{"id":335,"date":"2012-08-01T01:56:43","date_gmt":"2012-07-31T17:56:43","guid":{"rendered":"http:\/\/www.shuizilong.com\/house\/?p=335"},"modified":"2012-08-02T22:35:59","modified_gmt":"2012-08-02T14:35:59","slug":"bzoj-1095-zjoi2007hide-%e6%8d%89%e8%bf%b7%e8%97%8f","status":"publish","type":"post","link":"https:\/\/www.shuizilong.com\/house\/archives\/bzoj-1095-zjoi2007hide-%e6%8d%89%e8%bf%b7%e8%97%8f\/","title":{"rendered":"BZOJ 1095. [ZJOI2007]Hide \u6349\u8ff7\u85cf"},"content":{"rendered":"

Brief description: <\/h3>\n

\u7ed9\u5b9a\u4e00\u68f5\u6811\uff0c\u6bcf\u4e2a\u8282\u70b9\u8981\u4e48\u662f\u9ed1\u8272\uff0c\u8981\u4e48\u662f\u767d\u8272\uff0c\u80fd\u6267\u884c\u4e24\u4e2a\u64cd\u4f5c\uff1a
\n\u3002\u3002\u3002\u628a\u67d0\u4e00\u4e2a\u70b9\u53d6\u53cd\u8272\uff0c\u8fd4\u56de\u8ddd\u79bb\u6700\u8fdc\u7684\u9ed1\u8272\u70b9\u5bf9\u3002<\/p>\n

<\/p>\n

Analysis: <\/h3>\n

\u3002\u3002\u3002… \u3002\u3002\u94fe\u5206\u6cbb\u548c\u8fb9\u5206\u6cbb\u7684\u65b9\u6cd5\u53c2\u89c1 Qtree 4<\/a> \u90a3\u7bc7\u3002\u3002\uff09
\n\u3002\u3002\u8fd9\u91cc\u8bb0\u5f55\u4e00\u4e0b\u62ec\u53f7\u5e8f\u5217\u7684\u65b9\u6cd5\u3002\u3002\u3002\uff09<\/p>\n

\n\u5b9a\u4e49\u4e00\u79cd\u5bf9\u4e00\u68f5\u6811\u7684\u62ec\u53f7\u7f16\u7801\u3002\u8fd9\u79cd\u7f16\u7801\u65b9\u5f0f\u5f88\u76f4\u89c2\uff0c\u6240\u4ee5\uff0c\u8fd9\u91cc\u4e0d\u7ed9\u51fa\u4e25\u683c\u7684\u5b9a\u4e49\uff0c\u7528\u4ee5\u4e0b\u8fd9\u68f5\u6811\u4e3a\u4f8b\uff1a<\/p>\n

(\u56fe\u7247\u81ea\u884c\u8111\u8865\u3002\u3002\u3002\uff09<\/p>\n

\u53ef\u4ee5\u5148\u5e8f\u904d\u5386\u540e\u5199\u6210\uff1a[A[B[E][F[H][I]]][C][D[G]]]\r\n\u53bb\u6389\u5b57\u6bcd\u540e\u7684\u4e32\uff1a[[[][[][]]][][[]]]\r\n<\/pre>\n
\u5c31\u79f0\u4e3a\u8fd9\u68f5\u6811\u7684\u62ec\u53f7\u7f16\u7801\u3002\uff08\u8fd9\u4e2a\u7f16\u7801\u672c\u8d28\u4e0a\u662f\u7531\u6df1\u5ea6\u4f18\u5148\u904d\u5386\u5f97\u5230\u7684\uff09
\n\u8003\u5bdf\u4e24\u4e2a\u7ed3\u70b9\uff0c\u5982 E \u548c G \uff0c<\/p>\n
\u53d6\u51fa\u4ecb\u4e8e\u5b83\u4eec\u4e4b\u95f4\u7684\u90a3\u6bb5\u62ec\u53f7\u7f16\u7801 \uff1a][[][]]][][[\r\n\u628a\u5339\u914d\u7684\u62ec\u53f7\u53bb\u6389\uff0c\u5f97\u5230\uff1a]][[\r\n<\/pre>\n
\u6211\u4eec\u770b\u5230 2 \u4e2a ] \u548c 2 \u4e2a [\uff0c\u4e5f\u5c31\u662f\u8bf4\uff0c\u5728\u6811\u4e2d\uff0c\u4ece E \u5411\u4e0a\u722c 2 \u6b65\uff0c\u518d\u5411\u4e0b\u8d70 2 \u6b65\u5c31\u5230\u4e86 G\u3002
\n\u6ce8\u610f\u5230\uff0c\u9898\u76ee\u4e2d\u9700\u8981\u7684\u4fe1\u606f\u53ea\u6709\u8fd9\u68f5\u6811\u4e2d\u70b9\u4e0e\u70b9\u7684\u8ddd\u79bb\uff0c\u6240\u4ee5\uff0c\u8d2e\u5b58\u7f16\u7801\u4e2d\u5339\u914d\u7684\u62ec\u53f7\u662f\u6ca1\u6709\u610f\u4e49\u7684\u3002
\n\u56e0\u6b64\uff0c\u5bf9\u4e8e\u4ecb\u4e8e\u4e24\u4e2a\u8282\u70b9\u95f4\u7684\u4e00\u6bb5\u62ec\u53f7\u7f16\u7801 S\uff0c\u53ef\u4ee5\u7528\u4e00\u4e2a\u4e8c\u5143\u7ec4 (a, b) \u63cf\u8ff0\u5b83\uff0c\u5373\u8fd9\u6bb5\u7f16\u7801\u53bb\u6389\u5339\u914d\u62ec\u53f7\u540e\u6709 a \u4e2a ] \u548c b \u4e2a [\u3002
\n\u6240\u4ee5\uff0c\u5bf9\u4e8e\u4e24\u4e2a\u70b9 PQ\uff0c\u5982\u679c\u4ecb\u4e8e\u67d0\u4e24\u70b9 PQ \u4e4b\u95f4\u7f16\u7801 S \u53ef\u8868\u793a\u4e3a (a, b)\uff0cPQ \u4e4b\u95f4\u7684\u8ddd\u79bb\u5c31\u662f a+b\u3002<\/p><\/blockquote>\n
\n\u4e5f\u5c31\u662f\u8bf4\uff0c\u9898\u76ee\u53ea\u9700\u8981\u52a8\u6001\u7ef4\u62a4\uff1amax{a+b | S\u2019(a, b) \u662f S \u7684\u4e00\u4e2a\u5b50\u4e32\uff0c\u4e14 S\u2019 \u4ecb\u4e8e\u4e24\u4e2a\u9ed1\u70b9\u4e4b\u95f4}\uff0c
\n\u8fd9\u91cc S \u662f\u6574\u68f5\u6811\u7684\u62ec\u53f7\u7f16\u7801\u3002\u6211\u4eec\u628a\u8fd9\u4e2a\u91cf\u8bb0\u4e3a dis(s)\u3002<\/p>\n
\u73b0\u5728\uff0c\u5982\u679c\u53ef\u4ee5\u901a\u8fc7\u5de6\u8fb9\u4e00\u534a\u7684\u7edf\u8ba1\u4fe1\u606f\u548c\u53f3\u8fb9\u4e00\u534a\u7684\u7edf\u8ba1\u4fe1\u606f\uff0c\u5f97\u5230\u6574\u6bb5\u7f16\u7801\u7684\u7edf\u8ba1\uff0c\u8fd9\u9053\u9898\u5c31\u53ef\u4ee5\u7528\u719f\u6089\u7684\u7ebf\u6bb5\u6811\u89e3\u51b3\u4e86\u3002<\/p>\n
\u8fd9\u9700\u8981\u4e0b\u9762\u7684\u5206\u6790\u3002<\/p>\n
\u8003\u8651\u5bf9\u4e8e\u4e24\u6bb5\u62ec\u53f7\u7f16\u7801 S1(a1, b1) \u548c S2(a2, b2)\uff0c\u5982\u679c\u5b83\u4eec\u8fde\u63a5\u8d77\u6765\u5f62\u6210 S(a, b)\u3002
\n\u6ce8\u610f\u5230 S1\u3001S2 \u76f8\u8fde\u65f6\u53c8\u5f62\u6210\u4e86 min{b, c} \u5bf9\u6210\u5bf9\u7684\u62ec\u53f7\uff0c\u5408\u5e76\u540e\u5b83\u4eec\u4f1a\u88ab\u62b5\u6d88\u6389\u3002\uff08\uff1f..\u8fd9\u91cc b, c \u5e94\u8be5\u5206\u522b\u662f\u6307 b1 \u548c a2\u3002\u3002\u3002<\/span><\/p>\n
\u6240\u4ee5\uff1a<\/p>\n
\r\n\u5f53 a2 < b1 \u65f6\u7b2c\u4e00\u6bb5 [ \u5c31\u88ab\u6d88\u5b8c\u4e86\uff0c\u4e24\u6bb5 ] \u8fde\u5728\u4e00\u8d77\uff0c\u4f8b\u5982\uff1a\r\n] ] [ [  +  ] ] ] [ [  =  ] ] ] [ [\r\n\u5f53 a2 >= b1 \u65f6\u7b2c\u4e8c\u6bb5 ] \u5c31\u88ab\u6d88\u5b8c\u4e86\uff0c\u4e24\u6bb5 [ \u8fde\u5728\u4e00\u8d77\uff0c\u4f8b\u5982\uff1a\r\n] ] [ [ [  +  ] ] [ [  =  ] ] [ [ [ \uff08\uff1f..\u53cd\u4e86\uff1f\u3002\u3002\u3002<\/span>\r\n<\/pre>\n
\u8fd9\u6837\uff0c\u5c31\u5f97\u5230\u4e86\u4e00\u4e2a\u5341\u5206\u6709\u7528\u7684\u7ed3\u8bba\uff1a<\/p>\n
\r\n\u5f53 a2 < b1 \u65f6\uff0c(a,b) = (a1-b1+a2, b2)\uff0c\r\n\u5f53 a2 >= b1 \u65f6\uff0c(a,b) = (a1, b1-a2+b2)\u3002\r\n<\/pre>\n
\u7531\u6b64\uff0c\u53c8\u5f97\u5230\u51e0\u4e2a\u7b80\u5355\u7684\u63a8\u8bba\uff1a<\/p>\n
\r\n(i) a+b = a1+b2+|a2-b1| = max{(a1-b1)+(a2+b2), (a1+b1)+(b2-a2)}\r\n(ii) a-b = a1-b1+a2-b2\r\n(iii) b-a = b2-a2+b1-a1\r\n<\/pre>\n
\u7531 (i) \u5f0f\uff0c\u53ef\u4ee5\u53d1\u73b0\uff0c\u8981\u7ef4\u62a4 dis(s)\uff0c\u5c31\u5fc5\u987b\u5bf9\u5b50\u4e32\u7ef4\u62a4\u4ee5\u4e0b\u56db\u4e2a\u91cf\uff1a<\/p>\n
\r\nright_plus\uff1amax{a+b | S\u2019(a,b) \u662f S \u7684\u4e00\u4e2a\u540e\u7f00\uff0c\u4e14 S\u2019 \u7d27\u63a5\u5728\u4e00\u4e2a\u9ed1\u70b9\u4e4b\u540e}\r\nright_minus\uff1amax{a-b | S\u2019(a,b) \u662f S \u7684\u4e00\u4e2a\u540e\u7f00\uff0c\u4e14 S\u2019 \u7d27\u63a5\u5728\u4e00\u4e2a\u9ed1\u70b9\u4e4b\u540e}\r\nleft_plus\uff1amax{a+b | S\u2019(a,b) \u662f S \u7684\u4e00\u4e2a\u524d\u7f00\uff0c\u4e14\u6709\u4e00\u4e2a\u9ed1\u70b9\u7d27\u63a5\u5728 S \u4e4b\u540e}\r\nleft_minus\uff1amax{b-a | S\u2019(a,b) \u662f S \u7684\u4e00\u4e2a\u524d\u7f00\uff0c\u4e14\u6709\u4e00\u4e2a\u9ed1\u70b9\u7d27\u63a5\u5728 S \u4e4b\u540e}\r\n<\/pre>\n
\u8fd9\u6837\uff0c\u5bf9\u4e8e S = S1 + S2\uff0c\u5176\u4e2d S1(a, b)\u3001S2(c, d)\u3001S(e, f)\uff0c\u5c31\u6709<\/p>\n
\r\n(e, f) = b < c ? (a-b+c, d) : (a, b-c+d)\r\ndis(S) = max{dis(S1), left_minus(S2)+right_plus(S1), left_plus(S2)+right_minus(S1), dis(S2)}\r\n<\/pre>\n
\u90a3\u4e48\uff0c\u589e\u52a0\u8fd9\u56db\u4e2a\u53c2\u6570\u662f\u5426\u5c31\u591f\u4e86\u5462\uff1f
\n\u662f\u7684\uff0c\u56e0\u4e3a\uff1a<\/p>\n
\r\nright_plus(S) = max{right_plus(S1)-c+d, right_minus(S1)+c+d, right_plus(S2)}\r\nright_minus(S) = max{right_minus(S1)+c-d, right_minus(S2)}           \r\nleft_plus(S) = max{left_plus(S2)-b+a, left_minus(S2)+b+a, left_plus(S1)}   \r\nleft_minus(S) = max{left_minus(S2)+b-a, left_minus(S1)}               \r\n<\/pre>\n
\t\u8fd9\u6837\u4e00\u6765\uff0c\u5c31\u53ef\u4ee5\u7528\u7ebf\u6bb5\u6811\u5904\u7406\u7f16\u7801\u4e32\u4e86\u3002\u5b9e\u9645\u5b9e\u73b0\u7684\u65f6\u5019\uff0c\u5728\u7f16\u7801\u4e32\u4e2d\u52a0\u8fdb\u7ed3\u70b9\u6807\u53f7\u4f1a\u66f4\u65b9\u4fbf\uff0c\u5bf9\u4e8e\u5e95\u5c42\u7ed3\u70b9\uff0c\u5982\u679c\u5bf9\u5e94\u5b57\u7b26\u662f\u4e00\u4e2a\u62ec\u53f7\u6216\u8005\u4e00\u4e2a\u767d\u70b9\uff0c\u90a3 \u4e48right_plus\u3001right_minus\u3001left_plus\u3001left_minus\u3001dis \u7684\u503c\u5c31\u90fd\u662f -maxlongint\uff1b\u5982\u679c\u5bf9\u5e94\u5b57\u7b26\u662f\u4e00\u4e2a\u9ed1\u70b9\uff0c\u90a3\u4e48 right_plus\u3001right_minus\u3001left_plus\u3001left_minus \u90fd\u662f 0\uff0cdis \u662f -maxlongint\u3002<\/p>\n
\t\u73b0\u5728\u8fd9\u4e2a\u9898\u5f97\u5230\u5706\u6ee1\u89e3\u51b3\uff0c\u56de\u987e\u8fd9\u4e2a\u8fc7\u7a0b\uff0c\u53ef\u4ee5\u53d1\u73b0\u7528\u4e00\u4e2a\u4e32\u8868\u8fbe\u6574\u68f5\u6811\u7684\u4fe1\u606f\u662f\u5173\u952e\uff0c\u8fd9\u4e00\u201c\u538b\u201d\u4f7f\u5f97\u7ebf\u6bb5\u6811\u8fd9\u4e00\u5f3a\u5927\u5de5\u5177\u5f97\u4ee5\u5229\u7528.. .\n<\/p><\/blockquote>\n
\u2014\u2014\u2014\u2014 \u4ee5\u4e0a\u6458\u81ea NOI08 \u51ac\u4ee4\u8425\u8bba\u6587 \u300a\u6570\u636e\u7ed3\u6784\u7684\u63d0\u70bc\u4e0e\u538b\u7f29\u300b by cqx \u3002\u3002\u3002<\/p>\n
\u7ebf\u6bb5\u6811\u7ef4\u62a4\u62ec\u53f7\u5e8f\u5217\uff082s+- ...<\/a>
\n\u94fe\u5206\u6cbb\uff082.5s+ ...<\/a>
\n\u8fb9\u5206\u6cbb\u3002\uff0823.0s++ <\/a><\/p>\n
External link: <\/h3>\n
http:\/\/www.lydsy.com\/JudgeOnline\/problem.php?id=1095<\/a>
\nhttp:\/\/hi.baidu.com\/wjbzbmr\/blog\/item\/2b02ec1cda7abbfa1ad57656.html<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"
Brief description: \u7ed9\u5b9a\u4e00\u68f5\u6811\uff0c\u6bcf\u4e2a\u8282\u70b9\u8981\u4e48\u662f\u9ed1\u8272\uff0c\u8981\u4e48\u662f\u767d\u8272\uff0c\u80fd\u6267\u884c\u4e24\u4e2a\u64cd\u4f5c\uff1a \u3002\u3002\u3002\u628a\u67d0\u4e00\u4e2a\u70b9\u53d6\u53cd\u8272\uff0c\u8fd4\u56de\u8ddd\u79bb\u6700\u8fdc\u7684\u9ed1\u8272\u70b9\u5bf9\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":[22],"tags":[24],"class_list":["post-335","post","type-post","status-publish","format-standard","hentry","category-bzoj","tag-24"],"jetpack_publicize_connections":[],"jetpack_featured_media_url":"","jetpack_shortlink":"https:\/\/wp.me\/p2tdP7-5p","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/posts\/335","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=335"}],"version-history":[{"count":1,"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/posts\/335\/revisions"}],"predecessor-version":[{"id":336,"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/posts\/335\/revisions\/336"}],"wp:attachment":[{"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/media?parent=335"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/categories?post=335"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/tags?post=335"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}