{"id":1125,"date":"2024-02-19T09:16:48","date_gmt":"2024-02-19T01:16:48","guid":{"rendered":"http:\/\/ggapa.net:81\/?p=1125"},"modified":"2024-02-21T11:40:22","modified_gmt":"2024-02-21T03:40:22","slug":"%e5%81%9a%e9%a2%98%e7%ac%94%e8%ae%b0uva","status":"publish","type":"post","link":"http:\/\/ggapa.net:81\/2024\/02\/19\/%e5%81%9a%e9%a2%98%e7%ac%94%e8%ae%b0uva\/","title":{"rendered":"\u505a\u9898\u7b14\u8bb0(UVA)"},"content":{"rendered":"<h3><a href=\"https:\/\/www.luogu.com.cn\/problem\/UVA12661\">UVA 12661 Funny Car Racing<\/a><\/h3>\n<p>\u4e00\u4e2a\u6807\u51c6\u7684\u6700\u77ed\u8def\uff0c\u4f46\u662f\u5728\u8ba1\u7b97\u8ddd\u79bb\u8fd9\u4e00\u65b9\u9762\u9700\u8981\u6ce8\u610f\uff0c\u5f53\u6211\u4eec\u6765\u5f53\u4e00\u4e2a\u8d5b\u9053\u4e0a\u65f6\uff0c\u4f1a\u6709\u4ee5\u4e0b\u51e0\u79cd\u60c5\u51b5\uff1a<\/p>\n<ul>\n<li>\u8d5b\u9053\u6b63\u5728\u5f00\u653e\uff0c\u4e14\u5728\u901a\u8fc7\u8d5b\u9053\u4e4b\u524d\u8d5b\u9053\u4e0d\u4f1a\u5173\u95ed\uff0c\u65f6\u95f4\u5373\u4e3a\u901a\u8fc7\u8d5b\u9053\u7684\u65f6\u95f4<\/li>\n<li>\u8d5b\u9053\u6b63\u5728\u5f00\u653e\uff0c\u4f46\u662f\u5269\u4f59\u65f6\u95f4\u4e0d\u8db3\u4ee5\u901a\u8fc7\u8d5b\u9053\uff0c\u65f6\u95f4\u5373\u4e3a\u7b49\u5f85\u65f6\u95f4\u52a0\u4e0a\u5173\u95ed\u65f6\u95f4\u52a0\u4e0a\u901a\u8fc7\u65f6\u95f4\u3002<\/li>\n<li>\u6ce8\u610f\u8fde\u8fb9\u7684\u65f6\u5019\uff0c\u82e5\u5f00\u653e\u65f6\u95f4\u5c0f\u4e8e\u6240\u901a\u8fc7\u7684\u65f6\u95f4\uff0c\u90a3\u4e48\u8fd9\u6761\u8fb9\u5c31\u4e0d\u7528\u94fe\u63a5\u4e86\u3002<\/li>\n<\/ul>\n<p>\u603b\u7ed3\uff1a\u770b\u5230\u6700\u77ed\u8def\u7684\u9898\u76ee\uff0c\u8ba4\u771f\u5206\u6790\u65b0\u7684\u8ddd\u79bb\uff0c\u65e0\u9700\u591a\u8651\uff0c\u76f4\u63a5\u8dd1\u6700\u77ed\u8def\u5c31\u53ef\u4ee5\uff0c\u4f46\u662f\u5bf9\u4e8e2023\u5e74CSP\u7684\u4e00\u9053\u9898\u76ee\uff0c\u5c31\u9700\u8981\u8ba4\u771f\u5206\u6790\u6027\u8d28\uff0c\u7136\u540e\u4f5c\u7b54\u3002<br \/>\n\u6700\u77ed\u8def\u7684\u8d2a\u5fc3\u5df2\u7ecf\u662f\u8bc1\u660e\u8fc7\u7684\u4e86\uff0c\u65e0\u9700\u518d\u591a\u8651\u3002<\/p>\n<h3><a href=\"https:\/\/www.luogu.com.cn\/problem\/UVA12716\">UVA 12716 XOR GCD<\/a><\/h3>\n<p>\u6570\u8bba\u9898\uff0c\u6211\u4eec\u9700\u8981\u77e5\u9053\uff1a<\/p>\n<ul>\n<li>$a \\oplus b = c $ \u7b49\u4ef7\u4e8e $a\\oplus c = b$\u3002<\/li>\n<\/ul>\n<p>\u90a3\u4e48\u6211\u4eec\u5c31\u53ef\u4ee5\u679a\u4e3e $a$ \u548c\u679a\u4e3e $c$\uff0c\u7136\u540e\u7b97\u51fa $b$\uff0c\u63a5\u7740\u9a8c\u8bc1\u662f\u5426\u6709 $\\gcd(a, b) = c$, \u56e0\u4e3a $c$ \u65f6 $a$ \u7684\u7ea6\u6570\uff0c\u65f6\u95f4\u590d\u6742\u5ea6 $O(n\\log n)$\uff0c\u800c\u8ba1\u7b97 $\\gcd$ \u7684\u65f6\u95f4\u662f $O(\\log n)$\uff0c\u603b\u4f53\u65f6\u95f4\u590d\u6742\u5ea6 $O(n(\\log n)^2)$\u3002<\/p>\n<p>\u65f6\u95f4\u590d\u6742\u5ea6\u8fc7\u9ad8\uff0c\u65e0\u6cd5\u901a\u8fc7\u672c\u9898\uff0c\u8003\u8651\u5982\u4f55\u4f18\u5316\u3002<\/p>\n<p>\u6b64\u65f6\u6211\u4eec\u66b4\u529b\u6253\u51fa $a$\u3001$b$\u3001$c$ \u4e4b\u95f4\u7684\u5173\u7cfb\uff0c\u6211\u4eec\u53ef\u4ee5\u53d1\u73b0\u51fa\u4e00\u4e2a\u89c4\u5f8b $c = a - b$\u3002<\/p>\n<blockquote>\n<p>\u8bc1\u660e\uff1a\u6613\u5f97 $a  - b\\le a\\oplus b$\uff0c\u4e14 $a\\oplus b \\ge \\gcd(a, b) = c$\uff0c\u8003\u8651\u4f7f\u7528\u53cd\u8bc1\u6cd5\uff0c\u5047\u8bbe $a  -b &gt; c $\uff0c\u53ef\u4ee5\u5f97\u5230 $c &lt; a - b \\le a\\oplus b$\uff0c\u4e0e $c = a\\oplus b$ \u77db\u76fe\uff0c\u6545 $a - b = c$ \u5f97\u8bc1\u3002<\/p>\n<\/blockquote>\n<p>\u65f6\u95f4\u590d\u6742\u5ea6 $O(n \\log n)$\u3002<\/p>\n<p><strong>\u503c\u5f97\u6ce8\u610f\u7684\u662f\uff1a$\\oplus$ \u7684\u8fd0\u7b97\u4f18\u5148\u7ea7\u662f\u4f4e\u4e8e $=$ \uff0c\u5728\u8fdb\u884c\u5224\u65ad\u7684\u65f6\u5019\u9700\u8981\u52a0 $()$\u3002<\/strong><\/p>\n<hr \/>\n<p>\u4f46\u5728\u8003\u573a\u4e0a\uff0c\u6211\u4eec\u5c31\u4e0d\u80fd\u8fd9\u4e48\u505a\uff0c\u6211\u4eec\u4e0d\u9700\u8981\u7ba1\u8bc1\u660e\uff0c\u6211\u4eec\u76f4\u63a5\u6253\u8868\u770b\u89c4\u5f8b\uff01\uff01\uff01<\/p>\n<p>\u603b\u7ed3\uff1a<\/p>\n<ul>\n<li>\u6211\u4eec\u5e94\u5f53\u7262\u8bb0\uff1a<strong>\u66b4\u529b\u51fa\u5947\u8ff9\uff0c\u6253\u8868\u51fa\u7701\u4e00\uff01<\/strong> \u8c01\u544a\u8bc9\u4e86\u6211\u96be\u9898\u4e00\u5b9a\u8981\u63a8\u516c\u5f0f\u624d\u80fd\u505a\u5462\uff1f<\/li>\n<\/ul>\n<ul>\n<li>\u6253\u8868\u5e94\u8be5\u662f\u9762\u5bf9\u6570\u5b66\u9898\/\u6784\u9020\u9898\u7684\u7b2c\u4e00\u53cd\u5e94\u3002<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>UVA 12661 Funny Car Racing \u4e00\u4e2a\u6807\u51c6\u7684\u6700\u77ed\u8def\uff0c\u4f46\u662f\u5728\u8ba1\u7b97\u8ddd\u79bb\u8fd9\u4e00\u65b9\u9762\u9700\u8981\u6ce8\u610f\uff0c\u5f53\u6211\u4eec [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[12],"tags":[],"_links":{"self":[{"href":"http:\/\/ggapa.net:81\/wp-json\/wp\/v2\/posts\/1125"}],"collection":[{"href":"http:\/\/ggapa.net:81\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/ggapa.net:81\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/ggapa.net:81\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/ggapa.net:81\/wp-json\/wp\/v2\/comments?post=1125"}],"version-history":[{"count":4,"href":"http:\/\/ggapa.net:81\/wp-json\/wp\/v2\/posts\/1125\/revisions"}],"predecessor-version":[{"id":1143,"href":"http:\/\/ggapa.net:81\/wp-json\/wp\/v2\/posts\/1125\/revisions\/1143"}],"wp:attachment":[{"href":"http:\/\/ggapa.net:81\/wp-json\/wp\/v2\/media?parent=1125"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/ggapa.net:81\/wp-json\/wp\/v2\/categories?post=1125"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/ggapa.net:81\/wp-json\/wp\/v2\/tags?post=1125"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}