{"id":550,"date":"2012-10-31T05:36:45","date_gmt":"2012-10-30T21:36:45","guid":{"rendered":"http:\/\/www.shuizilong.com\/house\/?p=550"},"modified":"2012-11-02T05:06:05","modified_gmt":"2012-11-01T21:06:05","slug":"sgu-550-tree-queries-online","status":"publish","type":"post","link":"https:\/\/www.shuizilong.com\/house\/archives\/sgu-550-tree-queries-online\/","title":{"rendered":"SGU 550. Tree Queries Online"},"content":{"rendered":"

Brief description: <\/h3>\n

\u3002\u3002\u3002\u7ed9\u5b9a\u4e00\u68f5 N \u9636\u8fb9\u6743\u6811\uff0c\u6bcf\u6b21\u9009\u62e9\u4e00\u6761\u8fb9\u62c6\u5f00\uff0c\u8f93\u51fa\u5f53\u524d\u8fb9\u7684\u6743\u503c\u3002\u3002\u3002\u8bb0\u4f5c w\u3002\u3002
\n\u3002\u3002\u5e76\u5c06\u62c6\u5f00\u7684\u4e24\u9897\u5b50\u6811\u4e2d\uff0c\u8f83\u5c0f\u7684\u4e00\u9897\u5b50\u6811\u4e0a\u7684\u8fb9\u5168\u90e8 \u00d7 w\uff0c\u8f83\u5927\u5b50\u6811\u7684\u8fb9\u5168\u90e8 + w\u3002\u3002\u3002
\n\u3002\u3002\uff08 N <= 2e5, \u5f3a\u5236\u5728\u7ebf\u3002\u3002\uff09\u3002\u3002\n<\/p>\n

Analysis: <\/h3>\n

… \u524d\u56de Southern Subregional Programming Contest 2012<\/a> \u7684 Problem I\u3002\u3002
\n\u3002\u3002\u3002\u3002\u3002\u3002\u6bd4\u8d5b\u65f6\u7b2c\u4e00\u53cd\u5e94 dsu \u5012\u7740\u641e\u3002\u3002\u8bfb\u5230\u5f3a\u5236\u5728\u7ebf\u4ee5\u540e\u5c31 SB \u4e86\u3002\u3002\u3002\u3002\u3002 Euler Tour Tree \u786e\u5b9e\u4e00\u6b21\u90fd\u6ca1\u6709\u5199\u8fc7\u3002\u3002\uff08\u867d\u7136\u5c31\u5728\u524d\u4e00\u5929\u8fd8\u5728\u5403\u996d\u7684\u65f6\u5019\u548c \u4e8c\u59b9 \u8ba8\u8bba\u6765\u7740\u3002\u3002\u3002
\n\u3002\u3002\u6240\u4ee5\u8d5b\u540e\u5c31\u819c\u62dc\u4e86\u4e00\u4e0b CLJ \u7684\u4ee3\u7801<\/a>\u3002\u3002\u3002\u53d1\u73b0\u8fd9\u79cd\u975e\u5b8c\u5168\u5f62\u6001\u7684 ETT \u8fd8\u662f\u4e0d\u96be\u641e\u7684\u3002\u3002\u3002\uff08\u65e2\u6811\u7684\u5f62\u6001\u4e0d\u53d1\u751f\u6539\u53d8\u3002\u3002\u6ca1\u6709\u6362\u6839\u3002\u3002<\/p>\n

\u3002\u3002\u6b27\u62c9\u5e8f\u5217\u7684\u6bcf\u4e2a\u4f4d\u7f6e\u90fd\u662f\u4f38\u5c55\u6811\u7684\u4e00\u4e2a\u7ed3\u70b9\uff0c\u96be\u70b9\u662f\u7529\u533a\u95f4\u7684\u65f6\u5019\u3002\u3002\u3002\uff08\u8fd9\u91cc\u7531\u4e8e\u6700\u540e\u90fd\u662f\u4e00\u4e9b\u5c0f\u5757\u3002\u3002\u800c\u4e14\u5f15\u7528\u7684\u662f\u533a\u95f4\u4f4d\u7f6e\u3002\u3002\u4e5f\u4e0d\u592a\u597d\u76f4\u63a5\u5728\u5de6\u53f3\u52a0 -oo \u548c +oo \u54e8\u5175\u3002\u3002
\n\uff08CLJ \u8fd9\u91cc\u7684\u5904\u7406\u65b9\u6cd5\u3002\u3002\u5047\u8bbe\u5f53\u524d\u5b50\u6811\u662f [a, b], \u63d0\u53d6\u7684\u533a\u95f4\u662f [l, r] \u3002\u3002\u5219\u5206\u6210 [a, l-1] [l, r] [r+1, b] \u4e09\u5757\u3002\u3002\u3002\u5de6\u53f3\u4e24\u5757\u5207\u51fa\u53bb\u4ee5\u540e\u518d\u94fe\u63a5\u4e0a\u3002\u3002\u3002<\/p>\n

\uff08\u3002\u3002Euler Tour Tree\u3002\u3002\u3002<\/a><\/p>\n

\uff08..\u6211\u53d1\u73b0 CLJ \u7684\u4f38\u5c55\u6811<\/a> \u548c \u6211\u7684<\/a> \u540c\u6b65\u7387\u662f\u5f88\u9ad8\u7684\u3002\u3002\uff08\u6bd4\u5982\u6211\u4eec\u90fd\u5728\u7c7b\u91cc\u9762\u641e\u4e86\u4e00\u4e2a\u51fd\u6570\u5224\u65ad\u662f\u5de6\u5b69\u5b50\u8fd8\u662f\u53f3\u5b69\u5b50\u3002\u3002\uff08\u6211\u7684\u662f sgn() \u3002\u3002\u5979\u7684\u662f dir()\u3002\u3002\u3002\u3002<\/p>\n

.. \u7136\u540e\u770b\u4e0b\u9762\u8fd9\u6bb5\u3002\u3002<\/p>\n

\r\nvoid rot(Node*t) {\r\n\tNode*p = t->p;\r\n\tp->relax();\r\n\tt->relax();\r\n\tbool d = t->dir();\r\n\tp->p->setc(t, p->dir());\r\n\tp->setc(t->ch[!d], d);\r\n\tt->setc(p, !d);\r\n\tp->update();\r\n}\r\n\r\nvoid pushTo(Node*t) {\r\n\tstatic Node*stack[MAX_N * 2];\r\n\tint top = 0;\r\n\twhile (t != null) {\r\n\t\tstack[top++] = t;\r\n\t\tt = t->p;\r\n\t}\r\n\tfor (int i = top - 1; i >= 0; --i) {\r\n\t\tstack[i]->relax();\r\n\t}\r\n}\r\n\r\nvoid splay(Node*t, Node*f = null) {\r\n\tpushTo(t);\r\n\twhile (t->p != f) {\r\n\t\tif (t->p->p == f)\r\n\t\t\trot(t);\r\n\t\telse\r\n\t\t\t(t->dir() == t->p->dir()) ? (rot(t->p), rot(t)) : (rot(t), rot(t));\r\n\t}\r\n\tt->update();\r\n}\r\n<\/pre>\n
\uff08pushTo \u7591\u4f3c\u662f LCT \u91cc\u9762\u7684\u64cd\u4f5c\u3002\u3002\u53ef\u5220\u3002\u3002\u3002
\n\u3002\u3002\u7136\u540e CLJ \u8fd9\u91cc\u7684 rot \u548c splay \u51fd\u6570\u662f\u5b9e\u73b0\u5728\u5916\u90e8\u7684\u3002\u3002\uff08\u3002\u539f\u56e0\u4f3c\u4e4e\u662f\u9ed8\u8ba4\u5f62\u53c2\u5217\u8868\u91cc\u9762\u8981\u7528\u5230\u54e8\u5175 null\u3002\u3002
\n\u3002\u3002\u3002\u3002\u6211\u7684\u5904\u7406\u65b9\u6cd5\u662f\u5728\u5185\u90e8\u5b9a\u4e49\u4e86\u4e00\u4e2a static node* NIL \u3002\u3002\u3002\uff08\u7136\u540e\u5728 mian \u51fd\u6570\u521a\u5f00\u59cb\u7684\u65f6\u5019\u7ed9\u5979\u8d4b\u503c\u3002\u3002\u3002<\/p>\n
External link: <\/h3>\n
http:\/\/acm.sgu.ru\/problem.php?contest=0&problem=550<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"
Brief description: \u3002\u3002\u3002\u7ed9\u5b9a\u4e00\u68f5 N \u9636\u8fb9\u6743\u6811\uff0c\u6bcf\u6b21\u9009\u62e9\u4e00\u6761\u8fb9\u62c6\u5f00\uff0c\u8f93\u51fa\u5f53\u524d\u8fb9\u7684\u6743\u503c\u3002\u3002\u3002\u8bb0\u4f5c w\u3002\u3002 \u3002\u3002\u5e76\u5c06\u62c6\u5f00\u7684\u4e24\u9897\u5b50\u6811\u4e2d\uff0c\u8f83\u5c0f\u7684\u4e00\u9897\u5b50\u6811\u4e0a\u7684\u8fb9\u5168\u90e8 \u00d7 w\uff0c\u8f83\u5927\u5b50\u6811\u7684\u8fb9\u5168\u90e8 + w\u3002\u3002\u3002 \u3002\u3002\uff08 N<\/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":[61],"tags":[91],"class_list":["post-550","post","type-post","status-publish","format-standard","hentry","category-sgu","tag-euler-tour-tree"],"jetpack_publicize_connections":[],"jetpack_featured_media_url":"","jetpack_shortlink":"https:\/\/wp.me\/p2tdP7-8S","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/posts\/550","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=550"}],"version-history":[{"count":1,"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/posts\/550\/revisions"}],"predecessor-version":[{"id":551,"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/posts\/550\/revisions\/551"}],"wp:attachment":[{"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/media?parent=550"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/categories?post=550"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/tags?post=550"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}