\u5473\u7740\uff0c\u6811\u7684\u5d4c\u5165\u5173\u7cfb\u4e0d\u4ec5\u4ec5\u662f\u7b80\u5355\u7684\u6811\u7684\u5305\u542b\u5173\u7cfb\uff0c\u800c\u662f\u6d89\u53ca\u5230\u66f4\u591a\u7684\u7ed3\u6784\u548c\u6a21\u5f0f\u3002<\/li>\n\n\n\n<li><strong>\u6700\u5927\u6570\u91cf<\/strong>\uff1aTREE(3) \u8868\u793a\u5728\u6ee1\u8db3\u8fd9\u4e9b\u590d\u6742\u6761\u4ef6\u4e0b\uff0c\u53ef\u4ee5\u5728\u4e00\u884c\u4e2d\u5d4c\u5165\u7684\u4e0d\u540c\u65e0\u6807\u8bb0\u6811\u7684\u6700\u5927\u6570\u91cf\u3002\u8fd9\u662f\u4e00\u4e2a\u6781\u9650\u503c\uff0c\u5c55\u793a\u4e86\u5728\u8fd9\u4e9b\u6761\u4ef6\u4e0b\u80fd\u591f\u6784\u9020\u51fa\u7684\u6240\u6709\u4e0d\u540c\u6811\u7684\u6570\u91cf\u3002<\/li>\n\n\n\n<li><strong>\u89c4\u6a21\u7684\u4e0d\u53ef\u601d\u8bae<\/strong>\uff1aTREE(3) \u662f\u4e00\u4e2a\u6781\u5176\u5de8\u5927\u7684\u6570\u5b57\uff0c\u8fdc\u8fdc\u8d85\u51fa\u6211\u4eec\u65e5\u5e38\u6240\u80fd\u7406\u89e3\u7684\u8303\u56f4\u3002\u5b83\u5c55\u793a\u4e86\u7ec4\u5408\u6570\u5b66\u4e2d\u7684\u4e00\u4e9b\u6781\u7aef\u590d\u6742\u6027\u548c\u5de8\u5927\u7684\u89c4\u6a21\u3002<\/li>\n<\/ol>\n\n\n\n<h3 class=\"wp-block-heading\">\u793a\u4f8b\u5e2e\u52a9\u7406\u89e3<\/h3>\n\n\n\n<p>\u5c3d\u7ba1\u5177\u4f53\u8ba1\u7b97 TREE(3) \u662f\u4e0d\u53ef\u80fd\u7684\uff0c\u4f46\u6211\u4eec\u53ef\u4ee5\u901a\u8fc7\u4e00\u4e9b\u7b80\u5355\u7684\u4f8b\u5b50\u6765\u7406\u89e3\u5176\u6982\u5ff5\uff1a<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>TREE(1)<\/strong>\uff1a\u5047\u8bbe\u6211\u4eec\u6709\u4e00\u7ec4\u7b80\u5355\u7684\u65e0\u6807\u8bb0\u6811\uff0c\u8981\u6c42\u5b83\u4eec\u7684\u5d4c\u5165\u5173\u7cfb\u662f\u975e\u5e38\u57fa\u672c\u7684\u3002TREE(1) \u4f1a\u8868\u793a\u5728\u8fd9\u4e9b\u7b80\u5355\u6761\u4ef6\u4e0b\u7684\u6700\u5927\u65e0\u6807\u8bb0\u6811\u6570\u91cf\u3002<\/li>\n\n\n\n<li><strong>TREE(2)<\/strong>\uff1a\u5982\u679c\u6211\u4eec\u589e\u52a0\u5d4c\u5165\u6761\u4ef6\u7684\u590d\u6742\u6027\uff08\u4f8b\u5982\uff0c\u8981\u6c42\u6811\u7684\u67d0\u4e9b\u5b50\u7ed3\u6784\u5fc5\u987b\u6ee1\u8db3\u7279\u5b9a\u6a21\u5f0f\uff09\uff0c\u90a3\u4e48 TREE(2) \u5c31\u4f1a\u5728\u8fd9\u4e9b\u6761\u4ef6\u4e0b\u7ed9\u51fa\u6700\u5927\u7684\u65e0\u6807\u8bb0\u6811\u6570\u91cf\u3002<\/li>\n\n\n\n<li><strong>TREE(3)<\/strong>\uff1a\u8fdb\u4e00\u6b65\u589e\u52a0\u5d4c\u5165\u6761\u4ef6\u7684\u590d\u6742\u6027\uff0cTREE(3) \u5c31\u4f1a\u5728\u8fd9\u4e9b\u66f4\u590d\u6742\u6761\u4ef6\u4e0b\u7ed9\u51fa\u6700\u5927\u7684\u65e0\u6807\u8bb0\u6811\u6570\u91cf\u3002<\/li>\n<\/ul>\n\n\n\n<p>\u603b\u4e4b\uff0cTREE(3) \u662f\u5173\u4e8e\u5728\u6781\u5176\u590d\u6742\u7684\u5d4c\u5165\u5173\u7cfb\u4e0b\u80fd\u591f\u6784\u9020\u51fa\u7684\u6700\u5927\u65e0\u6807\u8bb0\u6811\u6570\u91cf\u7684\u5ea6\u91cf\u3002\u867d\u7136\u6211\u4eec\u65e0\u6cd5\u5177\u4f53\u8ba1\u7b97\u5b83\uff0c\u4f46\u5b83\u5728\u7406\u8bba\u4e0a\u5c55\u793a\u4e86\u7ec4\u5408\u6570\u5b66\u548c\u65e0\u6807\u8bb0\u6811\u5d4c\u5165\u95ee\u9898\u4e2d\u7684\u6781\u7aef\u590d\u6742\u6027\u548c\u5de8\u5927\u7684\u89c4\u6a21\u3002<\/p>\n\n\n\n<p><strong>\u8fd8\u6709tree4\u548ctree5\u5417\uff1f<\/strong><\/p>\n\n\n\n<p>\u662f\u7684\uff0cTREE\u5e8f\u5217\u662f\u53ef\u4ee5\u7ee7\u7eed\u5ef6\u4f38\u7684\uff0c\u6709 TREE(4)\u3001TREE(5) \u7b49\u7b49\u3002\u4e00\u822c\u6765\u8bf4\uff0c\u5bf9\u4e8e\u4efb\u610f\u81ea\u7136\u6570 nnn\uff0c\u90fd\u53ef\u4ee5\u5b9a\u4e49 TREE(n)\u3002\u4ee5\u4e0b\u662f\u5bf9\u8fd9\u4e9b\u66f4\u9ad8\u9636 TREE \u6570\u503c\u7684\u7b80\u8981\u63cf\u8ff0\uff1a<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">TREE(n) \u7684\u4e00\u822c\u5b9a\u4e49<\/h3>\n\n\n\n<p>TREE(n) \u662f\u5728\u7279\u5b9a\u5d4c\u5165\u6761\u4ef6\u4e0b\uff0c\u53ef\u4ee5\u5728\u4e00\u884c\u4e2d\u5d4c\u5165\u7684\u4e0d\u540c\u65e0\u6807\u8bb0\u6811\u7684\u6700\u5927\u6570\u91cf\u3002\u8fd9\u4e9b\u5d4c\u5165\u6761\u4ef6\u968f\u7740 nnn \u7684\u589e\u52a0\u53d8\u5f97\u8d8a\u6765\u8d8a\u590d\u6742\u3002\u56e0\u6b64\uff1a<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>TREE(1)<\/strong> \u548c <strong>TREE(2)<\/strong> \u76f8\u5bf9\u8f83\u5bb9\u6613\u7406\u89e3\u548c\u8ba1\u7b97\uff0c\u4f46\u6570\u503c\u5df2\u7ecf\u76f8\u5f53\u5927\u3002<\/li>\n\n\n\n<li><strong>TREE(3)<\/strong> \u6781\u5176\u5e9e\u5927\uff0c\u8fdc\u8d85\u6211\u4eec\u65e5\u5e38\u6240\u80fd\u7406\u89e3\u7684\u4efb\u4f55\u6570\u503c\u8303\u56f4\u3002<\/li>\n\n\n\n<li><strong>TREE(n)<\/strong> \u968f\u7740 nnn \u7684\u589e\u52a0\uff0c\u5d4c\u5165\u6761\u4ef6\u53d8\u5f97\u66f4\u52a0\u590d\u6742\uff0cTREE(n) \u7684\u6570\u503c\u4e5f\u53d8\u5f97\u66f4\u5927\uff0c\u8d85\u51fa\u4e86\u6211\u4eec\u65e5\u5e38\u6240\u80fd\u60f3\u8c61\u7684\u8303\u56f4\u3002<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">\u7406\u89e3\u66f4\u9ad8\u9636 TREE \u6570\u503c<\/h3>\n\n\n\n<p>\u66f4\u9ad8\u9636\u7684 TREE \u6570\u503c\u5982 TREE(4) \u548c TREE(5) \u7684\u89c4\u6a21\u8fdc\u8d85 TREE(3)\uff0c\u6211\u4eec\u4ecd\u7136\u53ef\u4ee5\u4ece\u6982\u5ff5\u4e0a\u7406\u89e3\u8fd9\u4e9b\u6570\u503c\uff1a<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>\u5d4c\u5165\u6761\u4ef6\u7684\u8fdb\u4e00\u6b65\u590d\u6742\u6027<\/strong>\uff1a\u968f\u7740 nnn \u7684\u589e\u52a0\uff0cTREE(n) \u4e2d\u7684\u5d4c\u5165\u6761\u4ef6\u53d8\u5f97\u66f4\u52a0\u590d\u6742\u548c\u4e25\u683c\u3002\u4f8b\u5982\uff0cTREE(4) \u6d89\u53ca\u7684\u5d4c\u5165\u6761\u4ef6\u6bd4 TREE(3) \u66f4\u52a0\u590d\u6742\uff0c\u8981\u6c42\u6811\u7684\u5d4c\u5165\u5173\u7cfb\u6ee1\u8db3\u66f4\u591a\u7684\u7ea6\u675f\u548c\u6a21\u5f0f\u3002<\/li>\n\n\n\n<li><strong>\u6570\u91cf\u7684\u4e0d\u53ef\u601d\u8bae\u6027<\/strong>\uff1aTREE(3) \u5df2\u7ecf\u662f\u4e00\u4e2a\u6781\u5176\u5e9e\u5927\u7684\u6570\u503c\uff0cTREE(4) \u548c TREE(5) \u751a\u81f3\u66f4\u5927\u3002\u5b83\u4eec\u8fdc\u8d85\u4efb\u4f55\u5b9e\u9645\u8ba1\u7b97\u548c\u8868\u793a\u7684\u80fd\u529b\u3002<\/li>\n<\/ol>\n\n\n\n<h3 class=\"wp-block-heading\">\u5bf9\u6bd4\u4e0e\u7406\u89e3<\/h3>\n\n\n\n<p>\u867d\u7136\u5177\u4f53\u7684\u6570\u503c\u65e0\u6cd5\u8ba1\u7b97\uff0c\u4f46\u6211\u4eec\u53ef\u4ee5\u901a\u8fc7\u4ee5\u4e0b\u65b9\u5f0f\u7406\u89e3\u8fd9\u4e9b\u6570\u503c\u7684\u76f8\u5bf9\u5927\u5c0f\uff1a<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>TREE(1)<\/strong> \u76f8\u5bf9\u7b80\u5355\uff0c\u53ef\u4ee5\u7406\u89e3\u4e3a\u57fa\u672c\u5d4c\u5165\u6761\u4ef6\u4e0b\u7684\u65e0\u6807\u8bb0\u6811\u6570\u91cf\u3002<\/li>\n\n\n\n<li><strong>TREE(2)<\/strong> \u589e\u52a0\u4e86\u5d4c\u5165\u6761\u4ef6\uff0c\u6570\u91cf\u663e\u8457\u589e\u52a0\u3002<\/li>\n\n\n\n<li><strong>TREE(3)<\/strong> \u6781\u5176\u5e9e\u5927\uff0c\u8fdc\u8d85\u6211\u4eec\u65e5\u5e38\u6240\u80fd\u7406\u89e3\u7684\u4efb\u4f55\u6570\u503c\u3002<\/li>\n\n\n\n<li><strong>TREE(4) \u548c TREE(5)<\/strong> \u66f4\u52a0\u4e0d\u53ef\u601d\u8bae\uff0c\u5c55\u793a\u4e86\u6781\u7aef\u6761\u4ef6\u4e0b\u7ec4\u5408\u6570\u5b66\u7684\u590d\u6742\u6027\u548c\u5de8\u5927\u7684\u89c4\u6a21\u3002<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">\u603b\u7ed3<\/h3>\n\n\n\n<p>TREE \u5e8f\u5217\u5c55\u793a\u4e86\u7ec4\u5408\u6570\u5b66\u4e2d\u4e00\u4e9b\u6781\u7aef\u590d\u6742\u6027\u548c\u5e9e\u5927\u6570\u503c\u7684\u6982\u5ff5\u3002\u867d\u7136\u5177\u4f53\u7684\u6570\u503c\u65e0\u6cd5\u8ba1\u7b97\uff0c\u4f46\u5b83\u4eec\u4e3a\u6211\u4eec\u63d0\u4f9b\u4e86\u7406\u89e3\u6570\u5b66\u4e2d\u6781\u7aef\u60c5\u51b5\u548c\u590d\u6742\u5d4c\u5165\u5173\u7cfb\u7684\u673a\u4f1a\u3002\u968f\u7740 nnn \u7684\u589e\u52a0\uff0cTREE(n) \u7684\u6570\u503c\u53d8\u5f97\u66f4\u52a0\u5e9e\u5927\u548c\u590d\u6742\uff0c\u8d85\u51fa\u4e86\u4efb\u4f55\u5b9e\u9645\u8ba1\u7b97\u548c\u8868\u793a\u7684\u80fd\u529b\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u600e\u4e48\u7b80\u5355\u7684\u8bc1\u660e\u56db\u8272\u5b9a\u7406\uff1a \u5373\u4efb\u4f55\u5e73\u9762\u5730\u56fe\u90fd\u53ef\u4ee5\u7528\u56db\u79cd\u989c\u8272\u7740\u8272\uff0c\u4f7f\u5f97\u76f8\u90bb\u7684\u533a\u57df\u989c\u8272\u4e0d\u540c\u3002 \u56db\u8272\u5b9a\u7406\u7684\u4e25\u683c\u8bc1\u660e\u975e\u5e38 [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_import_markdown_pro_load_document_selector":0,"_import_markdown_pro_submit_text_textarea":"","footnotes":""},"categories":[145],"tags":[191],"class_list":["post-5533","post","type-post","status-publish","format-standard","hentry","category-ai","tag-mathematica","entry"],"_links":{"self":[{"href":"https:\/\/www.xinyixx.com\/index.php\/wp-json\/wp\/v2\/posts\/5533","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.xinyixx.com\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.xinyixx.com\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.xinyixx.com\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.xinyixx.com\/index.php\/wp-json\/wp\/v2\/comments?post=5533"}],"version-history":[{"count":0,"href":"https:\/\/www.xinyixx.com\/index.php\/wp-json\/wp\/v2\/posts\/5533\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.xinyixx.com\/index.php\/wp-json\/wp\/v2\/media?parent=5533"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.xinyixx.com\/index.php\/wp-json\/wp\/v2\/categories?post=5533"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.xinyixx.com\/index.php\/wp-json\/wp\/v2\/tags?post=5533"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}