{"id":1924,"date":"2015-12-31T06:00:47","date_gmt":"2015-12-31T04:00:47","guid":{"rendered":"http:\/\/www.glc.us.es\/~jalonso\/exercitium\/?p=1924"},"modified":"2016-01-07T09:36:33","modified_gmt":"2016-01-07T07:36:33","slug":"elementos-optimos","status":"publish","type":"post","link":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/elementos-optimos\/","title":{"rendered":"Elementos \u00f3ptimos"},"content":{"rendered":"<p>Definir la funci\u00f3n<\/p>\n<pre lang=\"text\">\n   optimos :: Eq b => (b -> b -> Bool) -> (a -> b) -> [a] -> [a]\n<\/pre>\n<p>tal que (optimos r f xs) es la lista de los elementos de xs donde la funci\u00f3n f alcanza sus valores \u00f3ptimos respecto de la relaci\u00f3n r. Por ejemplo,<\/p>\n<pre lang=\"text\">\n   optimos (<) length [\"ab\",\"c\",\"de\",\"f\"]  ==  [\"c\",\"f\"]\n   optimos (>) length [\"ab\",\"c\",\"de\",\"f\"]  ==  [\"ab\",\"de\"]\n<\/pre>\n<h4>Soluciones<\/h4>\n<pre lang=\"haskell\">\n-- 1\u00aa definici\u00f3n\n-- =============\n\noptimos1 :: Eq a => (b -> b -> Bool) -> (a -> b) -> [a] -> [a]\noptimos1 r f xs = \n    [x | x <- xs, null [y | y <- xs, x \/= y, r (f y) (f x)]]\n\n-- 2\u00aa definici\u00f3n\n-- =============\n\noptimos2 :: Eq b => (b -> b -> Bool) -> (a -> b) -> [a] -> [a]\noptimos2 r f xs = [x | x <- xs, f x `elem` ms]\n    where ms = maximales r (map f xs) \n\n-- (maximales r xs) es la lista de los elementos de xs para los que no\n-- hay ning\u00fan otro elemento de xs mayor seg\u00fan la relaci\u00f3n r. Por\n-- ejemplo, \n--    maximales (>) [2,3,4,6]                     ==  [6]\n--    maximales (<) [2,3,4,6]                     ==  [2]\n--    maximales (\\x y -> mod x y == 0) [2,3,4,6]  ==  [4,6]\n--    maximales (\\x y -> mod y x == 0) [2,3,4,6]  ==  [2,3]\nmaximales :: Eq a => (a -> a -> Bool) -> [a] -> [a]\nmaximales r xs = [x | x <- xs, null [y | y <- xs, y \/= x, r y x]]\n\n-- Comparaci\u00f3n de eficiencia\n-- =========================\n\n--    \u03bb> length $ optimos1 (>) length [replicate n 'a' | n <- [1..1000]]\n--    1\n--    (16.74 secs, 153,957,400 bytes)\n--    \u03bb> length $ optimos2 (>) length [replicate n 'a' | n <- [1..1000]]\n--    1\n--    (0.64 secs, 85,520,896 bytes)\n<\/pre>\n","protected":false},"excerpt":{"rendered":"<p>Definir la funci\u00f3n optimos :: Eq b => (b -> b -> Bool) -> (a -> b) -> [a] -> [a] tal que (optimos r f xs) es la lista de los elementos de xs donde la funci\u00f3n f alcanza sus valores \u00f3ptimos respecto de la relaci\u00f3n r. Por ejemplo, optimos () length [\u00abab\u00bb,\u00bbc\u00bb,\u00bbde\u00bb,\u00bbf\u00bb] ==&#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":[5],"tags":[8,26,10,141,11],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/1924"}],"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=1924"}],"version-history":[{"count":4,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/1924\/revisions"}],"predecessor-version":[{"id":1959,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/1924\/revisions\/1959"}],"wp:attachment":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/media?parent=1924"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/categories?post=1924"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/tags?post=1924"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}