{"id":243,"date":"2006-10-15T11:55:00","date_gmt":"2006-10-15T03:55:00","guid":{"rendered":"http:\/\/114429"},"modified":"2006-10-15T11:55:00","modified_gmt":"2006-10-15T03:55:00","slug":"nwerc-2005-unequalled-consumption","status":"publish","type":"post","link":"https:\/\/www.yewen.us\/blog\/2006\/10\/nwerc-2005-unequalled-consumption\/","title":{"rendered":"NWERC 2005 Unequalled Consumption"},"content":{"rendered":"

\u4ee5\u4e0b\u5185\u5bb9\u5f15\u7528\u81eafrkstyc’s Blog<\/a>, \u539f\u6587\u5730\u5740:
\nhttp:\/\/www.blog.edu.cn\/user2\/frkstyc\/archives\/2006\/1180760.shtml<\/a><\/p>\n

——————————————————-\u6211\u662f\u5206\u9694\u7ebf——————————————————<\/p>\n

http:\/\/acm.pku.edu.cn\/JudgeOnline\/showproblem?problem_id=2764<\/a>
\nhttp:\/\/acm.xmu.edu.cn\/JudgeOnline\/showproblem?problem_id=1072<\/a><\/div>\n

\u6709\u4eba\u66fe\u7ecf\u5728POJ webboard\u4e0a\u58f0\u79f0\u751f\u6210\u51fd\u6570\u662f\u201c\u6ca1\u7528\u7684\u4e1c\u897f\u201d\u3002\u4f46\u8fd9\u4e2a\u9898\u5374\u662f\u5229\u7528\u751f\u6210\u51fd\u6570\u89e3\u51b3\u95ee\u9898\u7684\u4e00\u4e2a\u5f88\u597d\u7684\u4f8b\u5b50\u3002<\/p>\n

\u9898\u76ee\u7684\u5927\u610f\u662f\u6709\u4e0d\u8d85\u8fc75\u79cd\u91cd\u91cf\u572810\u4ee5\u5185\u7684\u7cd6\u679c\uff08\u4e0d\u540c\u7684\u7cd6\u679c\u53ef\u4ee5\u6709\u76f8\u540c\u91cd\u91cf\uff09\uff0c\u7ed9\u4e00\u4e2a\u6574\u6570P<\/em><= 1015\uff0c\u8981\u6c42\u4e00\u4e2a\u6700\u5c0f\u7684\u91cd\u91cfw<\/em>\uff0c\u53ea\u5f97\u505a\u4e00\u4e2a\u91cd\u91cf\u4e3aw<\/em>\u7684\u7cd6\u679c\u76d2\u7684\u4e0d\u540c\u65b9\u6cd5\u6570\u81f3\u5c11\u662fP<\/em>\u3002<\/p>\n

\u770b\u5230P<\/em>\u7684\u89c4\u6a21\u5c31\u53ef\u4ee5\u7acb\u5373\u5426\u51b3\u666e\u901a\u7684\u52a8\u6001\u89c4\u5212\u89e3\u6cd5\u3002\u5bb9\u6613\u8054\u60f3\u5230\u7684\u7b97\u6cd5\u662f\u4e8c\u5206\u6cd5\uff0c\u4f46\u8fd9\u4e2a\u9898\u4e4d\u770b\u4e4b\u4e0b\u6ca1\u6709\u660e\u663e\u7684\u5355\u8c03\u6027\u3002\u5c1d\u8bd5\u7528\u751f\u6210\u51fd\u6570\u89e3\u51b3\u3002\u4e3a\u63cf\u8ff0\u65b9\u4fbf\uff0c\u4ee5\u4e0b\u76f4\u63a5\u7528\u4e00\u4e2a\u5b9e\u4f8b\u6765\u8bf4\u660e\u3002<\/p>\n

\u5047\u8bbe\u67093\u79cd\u7cd6\u679c\uff0c\u91cd\u91cf\u5206\u522b\u4e3a2, 3, 5\u3002\u7528\u751f\u6210\u51fd\u6570\u4e2dxn<\/em>\u9879\u7684\u7cfb\u6570\u8868\u793a\u505a\u91cd\u91cf\u4e3an<\/em>\u7684\u7cd6\u679c\u76d2\u7684\u65b9\u6cd5\u6570\uff0c\u90a3\u4e48\u5bf9\u5e94\u7684\u751f\u6210\u51fd\u6570\u5c31\u662f<\/p>\n

f<\/em>(x<\/em>) = 1 \/ ((1 –\u00a0x<\/em>2)(1 –\u00a0x<\/em>3)(1 –\u00a0x<\/em>5))\u3002<\/p>\n

\u8fd9\u4e2a\u5f62\u5f0f\u662f\u6ca1\u6709\u529e\u6cd5\u76f4\u63a5\u5229\u7528\u7684\uff0c\u56e0\u4e3a\u91cc\u9762\u4e09\u4e2a\u56e0\u5b50\u7684\u5c55\u5f00\u5f0f\u90fd\u6709\u65e0\u7a77\u9879\uff0c\u8981\u76f4\u63a5\u627e\u7cfb\u6570\u7684\u901a\u9879\u516c\u5f0f\u4e5f\u4e0d\u5bb9\u6613\u3002\u4f46\u662f\u5229\u7528\u4e00\u4e2a\u5f88\u7b80\u5355\u7684\u6280\u5de7\u5c31\u53ef\u4ee5\u89e3\u51b3\u8fd9\u4e24\u4e2a\u95ee\u9898\u3002\uff08\u5e94\u5f53\u8bf4\u660e\uff0c\u8fd9\u4e2a\u6280\u5de7\u867d\u7136\u770b\u8d77\u6765\u5f88\u7b80\u5355\uff0c\u4f46\u7684\u786e\u662f\u8981\u8d39\u4e00\u756a\u601d\u8003\u7684\u3002\uff09\u6ce8\u610f\u52302, 3, 5\u7684\u6700\u5c0f\u516c\u500d\u6570[2, 3, 5] = 30\uff0c\u56e0\u6b64\u5c06\u4e0a\u9762\u7684\u5f0f\u5b50\u6539\u5199\u4e00\u4e0b\uff0c\u53d8\u6210<\/p>\n

g<\/em>(x<\/em>) = ((1 –\u00a0x<\/em>30) \/ (1 –\u00a0x<\/em>2)) ((1 –\u00a0x<\/em>30) \/ (1 –\u00a0x<\/em>3)) ((1 –\u00a0x<\/em>30) \/ (1 –\u00a0x<\/em>5))\uff0c
\nh<\/em>(x<\/em>) = 1 \/ (1 –\u00a0x<\/em>30)3\uff0c
\nf<\/em>(x<\/em>) =\u00a0g<\/em>(x<\/em>)\u00a0h<\/em>(x<\/em>)\u3002<\/p>\n

\u8fd9\u6837\uff0cg<\/em>(x<\/em>)\u662f\u4e00\u4e2a\u4e00\u822c\u7684\u591a\u9879\u5f0f\uff0ch<\/em>(x<\/em>)\u867d\u7136\u6709\u65e0\u7a77\u9879\u4f46\u5f62\u5f0f\u5f88\u89c4\u6574\uff0cf<\/em>(x<\/em>)\u53ea\u662fg<\/em>(x<\/em>)\u548ch<\/em>(x<\/em>)\u7684\u4e58\u79ef\u3002<\/p>\n

g<\/em>(x<\/em>)\u53ea\u9700\u76f4\u63a5\u5c55\u5f00\u5373\u53ef\uff0c\u5c55\u5f00\u7684\u7ed3\u679c\u662f\u4e00\u4e2a\u6b21\u6570\u5c0f\u4e8e3 * 30 = 90\u6b21\u7684\u591a\u9879\u5f0f\u3002\u5bf9\u4e8eh<\/em>(x<\/em>)\uff0c\u4e3a\u65b9\u4fbf\u8d77\u89c1\uff0c\u4f5c\u4e00\u4e2a\u6362\u5143\uff0c\u8bb0<\/p>\n

h’<\/em>(y<\/em>) = 1 \/ (1 –\u00a0y<\/em>)3\u3002<\/p>\n

\u901a\u8fc7\u8ba1\u7b97\u6216\u8005\u67e5\u9605\u5de5\u5177\u4e66\u53ef\u4ee5\u77e5\u9053h’<\/em>(y<\/em>)\u4e2dyn<\/em>\u9879\u7684\u7cfb\u6570\u4e3a\u7ec4\u5408\u6570C<\/em>(3 – 1,\u00a0n<\/em>\u00a0+ 3 – 1)\uff0c\u5176\u4e2d\u76843\u5c31\u662fh’<\/em>(y<\/em>)\u7684\u89e3\u6790\u5f0f\u4e2d1 –\u00a0y<\/em>\u7684\u6b21\u6570\u3002\u56e0\u6b64h<\/em>(x<\/em>)\u4e2dx<\/em>30\u00a0n<\/em>\u7684\u6b21\u6570\u4e5f\u662fC<\/em>(3 – 1,\u00a0n<\/em>\u00a0+ 3 – 1)\uff0c\u800c\u5176\u4ed6\u9879\u7684\u7cfb\u6570\u90fd\u662f0\u3002<\/p>\n

\u7efc\u5408\u4e0a\u9762\u7684\u8ba8\u8bba\uff0c\u53ef\u4ee5\u5f97\u5230\u8ba1\u7b97f<\/em>(x<\/em>)\u4e2dxn<\/em>\u9879\u7684\u7cfb\u6570\u7684\u65b9\u6cd5\u3002\u8bb0p<\/em>(x<\/em>)\u4e2dxn<\/em>\u9879\u7684\u7cfb\u6570\u4e3ac<\/em>(p<\/em>,\u00a0n<\/em>)\u3002\u5bf9\u4e8en<\/em>< 90\uff0cc<\/em>(f<\/em>,\u00a0n<\/em>)\u53ef\u4ee5\u76f4\u63a5\u5229\u7528\u52a8\u6001\u89c4\u5212\u6216\u8005\u9650\u5236\u6b21\u6570\u5730\u76f4\u63a5\u5c55\u5f00f<\/em>(x<\/em>)\u5f97\u5230\u3002\uff08\u6ce8\u610f\uff1a\u8fd9\u4e2a\u4e0d\u662fc<\/em>(g<\/em>,n<\/em>)\uff01\uff09\u5bf9\u4e8en<\/em>\u00a0>= 90\uff0c\u8bb0n<\/em>\u00a0=\u00a030\u00a0k<\/em>\u00a0+\u00a0r<\/em>\uff0c\u5176\u4e2d0 <=\u00a0r<\/em>\u00a0< 30\uff0c\u90a3\u4e48\u6839\u636ef<\/em>(x<\/em>) =\u00a0g<\/em>(x<\/em>)\u00a0h<\/em>(x<\/em>)\uff0c\u6709\u4ee5\u4e0b\u516c\u5f0f<\/p>\n

c<\/em>(f<\/em>,\u00a0n<\/em>) =\u00a0C<\/em>(2,\u00a0k<\/em>\u00a0+ 2)\u00a0c<\/em>(g<\/em>,\u00a0r<\/em>) +\u00a0C<\/em>(2,\u00a0k<\/em>\u00a0+ 1)\u00a0c<\/em>(g<\/em>,\u00a0r<\/em>\u00a0+ 30) +\u00a0C<\/em>(2,\u00a0\u00a0k<\/em>)\u00a0c<\/em>(g<\/em>,\u00a0r<\/em>\u00a0+ 60)\u3002<\/p>\n

\u548cf<\/em>(x<\/em>)\u76f4\u63a5\u76f8\u5173\u7684\u8ba1\u7b97\u5df2\u7ecf\u57fa\u672c\u89e3\u51b3\u3002\u5269\u4e0b\u6c42\u6700\u5c0f\u7684\u95ee\u9898\uff0c\u65b9\u6cd5\u8fd8\u662f\u4e8c\u5206\u6cd5\u3002\u867d\u7136\u4ece\u6574\u4f53\u770b\uff0cc<\/em>(f<\/em>,n<\/em>)\u5173\u4e8en<\/em>\u4e0d\u4e00\u5b9a\u662f\u5355\u8c03\u7684\uff0c\u4f46\u662f\u5047\u5982\u628an<\/em>\u5199\u6210n<\/em>\u00a0= 90\u00a0k<\/em>\u00a0+\u00a0r<\/em>\uff0c\u5176\u4e2d0 <=\u00a0r<\/em>\u00a0< 90\uff0c\u5c31\u53ef\u4ee5\u53d1\u73b0\u5bf9\u56fa\u5b9a\u7684r\uff0cc<\/em>(f, 90\u00a0k<\/em>\u00a0+\u00a0r<\/em>)\u5173\u4e8ek<\/em>\u662f\u5355\u8c03\u7684\u3002\u56e0\u6b64\u53ea\u9700\u679a\u4e3er<\/em>\uff0c\u5bf9k<\/em>\u5e94\u7528\u4e8c\u5206\u6cd5\uff0c\u7136\u540e\u4ece\u6240\u6709\u5019\u9009\u7684n<\/em>\u00a0= 90k<\/em>\u00a0+\u00a0r<\/em>\u4e2d\u9009\u53d6\u6700\u5c0f\u7684\u5373\u53ef\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"

\u4ee5\u4e0b\u5185\u5bb9\u5f15\u7528\u81eafrkstyc’s Blog, \u539f\u6587\u5730\u5740: http:\/\/www.blog.edu. […]<\/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":""},"categories":[11],"tags":[26,68,435],"class_list":["post-243","post","type-post","status-publish","format-standard","hentry","category-contests","tag-acm","tag-frkstyc","tag-435"],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"jetpack_shortlink":"https:\/\/wp.me\/p4aR5e-3V","_links":{"self":[{"href":"https:\/\/www.yewen.us\/blog\/wp-json\/wp\/v2\/posts\/243","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.yewen.us\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.yewen.us\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.yewen.us\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.yewen.us\/blog\/wp-json\/wp\/v2\/comments?post=243"}],"version-history":[{"count":0,"href":"https:\/\/www.yewen.us\/blog\/wp-json\/wp\/v2\/posts\/243\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.yewen.us\/blog\/wp-json\/wp\/v2\/media?parent=243"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.yewen.us\/blog\/wp-json\/wp\/v2\/categories?post=243"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.yewen.us\/blog\/wp-json\/wp\/v2\/tags?post=243"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}