{"id":1867,"date":"2015-12-16T06:00:16","date_gmt":"2015-12-16T04:00:16","guid":{"rendered":"http:\/\/www.glc.us.es\/~jalonso\/exercitium\/?p=1867"},"modified":"2015-12-23T09:33:08","modified_gmt":"2015-12-23T07:33:08","slug":"factorizable-respecto-de-una-lista","status":"publish","type":"post","link":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/factorizable-respecto-de-una-lista\/","title":{"rendered":"Factorizable respecto de una lista"},"content":{"rendered":"<p>Definir la funci\u00f3n<\/p>\n<pre lang=\"text\">\n   factorizable :: Integer -> [Integer] -> Bool\n<\/pre>\n<p>tal que (factorizable x ys) se verifica si x se puede escribir como producto de potencias de elementos de ys. Por ejemplo,<\/p>\n<pre lang=\"text\">\n   factorizable 1  [2,5,6]                           ==  True\n   factorizable 12 [2,5,3]                           ==  True\n   factorizable 12 [2,5,6]                           ==  True\n   factorizable 12 [7,5,12]                          ==  True\n   factorizable 12 [2,3,1]                           ==  True\n   factorizable 12 [2,3,0]                           ==  True\n   factorizable 24 [12,4,6]                          ==  True\n   factorizable 0  [2,3,0]                           ==  True\n   factorizable 12 [5,6]                             ==  False\n   factorizable 12 [2,5,1]                           ==  False\n   factorizable 0  [2,3,5]                           ==  False\n   factorizable (product [1..3000])     [1..100000]  ==  True\n   factorizable (1 + product [1..3000]) [1..100000]  ==  False\n<\/pre>\n<h4>Soluciones<\/h4>\n<pre lang=\"haskell\">\n-- 1\u00aa definici\u00f3n\nfactorizable1 :: Integer -> [Integer] -> Bool\nfactorizable1 1 _  = True\nfactorizable1 0 ys = 0 `elem` ys\nfactorizable1 x ys = \n    or [ factorizable1 (x `div` y) ys | y <- ys\n                                       , y \/= 0 &#038;&#038; y \/= 1\n                                       , x `mod` y == 0 ]\n\n-- 2\u00aa definici\u00f3n\nfactorizable2 :: Integer -> [Integer] -> Bool\nfactorizable2 1 _  = True\nfactorizable2 0 ys = 0 `elem` ys\nfactorizable2 x ys = \n    aux x [y | y <- ys, y > 1, x `mod` y == 0]\n    where aux _ [] = False\n          aux 1 _  = True\n          aux x ys | null zs   = False\n                   | otherwise = or [aux (x `div` z) ys | z <- zs] \n                   where zs = [y | y <- ys, x `mod` y == 0]\n\n-- 3\u00aa definici\u00f3n\nfactorizable3 :: Integer -> [Integer] -> Bool\nfactorizable3 1 _  = True\nfactorizable3 0 ys = 0 `elem` ys\nfactorizable3 x ys = \n    aux x [y | y <- ys, y > 1, x `mod` y == 0]\n    where aux _ [] = False\n          aux 1 _  = True\n          aux x (y:ys) \n              | rem x y == 0 = aux (div x y) (y:ys) || aux x ys\n              | otherwise    = aux x ys\n\n-- Comparaci\u00f3n de eficiencia\n-- =========================\n\n--    \u03bb> factorizable1 (product [1..3000]) [1..100000]\n--    True\n--    (3.55 secs, 322,471,488 bytes)\n--    \u03bb> factorizable2 (product [1..3000]) [1..100000]\n--    True\n--    (2.46 secs, 274,024,832 bytes)\n--    \u03bb> factorizable3 (product [1..3000]) [1..100000]\n--    True\n--    (0.30 secs, 47,606,400 bytes)\n--    \n--    \u03bb> factorizable1 (1 + product [1..3000]) [1..100000]\n--    False\n--    (2.41 secs, 147,221,760 bytes)\n--    \u03bb> factorizable2 (1 + product [1..3000]) [1..100000]\n--    False\n--    (0.45 secs, 40,472,168 bytes)\n--    \u03bb> factorizable3 (1 + product [1..3000]) [1..100000]\n--    False\n--    (0.43 secs, 29,949,680 bytes)\n<\/pre>\n","protected":false},"excerpt":{"rendered":"<p>Definir la funci\u00f3n factorizable :: Integer -> [Integer] -> Bool tal que (factorizable x ys) se verifica si x se puede escribir como producto de potencias de elementos de ys. Por ejemplo, factorizable 1 [2,5,6] == True factorizable 12 [2,5,3] == True factorizable 12 [2,5,6] == True factorizable 12 [7,5,12] == True factorizable 12 [2,3,1]&#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":[8,30,89,141,6],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/1867"}],"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=1867"}],"version-history":[{"count":4,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/1867\/revisions"}],"predecessor-version":[{"id":1902,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/1867\/revisions\/1902"}],"wp:attachment":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/media?parent=1867"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/categories?post=1867"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/tags?post=1867"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}