{"id":944,"date":"2014-08-21T11:36:49","date_gmt":"2014-08-21T03:36:49","guid":{"rendered":"http:\/\/www.shuizilong.com\/house\/?p=944"},"modified":"2014-08-21T11:36:49","modified_gmt":"2014-08-21T03:36:49","slug":"spoj-744-longest-permutation","status":"publish","type":"post","link":"https:\/\/www.shuizilong.com\/house\/archives\/spoj-744-longest-permutation\/","title":{"rendered":"SPOJ 744. Longest Permutation"},"content":{"rendered":"<p><a href=\"http:\/\/www.spoj.com\/problems\/LPERMUT\/\">http:\/\/www.spoj.com\/problems\/LPERMUT\/<\/a><\/p>\n<h3>Brief description:<\/h3>\n<p>\u7ed9\u51fa\u4e00\u4e2a\u5e8f\u5217\uff0c\u6c42\u6700\u5927\u7684 <code>mx<\/code>\uff0c\u4f7f\u5f97\u5b58\u5728\u4e00\u4e2a\u957f\u5ea6\u4e3a <code>mx<\/code> \u7684\u8fde\u7eed\u5b50\u5e8f\u5217\uff0c\u4f7f\u5176\u6070\u597d\u4e3a <code>1..mx<\/code> \u7684\u4e00\u4e2a\u6392\u5217\u3002<\/p>\n<h3>Analysis:<\/h3>\n<p>\u597d\u9898\u3002\u3002\u3002<a href=\"https:\/\/vijos.org\/p\/1381\">Vijos1381<\/a> \u6570\u636e\u592a\u5f31\uff0c\u6b63\u89e3\u5e94\u662f O(n) \u3002<\/p>\n<p>\u5c3d\u91cf\u907f\u514d\u4f7f\u7528\u6570\u636e\u7ed3\u6784\u3002\u3002\u3002\u6211\u4eec\u9700\u8981\u5145\u5206\u5229\u7528\u6392\u5217\u7684\u6027\u8d28\u3002\u3002\u3002<br \/>\n\u533a\u95f4 <code>[l, r]<\/code> \u6070\u597d\u662f <code>1..len<\/code> \uff08len = r-l+1\uff09\u7684\u6392\u5217\u7684\u5145\u5206\u5fc5\u8981\u6761\u4ef6\u662f\uff1a<\/p>\n<ul>\n<li>[l, r] \u533a\u95f4\u7684\u6570\u4e24\u4e24\u4e0d\u540c\u3002<\/li>\n<li>s[r]-s[l+1] = 1+2+&#8230;+len\u3002\u3002\u3002<\/li>\n<\/ul>\n<p>\u4e3a\u4e86\u786e\u4fdd\u533a\u95f4\u4e2d\u7684\u6570\u5b57\u4e24\u4e24\u4e0d\u540c\u3002\u3002\u3002\u6211\u4eec\u8bbe l[i] \u4e3a i \u5411\u5de6\u6700\u957f\u53ef\u4ee5\u5ef6\u4f38\u7684\u8ddd\u79bb\u3002\u3002\uff08\u8fb9\u754c\u8bbe l[0] = 0, l[n+1] = n+1\u3002\u3002\uff09<br \/>\n\u3002\u3002\u90a3\u4e48\u6709 l[i] = max(l[i],  p[a[i]]+1)\u3002\u3002\u3002\uff08p[a[i]] \u662f\u4e0a\u4e00\u4e2a a[i] \u7684\u4f4d\u7f6e\u3002\u3002\u3002\uff08\u4e5f\u53ef\u4ee5\u7528 two point \u5f97\u5230\u8fd9\u4e2a\u4e1c\u897f\u3002\u3002\u3002\u3002<\/p>\n<pre class=\"brush: cpp; light: false; title: ; toolbar: true; notranslate\" title=\"\">\r\nvoid upd(int l, int r, int len){\r\n    if (len &lt; ans) return;\r\n    if (::l&#x5B;r] &lt;= l &amp;&amp; (s&#x5B;r]-s&#x5B;l-1])*2 == (1+len)*len) ans = len;\r\n}\r\n<\/pre>\n<p>\u3002\u5e8f\u5217\u88ab 1 \u5206\u5272\u6210\u4e86\u4e00\u4e9b\u5c0f\u7684\u533a\u95f4\u3002\u3002\uff08\u4e0d\u80fd\u5305\u542b\u4e24\u4e2a\u76f8\u540c\u7684 1\u3002\u3002\u3002\uff09\u3002\u3002<\/p>\n<p>____ 1 ____ 1 _________ 1 _____<\/p>\n<p>\u6211\u4eec\u679a\u4e3e\u6bcf\u4e2a 1.\u3002\u3002\u8ba8\u8bba\u533a\u95f4\u4e2d\u6700\u5927\u7684\u6570\u5b57 mx \u51fa\u73b0\u5728 1 \u7684\u5de6\u8fb9\u8fd8\u662f\u53f3\u8fb9\u3002\u3002\u5bf9\u79f0\u5904\u7406\u3002\u3002<br \/>\n\u3002\u3002\u8003\u8651\u5de6\u8fb9\u3002\u3002<\/p>\n<pre class=\"brush: cpp; light: false; title: ; toolbar: true; notranslate\" title=\"\">\r\n        for (int j=i-1,mx=1;l&#x5B;i]&lt;=j;--j){\r\n            checkMax(mx, a&#x5B;j]);\r\n            upd(j,j+mx-1,mx);\r\n        }\r\n<\/pre>\n<p>\u7531\u4e8e <code>upd()<\/code> \u8fc7\u7a0b\u662f <code>O(1)<\/code> \u7684\u3002\u3002\u6240\u4ee5\u6574\u4e2a\u7b97\u6cd5\u662f <code>O(n)<\/code> \u7684\u3002\u3002\u3002 <\/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\n\r\nint a&#x5B;N], s&#x5B;N], l&#x5B;N], p&#x5B;N], n, ans;\r\n\r\nvoid upd(int l, int r, int len){\r\n    if (len &lt; ans) return;\r\n    if (::l&#x5B;r] &lt;= l &amp;&amp; (s&#x5B;r]-s&#x5B;l-1])*2 == (1+len)*len) ans = len;\r\n}\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    REP_1_C(i, RD(n)) s&#x5B;i] = s&#x5B;i-1] + RD(a&#x5B;i]);\r\n\r\n    RST(p); l&#x5B;0] = 0; REP_1(i, n){\r\n        l&#x5B;i] = max(l&#x5B;i-1], p&#x5B;a&#x5B;i]]+1); p&#x5B;a&#x5B;i]] = i;\r\n        \/\/cout &lt;&lt; l&#x5B;i] &lt;&lt; &quot; &quot;;\r\n    }\r\n    l&#x5B;n+1] = n+1;\r\n\r\n    \/\/puts(&quot;&quot;);\r\n\r\n    REP_1(i, n) if (a&#x5B;i] == 1){\r\n\r\n        upd(i, i, 1);\r\n\r\n        for (int j=i-1,mx=1;l&#x5B;i]&lt;=j;--j){\r\n            checkMax(mx, a&#x5B;j]);\r\n            upd(j,j+mx-1,mx);\r\n        }\r\n\r\n        for (int j=i+1,mx=1;l&#x5B;j]&lt;=i;++j){\r\n            checkMax(mx, a&#x5B;j]);\r\n            upd(j-mx+1,j,mx);\r\n        }\r\n    }\r\n\r\n    OT(ans);\r\n}\r\n\r\n<\/pre>\n","protected":false},"excerpt":{"rendered":"<p>http:\/\/www.spoj.com\/problems\/LPERMUT\/ Brief description: \u7ed9\u51fa\u4e00\u4e2a\u5e8f\u5217\uff0c\u6c42\u6700\u5927\u7684 mx\uff0c\u4f7f\u5f97\u5b58\u5728\u4e00\u4e2a\u957f\u5ea6\u4e3a mx \u7684\u8fde\u7eed\u5b50\u5e8f\u5217\uff0c\u4f7f\u5176\u6070\u597d\u4e3a 1..mx \u7684\u4e00\u4e2a\u6392\u5217\u3002 Analysis: \u597d\u9898\u3002\u3002\u3002Vijos1381 \u6570\u636e\u592a\u5f31\uff0c\u6b63\u89e3\u5e94\u662f O(n) \u3002 \u5c3d\u91cf\u907f\u514d\u4f7f\u7528\u6570\u636e\u7ed3\u6784\u3002\u3002\u3002\u6211\u4eec\u9700\u8981\u5145\u5206\u5229\u7528\u6392\u5217\u7684\u6027\u8d28\u3002\u3002\u3002 \u533a\u95f4 [l, r] \u6070\u597d\u662f 1..len \uff08len = r-l+1\uff09\u7684\u6392\u5217\u7684\u5145\u5206\u5fc5\u8981\u6761\u4ef6\u662f\uff1a [l, r] \u533a\u95f4\u7684\u6570\u4e24\u4e24\u4e0d\u540c\u3002 s[r]-s[l+1] = 1+2+&#8230;+len\u3002\u3002\u3002 \u4e3a\u4e86\u786e\u4fdd\u533a\u95f4\u4e2d\u7684\u6570\u5b57\u4e24\u4e24\u4e0d\u540c\u3002\u3002\u3002\u6211\u4eec\u8bbe l[i] \u4e3a i \u5411\u5de6\u6700\u957f\u53ef\u4ee5\u5ef6\u4f38\u7684\u8ddd\u79bb\u3002\u3002\uff08\u8fb9\u754c\u8bbe l[0] = 0, l[n+1] = n+1\u3002\u3002\uff09 \u3002\u3002\u90a3\u4e48\u6709 l[i] = max(l[i], p[a[i]]+1)\u3002\u3002\u3002\uff08p[a[i]] \u662f\u4e0a\u4e00\u4e2a a[i] \u7684\u4f4d\u7f6e\u3002\u3002\u3002\uff08\u4e5f\u53ef\u4ee5\u7528 two point \u5f97\u5230\u8fd9\u4e2a\u4e1c\u897f\u3002\u3002\u3002\u3002 void upd(int l, int [&hellip;]<\/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":[21],"tags":[],"class_list":["post-944","post","type-post","status-publish","format-standard","hentry","category-spoj"],"jetpack_publicize_connections":[],"jetpack_featured_media_url":"","jetpack_shortlink":"https:\/\/wp.me\/p2tdP7-fe","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/posts\/944","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=944"}],"version-history":[{"count":0,"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/posts\/944\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/media?parent=944"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/categories?post=944"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/tags?post=944"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}