{"id":788,"date":"2013-08-02T23:41:58","date_gmt":"2013-08-02T15:41:58","guid":{"rendered":"http:\/\/www.shuizilong.com\/house\/?p=788"},"modified":"2013-08-03T00:32:11","modified_gmt":"2013-08-02T16:32:11","slug":"srm-586","status":"publish","type":"post","link":"https:\/\/www.shuizilong.com\/house\/archives\/srm-586\/","title":{"rendered":"SRM 586"},"content":{"rendered":"

250. PiecewiseLinearFunction<\/h2>\n

Brief description: <\/h3>\n

… \u7ed9\u5b9a\u4e00\u4e2a\u5206\u6bb5\u7ebf\u6027 (piecewise linear) \u51fd\u6570\u3002\u3002
\n\u3002\u3002\u95ee f(x) = k \u6700\u591a\u53ef\u4ee5\u6709\u591a\u5c11\u4e2a\u89e3 \uff08k\u2208R\uff09\u3002\u82e5\u53ef\u4ee5\u6709\u65e0\u9650\u591a\u89e3\u5219\u8fd4\u56de -1\u3002
\n<\/p>\n

Analysis: <\/h3>\n

\u5148\u5224\u65ad\u65e0\u89e3\u3002\u3002\u7136\u540e\u7ebf\u6bb5\u6811\u6c42\u6700\u5927\u8986\u76d6\u6b21\u6570\u3002\u3002\u6ce8\u610f\u7aef\u70b9\u5904\u53ea\u88ab\u8986\u76d6\u4e00\u6b21\u3002\u9700\u8981\u5f00\u59cb\u5168\u90e8*2\u7136\u540e\u62c6\u70b9\u3002
\n\u3002\u3002\u5f53\u7136\u8fd9\u79cd\u9884\u5904\u7406\u540e\u4e00\u6b21\u8be2\u95ee\u7684\u95ee\u9898\u3002\u3002\u53ef\u4ee5\u7528\u79bb\u7ebf\u7b97\u6cd5 \u2014\u2014\u2014\u2014 +1-1 \u6807\u8bb0\u6570\u7ec4 + \u6392\u5e8f\u6765\u89e3\u51b3\u3002\u3002
\n\u3002\u3002\u5f53\u7136 O(n2) \u66b4\u529b\u4e0d\u5bb9\u6613\u5199\u9519\u3002\u3002\u3002<\/p>\n

500. History<\/h2>\n

Brief description: <\/h3>\n

… \u6709 n \u4e2a\u56fd\u5bb6\u3002\u3002\u6bcf\u4e2a\u56fd\u5bb6\u6709\u4e00\u4e9b\u671d\u4ee3\u3002\u671d\u4ee3\u90fd\u662f\u4ece 0 \u5f00\u59cb\u7eaa\u5e74\u3002
\n\u3002\u3002\u7ed9\u5b9a\u6bcf\u4e2a\u671d\u4ee3\u7684\u6301\u7eed\u65f6\u95f4\uff0c\u4e24\u4e2a\u671d\u4ee3\u88ab\u79f0\u4e3a\u540c\u65f6\u4ee3\u7684\u3002\u3002\u5982\u679c\u8fd9\u4e24\u4e2a\u671d\u4ee3\u4e2d\u5b58\u5728\u4e00\u5bf9\u7eaa\u5e74\u8868\u793a\u7684\u662f\u540c\u4e00\u5e74\u3002
\n\u3002\u73b0\u5728\u7ed9\u5b9a\u4e00\u4e9b\u540c\u65f6\u4ee3\u5173\u7cfb\u3002\u3002\u95ee\u662f\u5426\u53e6\u4e00\u4e9b\u671d\u4ee3\u4e4b\u95f4\u4e5f\u53ef\u80fd\u662f\u540c\u65f6\u4ee3\u7684\u3002\u3002\u3002<\/p>\n

Analysis: <\/h3>\n

\u3002\u3002\u5dee\u5206\u7ea6\u675f\u6a21\u578b\u3002\u3002<\/p>\n

1000. StringWeight<\/h2>\n

Brief description: <\/h3>\n

… \u4e00\u4e2a\u5b57\u7b26\u4e32\u542b\u6709 26 \u4e2a\u82f1\u6587\u5b57\u6bcd\u3002\u3002\u4e00\u4e2a\u5b57\u7b26\u4e32\u7684\u6743\u503c\u3002\u3002\u8bb0\u4f5c\u6240\u6709\u81f3\u5c11\u51fa\u73b0\u8fc7\u4e00\u6b21\u7684\u5b57\u7b26\u3001\u51fa\u73b0\u7684\u6700\u53f3\u8fb9\u4f4d\u7f6e\u51cf\u53bb\u6700\u5de6\u8fb9\u4f4d\u7f6e\u3002\u3002\u3002
\n\u3002\u3002\u4e00\u4e2a\u5b57\u7b26\u4e32\u88ab\u79f0\u4e3a\u662f \u201c\u8f7b\u7684\u201d\u3002\u3002\u5982\u679c\u5728\u6240\u6709\u76f8\u540c\u957f\u5ea6\u7684\u5b57\u7b26\u4e32\u4e2d\u3002\u3002\u6ca1\u6709\u6743\u503c\u6bd4\u5b83\u66f4\u5c0f\u7684\u3002\u3002\u3002\u3002
\n\u73b0\u5728\u7ed9\u5b9a\u4e00\u4e2a\u6570\u7ec4 L[0], L[1], … L[n-1] …
\n\u8981\u6c42\u4f60\u7528\u957f\u5ea6\u5206\u522b\u4e3a L[0], L[1], … L[n-1] \u7684 \u201c\u8f7b\u7684\u201d \u5b57\u7b26\u4e32\u4f9d\u6b21\u8fde\u63a5\u6210\u4e00\u4e2a\u5927\u5b57\u7b26\u4e32\u3002\u3002\u3002
\n\u3001\u3002\u3002\u3002\u6700\u5c0f\u5316\u8fd9\u4e2a\u5927\u5b57\u7b26\u4e32\u7684\u6743\u503c\u3002\u3002<\/p>\n

Analysis: <\/h3>\n

… \u9996\u5148\u3002\u3002\u5bf9\u4e8e\u4e00\u4e2a \u201c\u8f7b\u7684\u201d \u5b57\u7b26\u4e32\u3002\u3002\u4e00\u5b9a\u8981\u6700\u5927\u9650\u5ea6\u7684\u7528\u6ee1 26 \u7684\u5b57\u7b26\u3002\u3002
\n\u3002\u3002\u7136\u540e\u91cd\u590d\u591a\u6b21\u7684\u5b57\u7b26\u3002\u3002\u4e00\u5b9a\u90fd\u662f\u5728\u4e00\u5757\u8fde\u7eed\u7684\u4f4d\u7f6e\u3002\u3002\u3002<\/p>\n

\u5f53\u6211\u4eec\u4ee5\u53ca\u5904\u7406\u4e86\u4e00\u90e8\u5206\u5b57\u7b26\u4e32\u3002\u3002\u3002\u8003\u5bdf\u4e0b\u4e00\u4e2a\u5b57\u7b26\u4e32\u7684\u67d0\u4e2a\u5b57\u7b26\u65f6\u3002\u3002\u5b83\u53ef\u80fd\u5904\u4e8e\u4ee5\u4e0b\u4e09\u79cd\u72b6\u6001\u4e4b\u4e00\uff1a<\/p>\n

\u767d\u8272 (White)\uff1a\u5c1a\u672a\u51fa\u73b0\u3002
\n\u7070\u8272 (Gray): \u5df2\u7ecf\u51fa\u73b0\u3002
\n\u9ed1\u8272 (Black): \u5df2\u7ecf\u7ec8\u6b62\u3002<\/p>\n

\u77e5\u9053\u5176\u4e2d\u4e24\u4e2a\u5c31\u884c\u4e86\u3002\u3002<\/p>\n

\u6211\u4eec\u6709 White -> Gray, Gray -> Black \u4ee5\u53ca\u5728\u5f53\u524d\u8fd9\u4e2a\u5b57\u7b26\u4e32\u4e2d\u76f4\u63a5 White -> Black \u4e09\u79cd\u8f6c\u79fb\u3002\u3002
\n\u8fd9\u4e9b\u9700\u8981\u679a\u4e3e\u3002\u3002\u3002<\/p>\n

\u3002\u3002YY \u51fa\u72b6\u6001\u3002\u3002\u4ee5\u6bcf\u4e00\u6bb5\u5c0f\u5b57\u7b26\u4e32\u5212\u5206\u9636\u6bb5\u3002\u3002\u3002<\/p>\n

\r\nconst int N = 60, Z = 27;\r\nint dp[N][Z][Z]; \/\/Gray, White\r\n\r\nclass StringWeight {\r\npublic:\r\n  int getMinimum(vector <int> L) {\r\n\r\n\t    int n = SZ(L); FLC(dp, 0x3f), dp[0][0][26] = 0;\r\n\r\n\t    REP_3(i, j, k, n, 27, 27) if (dp[i][j][k] != INF){\r\n\t        REP_2(jj, kk, j+1, k+1){ \/\/ Black, Gray ..\r\n\t            if (j + kk < min(26, L[i]) || jj + kk > L[i]) continue;\r\n\t            int b = dp[i][j][k] + (jj-1)*jj\/2 + (j-jj)*L[i];\r\n\t            if (jj + kk == 26) b += L[i] - 26;\r\n\t            REP(jjj, kk+1) checkMin(dp[i+1][j-jj+jjj][k-kk], b += jjj);\r\n\t        }\r\n\t    }\r\n\r\n\t\tint res = INF; REP_2(i, j, Z, Z) checkMin(res, dp[n][i][j]);\r\n\t\treturn res;\r\n\t}\r\n};\r\n<\/pre>\n
dp[i][j][k]: \u8868\u793a\u5f53\u524d\u8003\u5bdf\u5230\u7b2c i \u4e2a\u5b57\u7b26\u4e32\uff0cj \u4e2a\u7070\u8272\u5b57\u7b26\uff0ck \u4e2a\u767d\u8272\u5b57\u7b26\u7684\u6700\u5c0f\u6743\u503c\u3002
\n\u3002\u3002\u72b6\u6001 O(NZ^2) \u3002\u3002\u8f6c\u79fb O(Z^3)\u3002\u3002<\/p>\n
\u6765\u5177\u4f53\u5206\u6790\u8f6c\u79fb\u3002\u3002Gray -> Black \u4e00\u5b9a\u662f\u4ece\u6700\u5de6\u8fb9\u5f00\u59cb\u5173\u95ed\u3002\u3002\u6240\u4ee5\u52a0\u7b49\u5dee\u6570\u5217 (jj-1)*jj\/2<\/code> \u5373\u53ef\u3002
\nGray -> Gray \u3002\u3002\u6bd4\u8f83\u7cdf\u7cd5\u3002\u3002\u6bcf\u4e00\u7c7b\u90fd\u8981\u589e\u52a0 L[i] \u7684\u635f\u8017\u3002\u3002
\nWhite -> Black \u3002\u3002\u65e0\u635f\u8017\u3002
\nWhite -> Gray \u3002\u3002\u8fd9\u7c7b\u5c3d\u91cf\u5f80\u53f3\u8fb9\u586b\u3002\u3002\u4e5f\u662f\u4e00\u4e2a\u7b49\u5dee\u6570\u5217\u3002\u3002\u3002<\/p>\n
External link: <\/h3>\n
https:\/\/apps.topcoder.com\/wiki\/display\/tc\/SRM+586<\/a>
\nhttps:\/\/gist.github.com\/lychees\/6140957<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"
250. PiecewiseLinearFunction Brief description: … \u7ed9\u5b9a\u4e00\u4e2a\u5206\u6bb5\u7ebf\u6027 (piecewise linear) \u51fd\u6570\u3002\u3002 \u3002\u3002\u95ee f(x) = k \u6700\u591a\u53ef\u4ee5\u6709\u591a\u5c11\u4e2a\u89e3 \uff08k\u2208R\uff09\u3002\u82e5\u53ef\u4ee5\u6709\u65e0\u9650\u591a\u89e3\u5219\u8fd4\u56de -1\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":[17],"tags":[],"class_list":["post-788","post","type-post","status-publish","format-standard","hentry","category-topcoder"],"jetpack_publicize_connections":[],"jetpack_featured_media_url":"","jetpack_shortlink":"https:\/\/wp.me\/p2tdP7-cI","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/posts\/788","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=788"}],"version-history":[{"count":1,"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/posts\/788\/revisions"}],"predecessor-version":[{"id":790,"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/posts\/788\/revisions\/790"}],"wp:attachment":[{"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/media?parent=788"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/categories?post=788"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.shuizilong.com\/house\/wp-json\/wp\/v2\/tags?post=788"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}