{"id":1024,"date":"2014-10-11T21:26:41","date_gmt":"2014-10-11T13:26:41","guid":{"rendered":"http:\/\/www.shuizilong.com\/house\/?p=1024"},"modified":"2014-10-11T21:29:06","modified_gmt":"2014-10-11T13:29:06","slug":"vijos-1676-%e6%b7%98%e6%b7%98%e5%90%83%e8%8b%b9%e6%9e%9c","status":"publish","type":"post","link":"https:\/\/www.shuizilong.com\/house\/archives\/vijos-1676-%e6%b7%98%e6%b7%98%e5%90%83%e8%8b%b9%e6%9e%9c\/","title":{"rendered":"Vijos 1676. \u6dd8\u6dd8\u5403\u82f9\u679c"},"content":{"rendered":"

<\/p>\n

\u3002\u3002 \u597d\u9898\u3002\u3002\u65e0\u9650\u4ef0\u6155\u5b8b\u795e\u725b\u3002\u3002\u3002<\/p>\n

\u9996\u5148\uff1a
\n\u8282\u70b9\u6570-\u9ad8\u5ea6 \u2264 k<\/p>\n

\u4ec0\u4e48\u610f\u601d\u5462\uff1f<\/p>\n

\u5c31\u662f\u80cc\u5305\u5bb9\u91cf\u4e3a k\u3002\u3002\u3002\u7136\u540e\u5176\u4e2d\u4e00\u6761\u94fe\u53ef\u4ee5\u514d\u8d39\u53d6\u3002\u3002\u3002
\n\u3002\u3002\u8bbe\u8fd9\u6761\u94fe\u4e3a free chain \u3002\u7136\u540e\u5c31\u53ef\u4ee5 O(n3) \u4e86\u3002\u3002\u3002<\/p>\n

g[u][i]:
\n\u4ee5 u \u4e3a\u6839\u7684\u5b50\u6811\u3002\u3002\u3002
\n\u5bb9\u91cf\u4e3a i\u3002\u3002\u3002<\/p>\n

f[u][i]:
\n\u4ee5 u \u4e3a\u6839\u7684\u5b50\u6811\u3002\u3002u \u5728 free chain \u4e0a\u3002\u3002
\n\u5bb9\u91cf\u4e3a i\u3002\u3002\u3002 <\/p>\n

https:\/\/vijos.org\/records\/5411e2a348c5fc1e1c8b4568<\/p>\n

\u6211\u4eec\u53d1\u73b0 g[][] \u5c31\u662f\u9009\u8bfe\u3002\u3002\u3002https:\/\/vijos.org\/records\/54062d6048c5fcbb348b4568
\n\u7ecf\u8fc7 doc \u7684\u6307\u5bfc\u3002\u3002\u3002\u6211\u5df2\u7ecf\u6307\u5bfc\u8fd9\u79cd\u6811\u5f62\u80cc\u5305\u662f\u53ef\u4ee5\u7528 dfs \u5e8f\u3002\u4f18\u5316\u5230 O(n2) \u7684\u3002\u3002\u3002<\/p>\n

\u8fd9\u4e2a\u6b65\u9aa4\u8fd8\u662f rather subtle\u3002\u3002\u3002\u3002\u5177\u4f53\u8bf4\u6765\u3002\u3002\u5c31\u662f<\/p>\n

g[u][i] \/ f[u][i] \u73b0\u5728\u8868\u793a\u3002\u3002\u3002\u4ece\u6839\u7ed3\u70b9 0 \u5f00\u59cb\uff0c\u6240\u6709 dfs \u5e8f <= r[u] \u7684\u7ed3\u70b9\u3002\u3002\u3002\n \uff08r[u]\u3002\u3002\u79bb\u5f00\u65f6\u523b\u3002\u3002\u4e5f\u5c31\u662f u \u7684\u5b50\u6811\u52a0\u4e4b\u524d\u8bbf\u95ee\u8fc7\u7684\u7ed3\u70b9\uff09\u3002\u3002\u3002\n\n\n\u521d\u59cb\u65f6\uff1a\n f[v][i] = max(g[u][i], i ? f[u][i-1] : 0) + val[v];\n\n\u5de6\u8fb9\u8868\u793a free_chain \u8fde\u63a5\u5230 v\u3002\u3002\n\u53f3\u8fb9\u8868\u793a free_chain \u4e0d\u7ecf\u8fc7 v\u3002\u3002\u3002\n\uff08\u8fd9\u91cc\u66f4 subtle \u4e86\u3002\u3002\u3002\u56e0\u4e3a f[v] \u8868\u793a\u65e0\u8bba\u5982\u4f55\u3002\u3002free_chain \u90fd\u7ecf\u8fc7 r->u->v \u7684\u3002\u3002
\n\u3002\u3002\u3002\u6211\u4eec\u60f3\u5f97\u5230 free_chain \u4e0d\u7ecf\u8fc7 v \u7684\u8f6c\u79fb\u3002\u3002\u5c31\u5f97\u901a\u8fc7\u5728\u521d\u59cb\u5316\u65f6\u5c31\u51cf\u5c11\u4e00\u683c\u5bb9\u91cf\u3002\u3002\uff09<\/p>\n

https:\/\/vijos.org\/records\/5411fad048c5fcd2208b4568<\/p>\n

\r\n\/\/}\/* .................................................................................................................................. *\/\r\n\r\n\r\nconst int N = int(4e3) + 9;\r\n\r\n\r\nVI adj[N]; LL g[N][N], f[N][N], val[N];\r\nint n, m;\r\n\r\n\r\nvoid dfs(int u = 0, int m = ::m){\r\n\r\n\r\n    ECH(it, adj[u]){\r\n        int v = *it;\r\n\r\n\r\n        REP(i, m+1){\r\n            g[v][i] = g[u][i] + val[v];\r\n            f[v][i] = max(g[u][i], i ? f[u][i-1] : 0) + val[v];\r\n        }\r\n\r\n\r\n        dfs(v);\r\n\r\n\r\n        REP(i, m+1){\r\n            if (i) checkMax(g[u][i], g[v][i-1]);\r\n            checkMax(f[u][i], f[v][i]);\r\n        }\r\n    }\r\n}\r\n\r\n\r\nint main(){\r\n\r\n\r\n#ifndef ONLINE_JUDGE\r\n    freopen("in.txt", "r", stdin);\r\n    \/\/freopen("out.txt", "w", stdout);\r\n#endif\r\n\r\n\r\n    REP_1_C(i, RD(n, m)){\r\n        adj[RD()].PB(i);\r\n        RD(val[i]);\r\n    }\r\n\r\n\r\n    dfs();\r\n    OT(f[0][m]);\r\n}\r\n\r\n\r\n<\/pre>\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":[1],"tags":[],"class_list":["post-1024","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"jetpack_publicize_connections":[],"jetpack_featured_media_url":"","jetpack_shortlink":"https:\/\/wp.me\/p2tdP7-gw","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/posts\/1024","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=1024"}],"version-history":[{"count":0,"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/posts\/1024\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/media?parent=1024"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/categories?post=1024"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/tags?post=1024"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}