{"id":394,"date":"2014-07-04T07:00:09","date_gmt":"2014-07-04T05:00:09","guid":{"rendered":"http:\/\/www.glc.us.es\/~jalonso\/exercitium\/?p=394"},"modified":"2022-03-26T12:13:52","modified_gmt":"2022-03-26T10:13:52","slug":"divide-si-todos-son-multiplos","status":"publish","type":"post","link":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/divide-si-todos-son-multiplos\/","title":{"rendered":"Divide si todos son m\u00faltiplos"},"content":{"rendered":"<p>Ejercicio. Definir la funci\u00f3n<\/p>\n<pre lang=\"text\">\n   divideSiTodosMultiplos :: Integral a => a -> [a] -> Maybe [a]\n<\/pre>\n<p>tal que (divideSiTodosMultiplos x ys) es justo la lista de los cocientes de los elementos de ys entre x si todos son m\u00faltiplos de x y Nothing en caso contrario. Por ejemplo,<\/p>\n<pre lang=\"text\">\n   divideSiTodosMultiplos 2 [6,10,4]  ==  Just [3,5,2]\n   divideSiTodosMultiplos 2 [6,10,5]  ==  Nothing\n<\/pre>\n<h4>Soluciones<\/h4>\n<pre lang=\"haskell\">\n-- 1\u00aa definici\u00f3n (por comprensi\u00f3n)\ndivideSiTodosMultiplos :: Integral a => a -> [a] -> Maybe [a]\ndivideSiTodosMultiplos x ys\n    | todosMultiplos x ys = Just [y `div` x | y <- ys]\n    | otherwise           = Nothing\n\n-- (todosMultiplos x ys) se verifica si todos los elementos de ys son\n-- m\u00faltiplos de x. Por ejemplo,\n--    todosMultiplos 2 [6,10,4]  ==  True\n--    todosMultiplos 2 [6,10,5]  ==  False\ntodosMultiplos :: Integral a => a -> [a] -> Bool\ntodosMultiplos x ys = and [y `mod` x == 0 | y <- ys]\n\n-- 2\u00aa definici\u00f3n (por recursi\u00f3n)\ndivideSiTodosMultiplos2 :: Integral a => a -> [a] -> Maybe [a]\ndivideSiTodosMultiplos2 _ [] = Just []\ndivideSiTodosMultiplos2 x (y:ys)\n    | y `mod` x \/= 0 = Nothing\n    | aux == Nothing  = Nothing\n    | otherwise       = Just ((y `div` x) : zs)\n    where aux     = divideSiTodosMultiplos2 x ys\n          Just zs = aux\n<\/pre>\n","protected":false},"excerpt":{"rendered":"<p>Ejercicio. Definir la funci\u00f3n divideSiTodosMultiplos :: Integral a => a -> [a] -> Maybe [a] tal que (divideSiTodosMultiplos x ys) es justo la lista de los cocientes de los elementos de ys entre x si todos son m\u00faltiplos de x y Nothing en caso contrario. Por ejemplo, divideSiTodosMultiplos 2 [6,10,4] == Just [3,5,2] divideSiTodosMultiplos 2&#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":[4],"tags":[100,8,500,30,89,6],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/394"}],"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=394"}],"version-history":[{"count":8,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/394\/revisions"}],"predecessor-version":[{"id":1386,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/394\/revisions\/1386"}],"wp:attachment":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/media?parent=394"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/categories?post=394"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/tags?post=394"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}