{"id":653,"date":"2013-01-27T08:40:56","date_gmt":"2013-01-27T00:40:56","guid":{"rendered":"http:\/\/www.shuizilong.com\/house\/?p=653"},"modified":"2014-09-22T21:37:40","modified_gmt":"2014-09-22T13:37:40","slug":"spoj-1479-the-gbaay-kingdom","status":"publish","type":"post","link":"https:\/\/www.shuizilong.com\/house\/archives\/spoj-1479-the-gbaay-kingdom\/","title":{"rendered":"SPOJ 1479. The GbAaY Kingdom"},"content":{"rendered":"

<\/p>\n

Problem C. The GbAaY Kingdom<\/h2>\n

Brief description: <\/h3>\n

… \u6700\u5c0f\u76f4\u5f84\u751f\u6210\u6811\u3002<\/p>\n

Analysis: <\/h3>\n

\u5bb9\u6613\u770b\u51fa\u6700\u5c0f\u76f4\u5f84\u751f\u6210\u6811\u5c31\u662f\u4ee5\u67d0\u4e2a\u300c\u4e2d\u5fc3\u300d\u4e3a\u6839\u7684\u6700\u77ed\u8def\u5f84\u6811\uff08shortest-paths tree\uff09\u3002\u3002
\n\u3002\u8fd9\u4e2a\u4e2d\u5fc3\u6ee1\u8db3\uff0c\u5230\u6811\u4e0a\u5176\u4ed6\u70b9\u7684\u8ddd\u79bb\u7684\u6700\u5927\u503c \u2014\u2014 \u300c\u504f\u5fc3\u7387\u300d\uff08eccentricity\uff09\u6700\u5c0f\u3002\u3002
\n..\u6211\u4eec\u79f0\u8fd9\u4e2a\u70b9\u4e3a\u300c\u7edd\u5bf9\u4e2d\u5fc3\u300d\uff08absolute center\uff09\u3002\u3002\u3002\u3002<\/p>\n

\u627e\u51fa\u7edd\u5bf9\u4e2d\u5fc3\u540e\u3002\u3002\u6211\u4eec\u53ea\u8981\u4ece\u8fd9\u4e2a\u70b9\u51fa\u53d1\u3002\u3002\u904d\u5386\u51fa\u6700\u77ed\u8def\u5f84\u6811\u5c31\u53ef\u4ee5\u6c42\u51fa\u6240\u6709\u9700\u8981\u7684\u4e1c\u897f\u3002\u3002\u3002
\n\u3002\u3002\u4e8e\u662f\u6700\u5c0f\u76f4\u5f84\u751f\u6210\u6811\u95ee\u9898\u73b0\u5728\u5c31\u5f52\u7ea6\u5230\u7edd\u5bf9\u4e2d\u5fc3\u7684\u5b9a\u4f4d\u95ee\u9898\u3002\u3002\u3002
\n\u3002\u3002\u6bd4\u8f83\u68d8\u624b\u7684\u662f\u3002\u300c\u7edd\u5bf9\u4e2d\u5fc3\u300d\u3002\u53ef\u4ee5\u51fa\u73b0\u5728\u67d0\u6761\u8fb9\u7684\u5185\u90e8\u3002\u3002<\/p>\n

\u3002\u3002\u3002\u5047\u8bbe\u7edd\u5bf9\u4e2d\u5fc3\u5728\u67d0\u6761\u8fb9\u4e0a E(x, y, w)\u3002\u3002\u4e14\u8ddd\u79bb x \u70b9\u7684\u504f\u79fb\u662f o\uff08\u4ee5\u4e0b\u628a\u8fd9\u4e2a\u70b9\u4e5f\u8bb0\u505a o\uff09\u3002\u3002
\n\u8ddd\u79bb y \u70b9\u504f\u79fb\u5c31\u662f o’ = w – o\u3002\u3002\u90a3\u4e48\u5bf9\u4e8e\u4efb\u610f\u4e00\u4e2a\u70b9 i\u3002\u3002\u5176\u5230 o \u70b9\u7684\u8ddd\u79bb\u5c31\u662f\u3002\u3002<\/p>\n

\u3002\u3002dist(i, a) = min(dist(i, x) + o, o’ + dist(y, i));<\/p>\n

\u90a3\u4e48\u5173\u4e8e\u4e00\u4e2a\u70b9\uff0c\u628a\u6240\u6709\u504f\u79fb\u4f4d\u7f6e\u7684\u8ddd\u79bb\u90fd\u7ed8\u51fa\u5c31\u662f\u4e24\u6761\u659c\u7387\u5206\u522b\u4e3a +1, -1 \u7684\u6298\u7ebf\u7684\u53d6 min\u3002\u3002
\n\u3002\u3002\u3002\u5173\u4e8e\u6240\u6709\u70b9\u3002\u3002\u5c31\u662f\u4e00\u7ec4 +1 -1 \u7684\u6298\u7ebf\u3002\u3002\uff08\u53d6 min \u540e\u518d\u53d6 max\u3002\u3002\u3002<\/p>\n

\"P1\"<\/a><\/p>\n

\u3002\u3002\u6298\u7ebf\u6bb5\u7531 dist(i, x) \u548c dist(i, y) \u552f\u4e00\u786e\u5b9a\u3002\u3002\u3002\u5e76\u4e14\u3002\u3002\u82e5\u67d0\u7ec4\u6298\u7ebf\u6bb5\u7684 dist(i, x) \u548c dist(i, y) \u90fd \u2264 \u53e6\u4e00\u7ec4\u6298\u7ebf\u6bb5\u3002\u3002
\n\u90a3\u4e48\u628a\u8fd9\u7ec4\u6298\u7ebf\u6bb5\u5220\u53bb\u5bf9\u6c42\u53d6\u300c\u5168\u5c40\u6700\u5c0f\u503c\u300d\uff08global minimum\uff09\u4e5f\u6ca1\u6709\u5f71\u54cd\u3002\u3002\u3002\u79f0\u5220\u53bb\u6240\u6709\u8fd9\u79cd\u7ebf\u6bb5\u7684\u8fc7\u7a0b\u4e3a\u300c\u5316\u7b80\u300d\uff08simplification\uff09\u3002
\n\u3002\u3002\u3002\u6ce8\u610f simplification \u540e\u7559\u4e0b\u7684\u90a3\u73a9\u610f\u4f3c\u4e4e\u4e0d\u662f \u51f8\u58f3\uff08Convex cone\uff09\u3002\u3002\u3002
\n\u4ec5\u4ec5\u53ea\u662f\u5916\u8fb9\u754c\uff08upper boundary\uff09\u3002\u3002\u3002<\/p>\n

\u7ea6\u5b9a\uff1a
\ndm\uff1a\u76f4\u5f84
\no\uff1a\u504f\u5fc3\u7387
\nde\uff1a\u7edd\u5bf9\u4e2d\u5fc3\u6240\u5728\u8fb9\u3002<\/p>\n

\r\n        REP(u, n) I[u] = MP(D[a][u], D[b][u]);\r\n        nn = 0; sort(I, I+n); REP(ii, n){\r\n            while (nn && II[nn].se <= I[ii].se) --nn;\r\n            II[++nn] = I[ii];\r\n        }\r\n        if (II[nn].fi < dm){\r\n            dm = II[nn].fi, de = MP(a, b), o = 0;\r\n        }\r\n        if (II[1].se < dm){\r\n            dm = II[1].se, de = MP(a, b), o = w;\r\n        }\r\n        FOR(ii, 1, nn) if ((w + II[ii].fi + II[ii+1].se) \/ 2 < dm){\r\n            dm = (w + II[ii].fi + II[ii+1].se) \/ 2, de = MP(a, b);\r\n            o  = (w - II[ii].fi + II[ii+1].se) \/ 2;\r\n        }\r\n<\/pre>\n
http:\/\/vjudge.net\/vjudge\/problem\/viewSource.action?id=2774287\uff081.82s<\/a><\/p>\n
External link: <\/h3>\n
A Distributed Algorithm for the Minimum Diameter Spanning Tree Problem<\/a><\/p>\n
\u3002\u3002\u6784\u9020\u751f\u6210\u6811\u7684\u90e8\u5206\u3002\u3002graphis \u795e\u7287\u4f7f\u7528\u4e86 SPFA\u3002<\/a>\u3002\u3002
\n\u3002\u3002lyd \u795e\u7287\u5904\u7406\u51fa\u8ddd\u79bb\u540e\u76f4\u63a5 dfs()\u3002\u3002\u3002\u4f46\u662f\u7528\u6811\u5f62 DP \u53c8\u91cd\u65b0\u8ba1\u7b97\u4e86\u904d dm\u3002\u3002\u3002<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"","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":[106,21],"tags":[],"class_list":["post-653","post","type-post","status-publish","format-standard","hentry","category-play-with-trees","category-spoj"],"jetpack_publicize_connections":[],"jetpack_featured_media_url":"","jetpack_shortlink":"https:\/\/wp.me\/p2tdP7-ax","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/posts\/653","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=653"}],"version-history":[{"count":1,"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/posts\/653\/revisions"}],"predecessor-version":[{"id":655,"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/posts\/653\/revisions\/655"}],"wp:attachment":[{"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/media?parent=653"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/categories?post=653"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/tags?post=653"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}