{"id":1851,"date":"2022-01-10T12:40:20","date_gmt":"2022-01-10T04:40:20","guid":{"rendered":"http:\/\/www.shuizilong.com\/house\/?p=1851"},"modified":"2022-01-11T14:12:30","modified_gmt":"2022-01-11T06:12:30","slug":"noi-2020","status":"publish","type":"post","link":"https:\/\/www.shuizilong.com\/house\/archives\/noi-2020\/","title":{"rendered":"NOI 2020"},"content":{"rendered":"<ul>\n<li><a href=\"https:\/\/kewth.github.io\/2020\/08\/05\/NOI2020\/\">https:\/\/kewth.github.io\/2020\/08\/05\/NOI2020\/<\/a><\/li>\n<li><a href=\"https:\/\/kewth.github.io\/2020\/09\/03\/NOI2020-%E9%A2%98%E8%A7%A3%E6%8A%A5%E5%91%8A\/\">https:\/\/kewth.github.io\/2020\/09\/03\/NOI2020-%E9%A2%98%E8%A7%A3%E6%8A%A5%E5%91%8A\/<\/a><\/li>\n<\/ul>\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-6a094aa93ed05\" 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-6a094aa93ed05\"  aria-label=\"Toggle\" \/><nav><ul class='ez-toc-list ez-toc-list-level-1 ' ><li class='ez-toc-page-1 ez-toc-heading-level-1'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/www.shuizilong.com\/house\/archives\/noi-2020\/#Day_1\" title=\"Day 1\">Day 1<\/a><ul class='ez-toc-list-level-2' ><li class='ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/www.shuizilong.com\/house\/archives\/noi-2020\/#%E7%BE%8E%E9%A3%9F%E5%AE%B6\" title=\"\u7f8e\u98df\u5bb6\">\u7f8e\u98df\u5bb6<\/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\/noi-2020\/#%E5%91%BD%E8%BF%90\" title=\"\u547d\u8fd0\">\u547d\u8fd0<\/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\/noi-2020\/#%E6%97%B6%E4%BB%A3%E7%9A%84%E7%9C%BC%E6%B3%AA\" title=\"\u65f6\u4ee3\u7684\u773c\u6cea\">\u65f6\u4ee3\u7684\u773c\u6cea<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-1'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/www.shuizilong.com\/house\/archives\/noi-2020\/#Day_2\" title=\"Day 2\">Day 2<\/a><ul class='ez-toc-list-level-2' ><li class='ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/www.shuizilong.com\/house\/archives\/noi-2020\/#%E5%88%B6%E4%BD%9C%E8%8F%9C%E5%93%81\" title=\"\u5236\u4f5c\u83dc\u54c1\">\u5236\u4f5c\u83dc\u54c1<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/www.shuizilong.com\/house\/archives\/noi-2020\/#%E8%B6%85%E7%8E%B0%E5%AE%9E%E6%A0%91\" title=\"\u8d85\u73b0\u5b9e\u6811\">\u8d85\u73b0\u5b9e\u6811<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-8\" href=\"https:\/\/www.shuizilong.com\/house\/archives\/noi-2020\/#%E7%BF%BB%E4%BF%AE%E9%81%93%E8%B7%AF\" title=\"\u7ffb\u4fee\u9053\u8def\">\u7ffb\u4fee\u9053\u8def<\/a><\/li><\/ul><\/li><\/ul><\/nav><\/div>\n\n<h1><span class=\"ez-toc-section\" id=\"Day_1\"><\/span>Day 1<span class=\"ez-toc-section-end\"><\/span><\/h1>\n<h2><span class=\"ez-toc-section\" id=\"%E7%BE%8E%E9%A3%9F%E5%AE%B6\"><\/span>\u7f8e\u98df\u5bb6<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<ul>\n<li><a href=\"https:\/\/www.luogu.com.cn\/problem\/P6772\">Luogu P6772 [NOI2020] \u7f8e\u98df\u5bb6<\/a><br \/>\n\u6734\u7d20 DP + \u77e9\u9635\u4f18\u5316<\/li>\n<\/ul>\n<p>40 \u5206\u6734\u7d20\u5206\u5341\u5206\u597d\u62ff\uff0c\u8003\u8651\u5230 T \u5341\u5206\u5927\uff0c\u4e5f\u5f88\u5bb9\u6613\u60f3\u5230\u63a5\u4e0b\u6765\u8981\u77e9\u9635\u4f18\u5316\u3002<br \/>\n\u5177\u4f53\u5b9e\u73b0\uff0c\u9996\u5148\u8fd9\u91cc\u9700\u8981\u4f7f\u7528\u5e7f\u4e49\u77e9\u9635\u4e58\u6cd5\u7ef4\u62a4 dp \u72b6\u6001\uff0c\u8fd9\u4e2a\u76f8\u4fe1\u5bf9\u4e8e\u719f\u6089 <a href=\"https:\/\/oi-wiki.org\/dp\/dynamic\/\">\u52a8\u6001\u7ef4\u62a4\u6811\u7684\u6700\u5927\u72ec\u7acb\u96c6<\/a> \u7684\u5c0f\u8bfb\u8005\u6765\u8bf4\u4e00\u5b9a\u4e0d\u662f\u4ec0\u4e48\u96be\u9898\u3002\u3002\u3002<br \/>\n\u7136\u540e\u5bf9\u4e8e\u7f8e\u98df\u8282\u8fd9\u4e9b\u7279\u6b8a\u4e8b\u4ef6\uff0c\u6ca1\u6709\u529e\u6cd5\u653e\u8fdb\u77e9\u9635\u91cc\u5904\u7406\uff0c\u4e0d\u8fc7\u7f8e\u98df\u8282\u6570\u76ee\u4e0d\u662f\u5f88\u591a\uff0c\u6211\u4eec\u53ef\u4ee5\u62c9\u51fa\u6765\u5355\u72ec\u5904\u7406\uff0c\u7f8e\u98df\u8282\u4e0e\u7f8e\u98df\u8282\u4e4b\u95f4\u5728\u7528\u77e9\u9635\u4e58\u6cd5\u3002<\/p>\n<h2><span class=\"ez-toc-section\" id=\"%E5%91%BD%E8%BF%90\"><\/span>\u547d\u8fd0<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u7ebf\u6bb5\u6811\u5408\u5e76\u5fc5\u505a\u4e60\u9898\u3002<\/p>\n<h2><span class=\"ez-toc-section\" id=\"%E6%97%B6%E4%BB%A3%E7%9A%84%E7%9C%BC%E6%B3%AA\"><\/span>\u65f6\u4ee3\u7684\u773c\u6cea<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<ul>\n<li><a href=\"https:\/\/www.luogu.com.cn\/problem\/P6774\">P6774 [NOI2020] \u65f6\u4ee3\u7684\u773c\u6cea<\/a><\/li>\n<\/ul>\n<p>\u7ed9\u5b9a\u4e00\u4e2a 1 \u5230 n \u7684\u6392\u5217\uff0cq \u6b21\u8be2\u95ee\uff0c\u6bcf\u6b21\u7ed9\u5b9a\u4e00\u4e2a\u4e0b\u6807\u533a\u95f4\u548c\u4e00\u4e2a\u503c\u57df\u533a\u95f4\u6c42\u5728\u7ed9\u5b9a\u533a\u95f4\u5185\u7684\u5143\u7d20\u7684\u9006\u5e8f\u5bf9\u6570\u3002<\/p>\n<p>\u5f88\u50cf\u4e0a\u4e2a\u6708 <a href=\"https:\/\/atcoder.jp\/contests\/abc233\/tasks\/abc233_h\">abc233 \u7684\u6700\u540e\u4e00\u9898<\/a>\uff0c\u4e0d\u8fc7\u533a\u95f4\u9006\u5e8f\u5bf9\u6ca1\u6709\u4ec0\u4e48\u592a\u597d\u7684\u6027\u8d28\uff0c\u8c8c\u4f3c\u53ea\u80fd\u5206\u5757\u4e71\u641e\u3002<\/p>\n<h1><span class=\"ez-toc-section\" id=\"Day_2\"><\/span>Day 2<span class=\"ez-toc-section-end\"><\/span><\/h1>\n<h2><span class=\"ez-toc-section\" id=\"%E5%88%B6%E4%BD%9C%E8%8F%9C%E5%93%81\"><\/span>\u5236\u4f5c\u83dc\u54c1<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>https:\/\/www.luogu.com.cn\/problem\/P6775<br \/>\n01-\u80cc\u5305<\/p>\n<p>\u6709 n \u79cd\u6750\u6599\uff0c\u7b2c i \u79cd\u6750\u6599\u6709 ai \u4e2a\u3002\u73b0\u8981\u5236\u4f5c m \u79cd\u83dc\uff0c\u6bcf\u79cd\u83dc\u6070\u597d\u4f7f\u7528 k \u4e2a\u6750\u6599\u5e76\u4e14\u4f7f\u7528\u81f3\u591a\u4e24\u79cd\u6750\u6599\u3002\u6c42\u662f\u5426\u5b58\u5728\u65b9\u6848\uff0c\u5982\u679c\u5b58\u5728\u5219\u7ed9\u51fa\u4efb\u610f\u4e00\u4e2a\u65b9\u6848\u3002<\/p>\n<p>\u4fdd\u8bc1  \\sigma ai = mk\u3002<\/p>\n<p>\u9996\u5148\u6211\u4eec\u5e0c\u671b\u6750\u6599\u8d8a\u5c11\u8d8a\u597d\uff0c\u518d\u6ce8\u610f\u5230\u6750\u6599\u6700\u591a\u53ea\u6709 m+2\u3002<br \/>\n\u4e8b\u5b9e\u4e0a\u66b4\u529b\u8d2a\u5fc3\u53ef\u4ee5\u89e3\u51b3 &lt;= m+1 \u7684\u60c5\u51b5\uff0c\u7136\u540e\u5bf9\u4e8e m+2 \u7684\u60c5\u51b5\u53ef\u4ee5\u7528\u80cc\u5305\u5206\u6210\u4e24\u4e2a &lt;= m+1 \u7684\u60c5\u51b5\uff0c\u5404\u79cd\u8bc1\u660e\u5373\u53ef\u3002<\/p>\n<h2><span class=\"ez-toc-section\" id=\"%E8%B6%85%E7%8E%B0%E5%AE%9E%E6%A0%91\"><\/span>\u8d85\u73b0\u5b9e\u6811<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<ul>\n<li><a href=\"https:\/\/www.luogu.com.cn\/problem\/P6776\">P6776 [NOI2020] \u8d85\u73b0\u5b9e\u6811<\/a><\/li>\n<\/ul>\n<p>\u9700\u8981\u4e00\u4e9b\u667a\u529b\u3002\u3002\u3002\u5bfb\u627e\u4e00\u4e9b\u6027\u8d28\u7528\u6709\u9650\u53bb\u523b\u753b\u65e0\u9650\u3002\u3002\u3002<br \/>\n\u611f\u89c9 <a href=\"https:\/\/www.cnblogs.com\/Troverld\/p\/14621898.html\">\u8fd9\u7bc7\u9898\u89e3<\/a> \u5199\u7684\u6700\u597d\u3002\u3002<\/p>\n<p>Observation 9. \u94fe\u6811\u68ee\u6797\u4e2d\uff0c\u82e5\u4ee5\u5f53\u524d\u8282\u70b9\u4e3a\u6839\u7684\u5b50\u6811\u4e2d\u4ec5\u6709\u6709\u9650\u68f5\u94fe\u6811\u65e0\u6cd5\u88ab\u751f\u6210\uff0c\u5f53\u4e14\u4ec5\u5f53\uff1a<br \/>\n&#8211; \u8be5\u70b9\u5728\u67d0\u4e00\u68f5\u94fe\u6811\u4e2d\u662f\u53f6\u5b50\u8282\u70b9\uff0c\u6216<br \/>\n&#8211; \u8be5\u70b9\u62e5\u6709\u5168\u90e8\u56db\u4e2a\u513f\u5b50\uff0c\u4e14\u56db\u4e2a\u513f\u5b50\u4ee3\u8868\u7684\u5b50\u6811\u4e2d\u90fd\u4ec5\u6709\u6709\u9650\u68f5\u6811\u65e0\u6cd5\u88ab\u751f\u6210\u3002<\/p>\n<p>\u8fd9\u91cc\u7684\u56db\u4e2a\u513f\u5b50\u5206\u8868\u8868\u793a\u4e86\u94fe\u6811\u4e2d\u56db\u79cd\u60c5\u51b5\uff0c\u65e2\u533a\u5206\u5144\u5f1f\u8282\u70b9\u662f\u53f6\u5b50\u8fd8\u662f\u7a7a\u3002<br \/>\n\u5982\u679c\u65e2\u4e0d\u662f\u53f6\u5b50\uff0c\u4e5f\u4e0d\u662f\u7a7a\uff0c\u90a3\u4e48\u5c40\u90e8\u4e0d\u5728\u94fe\u6811\u4e2d\u3002<br \/>\n\u53ef\u4ee5\u63d0\u524d\u628a\u8fd9\u975e\u94fe\u6811\u7684\u8f93\u5165\u8fc7\u6ee4\u6389\uff0c\u6216\u8005\u66f4\u65b9\u4fbf\u7684\u5408\u5e76\u7684\u65f6\u5019\u4e0d\u5f80\u4e0b\u4e00\u5c42\u9012\u5f52\u3002<\/p>\n<h2><span class=\"ez-toc-section\" id=\"%E7%BF%BB%E4%BF%AE%E9%81%93%E8%B7%AF\"><\/span>\u7ffb\u4fee\u9053\u8def<span class=\"ez-toc-section-end\"><\/span><\/h2>\n","protected":false},"excerpt":{"rendered":"<p>https:\/\/kewth.github.io\/2020\/08\/05\/NOI2020\/ https:\/\/kewth.github.io\/2020\/09\/03\/NOI2020-%E9%A2%98%E8%A7%A3%E6%8A%A5%E5%91%8A\/ Day 1 \u7f8e\u98df\u5bb6 Luogu P6772 [NOI2020] \u7f8e\u98df\u5bb6 \u6734\u7d20 DP + \u77e9\u9635\u4f18\u5316 40 \u5206\u6734\u7d20\u5206\u5341\u5206\u597d\u62ff\uff0c\u8003\u8651\u5230 T \u5341\u5206\u5927\uff0c\u4e5f\u5f88\u5bb9\u6613\u60f3\u5230\u63a5\u4e0b\u6765\u8981\u77e9\u9635\u4f18\u5316\u3002 \u5177\u4f53\u5b9e\u73b0\uff0c\u9996\u5148\u8fd9\u91cc\u9700\u8981\u4f7f\u7528\u5e7f\u4e49\u77e9\u9635\u4e58\u6cd5\u7ef4\u62a4 dp \u72b6\u6001\uff0c\u8fd9\u4e2a\u76f8\u4fe1\u5bf9\u4e8e\u719f\u6089 \u52a8\u6001\u7ef4\u62a4\u6811\u7684\u6700\u5927\u72ec\u7acb\u96c6 \u7684\u5c0f\u8bfb\u8005\u6765\u8bf4\u4e00\u5b9a\u4e0d\u662f\u4ec0\u4e48\u96be\u9898\u3002\u3002\u3002 \u7136\u540e\u5bf9\u4e8e\u7f8e\u98df\u8282\u8fd9\u4e9b\u7279\u6b8a\u4e8b\u4ef6\uff0c\u6ca1\u6709\u529e\u6cd5\u653e\u8fdb\u77e9\u9635\u91cc\u5904\u7406\uff0c\u4e0d\u8fc7\u7f8e\u98df\u8282\u6570\u76ee\u4e0d\u662f\u5f88\u591a\uff0c\u6211\u4eec\u53ef\u4ee5\u62c9\u51fa\u6765\u5355\u72ec\u5904\u7406\uff0c\u7f8e\u98df\u8282\u4e0e\u7f8e\u98df\u8282\u4e4b\u95f4\u5728\u7528\u77e9\u9635\u4e58\u6cd5\u3002 \u547d\u8fd0 \u7ebf\u6bb5\u6811\u5408\u5e76\u5fc5\u505a\u4e60\u9898\u3002 \u65f6\u4ee3\u7684\u773c\u6cea P6774 [NOI2020] \u65f6\u4ee3\u7684\u773c\u6cea \u7ed9\u5b9a\u4e00\u4e2a 1 \u5230 n \u7684\u6392\u5217\uff0cq \u6b21\u8be2\u95ee\uff0c\u6bcf\u6b21\u7ed9\u5b9a\u4e00\u4e2a\u4e0b\u6807\u533a\u95f4\u548c\u4e00\u4e2a\u503c\u57df\u533a\u95f4\u6c42\u5728\u7ed9\u5b9a\u533a\u95f4\u5185\u7684\u5143\u7d20\u7684\u9006\u5e8f\u5bf9\u6570\u3002 \u5f88\u50cf\u4e0a\u4e2a\u6708 abc233 \u7684\u6700\u540e\u4e00\u9898\uff0c\u4e0d\u8fc7\u533a\u95f4\u9006\u5e8f\u5bf9\u6ca1\u6709\u4ec0\u4e48\u592a\u597d\u7684\u6027\u8d28\uff0c\u8c8c\u4f3c\u53ea\u80fd\u5206\u5757\u4e71\u641e\u3002 Day 2 \u5236\u4f5c\u83dc\u54c1 https:\/\/www.luogu.com.cn\/problem\/P6775 01-\u80cc\u5305 \u6709 n \u79cd\u6750\u6599\uff0c\u7b2c i \u79cd\u6750\u6599\u6709 ai \u4e2a\u3002\u73b0\u8981\u5236\u4f5c m \u79cd\u83dc\uff0c\u6bcf\u79cd\u83dc\u6070\u597d\u4f7f\u7528 k \u4e2a\u6750\u6599\u5e76\u4e14\u4f7f\u7528\u81f3\u591a\u4e24\u79cd\u6750\u6599\u3002\u6c42\u662f\u5426\u5b58\u5728\u65b9\u6848\uff0c\u5982\u679c\u5b58\u5728\u5219\u7ed9\u51fa\u4efb\u610f\u4e00\u4e2a\u65b9\u6848\u3002 \u4fdd\u8bc1 [&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-1851","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"jetpack_publicize_connections":[],"jetpack_featured_media_url":"","jetpack_shortlink":"https:\/\/wp.me\/p2tdP7-tR","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/posts\/1851","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=1851"}],"version-history":[{"count":1,"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/posts\/1851\/revisions"}],"predecessor-version":[{"id":1852,"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/posts\/1851\/revisions\/1852"}],"wp:attachment":[{"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/media?parent=1851"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/categories?post=1851"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/tags?post=1851"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}