{"id":3377,"date":"2025-01-03T01:55:17","date_gmt":"2025-01-02T17:55:17","guid":{"rendered":"https:\/\/www.shuizilong.com\/house\/?p=3377"},"modified":"2025-01-06T08:11:33","modified_gmt":"2025-01-06T00:11:33","slug":"range-substring-query","status":"publish","type":"post","link":"https:\/\/www.shuizilong.com\/house\/archives\/range-substring-query\/","title":{"rendered":"\u533a\u95f4\u5b50\u4e32\u8be2\u95ee"},"content":{"rendered":"<ul>\n<li><a href=\"https:\/\/codeforces.com\/blog\/entry\/62331\">Codeforces, The history of some recurring problem<\/a><\/li>\n<li><a href=\"https:\/\/www.luogu.com.cn\/problem\/P6292\">Luogu P6292 \u533a\u95f4\u672c\u8d28\u4e0d\u540c\u5b50\u4e32\u4e2a\u6570<\/a><\/li>\n<li><a href=\"https:\/\/uoj.ac\/problem\/608\">https:\/\/uoj.ac\/problem\/608<\/a><\/li>\n<li><a href=\"https:\/\/www.fzoi.top\/problem\/4449\">https:\/\/www.fzoi.top\/problem\/4449<\/a><\/li>\n<\/ul>\n<p>\u521d\u89c1\u6740\uff0c\u5b9e\u9645\u5957\u8def\uff0c\u5e94\u8be5\u653e\u4e00\u8d77\u505a\uff01<\/p>\n<p>\u9996\u5148\u80fd\u79bb\u7ebf\u5f53\u7136\u8003\u8651\u79bb\u7ebf\uff08Ukkonen \u53ef\u4ee5\u9b54\u6539\u652f\u6301\u5de6\u5220\uff0c\u4f46\u662f\u597d\u50cf\u8fd8\u662f\u4e0d\u80fd\u5f88\u597d\u7684\u652f\u6301\u5de6\u52a0\u548c\u53f3\u5220\uff0c\u5426\u5219\u6211\u4eec\u751a\u81f3\u80fd\u83ab\u961f\uff1f\uff09\uff0c<br \/>\n\u90a3\u4e48\u6211\u4eec\u53ea\u8981\u7ef4\u62a4\u4e00\u4e2a\u7ebf\u6bb5\u6811\u8bb0\u5f55\u8be2\u95ee\u5de6\u7aef\u70b9\u5728\u4e0d\u540c\u4f4d\u7f6e\u7684\u7b54\u6848\uff0c\u8003\u5bdf\u589e\u52a0\u64cd\u4f5c\u5bf9\u7ebf\u6bb5\u6811\u7684\u5f71\u54cd\uff0c\u53d1\u73b0\u53ea\u5f71\u54cd fail \u6811\u5411\u4e0a\u7684\u8282\u70b9\uff0c\u6700\u540e\u4e00\u6b65\u52a8\u6001\u6811\u4f18\u5316\u5373\u53ef\uff0c\u590d\u6742\u5ea6 O(nlog2n + mlogn)\u3002<\/p>\n<p>\u548c BZOJ_2555 \u76f8\u6bd4\uff0c\u8fd9\u91cc\u7531\u4e8e\u6211\u4eec\u4e0d\u9700\u8981\u5f3a\u5236\u5728\u7ebf\uff0c\u52a8\u6001\u6811\u4e0d\u9700\u8981\u5728\u540e\u7f00\u81ea\u52a8\u673a\u63d2\u5165\u5b57\u7b26\u65f6\u5019\u8ddf\u968f SAM \u53d8\u5316\u5f62\u6001\uff0c\u53ea\u9700\u8981\u5728\u5168\u90e8\u63d2\u5165\u5b8c\u540e\u6839\u636e fail \u6811\u6784\u5efa\u5373\u53ef\uff0c\u56e0\u800c\u4e5f\u53ef\u4ee5\u6811\u94fe\u5256\u5206\u554a\u542f\u53d1\u5f0f\u5408\u5e76\u554a\u66ff\u4ee3\u52a8\u6001\u6811\u7684\u73af\u8282\u3002<\/p>\n<p>\u5177\u4f53\u6765\u770b\uff0c\u5148\u8003\u5bdf <a href=\"https:\/\/www.luogu.com.cn\/problem\/P6292\">Luogu P6292 \u533a\u95f4\u672c\u8d28\u4e0d\u540c\u5b50\u4e32\u4e2a\u6570<\/a>\uff0c\u6bcf\u6b21\u6dfb\u52a0\u65b0\u5b57\u7b26\u65f6\uff0c\u5148\u628a\u6240\u6709\u4f4d\u7f6e\u90fd\u52a0 1\uff0c\u7136\u540e\u7c7b\u4f3c <a href=\"https:\/\/www.spoj.com\/problems\/DQUERY\/\">dquery<\/a> \u4e00\u9898\u7684\u641e\u6cd5\uff0c\u6211\u4eec\u8bb0\u5f55\u4e0a\u6b21\u6dfb\u52a0\u7684\u65f6\u523b\u4ee5\u53bb\u6389\u91cd\u590d\u8ba1\u6570\u7684\u90e8\u5206\uff0c\u800c\u8fd9\u53ea\u9700\u8981\u6cbf\u7740 fail \u6811\u5411\u4e0a\uff0c\u5e76\u8bb0\u5f55\u6bcf\u4e2a\u72b6\u6001\u4e0a\u6b21\u8ba1\u6570\u7684\u65f6\u523b\u5373\u53ef\u3002\u8fd9\u91cc\u7684\u7ebf\u6bb5\u6811\u53ea\u9700\u8981\u652f\u6301\u533a\u95f4\u52a0\u51cf\uff0c\u533a\u95f4\u6c42\u548c\uff0c\u56e0\u800c\u4e5f\u53ef\u4ee5\u7528\u6811\u72b6\u6811\u7ec4\u66ff\u4ee3\u3002<\/p>\n<p>\u89c2\u5bdf\u8fd9\u91cc\u7684\u52a8\u6001\u6811\u8fd9\u91cc\u5176\u5b9e\u552f\u4e00\u7684\u7528\u5904\u5c31\u53ea\u6709\u538b\u7f29 fail \u6811 = =\uff0c\u6211\u4eec\u53ea\u9700\u8981\u7ef4\u62a4\u4e0a\u6b21\u8bbf\u95ee\u7684\u6807\u8bb0\u5373\u53ef\uff0c\u5176\u5b83\u4fe1\u606f\u90fd\u53ef\u4ee5\u4ece SAM \u4e2d\u62ff\u5230\uff0c\u56e0\u4e3a Splay \u4e4b\u540e\u7236\u8282\u70b9\u548c\u81ea\u5df1\u521a\u597d\u5f62\u6210\u538b\u7f29\u540e\u7684 endpos \u533a\u95f4\u3002<\/p>\n<p>fzoi \u90a3\u679a\u53ea\u9700\u8981\u628a\u7ebf\u6bb5\u6811\u4ece\u533a\u95f4\u52a0\u5e38\u6570\u53d8\u6210\u52a0\u7b49\u5dee\u6570\u5217\u3002\u518d\u770b uoj 608\uff0c\u8fd9\u91cc\u6211\u4eec\u7ebf\u6bb5\u6811\u9700\u8981\u652f\u6301\u7684\u662f\u533a\u95f4\u7b49\u5dee\u6570\u5217 checkMax\uff0c\u7531\u4e8e\u8fd9\u4e2a\u6807\u8bb0\u662f\u5355\u8c03\u7684\uff0c\u6240\u4ee5\u53ef\u4ee5\u7b80\u5355\u6807\u8bb0\u6301\u4e45\u5316\uff0c\u52a8\u6001\u6811\u540c\u6837\u53ea\u8d77\u5230\u538b\u7f29 fail \u6811\u7684\u529f\u80fd\uff0c\u5b8c\u5168\u4e0d\u7528\u6539\uff01<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Codeforces, The history of some recurring problem Luogu P6292 \u533a\u95f4\u672c\u8d28\u4e0d\u540c\u5b50\u4e32\u4e2a\u6570 https:\/\/uoj.ac\/problem\/608 https:\/\/www.fzoi.top\/problem\/4449 \u521d\u89c1\u6740\uff0c\u5b9e\u9645\u5957\u8def\uff0c\u5e94\u8be5\u653e\u4e00\u8d77\u505a\uff01 \u9996\u5148\u80fd\u79bb\u7ebf\u5f53\u7136\u8003\u8651\u79bb\u7ebf\uff08Ukkonen \u53ef\u4ee5\u9b54\u6539\u652f\u6301\u5de6\u5220\uff0c\u4f46\u662f\u597d\u50cf\u8fd8\u662f\u4e0d\u80fd\u5f88\u597d\u7684\u652f\u6301\u5de6\u52a0\u548c\u53f3\u5220\uff0c\u5426\u5219\u6211\u4eec\u751a\u81f3\u80fd\u83ab\u961f\uff1f\uff09\uff0c \u90a3\u4e48\u6211\u4eec\u53ea\u8981\u7ef4\u62a4\u4e00\u4e2a\u7ebf\u6bb5\u6811\u8bb0\u5f55\u8be2\u95ee\u5de6\u7aef\u70b9\u5728\u4e0d\u540c\u4f4d\u7f6e\u7684\u7b54\u6848\uff0c\u8003\u5bdf\u589e\u52a0\u64cd\u4f5c\u5bf9\u7ebf\u6bb5\u6811\u7684\u5f71\u54cd\uff0c\u53d1\u73b0\u53ea\u5f71\u54cd fail \u6811\u5411\u4e0a\u7684\u8282\u70b9\uff0c\u6700\u540e\u4e00\u6b65\u52a8\u6001\u6811\u4f18\u5316\u5373\u53ef\uff0c\u590d\u6742\u5ea6 O(nlog2n + mlogn)\u3002 \u548c BZOJ_2555 \u76f8\u6bd4\uff0c\u8fd9\u91cc\u7531\u4e8e\u6211\u4eec\u4e0d\u9700\u8981\u5f3a\u5236\u5728\u7ebf\uff0c\u52a8\u6001\u6811\u4e0d\u9700\u8981\u5728\u540e\u7f00\u81ea\u52a8\u673a\u63d2\u5165\u5b57\u7b26\u65f6\u5019\u8ddf\u968f SAM \u53d8\u5316\u5f62\u6001\uff0c\u53ea\u9700\u8981\u5728\u5168\u90e8\u63d2\u5165\u5b8c\u540e\u6839\u636e fail \u6811\u6784\u5efa\u5373\u53ef\uff0c\u56e0\u800c\u4e5f\u53ef\u4ee5\u6811\u94fe\u5256\u5206\u554a\u542f\u53d1\u5f0f\u5408\u5e76\u554a\u66ff\u4ee3\u52a8\u6001\u6811\u7684\u73af\u8282\u3002 \u5177\u4f53\u6765\u770b\uff0c\u5148\u8003\u5bdf Luogu P6292 \u533a\u95f4\u672c\u8d28\u4e0d\u540c\u5b50\u4e32\u4e2a\u6570\uff0c\u6bcf\u6b21\u6dfb\u52a0\u65b0\u5b57\u7b26\u65f6\uff0c\u5148\u628a\u6240\u6709\u4f4d\u7f6e\u90fd\u52a0 1\uff0c\u7136\u540e\u7c7b\u4f3c dquery \u4e00\u9898\u7684\u641e\u6cd5\uff0c\u6211\u4eec\u8bb0\u5f55\u4e0a\u6b21\u6dfb\u52a0\u7684\u65f6\u523b\u4ee5\u53bb\u6389\u91cd\u590d\u8ba1\u6570\u7684\u90e8\u5206\uff0c\u800c\u8fd9\u53ea\u9700\u8981\u6cbf\u7740 fail \u6811\u5411\u4e0a\uff0c\u5e76\u8bb0\u5f55\u6bcf\u4e2a\u72b6\u6001\u4e0a\u6b21\u8ba1\u6570\u7684\u65f6\u523b\u5373\u53ef\u3002\u8fd9\u91cc\u7684\u7ebf\u6bb5\u6811\u53ea\u9700\u8981\u652f\u6301\u533a\u95f4\u52a0\u51cf\uff0c\u533a\u95f4\u6c42\u548c\uff0c\u56e0\u800c\u4e5f\u53ef\u4ee5\u7528\u6811\u72b6\u6811\u7ec4\u66ff\u4ee3\u3002 \u89c2\u5bdf\u8fd9\u91cc\u7684\u52a8\u6001\u6811\u8fd9\u91cc\u5176\u5b9e\u552f\u4e00\u7684\u7528\u5904\u5c31\u53ea\u6709\u538b\u7f29 fail \u6811 = =\uff0c\u6211\u4eec\u53ea\u9700\u8981\u7ef4\u62a4\u4e0a\u6b21\u8bbf\u95ee\u7684\u6807\u8bb0\u5373\u53ef\uff0c\u5176\u5b83\u4fe1\u606f\u90fd\u53ef\u4ee5\u4ece SAM \u4e2d\u62ff\u5230\uff0c\u56e0\u4e3a Splay \u4e4b\u540e\u7236\u8282\u70b9\u548c\u81ea\u5df1\u521a\u597d\u5f62\u6210\u538b\u7f29\u540e\u7684 endpos \u533a\u95f4\u3002 fzoi \u90a3\u679a\u53ea\u9700\u8981\u628a\u7ebf\u6bb5\u6811\u4ece\u533a\u95f4\u52a0\u5e38\u6570\u53d8\u6210\u52a0\u7b49\u5dee\u6570\u5217\u3002\u518d\u770b uoj 608\uff0c\u8fd9\u91cc\u6211\u4eec\u7ebf\u6bb5\u6811\u9700\u8981\u652f\u6301\u7684\u662f\u533a\u95f4\u7b49\u5dee\u6570\u5217 checkMax\uff0c\u7531\u4e8e\u8fd9\u4e2a\u6807\u8bb0\u662f\u5355\u8c03\u7684\uff0c\u6240\u4ee5\u53ef\u4ee5\u7b80\u5355\u6807\u8bb0\u6301\u4e45\u5316\uff0c\u52a8\u6001\u6811\u540c\u6837\u53ea\u8d77\u5230\u538b\u7f29 fail \u6811\u7684\u529f\u80fd\uff0c\u5b8c\u5168\u4e0d\u7528\u6539\uff01<\/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-3377","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"jetpack_publicize_connections":[],"jetpack_featured_media_url":"","jetpack_shortlink":"https:\/\/wp.me\/p2tdP7-St","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/posts\/3377","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=3377"}],"version-history":[{"count":14,"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/posts\/3377\/revisions"}],"predecessor-version":[{"id":3392,"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/posts\/3377\/revisions\/3392"}],"wp:attachment":[{"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/media?parent=3377"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/categories?post=3377"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/tags?post=3377"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}