{"id":267,"date":"2012-06-20T13:10:20","date_gmt":"2012-06-20T05:10:20","guid":{"rendered":"http:\/\/www.shuizilong.com\/house\/?p=267"},"modified":"2012-07-17T01:36:18","modified_gmt":"2012-07-16T17:36:18","slug":"zoj-2112-dynamic-rankings","status":"publish","type":"post","link":"https:\/\/www.shuizilong.com\/house\/archives\/zoj-2112-dynamic-rankings\/","title":{"rendered":"ZOJ 2112. Dynamic Rankings"},"content":{"rendered":"<h3>Brief description: <\/h3>\n<p>\u7ed9\u5b9a\u4e00\u4e2a\u957f\u5ea6\u4e3a N \u7684\u5df2\u77e5\u5e8f\u5217 A[i] (1\u2264i\u2264N)\uff0c\u8981\u6c42\u52a8\u6001\u7ef4\u62a4 M \u6b21\u4ee5\u4e0b\u64cd\u4f5c\uff1a<br \/>\n1\u3001Q a b k \u67e5\u8be2 A[a], A[a+1], A[a+2], \u2026, A[b] (1\u2264a\u2264b\u2264N) \u4e2d\uff0c\u7b2c k \u5c0f\u7684\u6570\u3002\uff08Start From 1 &#8230;<br \/>\n2\u3001C x y \u4fee\u6539 A[x] \u7684\u503c\u4e3a y\u3002<br \/>\n( .. N \u2264 50, 000 .. M \u2264 10, 000 .. \u4fdd\u8bc1 A[i] \u5728\u4efb\u4f55\u4e2d\u95f4\u65f6\u523b\u7684\u7edd\u5bf9\u503c\u90fd\u4e0d\u8d85\u8fc7 10^9 ..)<\/p>\n<p><!--more--><\/p>\n<h3>Analysis: <\/h3>\n<blockquote><p>\u89e3\u51b3\u8fd9\u4e2a\u95ee\u9898\uff0c\u9700\u8981\u7528\u5230\u201c\u6811\u5957\u6811\u201d\u3002\u5efa\u7acb\u4e00\u68f5\u7ebf\u6bb5\u6811\uff0c\u7ef4\u62a4 N \u7684\u8282\u70b9\u7684\u6240\u6709\u533a\u95f4\uff0c\u6bcf\u4e2a\u7ebf\u6bb5\u6811\u8282\u70b9\u4e0a\u6709\u4e00\u4e2a\u5e73\u8861\u6811\uff0c\u7528\u6765\u7ef4\u62a4\u5f53\u524d\u533a\u95f4\u5185\u6240\u6709\u6570\u7684\u52a8\u6001\u6392\u540d\u3002\u5f88\u663e\u7136\uff0c\u6bcf\u4e2a\u7ebf\u6bb5\u6811\u8282\u70b9\u4e0a\u7684\u5e73\u8861\u6811\uff0c\u90fd\u662f\u8fd9\u4e2a\u7ebf\u6bb5\u6811\u8282\u70b9\u7684\u4e24\u4e2a\u5b50\u8282\u70b9\u7684\u5e73\u8861\u6811\u7684\u5408\u5e76\u3002\u7531\u4e8e\u6211\u4eec\u65e0\u6cd5\u5b9e\u73b0\u9ad8\u6548\u7684\u5e73\u8861\u6811\u5408\u5e76\uff0c\u53ea\u597d\u7528\u8fd9\u79cd\u4ee5\u7a7a\u95f4\u6362\u65f6\u95f4\u7684\u65b9\u6cd5\u3002<br \/>\n\u2014\u2014 <a href=\"http:\/\/www.byvoid.com\/blog\/zju-2112\/\">http:\/\/www.byvoid.com\/blog\/zju-2112\/<\/a>\n<\/p><\/blockquote>\n<p>\u5f53\u7136\u8fd9\u6837\u505a\u6cd5\u5c31\u5f88\u660e\u786e\u4e86\uff0c\uff08\u6811\u72b6\u6570\u7ec4\u5957\u5e73\u8861\u6811\u601d\u60f3\u4e5f\u7c7b\u4f3c\u3002\uff09<br \/>\n\u5bf9\u4e8e\u67e5\u8be2\u64cd\u4f5c Q a b k\uff0c\u7531\u4e8e\u65e0\u6cd5\u5bf9\u7ebf\u6bb5\u6811\u4e0a\u9ad8\u6548\u7684\u76f4\u63a5\u5b8c\u6210\u8be2\u95ee\uff0c<br \/>\n\u53ea\u6709\u91c7\u53d6\u4e8c\u5206\u7b54\u6848\u7684\u65b9\u6cd5\uff0c\u8fd9\u4e2a\u8fc7\u7a0b\u4e5f\u53ef\u4ee5\u5148\u9884\u5904\u7406\u628a\u6240\u6709\u533a\u95f4\u627e\u5230\u3002<\/p>\n<p>\u6ce8\u610f\uff0c\u5bf9\u4e8e\u8be2\u95ee\u5173\u952e\u5b57\u4e3a v \u7684\u7ed3\u70b9\u7684 Rank \u503c\uff0c\u5f88\u53ef\u80fd\u6ca1\u6709\u5173\u952e\u5b57\u4e3a x \u7684\u7ed3\u70b9\uff0c\u6216\u8005\u6709\u5f88\u591a\u5173\u952e\u5b57\u4e3a x \u7684\u7ed3\u70b9\u3002\u3002<br \/>\n\uff08\u8fd9\u91cc\u5373\u4fbf\u662f\u8fdb\u884c\u9884\u5904\u7406\uff0c\u8fdb\u884c\u79bb\u6563\u5316\u7684\u4e8c\u5206\u7b54\u6848\uff0c\u4ecd\u7136\u6709\u53ef\u80fd\u51fa\u73b0\u5355\u4e2a\u5b50\u6811\u4e0a\u4e0d\u5b58\u5728 x \u7ed3\u70b9\u7684\u60c5\u51b5\u3002\uff09<br \/>\n\u4e5f\u5c31\u662f\u8bf4\u5f97\u5230\u7684 Rank \u503c\u5e94\u8be5\u662f\u4e00\u4e2a\u533a\u95f4\uff0c\u8fd9\u91cc\u6211\u4eec\u8fd4\u56de\u7b2c\u4e00\u4e2a\u5927\u4e8e\u7b49\u4e8e x \u7684\u7ed3\u70b9\u3002\uff08upper_bound &#8230; )<\/p>\n<p>\u8fd9\u6837\u8bbe\u8ba1\u540e\u5148\u628a\u5916\u90e8\u4e8c\u5206\u7b54\u6848\u7684\u8fc7\u7a0b\u786e\u5b9a\u4e0b\u6765\uff1a<br \/>\n\u5982\u679c f(x) > k\uff0c\u90a3\u4e48\u5f53\u524d\u7684\u7b54\u6848\u4e00\u5b9a\u662f\u4e0d\u6ee1\u8db3\u6761\u4ef6\u7684\uff0cr = x &#8211; 1;<br \/>\n\u5982\u679c f(x) <= k\uff0c\u90a3\u4e48\u6700\u540e\u7684\u7b54\u6848\u81f3\u5c11 >= x\uff0c l = x;<\/p>\n<pre class=\"brush: cpp; collapse: false; first-line: 1; light: false; title: ; toolbar: true; notranslate\" title=\"\">\r\n...\r\n        RC(cmd); if (cmd =='Q'){\r\n            RD(a, b, k); --k; int l = 0, r = INF;\r\n            while (l &lt; r){\r\n                _x = (l + r + 1) &gt;&gt; 1;\r\n                if (f() &gt; k) r = _x - 1;\r\n                else l = _x;\r\n            }\r\n            OT(l);\r\n        }\r\n...\r\n<\/pre>\n<p><a href=\"http:\/\/ideone.com\/EfF8G\">A. \u7ebf\u6bb5\u6811\u5957 Splay<\/a><br \/>\n<a href=\"http:\/\/ideone.com\/UV6We\">B. \u6811\u72b6\u6570\u7ec4\u5957 Splay<\/a><\/p>\n<h3>Further discuss: <\/h3>\n<p>\u4f46\u662f\u8fd9\u4e9b\u5199\u6cd5\u90fd\u5f31\u7206\u4e86\u3002\u3002\u3002\u4e0b\u4e00\u8282\u8be6\u7ec6\u4ecb\u7ecd\u4e3b\u5e2d\u6811\u3002\u3002\u3002<br \/>\n\u5148\u8d34\u4e2a <a href=\"http:\/\/seter.is-programmer.com\/posts\">Seter<\/a> \u7684\u4ee3\u7801\u819c\u62dc\u4e00\u4e0b\u3002\u3002\u3002<br \/>\n(Seter \u4e0d\u4ec5\u7f29\u4ee3\u7801\u3002\u3002\u800c\u4e14\u8fd8\u7f29\u5185\u5b58\u3002\u3002\u3002Orz\uff09\u3002\u3002\u3002\u3002<\/p>\n<p><a href=\"http:\/\/ideone.com\/2Jp5W\">Seter&#8217;s \u4e3b\u5e2d\u6811<\/a><br \/>\n&#8230;<\/p>\n<h3>External link: <\/h3>\n<p><a href=\"http:\/\/acm.zju.edu.cn\/onlinejudge\/showProblem.do?problemCode=2112\">http:\/\/acm.zju.edu.cn\/onlinejudge\/showProblem.do?problemCode=2112<\/a><br \/>\n<a href=\"http:\/\/www.lydsy.com\/JudgeOnline\/problem.php?id=1901\">http:\/\/www.lydsy.com\/JudgeOnline\/problem.php?id=1901<\/a><\/p>\n<p><a href=\"http:\/\/seter.is-programmer.com\/posts\/31907.html\">http:\/\/seter.is-programmer.com\/posts\/31907.html<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Brief description: \u7ed9\u5b9a\u4e00\u4e2a\u957f\u5ea6\u4e3a N \u7684\u5df2\u77e5\u5e8f\u5217 A[i] (1\u2264i\u2264N)\uff0c\u8981\u6c42\u52a8\u6001\u7ef4\u62a4 M \u6b21\u4ee5\u4e0b\u64cd\u4f5c\uff1a 1\u3001Q a b k \u67e5\u8be2 A[a], A[a+1], A[a+2], \u2026, A[b] (1\u2264a\u2264b\u2264N) \u4e2d\uff0c\u7b2c k \u5c0f\u7684\u6570\u3002\uff08Start From 1 &#8230; 2\u3001C x y \u4fee\u6539 A[x] \u7684\u503c\u4e3a y\u3002 ( .. N \u2264 50, 000 .. M \u2264 10, 000 .. \u4fdd\u8bc1 A[i] \u5728\u4efb\u4f55\u4e2d\u95f4\u65f6\u523b\u7684\u7edd\u5bf9\u503c\u90fd\u4e0d\u8d85\u8fc7 10^9 ..)<\/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":[55],"tags":[78,77],"class_list":["post-267","post","type-post","status-publish","format-standard","hentry","category-zoj","tag-78","tag-77"],"jetpack_publicize_connections":[],"jetpack_featured_media_url":"","jetpack_shortlink":"https:\/\/wp.me\/p2tdP7-4j","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/posts\/267","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=267"}],"version-history":[{"count":1,"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/posts\/267\/revisions"}],"predecessor-version":[{"id":268,"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/posts\/267\/revisions\/268"}],"wp:attachment":[{"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/media?parent=267"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/categories?post=267"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/tags?post=267"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}