{"id":2216,"date":"2016-03-10T06:00:36","date_gmt":"2016-03-10T04:00:36","guid":{"rendered":"http:\/\/www.glc.us.es\/~jalonso\/exercitium\/?p=2216"},"modified":"2016-03-17T07:10:54","modified_gmt":"2016-03-17T05:10:54","slug":"paridad-del-numero-de-divisores","status":"publish","type":"post","link":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/paridad-del-numero-de-divisores\/","title":{"rendered":"Paridad del n\u00famero de divisores"},"content":{"rendered":"<p>Definir la funci\u00f3n<\/p>\n<pre lang=\"text\">\n   nDivisoresPar :: Integer -> Bool\n<\/pre>\n<p>tal que (nDivisoresPar n) se verifica si n tiene un n\u00famero par de divisores. Por ejemplo,<\/p>\n<pre lang=\"text\">\n   nDivisoresPar 12                     ==  True\n   nDivisoresPar 16                     ==  False\n   nDivisoresPar (product [1..2*10^4])  ==  True\n<\/pre>\n<h4>Soluciones<\/h4>\n<pre lang=\"haskell\">\nimport Data.List (group)\nimport Data.Numbers.Primes (primeFactors)\n\n-- 1\u00aa definici\u00f3n\n-- =============\n\nnDivisoresPar1 :: Integer -> Bool\nnDivisoresPar1 = even . length . divisores\n\n-- (divisores n) es la lista de los divisores de n. Por ejemplo,\n--    divisores 12  ==  [1,2,3,4,6,12]\n--    divisores 16  ==  [1,2,4,8,16]\ndivisores :: Integer -> [Integer]\ndivisores n =\n    [x | x <- [1..n], n `mod` x == 0]\n\n-- 2\u00aa definici\u00f3n\n-- =============\n\nnDivisoresPar2 :: Integer -> Bool\nnDivisoresPar2 n =\n    any odd (map length (group (primeFactors n)))\n\n-- Comparaci\u00f3n de eficiencia\n-- =========================\n\n--    \u03bb> nDivisoresPar1 (10^7)\n--    True\n--    (14.18 secs, 2,078,736,992 bytes)\n--    \u03bb> nDivisoresPar2 (10^7)\n--    True\n--    (0.01 secs, 0 bytes)\n--\n--    \u03bb> nDivisoresPar2 (product [1..2*10^4])\n--    True\n--    (2.30 secs, 1,003,013,112 bytes)\n<\/pre>\n<h4>Soluci\u00f3n en Maxima<\/h4>\n<pre lang=\"text\">\n\/* concat(xs) es la lista obtenida concatenado los elementos de xss. Por\n   ejemplo,\n      concat([[1,3],[2,4],[5,7]])  ==  [1, 3, 2, 4, 5, 7]             *\/\nconcat (xs) := block ([r:[]],\n  for x in reverse (xs) do r : append (x,r),\n  r)$\n\nnDivisoresPares (n) := block(\n  [xs : concat (map (rest, ifactors (n))), p : false],\n  for x in xs do p: oddp (x) or p,\n  p)$\n<\/pre>\n","protected":false},"excerpt":{"rendered":"<p>Definir la funci\u00f3n nDivisoresPar :: Integer -> Bool tal que (nDivisoresPar n) se verifica si n tiene un n\u00famero par de divisores. Por ejemplo, nDivisoresPar 12 == True nDivisoresPar 16 == False nDivisoresPar (product [1..2*10^4]) == True Soluciones import Data.List (group) import Data.Numbers.Primes (primeFactors) &#8212; 1\u00aa definici\u00f3n &#8212; ============= nDivisoresPar1 :: Integer -> Bool nDivisoresPar1&#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":[163,8,91,13,28,10,89,92,11,247,6],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/2216"}],"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=2216"}],"version-history":[{"count":3,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/2216\/revisions"}],"predecessor-version":[{"id":2246,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/2216\/revisions\/2246"}],"wp:attachment":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/media?parent=2216"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/categories?post=2216"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/tags?post=2216"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}