{"id":595,"date":"2012-12-14T07:13:46","date_gmt":"2012-12-13T23:13:46","guid":{"rendered":"http:\/\/www.shuizilong.com\/house\/?p=595"},"modified":"2012-12-14T07:18:55","modified_gmt":"2012-12-13T23:18:55","slug":"codechef-december-challenge-2012","status":"publish","type":"post","link":"https:\/\/www.shuizilong.com\/house\/archives\/codechef-december-challenge-2012\/","title":{"rendered":"CodeChef December Challenge 2012"},"content":{"rendered":"<p>\u3002\u6c34\u9898\u7565\u3002\u3002\uff09<\/p>\n<p><!--more--><\/p>\n<h2 style=\"color: #7B5E47;\">Sereja and Data Structures<\/h2>\n<h3>Brief description: <\/h3>\n<p>\u3002\u3002\u7ed9\u5b9a\u957f\u5ea6\u4e3a n \u7684\u6570\u5217 {an}\u3002\u3002\u8bb0 s(l, r) \u4e3a [l, r] \u533a\u95f4\u91cc\u6700\u5927\u6570\u4e0e\u6700\u5c0f\u6570\u7684\u5dee\u3002\u3002\u3002<br \/>\n\u3002\u3002\u3002\u8be2\u95ee\u6240\u6709 s(l, r) \u7684\u7684\u79ef\u3002\u3002\uff08\u3002\u3002\u6570\u636e\u4fdd\u8bc1\u662f\u968f\u673a\u751f\u6210\u7684\u3002\u3002\u3002<\/p>\n<h3>Analysis: <\/h3>\n<p>\u3002\u3002\u5206\u6cbb\u3002\u3002\u6bcf\u6b21\u627e\u5230\u5f53\u524d\u533a\u95f4\u7684\u6700\u5927\u503c\u8bb0\u4f5c m\uff08\u3002\u3002\u6216\u6700\u5c0f\u503c\u3002\u3002\u53ef\u4ee5\u6bd4\u8f83\u54ea\u4e00\u4e2a\u66f4\u63a5\u8fd1\u4e2d\u70b9\u3002\u3002<br \/>\n\u3002\u5219\u6309\u4ece\u5c0f\u5230\u5927\u7684\u987a\u5e8f\u63d2\u5165\u5176\u4ed6\u6570\u5b57\u3002\u3002\uff08\u3002\u8fd9\u4e00\u6b65\u66b4\u529b\u6392\u5e8f\u3002\u3002<br \/>\n\u3002\u3002\u3002\u3002\u5de6\u53f3\u5404\u7ef4\u62a4\u5f53\u524d\u6700\u8fdc\u7684\u53ef\u7528\u8ddd\u79bb\u3002\u3002\u3002\u590d\u6742\u5ea6 O(nlog^2n)<br \/>\n\u3002\uff08Remark\uff1a\u548c <a href=\"https:\/\/www.shuizilong.com\/house\/archives\/spoj-9392-play-with-sequence\/\">N \u5e74\u524d\u6211\u51fa\u7684\u4e00\u4e2a\u9898<\/a> \u4e00\u6837\u3002\u3002\u4f9d\u8d56\u4e8e\u6570\u636e\u7684\u968f\u673a\u6027\u3002\u3002\u4e0d\u8fc7\u8fd9\u4e2a\u9898\u7684 Killer \u4f3c\u4e4e\u5f88\u597d\u6784\u9020\uff1f\u3002\u3002\u7ed9\u4e2a\u9012\u589e\u7684\u6570\u5217\u5c31\u884c\u4e86\u3002\u3002<\/p>\n<h2 style=\"color: #7B5E47;\">Arigeom Beats<\/h2>\n<h3>Brief description: <\/h3>\n<p>\u3002\u7ed9\u5b9a n \u4e2a\u6b63\u6574\u6570 {An}\uff0c\u5c06\u8fd9\u4e9b\u6570\u5206\u89e3\u6210\u4e00\u4e2a AP\uff08\u7b97\u6570\u5e8f\u5217\uff09 \u548c\u4e00\u4e2a GP \uff08\u51e0\u4f55\u6570\u5217\uff09\u3002\u3002\u3002<br \/>\n\u5141\u8bb8\u4e00\u4e2a\u6570\u540c\u65f6\u51fa\u73b0\u5728 AP \u548c GP \u4e2d\u3002\u3002\u3002 p \u53ef\u4ee5\u662f\u6709\u7406\u6570\u3002\u3002\uff08\u8bb0 d \u4e3a \u8be5 AP \u7684\u516c\u5dee\u3002\u3002p \u4e3a\u8be5 GP \u6570\u5217\u7684\u516c\u6bd4\u3002\u3002\u4e0b\u540c\u3002\u3002<br \/>\n\uff08\u3002\u3002{An} \u9012\u589e\u7ed9\u51fa\u4e14\u4e92\u4e0d\u76f8\u540c\u3002\u3002\u3002\u3002n <= 1e4, Ai <= 1e5 ... \u3002\u3002)\n\n\n\n<h3>Analysis: <\/h3>\n<p>\uff08\u3002\u3002\u3002\u505a\u6cd5\u7c7b\u4f3c <a href=\"http:\/\/codeforces.com\/contest\/125\/problem\/D \">CF \u8fd9\u9898<\/a>\u3002\u3002<br \/>\n\u3002\u3002<\/p>\n<p> \u7531\u4e8e\u6bcf\u9879\u81f3\u5c11\u5b58\u5728\u5728 AP \u548c GP \u4e2d\u7684\u4e00\u4e2a\u3002\u3002\u3002<br \/>\n\u3002\u3002\u8003\u5bdf\u524d 3 \u4e2a\u6570\u3002\u3002\u5fc5\u7136\u6709 2 \u4e2a\u4f1a\u843d\u5728 AP \u6216\u8005 GP \u4e2d\u3002\u3002\u4e14\u662f\u8be5\u6570\u5217\u4e2d\u6700\u5c0f\u7684\u4e24\u9879\uff08\u5916\u5c42\u5171\u9700\u679a\u4e3e 6 \u79cd\u60c5\u51b5\u3002\u3002<br \/>\n\u3002\u3002\u3002\u3002\u3002\u90a3\u4e48 Sub Task \u662f\u9a8c\u8bc1\u662f\u5426\u5b58\u5728\u4e00\u4e2a AP \uff08\u6216\u8005 GP \u6570\u5217\uff09\u3002\u3002\u4f7f\u5f97\u3002\u3002\u67d0\u4e9b\u6570\u5b57\u5fc5\u987b\u51fa\u73b0\u3002\u3002\u67d0\u4e9b\u6570\u5b57\u53ef\u4ee5\u51fa\u73b0\u3002\u3002<\/p>\n<ul>\n<li>\u5bf9\u4e8e AP\u3002\u3002\u3002<\/li>\n<p>\u3002\u3002\u5982\u679c\u5b58\u5728\uff0c\u5219\u5bf9\u6240\u6709\u5fc5\u987b\u51fa\u73b0\u7684\u6570\u5b57\u6392\u5e8f\u3002\u3002d \u4e00\u5b9a\u662f\u6240\u6709\u76f8\u90bb\u6570\u5b57\u7684\u5dee\u7684 gcd \u3002\u3002\u3002<\/p>\n<li>\u5bf9\u4e8e GP\u3002\u3002\u3002<\/li>\n<p>\u3002\u3002\u5982\u679c\u5b58\u5728\uff0c\u5219\u5bf9\u6240\u6709\u5fc5\u987b\u51fa\u73b0\u7684\u6570\u5b57\u6392\u5e8f\u3002\u3002\u5219 \u6700\u5c0f\u6570 \u548c \u6700\u5927\u6570 \u5fc5\u7136\u53ef\u4ee5\u662f GP \u6570\u5217\u7684\u7b2c\u4e00\u9879\u548c\u6700\u540e\u4e00\u9879\u3002\u3002<br \/>\n\u8bbe\u6700\u5927\u6570 \/ \u6700\u5c0f\u6570\u7684\u6700\u7b80\u5206\u6570\u4e3a  A \/ B \u3002\u3002GP \u6570\u5217\u6709 m+1 \u9879\u3002\u3002\u90a3\u4e48 a \u548c b \u7684 m \u6b21\u65b9\u6839\u90fd\u5fc5\u987b\u662f\u6709\u7406\u6570\u3002\u3002\u3002<br \/>\n\u3002\u3002\u5373\u5408\u6cd5\u7684 m  \u4e3a  \u3002\u3002\u3002 A \u548c B \u7684\u6240\u6709\u8d28\u56e0\u5b50\u7684\u5e42\u7684 gcd  \u7684\u7ea6\u6570\u3002\u3002\u3002\u3002\n<\/ul>\n<p><a href=\"http:\/\/www.codechef.com\/DEC12\/problems\/DIFTRIP\"  style=\"color: #7B5E47;\"><\/p>\n<h2>Different Trips<\/h2>\n<p><\/a><\/p>\n<h3>Brief description: <\/h3>\n<p>\u3002\u3002\u7ed9\u5b9a\u4e00\u9897\u6709\u6839\u6811\u3002\u3002\u95ee\u6240\u6709\u6839\u5230\u53f6\u5b50\u7ed3\u70b9\u6240\u6784\u6210\u7684\u5b57\u7b26\u4e32\u96c6\u5408\u3002\u6709\u591a\u5c11\u4e0d\u540c\u7684\u5b50\u4e32\u3002\u3002\u3002<br \/>\n\u3002\u7ed3\u70b9\u6240\u8868\u793a\u5b57\u7b26\u7b49\u4e8e\u8fd9\u4e2a\u7ed3\u70b9\u7684\u5ea6\u6570\u3002\u3002<\/p>\n<h3>Analysis: <\/h3>\n<p>\u3002\u3002\u5f00\u59cb\u4e00\u76f4\u4ece\u52a8\u6001\u6dfb\u52a0\u5b57\u7b26\u7684\u89d2\u5ea6\u8003\u5bdf\u8fd9\u4e2a\u95ee\u9898\u3002\u3002\uff08\u3002\u3002<a href=\"http:\/\/user.qzone.qq.com\/251815992\/main#!app=2&#038;via=QZ.HashRefresh&#038;pos=1354652974\">\u5475\u5475\u5475\u3002\u3002<\/a><br \/>\n\u3002\u540e\u6765\u5728\u8457\u540d\u56fe\u8bba\u5dc5\u5cf0\u4eba\u7269 <a href=\"http:\/\/acmdiy.org\/wiki\/index.php?title=%E6%88%B4%E6%8C%AF%E9%98%B3\">Daizhenyang<\/a> \u7684\u6ce8\u89c6\u4e0b\u7ec8\u4e8e\u8ba4\u8bc6\u5230\u4e86\u6211\u7684\u5f31\u83dc\u672c\u8d28\u3002\u3002\u3002<\/p>\n<p>\u3002\u5176\u5b9e\u628a\u6839\u5230\u6bcf\u4e2a\u7ed3\u70b9\u7684\u8def\u5f84\u3002\u3002\u7ec4\u7ec7\u6210\u4e00\u9897\u9759\u6001\u7684\u540e\u7f00\u6570\u7ec4\u5c31\u884c\u4e86\u3002\u3002\u3002<br \/>\n\u3002\u3002\u8981\u5bf9\u500d\u589e\u7b97\u6cd5\u8fdb\u884c\u5c11\u91cf\u7684 Modification\u3002\u3002\u3002\uff08\u3002\u3002\u4f7f\u7528\u500d\u589e\u7956\u5148\u3002\u3002\u5176\u4ed6\u5168\u90e8\u7c7b\u6bd4\u539f\u7b97\u6cd5\u5373\u53ef\u3002\u8279\uff1f\u3002\u3002\u8fd9\u4f3c\u4e4e\u662f\u4e2a\u7ecf\u5178\u7684\u9898\u554a\uff1f<\/p>\n<p> \u3002\u3002\u6309\u7167\u53f6\u5b50\u5230\u6839\u7ed3\u70b9\u7684\u987a\u5e8f\u8ba1\u7b97 height \u6570\u7ec4\u7684\u3002\u3002\u4ee5\u4fdd\u8bc1\u7ebf\u6027\u590d\u6742\u5ea6\u3002\u3002<br \/>\n1. \u9047\u5230\u5df2\u7ecf\u8ba1\u7b97\u8fc7\u7684\u3002\u3002\u5219\u76f4\u63a5 break \u6389\uff1b<br \/>\n2. \u82e5\u67d0\u65f6\u523b u, v \u76f8\u540c\u3002\u3002\u5219\u76f4\u63a5 height += dep[u]\uff1b  break \u6389\u3002\u3002 <\/p>\n<p>(Remark: <a href=\"http:\/\/www.lydsy.com\/JudgeOnline\/problem.php?id=1921 \">http:\/\/www.lydsy.com\/JudgeOnline\/problem.php?id=1921 <\/a><\/p>\n<h2 style=\"color: #7B5E47;\">Quasi-Polynomial Sum: <\/h2>\n<p> .. \u8fd9\u4e2a\u9898\u9700\u8981\u7528\u5230\u3002\u4e8c\u9879\u5f0f\u5b9a\u7406 (Binomial theorem)\u3002\u3002\u970d\u7eb3\u89c4\u5219(Horner&#8217;s method)\u3002\u6269\u5c55\u6b27\u51e0\u91cc\u5fb7\u7b97\u6cd5(Extended Euclid&#8217;s algorithm)\u3002\u3002\u6570\u8bba\u53d8\u6362(Number-theoretic transform)\u3002\u3002\u5feb\u901f\u5085\u91cc\u53f6\u53d8\u6362(Fast Fourier transform)\u3002\u548c\u4e2d\u56fd\u5269\u4f59\u5b9a\u7406(Chinese remainder theorem)<br \/>\n\u3002\u3002\u3002\u8fd9\u4e2a\u9898\u8d85\u51fa\u4e86\u672c\u83dc\u7684\u80fd\u529b\u8303\u56f4\u3002\u3002\u3002\uff08\u5475\u5475\u5475\u5475\u3002\u3002\u3002<br \/>\n\u3002\u3002\u3002\uff08<a href=\"http:\/\/discuss.codechef.com\/questions\/4505\/qpolysum-editorial \">\u9898\u89e3<\/a> \u770b\u90fd\u770b\u4e0d\u61c2\u6211\u4f1a\u4e71\u8bf4\uff1f\u3002\u3002 \u3002\u3002<\/p>\n<h2 style=\"color: #7B5E47;\">WordNinjas: <\/h2>\n<p>\u3002\u3002\u3002\u8003\u8651\u5230\u6700\u540e\u9644\u52a0\u9898\u672c\u83dc\u7684\u7b97\u6cd5\u975e\u5e38\u5f31\u667a\u3002\u3002\u5c31\u4e0d\u548c\u5927\u5bb6\u5206\u4eab\u4e86\u3002\uff01\uff01\u3002\u3002<br \/>\n\u7531\u4e8e\u6211\u6ca1\u80fd\u628a\u62df\u591a\u9879\u5f0f\u548c\u7ed9\u64b8\u51fa\u6765\u3002\u3002\u6700\u7ec8\u8fd8\u662f\u50bb\u903c\u7684\u6eda\u51fa\u4e86\u7b2c\u4e00\u7248\u4e3b\u8981\u8fd8\u662f\u81ea\u5df1\u5f31\u4e5f\u6ca1\u4ec0\u4e48\u597d\u96be\u8fc7\u7684\u3002<br \/>\n\u3002\u3002\uff08\u3002\u3002\u5565\u65f6\u5019\u6211\u624d\u80fd\u50cf<a href=\"http:\/\/acmdiy.org\/wiki\/index.php?title=%E6%88%B4%E6%8C%AF%E9%98%B3\">\u6234\u725b<\/a>\u90a3\u6837\u8650\u7206\u5168\u4e16\u754c\u5462\uff1f\u3002\u3002\u3002 \uff09\u3002\u3002\u3002<\/p>\n<h3>External link: <\/h3>\n<p><a href=\"http:\/\/www.codechef.com\/DEC12\">http:\/\/www.codechef.com\/DEC12<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u3002\u6c34\u9898\u7565\u3002\u3002\uff09<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"jetpack_post_was_ever_published":false,"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"_jetpack_memberships_contains_paid_content":false,"footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":false,"jetpack_social_options":{"image_generator_settings":{"template":"highway","enabled":false}}},"categories":[83],"tags":[],"class_list":["post-595","post","type-post","status-publish","format-standard","hentry","category-codechef"],"jetpack_publicize_connections":[],"jetpack_featured_media_url":"","jetpack_shortlink":"https:\/\/wp.me\/p2tdP7-9B","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/posts\/595","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/comments?post=595"}],"version-history":[{"count":1,"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/posts\/595\/revisions"}],"predecessor-version":[{"id":596,"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/posts\/595\/revisions\/596"}],"wp:attachment":[{"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/media?parent=595"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/categories?post=595"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/tags?post=595"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}