{"id":3351,"date":"2017-06-06T06:00:00","date_gmt":"2017-06-06T04:00:00","guid":{"rendered":"http:\/\/www.glc.us.es\/~jalonso\/exercitium\/?p=3351"},"modified":"2017-06-05T16:14:53","modified_gmt":"2017-06-05T14:14:53","slug":"problema-de-ullman","status":"publish","type":"post","link":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/problema-de-ullman\/","title":{"rendered":"Problema de Ullman"},"content":{"rendered":"<p>Definir la funci\u00f3n<\/p>\n<pre lang=\"text\">\n   ullman :: (Num a, Ord a) => a -> Int -> [a] -> Bool\n<\/pre>\n<p>tal que (ullman t k xs) se verifica si xs tiene un subconjunto con k  elementos cuya suma sea menor que t. Por ejemplo,<\/p>\n<pre lang=\"text\">\n   ullman  9 3 [1..10]    ==  True\n   ullman  5 3 [1..10]    ==  False\n   ullman  9 5 [1..10^6]  ==  False\n   ullman 29 5 [1..10^6]  ==  True\n<\/pre>\n<h4>Soluciones<\/h4>\n<p>[schedule expon=&#8217;2017-06-13&#8242; expat=\u00bb06:00&#8243;]<\/p>\n<ul>\n<li>Las soluciones se pueden escribir en los comentarios hasta el 13 de junio.\n<li>El c\u00f3digo se debe escribir entre una l\u00ednea con &#60;pre lang=\u00bbhaskell\u00bb&#62; y otra con &#60;\/pre&#62;\n<\/ul>\n<p>[\/schedule]<\/p>\n<p>[schedule on=&#8217;2017-06-13&#8242; at=\u00bb06:00&#8243;]<\/p>\n<pre lang=\"haskell\">\r\nimport Data.List (sort, subsequences)\r\n\r\n-- 1\u00aa soluci\u00f3n\r\nullman1 :: (Num a, Ord a) => a -> Int -> [a] -> Bool\r\nullman1 t k xs = \r\n  (not . null) [ys | ys <- subsequences xs, length ys == k, sum ys < t]\r\n\r\n-- 2\u00aa soluci\u00f3n\r\nullman2 :: (Ord a, Num a) => a -> Int -> [a] -> Bool\r\nullman2 t k xs = sum (take k (sort xs)) < t\r\n\r\n-- Comparaci\u00f3n de eficiencia\r\n--    \u03bb> ullman1 9 5 [1..23]\r\n--    False\r\n--    (10.73 secs, 1,761,726,376 bytes)\r\n--    \u03bb> ullman2 9 5 [1..23]\r\n--    False\r\n--    (0.01 secs, 0 bytes)\r\n<\/pre>\n<p>[\/schedule]<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Definir la funci\u00f3n ullman :: (Num a, Ord a) => a -> Int -> [a] -> Bool tal que (ullman t k xs) se verifica si xs tiene un subconjunto con k elementos cuya suma sea menor que t. Por ejemplo, ullman 9 3 [1..10] == True ullman 5 3 [1..10] == False ullman 9&#8230;<\/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,"_kad_post_transparent":"","_kad_post_title":"","_kad_post_layout":"","_kad_post_sidebar_id":"","_kad_post_content_style":"","_kad_post_vertical_padding":"","_kad_post_feature":"","_kad_post_feature_position":"","_kad_post_header":false,"_kad_post_footer":false,"_jetpack_newsletter_access":"","_jetpack_dont_email_post_to_subs":false,"_jetpack_newsletter_tier_id":0,"_jetpack_memberships_contains_paywalled_content":false,"footnotes":"","_jetpack_memberships_contains_paid_content":false},"categories":[2],"tags":[],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/3351"}],"collection":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/comments?post=3351"}],"version-history":[{"count":1,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/3351\/revisions"}],"predecessor-version":[{"id":3352,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/3351\/revisions\/3352"}],"wp:attachment":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/media?parent=3351"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/categories?post=3351"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/tags?post=3351"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}