{"id":2902,"date":"2017-02-09T06:00:19","date_gmt":"2017-02-09T04:00:19","guid":{"rendered":"http:\/\/www.glc.us.es\/~jalonso\/exercitium\/?p=2902"},"modified":"2017-02-16T07:03:20","modified_gmt":"2017-02-16T05:03:20","slug":"maximo-comun-divisor-de-x-e-y-veces-n","status":"publish","type":"post","link":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/maximo-comun-divisor-de-x-e-y-veces-n\/","title":{"rendered":"M\u00e1ximo com\u00fan divisor de x e y veces n"},"content":{"rendered":"<p>Definir las funciones<\/p>\n<pre lang=\"text\">\n   repite :: Int -> Integer -> Integer\n   mcdR   :: Integer -> Int -> Int -> Integer\n<\/pre>\n<p>tales que<\/p>\n<ul>\n<li>(repite x n) es el n\u00famero obtenido repitiendo x veces el n\u00famero n. Por ejemplo.<\/li>\n<\/ul>\n<pre lang=\"text\">\n     repite 3 123  ==  123123123\n<\/pre>\n<ul>\n<li>(mcdR n x y) es el m\u00e1ximo com\u00fan divisor de los n\u00fameros obtenidos repitiendo x veces e y veces el n\u00famero n. Por ejemplo. <\/li>\n<\/ul>\n<pre lang=\"text\">\n     mcdR 123 2 3                     ==  123\n     mcdR 4 4 6                       ==  44\n     mcdR 2017 (10^1000) (2+10^1000)  ==  20172017\n<\/pre>\n<h4>Soluciones<\/h4>\n<pre lang=\"haskell\">\nimport Test.QuickCheck\n\nrepite :: Int -> Integer -> Integer\nrepite x n =\n  read (concat (replicate x (show n)))\n\n-- 1\u00aa definici\u00f3n\nmcdR :: Integer -> Int -> Int -> Integer\nmcdR n x y =\n  gcd (repite x n) (repite y n)\n\n-- 2\u00aa definici\u00f3n\nmcdR2 :: Integer -> Int -> Int -> Integer\nmcdR2 n x y =\n  repite (gcd x y) n\n\n-- Comprobaci\u00f3n de equivalencia\n-- ============================\n\n-- La propiedad es\nprop_equivalencia :: (Positive Integer) -> (Positive Int) -> (Positive Int)\n                     -> Bool\nprop_equivalencia (Positive n) (Positive x) (Positive y) =\n  mcdR n x y == mcdR2 n x y\n\n-- La comprobaci\u00f3n es\n--    \u03bb> quickCheck prop_equivalencia\n--    +++ OK, passed 100 tests.\n\n-- Comparaci\u00f3n de eficiencia\n-- =========================\n\n--    \u03bb> mcdR 2017 (10^6) (2+10^6)\n--    20172017\n--    (18.92 secs, 6,012,285,224 bytes)\n--    \u03bb> mcdR2 2017 (10^6) (2+10^6)\n--    20172017\n--    (0.01 secs, 0 bytes)\n<\/pre>\n","protected":false},"excerpt":{"rendered":"<p>Definir las funciones repite :: Int -> Integer -> Integer mcdR :: Integer -> Int -> Int -> Integer tales que (repite x n) es el n\u00famero obtenido repitiendo x veces el n\u00famero n. Por ejemplo. repite 3 123 == 123123123 (mcdR n x y) es el m\u00e1ximo com\u00fan divisor de los n\u00fameros obtenidos repitiendo&#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":[12,155,95,19],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/2902"}],"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=2902"}],"version-history":[{"count":3,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/2902\/revisions"}],"predecessor-version":[{"id":2957,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/2902\/revisions\/2957"}],"wp:attachment":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/media?parent=2902"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/categories?post=2902"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/tags?post=2902"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}