{"id":2987,"date":"2023-06-06T23:11:44","date_gmt":"2023-06-06T15:11:44","guid":{"rendered":"https:\/\/www.shuizilong.com\/house\/?p=2987"},"modified":"2023-06-07T01:47:27","modified_gmt":"2023-06-06T17:47:27","slug":"luogu-p8500-noi2022-%e5%86%92%e6%b3%a1%e6%8e%92%e5%ba%8f","status":"publish","type":"post","link":"https:\/\/www.shuizilong.com\/house\/archives\/luogu-p8500-noi2022-%e5%86%92%e6%b3%a1%e6%8e%92%e5%ba%8f\/","title":{"rendered":"Luogu P8500. [NOI2022] \u5192\u6ce1\u6392\u5e8f"},"content":{"rendered":"<ul>\n<li><a href=\"https:\/\/uoj.ac\/problem\/768\">https:\/\/uoj.ac\/problem\/768<\/a><\/li>\n<li><a href=\"https:\/\/www.luogu.com.cn\/problem\/P8500\">https:\/\/www.luogu.com.cn\/problem\/P8500<\/a><\/li>\n<\/ul>\n<p>\u533a\u95f4\u76f8\u4ea4\u5f53\u7136\u662f\u5f88\u9ebb\u70e6\u7684\u3002\u3002\u524d\u51e0\u5929 <a href=\"https:\/\/www.shuizilong.com\/house\/archives\/codeforces-round-875\/\">CF #875 C<\/a> \u7684\u65f6\u5019\u8fd8\u80fd\u7528 hash \u5927\u6cd5\u8499\u6df7\u8fc7\u5173\u3002\u3002\u8fd9\u6b21\u80af\u5b9a\u4e0d\u884c\u4e86\u3002\u3002<\/p>\n<p>\u6211\u4eec\u5148\u628a\u8fd9\u79cd\u60c5\u51b5\u653e\u5728\u6700\u540e\u5904\u7406\uff0c\u5148\u5199\u4e00\u4e2a <a href=\"https:\/\/uoj.ac\/submission\/626758\">28 \u5206\u7684\u4ee3\u7801<\/a>\u3002<\/p>\n<h3>Lemma 1. \u6211\u4eec\u53ea\u9700\u8981\u5229\u7528\u6761\u4ef6\u4e2d\u51fa\u73b0\u7684\u503c\u3002<\/h3>\n<p>\u8fd9\u4e2a\u6027\u8d28\u53ef\u4ee5\u6307\u5bfc\u6211\u4eec\u8fdb\u884c\u79bb\u6563\u5316\uff0c\u4ece\u800c\u65b9\u4fbf\u4f7f\u7528\u5404\u79cd\u6570\u636e\u7ed3\u6784\u3002<\/p>\n<h3>Lemma 2. \u5bf9\u4e8e\u6027\u8d28 B \u7684\u60c5\u51b5\uff0c\u672a\u786e\u5b9a\u7684\u6570\u5355\u8c03\u9012\u589e\u3002<\/h3>\n<p>\u53ef\u4ee5\u7b80\u5355\u8c03\u6574\u5f97\u5230\uff0c<a href=\"https:\/\/www.shuizilong.com\/house\/archives\/vijos-1893-%E7%AD%BE%E5%88%B0%E9%A2%98\/\">Vijos 1893<\/a> \u4e5f\u8003\u5bdf\u4e86\u4ea4\u6362\u5e26\u6765\u7684\u5177\u4f53\u5f71\u54cd\u3002<\/p>\n<p>\u6240\u4ee5\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\u6211\u4eec\u53ef\u4ee5\u4e0d\u7edf\u8ba1 \u672a\u786e\u5b9a\u6570\u548c\u672a\u786e\u5b9a\u6570\u4e4b\u95f4 \u7684\u9006\u5e8f\u5bf9\uff0c\u56e0\u4e3a\u5fc5\u7136\u662f 0\uff0c\u4f46\u662f\u8fd9\u4e2a\u6027\u8d28\u4e0d\u662f\u901a\u7528\u7684\uff0c\u6211\u4eec\u4e0d\u5982\u5148\u628a\u6240\u6709\u6570\u586b\u51fa\u6765\uff0c\u6700\u540e\u7edf\u4e00\u8dd1\u4e00\u904d\u6c42\u9006\u5e8f\u5bf9\u7684\u4ee3\u7801\uff0c\u8fd9\u6837\u53ef\u4ee5\u51cf\u5c11\u8ba8\u8bba\u3002<\/p>\n<h3>Lemma 3. \u4ece\u5de6\u5230\u53f3\u626b\u63cf\u65f6\uff0c\u5bf9\u4e8e\u80fd\u586b\u7684\u6570\uff0c\u5c3d\u91cf\u5728\u6700\u4f18\u60c5\u51b5\u4e0b\u586b\u66f4\u5c0f\u7684\u503c\u3002<\/h3>\n<p>\u8fd9\u4e2a\u662f\u4e0a\u9762\u7684\u6027\u8d28\u7684\u63a8\u5e7f\uff0c\u663e\u7136\u5bf9\u6211\u4eec\u66f4\u6709\u7528\u3002<\/p>\n<p>\u6240\u4ee5\u7efc\u4e0a\u6240\u8ff0\uff0c\u6211\u4eec\u53ea\u9700\u8981\u5f00\u4e00\u68f5\u7ebf\u6bb5\u6811\uff0c\u8bb0\u5f55\u5f53\u524d\u586b\u6bcf\u4e2a\u6570\u65f6\u7684\u4ee3\u4ef7\uff0c\u7136\u540e\u6bcf\u6b21\u533a\u95f4\u4fee\u6539\uff0c\u533a\u95f4\u6c42\u6700\u5c0f\u503c\u5373\u53ef\u3002<\/p>\n<p>\u6700\u540e\u53ea\u8981\u8003\u8651\u533a\u95f4\u4ea4\u5c31\u53ef\u4ee5\u4e86\u3002<\/p>\n<p>\u6211\u4eec\u6700\u7ec8\u7684\u76ee\u6807\u662f\u5904\u7406\u51fa\u4e24\u4e2a\u6570\u7ec4\uff0cA[] \u8868\u793a\u6240\u6709\u5df2\u7ecf\u88ab\u586b\u7684\u6570\uff0cB[] \u8868\u793a\u672a\u586b\u6570\u7684\u4e0b\u754c\u3002<br \/>\n\u7136\u540e\u7528\u7ebf\u6bb5\u6811\u626b\u4e00\u904d\uff0c\u5f97\u5230\u5b8c\u6574\u7684 A[] \u5373\u53ef\u3002<\/p>\n<p>\u518d\u770b\u770b\u6027\u8d28 A\uff0c1 \u7684\u60c5\u51b5\u90a3\u4e48\u5168\u90e8\u53ea\u80fd\u586b 1\uff0c\u76f4\u63a5\u586b\u8fdb A[] \u91cc\uff0c\u5bf9\u4e8e 0 \u7684\u60c5\u51b5\uff0c\u6211\u4eec\u5e0c\u671b\u7ee7\u7eed\u5229\u7528 Lemma 3\uff0c\u4ece\u53f3\u5411\u5de6\u626b\u63cf\u533a\u95f4\uff0c\u5c3d\u53ef\u80fd\u665a\u7684\u53bb\u586b\u6570\u3002<\/p>\n<p>\u6700\u540e\u53bb\u6389\u6027\u8d28 A \u53ea\u8981\u6309\u6743\u503c\u4ece\u5927\u5230\u5c0f\u7136\u540e\u7528\u5e76\u67e5\u96c6\u6316\u53bb\u6bcf\u4e2a\u9636\u6bb5\u5904\u7406\u8fc7\u7684\u4f4d\u7f6e\u5373\u53ef\u3002<\/p>\n<p><a href=\"https:\/\/uoj.ac\/submission\/626775\">https:\/\/uoj.ac\/submission\/626775<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>https:\/\/uoj.ac\/problem\/768 https:\/\/www.luogu.com.cn\/problem\/P8500 \u533a\u95f4\u76f8\u4ea4\u5f53\u7136\u662f\u5f88\u9ebb\u70e6\u7684\u3002\u3002\u524d\u51e0\u5929 CF #875 C \u7684\u65f6\u5019\u8fd8\u80fd\u7528 hash \u5927\u6cd5\u8499\u6df7\u8fc7\u5173\u3002\u3002\u8fd9\u6b21\u80af\u5b9a\u4e0d\u884c\u4e86\u3002\u3002 \u6211\u4eec\u5148\u628a\u8fd9\u79cd\u60c5\u51b5\u653e\u5728\u6700\u540e\u5904\u7406\uff0c\u5148\u5199\u4e00\u4e2a 28 \u5206\u7684\u4ee3\u7801\u3002 Lemma 1. \u6211\u4eec\u53ea\u9700\u8981\u5229\u7528\u6761\u4ef6\u4e2d\u51fa\u73b0\u7684\u503c\u3002 \u8fd9\u4e2a\u6027\u8d28\u53ef\u4ee5\u6307\u5bfc\u6211\u4eec\u8fdb\u884c\u79bb\u6563\u5316\uff0c\u4ece\u800c\u65b9\u4fbf\u4f7f\u7528\u5404\u79cd\u6570\u636e\u7ed3\u6784\u3002 Lemma 2. \u5bf9\u4e8e\u6027\u8d28 B \u7684\u60c5\u51b5\uff0c\u672a\u786e\u5b9a\u7684\u6570\u5355\u8c03\u9012\u589e\u3002 \u53ef\u4ee5\u7b80\u5355\u8c03\u6574\u5f97\u5230\uff0cVijos 1893 \u4e5f\u8003\u5bdf\u4e86\u4ea4\u6362\u5e26\u6765\u7684\u5177\u4f53\u5f71\u54cd\u3002 \u6240\u4ee5\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\u6211\u4eec\u53ef\u4ee5\u4e0d\u7edf\u8ba1 \u672a\u786e\u5b9a\u6570\u548c\u672a\u786e\u5b9a\u6570\u4e4b\u95f4 \u7684\u9006\u5e8f\u5bf9\uff0c\u56e0\u4e3a\u5fc5\u7136\u662f 0\uff0c\u4f46\u662f\u8fd9\u4e2a\u6027\u8d28\u4e0d\u662f\u901a\u7528\u7684\uff0c\u6211\u4eec\u4e0d\u5982\u5148\u628a\u6240\u6709\u6570\u586b\u51fa\u6765\uff0c\u6700\u540e\u7edf\u4e00\u8dd1\u4e00\u904d\u6c42\u9006\u5e8f\u5bf9\u7684\u4ee3\u7801\uff0c\u8fd9\u6837\u53ef\u4ee5\u51cf\u5c11\u8ba8\u8bba\u3002 Lemma 3. \u4ece\u5de6\u5230\u53f3\u626b\u63cf\u65f6\uff0c\u5bf9\u4e8e\u80fd\u586b\u7684\u6570\uff0c\u5c3d\u91cf\u5728\u6700\u4f18\u60c5\u51b5\u4e0b\u586b\u66f4\u5c0f\u7684\u503c\u3002 \u8fd9\u4e2a\u662f\u4e0a\u9762\u7684\u6027\u8d28\u7684\u63a8\u5e7f\uff0c\u663e\u7136\u5bf9\u6211\u4eec\u66f4\u6709\u7528\u3002 \u6240\u4ee5\u7efc\u4e0a\u6240\u8ff0\uff0c\u6211\u4eec\u53ea\u9700\u8981\u5f00\u4e00\u68f5\u7ebf\u6bb5\u6811\uff0c\u8bb0\u5f55\u5f53\u524d\u586b\u6bcf\u4e2a\u6570\u65f6\u7684\u4ee3\u4ef7\uff0c\u7136\u540e\u6bcf\u6b21\u533a\u95f4\u4fee\u6539\uff0c\u533a\u95f4\u6c42\u6700\u5c0f\u503c\u5373\u53ef\u3002 \u6700\u540e\u53ea\u8981\u8003\u8651\u533a\u95f4\u4ea4\u5c31\u53ef\u4ee5\u4e86\u3002 \u6211\u4eec\u6700\u7ec8\u7684\u76ee\u6807\u662f\u5904\u7406\u51fa\u4e24\u4e2a\u6570\u7ec4\uff0cA[] \u8868\u793a\u6240\u6709\u5df2\u7ecf\u88ab\u586b\u7684\u6570\uff0cB[] \u8868\u793a\u672a\u586b\u6570\u7684\u4e0b\u754c\u3002 \u7136\u540e\u7528\u7ebf\u6bb5\u6811\u626b\u4e00\u904d\uff0c\u5f97\u5230\u5b8c\u6574\u7684 A[] \u5373\u53ef\u3002 \u518d\u770b\u770b\u6027\u8d28 A\uff0c1 \u7684\u60c5\u51b5\u90a3\u4e48\u5168\u90e8\u53ea\u80fd\u586b 1\uff0c\u76f4\u63a5\u586b\u8fdb A[] \u91cc\uff0c\u5bf9\u4e8e 0 \u7684\u60c5\u51b5\uff0c\u6211\u4eec\u5e0c\u671b\u7ee7\u7eed\u5229\u7528 Lemma 3\uff0c\u4ece\u53f3\u5411\u5de6\u626b\u63cf\u533a\u95f4\uff0c\u5c3d\u53ef\u80fd\u665a\u7684\u53bb\u586b\u6570\u3002 \u6700\u540e\u53bb\u6389\u6027\u8d28 A \u53ea\u8981\u6309\u6743\u503c\u4ece\u5927\u5230\u5c0f\u7136\u540e\u7528\u5e76\u67e5\u96c6\u6316\u53bb\u6bcf\u4e2a\u9636\u6bb5\u5904\u7406\u8fc7\u7684\u4f4d\u7f6e\u5373\u53ef\u3002 https:\/\/uoj.ac\/submission\/626775<\/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-2987","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"jetpack_publicize_connections":[],"jetpack_featured_media_url":"","jetpack_shortlink":"https:\/\/wp.me\/p2tdP7-Mb","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/posts\/2987","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=2987"}],"version-history":[{"count":6,"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/posts\/2987\/revisions"}],"predecessor-version":[{"id":2993,"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/posts\/2987\/revisions\/2993"}],"wp:attachment":[{"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/media?parent=2987"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/categories?post=2987"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/tags?post=2987"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}