{"id":633,"date":"2013-01-20T07:11:00","date_gmt":"2013-01-19T23:11:00","guid":{"rendered":"http:\/\/www.shuizilong.com\/house\/?p=633"},"modified":"2013-01-20T10:33:36","modified_gmt":"2013-01-20T02:33:36","slug":"poj-3666-making-the-grade","status":"publish","type":"post","link":"https:\/\/www.shuizilong.com\/house\/archives\/poj-3666-making-the-grade\/","title":{"rendered":"POJ 3666. Making the Grade"},"content":{"rendered":"<p><a href=\"http:\/\/acm.hust.edu.cn:8080\/judge\/problem\/viewProblem.action?id=10721\">http:\/\/acm.hust.edu.cn:8080\/judge\/problem\/viewProblem.action?id=10721<\/a><\/p>\n<h3>Brief description: <\/h3>\n<p>\u7ed9\u5b9a\u4e00\u4e2a\u6574\u6570\u5e8f\u5217 {an} \u6c42\u4e00\u4e2a\u4e0d\u964d\u5e8f\u5217 {bn}\uff0c\u6700\u5c0f\u5316 {an} \u548c {bn} \u5404\u9879\u5dee\u7edd\u5bf9\u503c\u4e4b\u548c\uff1a<br \/>\nS = |a1 &#8211; b1| + |a2 &#8211; b2| + \u2026 + |an &#8211; bn|\u3002<\/p>\n<p><!--more--><\/p>\n<h3>Analysis: <\/h3>\n<p>\u7b97\u6cd5 1\uff1a\u52a8\u6001\u89c4\u5212\uff082D\/0D\u3002\u3002<br \/>\n\u3002\u3002f[i][j]: \u5f53\u524d\u8003\u5bdf\u5230 ai\uff0c\u6700\u540e\u4e00\u4e2a bi \u4e3a a[o[j]]\u3002\uff08\u5176\u4e2d o \u6570\u5b57 \u4e3a a \u6570\u7ec4\u6392\u5e8f\u540e\u6bcf\u4e2a\u540d\u6b21\u6240\u5bf9\u5e94\u7684\u4e0b\u6807\u3002<\/p>\n<p><a href=\"http:\/\/acm.hust.edu.cn:8080\/judge\/problem\/viewSource.action?id=901783\">http:\/\/acm.hust.edu.cn:8080\/judge\/problem\/viewSource.action?id=901783<\/a><\/p>\n<p>\u7b97\u6cd5 2\uff1a\u53ef\u5408\u5e76\u5806\u3002<\/p>\n<blockquote><p>\n\u6211\u4eec\u5148\u6765\u770b\u770b\u4e24\u4e2a\u6700\u7279\u6b8a\u7684\u60c5\u51b5\uff1a<\/p>\n<ol>\n<li>a[1]\u2264a[2]\u2264\u2026\u2264a[n]\uff0c\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b\uff0c\u663e\u7136\u6700\u4f18\u89e3\u4e3a b[i] = a[i]\uff1b<\/li>\n<li>a[1]\u2265a[2]\u2265\u2026\u2265a[n]\uff0c\u8fd9\u65f6\uff0c\u6700\u4f18\u89e3\u4e3a b[i] = x\uff0c\u5176\u4e2d x \u662f\u6570\u5217 a \u7684\u4e2d\u4f4d\u6570 \u3002<\/li>\n<\/ol>\n<p>\u4e8e\u662f\u6211\u4eec\u53ef\u4ee5\u521d\u6b65\u5efa\u7acb\u8d77\u8fd9\u6837\u4e00\u4e2a\u601d\u8def\uff1a<br \/>\n\u628a 1 \u2026 n \u5212\u5206\u6210 m \u4e2a\u533a\u95f4\uff1a[q[1], q[2]\uff09\uff0c[q[2], q[3]\uff09\uff0c\u2026\u2026\uff0c[q[m], q[m+1]\uff09 \u3002\u6bcf\u4e2a\u533a\u95f4\u5bf9\u5e94\u4e00\u4e2a\u89e3\uff0cb[q[i]] = b[q[i]+1] = \u2026 = b[q[i+1]-1] = w[i]\uff0c\u5176\u4e2d w[i] \u4e3a a[q[i]], a[q[i]+1], &#8230; , a[q[i+1]-1] \u7684\u4e2d\u4f4d\u6570\u3002<br \/>\n\u663e\u7136\uff0c\u5728\u4e0a\u9762\u7b2c\u4e00\u79cd\u60c5\u51b5\u4e0b m=n\uff0cq[i]=i\uff1b\u5728\u7b2c\u4e8c\u79cd\u60c5\u51b5\u4e0b m=1\uff0cq[1]=1\u3002<br \/>\n\u8fd9\u6837\u7684\u60f3\u6cd5\u7a76\u7adf\u5bf9\u4e0d\u5bf9\u5462\uff1f\u5e94\u8be5\u600e\u6837\u5b9e\u73b0\uff1f<\/p>\n<p>\u82e5\u67d0\u5e8f\u5217\u524d\u534a\u90e8\u5206 a[1], a[2], \u2026 , a[m-1] \u7684\u6700\u4f18\u89e3\u4e3a (u,u,\u2026,u)\uff0c\u540e\u534a\u90e8\u5206a[m], a[n+2], &#8230; , a[n] \u7684\u6700\u4f18\u89e3\u4e3a (v,v,\u2026,v)\uff0c\u90a3\u4e48\u6574\u4e2a\u5e8f\u5217\u7684\u6700\u4f18\u89e3\u662f\u4ec0\u4e48\u5462\uff1f<br \/>\n\u82e5 u \u2264 v\uff0c\u663e\u7136\u6574\u4e2a\u5e8f\u5217\u7684\u6700\u4f18\u89e3\u4e3a (u,u,\u2026,u,v,v,\u2026,v)\u3002\u5426\u5219\uff0c\u8bbe\u6574\u4e2a\u5e8f\u5217\u7684\u6700\u4f18\u89e3\u4e3a (b[1],\u2026,b[m],b[m+1],\u2026,b[n])\uff0c\u5219\u663e\u7136 b[m] \u2264 u<br \/>\n\uff08\u5426\u5219\u6211\u4eec\u628a\u524d\u534a\u90e8\u5206\u7684\u89e3 (b[1],b[2],\u2026,b[m-1]) \u6539\u4e3a (u,u,\u2026,u)\uff0c\u7531\u9898\u8bbe\u77e5\u6574\u4e2a\u5e8f\u5217\u7684\u89e3\u4e0d\u4f1a\u53d8\u574f\uff09\uff0c\u540c\u7406 b[m+1] \u2265 v\u3002<br \/>\n\u63a5\u4e0b\u6765\uff0c\u6211\u4eec\u5c06\u770b\u5230\u4e0b\u9762\u8fd9\u4e2a\u4e8b\u5b9e\uff1a<br \/>\n\u5bf9\u4e8e\u4efb\u610f\u4e00\u4e2a\u5e8f\u5217 a[1],a[2],\u2026,a[n]\uff0c\u5982\u679c\u6700\u4f18\u89e3\u4e3a (u,u,\u2026,u)\uff0c\u90a3\u4e48\u5728\u6ee1\u8db3 u\u2264u\u2032\u2264b[1] \u6216 b[n]\u2264u\u2032\u2264u \u7684\u60c5\u51b5\u4e0b\uff0c(b[1],b[2],\u2026,b[n]) \u4e0d\u4f1a\u6bd4 (u\u2032,u\u2032,\u2026,u\u2032) \u66f4\u4f18\u3002<\/p>\n<p>\u6211\u4eec\u7528\u5f52\u7eb3\u6cd5\u8bc1\u660eu\u2264u\u2032\u2264b[1] \u7684\u60c5\u51b5\uff0cb[n]\u2264u\u2032\u2264u\u7684\u60c5\u51b5\u53ef\u4ee5\u7c7b\u4f3c\u8bc1\u660e\u3002<br \/>\n\u5f53n=1\u65f6\uff0cu=a[1]\uff0c\u547d\u9898\u663e\u7136\u6210\u7acb\u3002<br \/>\n\u5f53n>1\u65f6\uff0c\u5047\u8bbe\u5bf9\u4e8e\u4efb\u610f\u957f\u5ea6\u5c0f\u4e8en\u7684\u5e8f\u5217\u547d\u9898\u90fd\u6210\u7acb\uff0c\u73b0\u5728\u8bc1\u660e\u5bf9\u4e8e\u957f\u5ea6\u4e3an\u7684\u5e8f\u5217\u547d\u9898\u4e5f\u6210\u7acb\u3002\u9996\u5148\u628a (b[1], b[2], \u2026 b[n]) \u6539\u4e3a (b[1], b[1], \u2026 b[1])\uff0c\u8fd9\u4e00\u6539\u52a8\u5c06\u4e0d\u4f1a\u5bfc\u81f4\u89e3\u53d8\u574f\uff0c\u56e0\u4e3a\u5982\u679c\u89e3\u53d8\u574f\u4e86\uff0c\u7531\u5f52\u7eb3\u5047\u8bbe\u53ef\u77e5a[2],a[3],\u2026,a[n]\u7684\u4e2d\u4f4d\u6570w>u\uff0c\u8fd9\u6837\u7684\u8bdd\uff0c\u6700\u4f18\u89e3\u5c31\u5e94\u8be5\u4e3a(u,u,\u2026,u,w,w,\u2026,w)\uff0c\u77db\u76fe\u3002\u7136\u540e\u6211\u4eec\u518d\u628a(b[1],b[1],\u2026,b[1])\u6539\u4e3a (u\u2032,u\u2032,\u2026,u\u2032)\uff0c\u7531\u4e8e| a[1] &#8211; x | + | a[2] &#8211; x | + \u2026 + | a[n] &#8211; x | \u7684\u51e0\u4f55\u610f\u4e49\u4e3a\u6570\u8f74\u4e0a\u70b9x\u5230\u70b9a[1], a[2], \u2026 a[n]\u7684\u8ddd\u79bb\u4e4b\u548c\uff0c\u4e14u\u2264u\u2032\u2264b[1]\uff0c\u663e\u7136\u70b9u\u2032\u5230\u5404\u70b9\u7684\u8ddd\u79bb\u4e4b\u548c\u4e0d\u4f1a\u6bd4\u70b9b[1]\u5230\u5404\u70b9\u7684\u8ddd\u79bb\u4e4b\u548c\u5927\uff0c\u4e5f\u5c31\u662f\u8bf4\uff0c(b[1],b[1],\u2026,b[n]) \u4e0d\u4f1a\u6bd4 (v,v,\u2026,v) \u66f4\u4f18\u3002\uff08\u8bc1\u6bd5\uff09<br \/>\n\u518d\u56de\u5230\u4e4b\u524d\u7684\u8bba\u8ff0\uff0c\u7531\u4e8eb[n]\u2264u\uff0c\u4f5c\u4e3a\u4e0a\u8ff0\u4e8b\u5b9e\u7684\u7ed3\u8bba\uff0c\u6211\u4eec\u53ef\u4ee5\u5f97\u77e5\uff0c\u5c06(b[1],b[2],\u2026,b[n])\u6539\u4e3a(b[n],b[n],\u2026,b[n])\uff0c\u518d\u5c06(b[n+1],b[n+2],\u2026,b[m])\u6539\u4e3a(b[n+1],b[n+1],\u2026,b[n+1])\uff0c\u5e76\u4e0d\u4f1a\u4f7f\u89e3\u53d8\u574f\u3002\u4e5f\u5c31\u662f\u8bf4\uff0c\u6574\u4e2a\u5e8f\u5217\u7684\u6700\u4f18\u89e3\u4e3a(b[n],b[n],\u2026,b[n],b[n+1],b[n+1],\u2026,b[n+1])\u3002\u518d\u8003\u8651\u4e00\u4e0b\u8be5\u89e3\u7684\u51e0\u4f55\u610f\u4e49\uff0c\u8bbe\u6574\u4e2a\u5e8f\u5217\u7684\u4e2d\u4f4d\u6570\u4e3aw\uff0c\u5219\u663e\u7136\u4ee4b[n]=b[n+1]=w\u5c06\u5f97\u5230\u6574\u4e2a\u5e8f\u5217\u7684\u6700\u4f18\u89e3\uff0c\u5373\u6700\u4f18\u89e3\u4e3a (w,w,\u2026,w)\u3002<br \/>\n\u5206\u6790\u5230\u8fd9\u91cc\uff0c\u6211\u4eec\u4e00\u5f00\u59cb\u7684\u60f3\u6cd5\u5df2\u7ecf\u6709\u4e86\u7406\u8bba\u4f9d\u636e\uff0c\u7b97\u6cd5\u4e5f\u4e0d\u96be\u6784\u601d\u4e86\u3002\n<\/p><\/blockquote>\n<p>\u2014\u2014 \u5f15\u81ea \u300a\u5de6\u504f\u6811\u7684\u7279\u70b9\u53ca\u5176\u5e94\u7528\u300b\uff0c\u9ec4\u6e90\u6cb3<\/p>\n<p><a href=\"http:\/\/acm.hust.edu.cn:8080\/judge\/problem\/viewSource.action?id=901802\">\u5de6\u504f\u6811\u3002\u3002<\/a><\/p>\n<p>\u7b97\u6cd5 3\uff1a\u5212\u5206\u6811\u3002<br \/>\n<a href=\"http:\/\/acm.hust.edu.cn:8080\/judge\/problem\/viewSource.action?id=901844\">\uff08\u3002\u3002Orz\u3002<\/a><\/p>\n<h3>External link: <\/h3>\n<p><a href=\"http:\/\/blog.163.com\/hacker_james\/blog\/static\/659024432011711105241183\/\">http:\/\/blog.163.com\/hacker_james\/blog\/static\/659024432011711105241183\/<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>http:\/\/acm.hust.edu.cn:8080\/judge\/problem\/viewProblem.action?id=10721 Brief description: \u7ed9\u5b9a\u4e00\u4e2a\u6574\u6570\u5e8f\u5217 {an} \u6c42\u4e00\u4e2a\u4e0d\u964d\u5e8f\u5217 {bn}\uff0c\u6700\u5c0f\u5316 {an} \u548c {bn} \u5404\u9879\u5dee\u7edd\u5bf9\u503c\u4e4b\u548c\uff1a S = |a1 &#8211; b1| + |a2 &#8211; b2| + \u2026 + |an &#8211; bn|\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":true,"jetpack_social_options":{"image_generator_settings":{"template":"highway","enabled":false}}},"categories":[19],"tags":[28],"class_list":["post-633","post","type-post","status-publish","format-standard","hentry","category-poj","tag-28"],"jetpack_publicize_connections":[],"jetpack_featured_media_url":"","jetpack_shortlink":"https:\/\/wp.me\/p2tdP7-ad","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/posts\/633","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=633"}],"version-history":[{"count":1,"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/posts\/633\/revisions"}],"predecessor-version":[{"id":634,"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/posts\/633\/revisions\/634"}],"wp:attachment":[{"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/media?parent=633"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/categories?post=633"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/tags?post=633"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}