{"id":1846,"date":"2021-12-30T19:50:59","date_gmt":"2021-12-30T11:50:59","guid":{"rendered":"http:\/\/www.shuizilong.com\/house\/?p=1846"},"modified":"2022-01-03T09:31:14","modified_gmt":"2022-01-03T01:31:14","slug":"good-bye-2021-2022-is-near","status":"publish","type":"post","link":"https:\/\/www.shuizilong.com\/house\/archives\/good-bye-2021-2022-is-near\/","title":{"rendered":"Good Bye 2021: 2022 is NEAR"},"content":{"rendered":"<h2><span class=\"ez-toc-section\" id=\"%E4%BC%A0%E9%80%81%E9%97%A8\"><\/span>\u4f20\u9001\u95e8<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><a href=\"https:\/\/codeforces.com\/contest\/1616\">https:\/\/codeforces.com\/contest\/1616<\/a><\/p>\n<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_65 counter-hierarchy ez-toc-counter ez-toc-grey ez-toc-container-direction\">\n<p class=\"ez-toc-title\">Table of Contents<\/p>\n<label for=\"ez-toc-cssicon-toggle-item-6a0934f9275a7\" class=\"ez-toc-cssicon-toggle-label\"><span class=\"\"><span class=\"eztoc-hide\" style=\"display:none;\">Toggle<\/span><span class=\"ez-toc-icon-toggle-span\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/span><\/label><input type=\"checkbox\"  id=\"ez-toc-cssicon-toggle-item-6a0934f9275a7\"  aria-label=\"Toggle\" \/><nav><ul class='ez-toc-list ez-toc-list-level-1 ' ><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/www.shuizilong.com\/house\/archives\/good-bye-2021-2022-is-near\/#%E4%BC%A0%E9%80%81%E9%97%A8\" title=\"\u4f20\u9001\u95e8\">\u4f20\u9001\u95e8<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/www.shuizilong.com\/house\/archives\/good-bye-2021-2022-is-near\/#Problem_D_Keep_the_Average_High\" title=\"Problem D. Keep the Average High\">Problem D. Keep the Average High<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/www.shuizilong.com\/house\/archives\/good-bye-2021-2022-is-near\/#Problem_E_Lexicographically_Small_Enough\" title=\"Problem E. Lexicographically Small Enough\">Problem E. Lexicographically Small Enough<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/www.shuizilong.com\/house\/archives\/good-bye-2021-2022-is-near\/#Problem_F_Tricolor_Triangles\" title=\"Problem F. Tricolor Triangles\">Problem F. Tricolor Triangles<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/www.shuizilong.com\/house\/archives\/good-bye-2021-2022-is-near\/#Problem_G_Just_Add_an_Edge\" title=\"Problem G. Just Add an Edge\">Problem G. Just Add an Edge<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/www.shuizilong.com\/house\/archives\/good-bye-2021-2022-is-near\/#Problem_H_Keep_XOR_Low\" title=\"Problem H. Keep XOR Low\">Problem H. Keep XOR Low<\/a><\/li><\/ul><\/nav><\/div>\n\n<p>\u548c <a href=\"https:\/\/t.me\/TwilightParliament\/65222\">\u53bb\u5e74\u4e00\u6837<\/a> \u3002\u3002\u3002\u4eca\u5e74\u7684 GoodBye Round \u7684 Pretest \u4e5f\u5f88\u5f3a\u3002\u3002\u3002<br \/>\n\u5927\u5bb6\u65b0\u5e74\u5feb\u4e50\u5566\u3002\u3002\u3002<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Problem_D_Keep_the_Average_High\"><\/span>Problem D. Keep the Average High<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u6570\u5217\u9009\u6570\uff0c\u8981\u6c42\u5982\u679c\u539f\u5e8f\u5217\u4e2d\u591a\u4e8e1\u4e2a\u8fde\u7eed\u7684\u5168\u88ab\u6311\u4e2d\uff0c\u5219\u6ee1\u8db3\u5e73\u5747\u503c\u5927\u4e8e\u7ed9\u5b9a\u7684 x\uff0c\u95ee\u6700\u591a\u53ef\u4ee5\u9009\u591a\u5c11<br \/>\ndp\uff0c\u53ea\u8981\u8003\u8651\u957f\u5ea6\u4e3a 2\u30013 \u7684\u6bb5\u6ee1\u8db3\u6761\u4ef6\u5373\u53ef\uff0c\u5176\u5b83\u957f\u5ea6\u81ea\u52a8\u6ee1\u8db3\u3002<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Problem_E_Lexicographically_Small_Enough\"><\/span>Problem E. Lexicographically Small Enough<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u7ed9\u5b9a\u4e24\u4e2a\u5b57\u7b26\u4e32 s, t \uff0c\u6bcf\u6b21\u53ef\u4ee5\u4ea4\u6362\u4e24\u4e2a\u76f8\u90bb\u5b57\u7b26\uff0c\u95ee\u81f3\u5c11\u51e0\u6b21\u4ea4\u6362\u53ef\u4ee5\u4f7f\u5f97 s \u5b57\u5178\u5e8f\u5c0f\u4e8e t\u3002<\/p>\n<p>\u8003\u5bdf t[0]\uff0c\u65b9\u6848\u4e00\uff1a\u627e\u5c0f\u4e8e t[0] \u7684\u5b57\u7b26\u4ea4\u6362\u5230 s[0] \u4f4d\u7f6e\u3002\u65b9\u6848\u4e8c\uff1a\u627e\u7b49\u4e8e t[0] \u7684\u5b57\u7b26\u4ea4\u6362\u5230 s[0] \u4f4d\u7f6e\uff0c\u4e4b\u540e\u8fed\u4ee3\u5230\u4e0b\u4e2a\u4f4d\u7f6e\u3002<br \/>\n\u6bcf\u6b21\u90fd\u8d2a\u5fc3\u7684\u627e\u6700\u9760\u524d\u7684\uff0c\u53ef\u4ee5\u5f00 26 \u4e2a deque<int> \u53bb\u8bb0\u5f55\u8fd9\u4e9b\u4f4d\u7f6e\uff0c\u540c\u65f6\u7528\u6811\u72b6\u6570\u7ec4\u7ef4\u62a4\u5220\u9664\u4e8b\u4ef6\u3002<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Problem_F_Tricolor_Triangles\"><\/span>Problem F. Tricolor Triangles<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u7ed9\u5b9a\u4e00\u4e2a\u65e0\u5411\u56fe (n &lt;= 64,m &lt;= 256) \u8981\u6c42\u5bf9\u8fb9\u8fdb\u884c\u4e09\u67d3\u8272\uff0c\u4f7f\u5f97\u5bf9\u4e8e\u4efb\u610f\u4e09\u5143\u7ec4\uff0c\u5982\u679c\u5b58\u5728\u4e09\u6761\u8fb9\u7684\u8bdd\uff0c\u8981\u4e48\u989c\u8272\u5168\u76f8\u7b49\uff0c\u8981\u4e48\u5168\u90e8\u4e0d\u76f8\u7b49\u3002<\/p>\n<p>\u8c8c\u4f3c\u53ef\u4ee5\u968f\u673a\u5316\u4e71\u641e\u6216\u8005\u9ad8\u65af\u6d88\u5143\uff0c\u540e\u8005\u975e\u5e38\u76f4\u63a5\uff0c\u6211\u4eec\u7684\u5fc5\u8981\u6761\u4ef6\u5c31\u662f xi + xj + xk = 0\uff0c\u6211\u4eec\u5efa\u7acb\u6a21 3 \u975e\u9f50\u6b21\u7ebf\u6027\u65b9\u7a0b\u7ec4\u5417\uff0c\u5bf9\u5176\u589e\u5e7f\u77e9\u9635\u8fdb\u884c\u9ad8\u65af\u6d88\u5143\u5373\u53ef\uff0c\u672a\u77e5\u6570\u89c4\u6a21\u662f m\uff0c\u65b9\u7a0b\u7ec4\u6570\u4e3a $n^3$ = $m\\sqrt(m) $\u3002\u3002\u6700\u540e\u5355\u7ec4 Case \u7684\u590d\u6742\u5ea6\u5e94\u8be5\u662f $O(m^3\\sqrt(m))$\uff0c\u590d\u6742\u5ea6\u7206\u70b8\u3002\u3002\u3002\u4f46\u662f\u56e0\u4e3a\u8fd9\u4e2a\u77e9\u9635\u975e\u5e38\u7a00\u758f\uff0c\u5927\u5bb6\u90fd\u8fd9\u4e48\u7206\u8fc7\u53bb\u4e86\u3002\u3002\u3002\u3002\u3002<\/p>\n<p>\uff08\u76f4\u64ad\u91cc Neal Wu \u8bf4\u4e00\u773c\u5c31\u770b\u51fa\u8981 Gauss \u4f46\u662f\u4f30\u8ba1\u4e86\u4e00\u4e0b\u590d\u6742\u5ea6\u8ba4\u4e3a\u4e0d\u53ef\u505a\u5c31\u8df3\u53bb\u505a H \u4e86\u56e7\uff09\u3002<br \/>\n\uff08\u8d5b\u540e\u53bb\u722c\u4e86\u4e00\u4e0b <a href=\"https:\/\/codeforces.com\/blog\/entry\/98471?#comment-872952\">Neal Wu \u7684\u5410\u69fd<\/a>\uff0c\u679c\u7136\u88ab\u4ed6\u6210\u529f cha \u6389\u4e86 AC \u7684\u7a0b\u5e8f\uff0c\u770b\u6765 300iq \u7684\u6570\u636e\u8fd8\u662f\u6709\u70b9\u5f31\u7684\u3002\u3002\u3002\uff09<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Problem_G_Just_Add_an_Edge\"><\/span>Problem G. Just Add an Edge<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u7ed9\u5b9a\u4e00\u4e2a dag\uff0c\u95ee\u6709\u591a\u5c11\u79cd\u52a0\u4e00\u6761\u8fb9\u7684\u65b9\u6848\uff0c\u4f7f\u5f97\u52a0\u5b8c\u540e\u56fe\u4e2d\u5b58\u5728 Hamiltonian path\u3002<\/p>\n<p>dp\uff1f<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Problem_H_Keep_XOR_Low\"><\/span>Problem H. Keep XOR Low<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u7ed9\u4e00\u4e2a\u6570\u96c6\uff0c\u95ee\u6709\u591a\u5c11\u79cd subset \u65b9\u6848\uff0c\u4f7f\u5f97 subset \u79cd\u4efb\u610f\u4e24\u4e2a\u6570\u7684 xor &lt; \u7ed9\u5b9a\u7684\u6570 x\u3002<\/p>\n<p>2-sat\uff1f\u4e8c\u8fdb\u5236 tire?<\/p>\n<p>\u770b\u4e86\u4e00\u4e0b <a href=\"https:\/\/codeforces.com\/contest\/1616\/submission\/141359051\">\u8fd9\u4e2a python \u4ee3\u7801<\/a>\uff0c\u679c\u7136\u5bb9\u6613\u4e3d\u6d01\u3002\u3002<\/p>\n<p>\u7b80\u5355\u6765\u8bf4\u3002\u3002\u5148\u8003\u8651 x = 000111.. \u8fd9\u6837\u7684\u60c5\u51b5\u3002\u90a3\u4e48\u663e\u7136\u6211\u4eec\u53ea\u8981\u8fdb\u884c\u5206\u7ec4\u5373\u53ef\uff0c\u7ec4\u4e0e\u7ec4\u4e4b\u95f4\u76f8\u4e92\u72ec\u7acb\uff0c\u6bcf\u4e2a\u7ec4\u91cc\u53ef\u4ee5\u968f\u4fbf\u9009\u3002\u8003\u8651\u4e00\u822c\u60c5\u51b5\uff0c\u76f8\u5f53\u4e8e\u5728\u4e00\u4e2a binary tire \u6811\u4e0a dp\uff0c\u5b9e\u9645\u4e2d\uff0c\u6211\u4eec\u4e0d\u9700\u8981\u628a\u8fd9\u4e2a tire \u6784\u5efa\u51fa\u6765\u3002\u3002\u3002\u53ea\u8981\u7528 std::sort() + std::partition_point() \u9012\u5f52\u5904\u7406\u4e0b\u53bb\u5373\u53ef\u3002\u3002\u3002<\/p>\n<p>\u8fd9\u91cc\u6709\u4e24\u79cd\u5b9a\u4e49\u9012\u5f52\u51fd\u6570\u7684\u65b9\u5f0f\uff1a<br \/>\n&#8211; f(a,b,i) \u8868\u793a a \u96c6\u5408\u548c b \u96c6\u5408\u81f3\u5c11\u90fd\u9009\u4e86\u4e00\u79cd\u6570\uff0c\u5f53\u524d\u8003\u5bdf\u5230 x \u7684\u7b2c i  \u4f4d\u7684\u65b9\u6848\u6570\u3002<br \/>\n&#8211; g(a,b,i) \u8868\u793a\u5141\u8bb8\u4e0d\u9009 a \u96c6\u5408\u6216 b \u96c6\u5408\u7684\u65b9\u6848\u6570\u3002<\/p>\n<p>\u663e\u7136\u6211\u4eec\u6709 g = f + 2^|a| + 2^|b| &#8211; 1\u3002<\/p>\n<p>\u7136\u540e\u6211\u4eec\u5bf9\u7b2c i \u4f4d\u8fdb\u884c\u8ba8\u8bba\uff0c\u6211\u4eec\u53d1\u73b0\u4e00\u79cd\u60c5\u51b5\u4e0b\u7528 f \u8868\u793a\u66f4\u65b9\u4fbf\uff0c\u53e6\u4e00\u79cd\u60c5\u51b5\u4e0b\u7528 g \u8868\u793a\u66f4\u65b9\u4fbf\u3002\u3002\u7136\u540e f \u548c g \u53ef\u4ee5\u7528\u4e0a\u9762\u7b80\u5355\u7684\u5f0f\u5b50\u8fdb\u884c\u4e92\u76f8\u6362\u7b97\uff0c\u6240\u4ee5\u6211\u4eec\u73b0\u5728\u90fd\u53ea\u770b\u6bd4\u8f83\u77ed\u7684\u90a3\u4e00\u79cd\u8f6c\u79fb\u5373\u53ef\uff0c\u4e5f\u5c31\u662f\uff1a<\/p>\n<ul>\n<li>f(a,b,i) = f(a0, b0,i-1) + f(a1, b1,i-1) | x \u7684\u7b2c i \u4f4d\u4e3a 0\u3002<\/li>\n<li>g(a,b,i) = g(a0, b1,i-1) * g(a1, b0,i-1) | x \u7684\u7b2c i \u4f4d\u4e3a 1\u3002<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>\u4f20\u9001\u95e8 https:\/\/codeforces.com\/contest\/1616 \u548c \u53bb\u5e74\u4e00\u6837 \u3002\u3002\u3002\u4eca\u5e74\u7684 GoodBye Round \u7684 Pretest \u4e5f\u5f88\u5f3a\u3002\u3002\u3002 \u5927\u5bb6\u65b0\u5e74\u5feb\u4e50\u5566\u3002\u3002\u3002 Problem D. Keep the Average High \u6570\u5217\u9009\u6570\uff0c\u8981\u6c42\u5982\u679c\u539f\u5e8f\u5217\u4e2d\u591a\u4e8e1\u4e2a\u8fde\u7eed\u7684\u5168\u88ab\u6311\u4e2d\uff0c\u5219\u6ee1\u8db3\u5e73\u5747\u503c\u5927\u4e8e\u7ed9\u5b9a\u7684 x\uff0c\u95ee\u6700\u591a\u53ef\u4ee5\u9009\u591a\u5c11 dp\uff0c\u53ea\u8981\u8003\u8651\u957f\u5ea6\u4e3a 2\u30013 \u7684\u6bb5\u6ee1\u8db3\u6761\u4ef6\u5373\u53ef\uff0c\u5176\u5b83\u957f\u5ea6\u81ea\u52a8\u6ee1\u8db3\u3002 Problem E. Lexicographically Small Enough \u7ed9\u5b9a\u4e24\u4e2a\u5b57\u7b26\u4e32 s, t \uff0c\u6bcf\u6b21\u53ef\u4ee5\u4ea4\u6362\u4e24\u4e2a\u76f8\u90bb\u5b57\u7b26\uff0c\u95ee\u81f3\u5c11\u51e0\u6b21\u4ea4\u6362\u53ef\u4ee5\u4f7f\u5f97 s \u5b57\u5178\u5e8f\u5c0f\u4e8e t\u3002 \u8003\u5bdf t[0]\uff0c\u65b9\u6848\u4e00\uff1a\u627e\u5c0f\u4e8e t[0] \u7684\u5b57\u7b26\u4ea4\u6362\u5230 s[0] \u4f4d\u7f6e\u3002\u65b9\u6848\u4e8c\uff1a\u627e\u7b49\u4e8e t[0] \u7684\u5b57\u7b26\u4ea4\u6362\u5230 s[0] \u4f4d\u7f6e\uff0c\u4e4b\u540e\u8fed\u4ee3\u5230\u4e0b\u4e2a\u4f4d\u7f6e\u3002 \u6bcf\u6b21\u90fd\u8d2a\u5fc3\u7684\u627e\u6700\u9760\u524d\u7684\uff0c\u53ef\u4ee5\u5f00 26 \u4e2a deque \u53bb\u8bb0\u5f55\u8fd9\u4e9b\u4f4d\u7f6e\uff0c\u540c\u65f6\u7528\u6811\u72b6\u6570\u7ec4\u7ef4\u62a4\u5220\u9664\u4e8b\u4ef6\u3002 Problem F. Tricolor Triangles \u7ed9\u5b9a\u4e00\u4e2a\u65e0\u5411\u56fe (n [&hellip;]<\/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":true,"jetpack_social_options":{"image_generator_settings":{"template":"highway","enabled":false}}},"categories":[1],"tags":[],"class_list":["post-1846","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"jetpack_publicize_connections":[],"jetpack_featured_media_url":"","jetpack_shortlink":"https:\/\/wp.me\/p2tdP7-tM","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/posts\/1846","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=1846"}],"version-history":[{"count":1,"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/posts\/1846\/revisions"}],"predecessor-version":[{"id":1847,"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/posts\/1846\/revisions\/1847"}],"wp:attachment":[{"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/media?parent=1846"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/categories?post=1846"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/tags?post=1846"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}