{"id":544,"date":"2014-11-04T07:00:54","date_gmt":"2014-11-04T05:00:54","guid":{"rendered":"http:\/\/www.glc.us.es\/~jalonso\/exercitium\/?p=544"},"modified":"2014-12-27T21:46:34","modified_gmt":"2014-12-27T19:46:35","slug":"maximo-de-una-funcion","status":"publish","type":"post","link":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/maximo-de-una-funcion\/","title":{"rendered":"M\u00e1ximo de una funci\u00f3n"},"content":{"rendered":"<h4>Enunciado<\/h4>\n<pre lang=\"text\">\n-- Se considera la siguiente funci\u00f3n\n--    g :: Integer -> Integer\n--    g n = if n < 10 then n*n else n\n-- \n-- Definir la funci\u00f3n \n--    max_g :: Integer -> Integer\n-- tal que (max_g n) es el punto i del intervalo [0,n] donde g alcanza\n-- el m\u00e1ximo de sus valores, si n es positivo y 0 en caso contrario. Por\n-- ejemplo,\n--    max_g (-7)  ==  0\n--    max_g 7     ==  7\n--    max_g 14    ==  9\n--    max_g 84    ==  84\n-- \n-- Comprobar con QuickCheck que la funci\u00f3n max_g es equivalente a la\n-- funci\u00f3n f definida por  \n--    f :: Integer -> Integer\n--    f n | n < 0             = 0\n--        | n >= 10 && n < 81 = 9\n--        | otherwise         = n\n--\n-- Nota: Se piden dos definiciones de max_g, una por comprensi\u00f3n y otra\n-- por recursi\u00f3n.\n<\/pre>\n<h4>Soluciones<\/h4>\n<pre lang=\"haskell\">\nimport Test.QuickCheck\n\ng :: Integer -> Integer\ng n = if n < 10 then n*n else n\n\n-- 1\u00aa definici\u00f3n (por comprensi\u00f3n):\nmax_gC :: Integer -> Integer\nmax_gC n | n < 0     = 0 \n         | otherwise = snd (maximum [(g i,i) | i <- [0..n]])\n\n-- 2\u00aa definici\u00f3n (por recursi\u00f3n):\nmax_gR :: Integer -> Integer\nmax_gR n | n < 0      = 0\n         | g m > g n  = m \n         | otherwise  = n\n         where m = max_gR (n - 1)\n\nf :: Integer -> Integer\nf n | n < 0             = 0\n    | n >= 10 && n < 81 = 9\n    | otherwise         = n\n\n-- La propiedad con max_gR es\nprop_max_gR n = max_gR n == f n\n\n-- La comprobaci\u00f3n es\n--    ghci> quickCheck prop_max_gR\n--    +++ OK, passed 100 tests.\n\n-- La propiedad con max_gC es\nprop_max_gC n = max_gC n == f n\n\n-- La comprobaci\u00f3n es\n--    ghci> quickCheck prop_max_gC\n--    +++ OK, passed 100 tests.\n<\/pre>\n","protected":false},"excerpt":{"rendered":"<p>Enunciado &#8212; Se considera la siguiente funci\u00f3n &#8212; g :: Integer -> Integer &#8212; g n = if n < 10 then n*n else n -- -- Definir la funci\u00f3n -- max_g :: Integer -> Integer &#8212; tal que (max_g n) es el punto i del intervalo [0,n] donde g alcanza &#8212; el m\u00e1ximo de&#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":[7],"tags":[8,15,6,16,146],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/544"}],"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=544"}],"version-history":[{"count":6,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/544\/revisions"}],"predecessor-version":[{"id":747,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/544\/revisions\/747"}],"wp:attachment":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/media?parent=544"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/categories?post=544"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/tags?post=544"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}