{"id":618,"date":"2012-12-28T04:52:35","date_gmt":"2012-12-27T20:52:35","guid":{"rendered":"http:\/\/www.shuizilong.com\/house\/?p=618"},"modified":"2014-10-11T22:53:46","modified_gmt":"2014-10-11T14:53:46","slug":"hdu-3842-machine-works","status":"publish","type":"post","link":"https:\/\/www.shuizilong.com\/house\/archives\/hdu-3842-machine-works\/","title":{"rendered":"HDU 3842. Machine Works"},"content":{"rendered":"<p><a href=\"http:\/\/acm.hust.edu.cn:8080\/judge\/problem\/viewProblem.action?id=23094\">http:\/\/acm.hust.edu.cn:8080\/judge\/problem\/viewProblem.action?id=23094<\/a><\/p>\n<h3>Brief description: <\/h3>\n<p>\u3002\u3002\u3002\u67d0\u4e2a\u5de5\u5382\u540c\u4e00\u65f6\u523b\u6700\u591a\u53ea\u53ef\u4ee5\u88c5\u8f7d\u4e00\u79cd\u673a\u5668\uff0c<br \/>\n\u3002\u3002\u3002\u673a\u5668\u6709\u4e70\u5165\u4ef7\u683c\uff0c\u5356\u51fa\u4ef7\u683c\uff0c\u548c\u6bcf\u65e5\u5229\u6da6\u3002<br \/>\n\u3002\u3002\u3002\u6709 n \u4e2a\u53ef\u4ee5\u4e70\u5165\u673a\u5668\u7684\u65f6\u70b9\u3002\u3002\u6bcf\u4e2a\u65f6\u70b9\u5f62\u5982\uff0cd, p, r, g \u3002\u3002\u3002<br \/>\n\u3002\u3002\u3002\u5206\u522b\u8868\u793a\u65f6\u523b\uff0c\u4e70\u5165\u4ef7\u683c\uff0c\u5356\u51fa\u4ef7\u683c\u548c\u8be5\u673a\u5668\u7684\u65e5\u5229\u6da6\u3002<\/p>\n<p>\u3002\u4e70\u5165\u53ea\u80fd\u5728\u90a3\u4e2a\u65f6\u523b\u8fdb\u884c\uff0c\u800c\u5356\u51fa\u53ef\u4ee5\u9009\u62e9\u4e70\u5165\u540e\u7684\u4efb\u610f\u65f6\u523b\u3002<br \/>\n\u3002\u7ed9\u5b9a\u521d\u59cb\u65f6\u523b\u7684\u91d1\u5e01\uff0c\u95ee d \u5929\u540e\u6240\u80fd\u83b7\u5f97\u91d1\u5e01\u7684\u6700\u5927\u503c\u3002<\/p>\n<p><!--more--><\/p>\n<h3>Analysis: <\/h3>\n<p>\u539f\u9898\u4e2d\u7684\u4e24\u4e2a\u4e0d\u592a\u81ea\u7136\u7684\u6761\u4ef6\u3002\u3002<br \/>\n1. \u4efb\u4f55\u65f6\u523b\u53ea\u80fd\u4fdd\u7559\u81f3\u591a\u4e00\u53f0\u673a\u5668\u3002<br \/>\n2. \u673a\u5668\u5356\u51fa\u7684\u6536\u76ca\u662f\u56fa\u5b9a\u7684\uff0c\u4e0e\u65e5\u671f\u65e0\u5173\u3002\u3002<\/p>\n<p>\u7efc\u5408\u4e0a\u8ff0\u4e24\u4e2a\u6761\u4ef6\u4e0d\u96be\u5f97\u5230 O(n2) \u7684\u66b4\u529b DP\u3002\u3002\u3002<br \/>\nhttp:\/\/acm.hust.edu.cn\/vjudge\/problem\/viewSource.action?id=2838582<\/p>\n<pre class=\"brush: cpp; light: false; title: ; toolbar: true; notranslate\" title=\"\">\r\n\/\/}\/* .................................................................................................................................. *\/\r\n\r\nconst int N = int(1e5) + 9;\r\nLL f&#x5B;N];\r\n\r\nstruct Event{\r\n    int d,p,r,g; \/\/ \u4e70\u5165\u65f6\u95f4\uff0c\u4e70\u5165\u4ef7\u683c\uff0c\u5356\u51fa\u4ef7\u683c\uff0c\u65e5\u5229\u6da6\u3002\r\n    bool operator &lt;(const Event&amp; rhs)const{\r\n        return d &lt; rhs.d;\r\n    }\r\n    void in(){\r\n        RD(d,p,r,g);\r\n    }\r\n} E&#x5B;N];\r\n\r\nint n, d;\r\n\r\nint main(){\r\n\r\n#ifndef ONLINE_JUDGE\r\n    freopen(&quot;in.txt&quot;, &quot;r&quot;, stdin);\r\n    \/\/freopen(&quot;out.txt&quot;, &quot;w&quot;, stdout);\r\n#endif\r\n\r\n    while (RD(n, f&#x5B;0], d)){\r\n        REP_1(i, n) E&#x5B;i].in(); sort(E+1, E+n+1); ++n; E&#x5B;n].d = d+1; E&#x5B;n].p = E&#x5B;n].g = 0;\r\n\r\n\/\/ b = kx + y\r\n\r\n#define k (LL)E&#x5B;i].d\r\n#define x E&#x5B;j].g\r\n#define y (f&#x5B;j]+E&#x5B;j].r-E&#x5B;j].p-(LL)x*(E&#x5B;j].d+1))\r\n\r\n        REP_1(i, n){\r\n            f&#x5B;i] = f&#x5B;i-1]; REP(j, i) if (f&#x5B;j] &gt;= E&#x5B;j].p){\r\n                checkMax(f&#x5B;i], k*x + y);\r\n            }\r\n        }\r\n        OT(f&#x5B;n]);\r\n    }\r\n}\r\n<\/pre>\n<p>\u5199\u6210\u659c\u7387 DP \u7684\u6807\u51c6\u5f62\u5f0f\uff0c\u6ce8\u610f\u5230\u8fd9\u91cc k, x \u5747\u4e0d\u5355\u8c03\uff0c\u65e0\u6cd5\u4f7f\u7528\u5355\u8c03\u961f\u5217\u4f18\u5316\u3002\u3002<\/p>\n<p>\u65b9\u6cd5\u4e00\uff1a<br \/>\nSplay \u7ef4\u62a4\u51f8\u58f3\u3002<br \/>\nhttp:\/\/acm.hust.edu.cn\/vjudge\/problem\/viewSource.action?id=880923 \uff08\u6ce8\u610f\u7528\u53c9\u79ef\u3002\u3002\u3002<br \/>\n500ms O(nlogn)<\/p>\n<p>\u65b9\u6cd5\u4e8c\uff1a<br \/>\ncdq \u5206\u6cbb<\/p>\n<p>\u6d32\u59b9\u544a\u8bc9\u6211\u4eec\u3002\u3002\u8fd9\u7c7b\u95ee\u9898\u90fd\u53ef\u4ee5\u7528 cdq \u5206\u6cbb\u6765\u89e3\u51b3\u3002\u3002\u3002<br \/>\n\u3002\u3002\u3002<br \/>\n\u901a\u8fc7 cdq \u5206\u6cbb\u3002\u3002\u5c06\u539f\u672c\u9700\u8981\u5f3a\u5236\u5728\u7ebf\u7684\u8be2\u95ee\u3002\u3002\u53ef\u4ee5\u79bb\u7ebf\u5904\u7406\u3002\u3002\u3002\u4e8e\u662f\u53ef\u4ee5\u901a\u8fc7\u6392\u5e8f\u3001\u91cd\u65b0\u8ba9\u8be2\u95ee\u5355\u8c03\u3002\u3002<br \/>\n\u3002\u3002\u91cd\u65b0\u8ba9\u6808\u968f\u4fbf\u641e\u641e\u5c31\u80fd\u89e3\u51b3\u3001\u3001\u3002\u3002\u3002\u3002\u3002\u3002\u3002\u3002\u4ece\u800c\u6781\u5927\u7684\u964d\u4f4e\u4e86\u7f16\u7a0b\u96be\u5ea6\u3002\u3002<\/p>\n<p>http:\/\/acm.hust.edu.cn\/vjudge\/problem\/viewSource.action?id=2795801<br \/>\n\uff081640ms\u3002\u3002\u3002O(nlog2n)<\/p>\n","protected":false},"excerpt":{"rendered":"<p>http:\/\/acm.hust.edu.cn:8080\/judge\/problem\/viewProblem.action?id=23094 Brief description: \u3002\u3002\u3002\u67d0\u4e2a\u5de5\u5382\u540c\u4e00\u65f6\u523b\u6700\u591a\u53ea\u53ef\u4ee5\u88c5\u8f7d\u4e00\u79cd\u673a\u5668\uff0c \u3002\u3002\u3002\u673a\u5668\u6709\u4e70\u5165\u4ef7\u683c\uff0c\u5356\u51fa\u4ef7\u683c\uff0c\u548c\u6bcf\u65e5\u5229\u6da6\u3002 \u3002\u3002\u3002\u6709 n \u4e2a\u53ef\u4ee5\u4e70\u5165\u673a\u5668\u7684\u65f6\u70b9\u3002\u3002\u6bcf\u4e2a\u65f6\u70b9\u5f62\u5982\uff0cd, p, r, g \u3002\u3002\u3002 \u3002\u3002\u3002\u5206\u522b\u8868\u793a\u65f6\u523b\uff0c\u4e70\u5165\u4ef7\u683c\uff0c\u5356\u51fa\u4ef7\u683c\u548c\u8be5\u673a\u5668\u7684\u65e5\u5229\u6da6\u3002 \u3002\u4e70\u5165\u53ea\u80fd\u5728\u90a3\u4e2a\u65f6\u523b\u8fdb\u884c\uff0c\u800c\u5356\u51fa\u53ef\u4ee5\u9009\u62e9\u4e70\u5165\u540e\u7684\u4efb\u610f\u65f6\u523b\u3002 \u3002\u7ed9\u5b9a\u521d\u59cb\u65f6\u523b\u7684\u91d1\u5e01\uff0c\u95ee d \u5929\u540e\u6240\u80fd\u83b7\u5f97\u91d1\u5e01\u7684\u6700\u5927\u503c\u3002<\/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":[1],"tags":[],"class_list":["post-618","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"jetpack_publicize_connections":[],"jetpack_featured_media_url":"","jetpack_shortlink":"https:\/\/wp.me\/p2tdP7-9Y","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/posts\/618","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=618"}],"version-history":[{"count":1,"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/posts\/618\/revisions"}],"predecessor-version":[{"id":620,"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/posts\/618\/revisions\/620"}],"wp:attachment":[{"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/media?parent=618"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/categories?post=618"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/tags?post=618"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}