{"id":6887,"date":"2022-04-08T06:00:52","date_gmt":"2022-04-08T04:00:52","guid":{"rendered":"http:\/\/www.glc.us.es\/~jalonso\/exercitium\/?p=6887"},"modified":"2022-04-16T18:26:01","modified_gmt":"2022-04-16T16:26:01","slug":"reiteracion-de-una-funcion","status":"publish","type":"post","link":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/reiteracion-de-una-funcion\/","title":{"rendered":"Reiteraci\u00f3n de una funci\u00f3n"},"content":{"rendered":"<p>Definir la funci\u00f3n<\/p>\n<pre lang=\"text\">\n   reiteracion :: (a -> a) -> Int -> a -> a\n   <\/pre>\n<p>tal que <code>(reiteracion f n x)<\/code> es el resultado de aplicar <code>n<\/code> veces la funci\u00f3n <code>f<\/code> a <code>x<\/code>. Por ejemplo,<\/p>\n<pre lang=\"text\">\n   reiteracion (+1) 10 5  ==  15\n   reiteracion (+5) 10 0  ==  50\n   reiteracion (*2)  4 1  ==  16\n   reiteracion (5:)  4 [] ==  [5,5,5,5]\n<\/pre>\n<h4>Soluciones<\/h4>\n<pre lang=\"haskell\">\nimport Test.QuickCheck (Fun (..), Positive (..), quickCheck)\n\n-- 1\u00aa soluci\u00f3n\n-- ===========\n\nreiteracion1 :: (a -> a) -> Int -> a -> a\nreiteracion1 _ 0 x = x\nreiteracion1 f n x = f (reiteracion1 f (n-1) x)\n\n-- 2\u00aa soluci\u00f3n\n-- ===========\n\nreiteracion2 :: (a -> a) -> Int -> a -> a\nreiteracion2 _ 0 = id\nreiteracion2 f n = f . reiteracion2 f (n-1)\n\n-- 3\u00aa soluci\u00f3n\n-- ===========\n\nreiteracion3 :: (a -> a) -> Int -> a -> a\nreiteracion3 _ 0 = id\nreiteracion3 f n\n  | even n    = reiteracion3 (f . f) (n `div` 2)\n  | otherwise = f . reiteracion3 (f . f) (n `div` 2)\n\n-- 4\u00aa soluci\u00f3n\n-- ===========\n\nreiteracion4 :: (a -> a) -> Int -> a -> a\nreiteracion4 f n x = reiteraciones f x !! n\n\nreiteraciones :: (a -> a) -> a -> [a]\nreiteraciones f x = x : reiteraciones f (f x)\n\n-- 5\u00aa soluci\u00f3n\n-- ===========\n\nreiteracion5 :: (a -> a) -> Int -> a -> a\nreiteracion5 f n x = (iterate f x) !! n\n\n-- 6\u00aa soluci\u00f3n\n-- ===========\n\n-- Se puede eliminar los argumentos de la definici\u00f3n anterior como sigue:\n--    reiteracion4 f n x = iterate f x !! n\n--    reiteracion4 f n x = ((!!) (iterate f x)) n\n--    reiteracion4 f n x = (((!!) . (iterate f)) x) n\n--    reiteracion4 f n x = ((!!) . (iterate f)) x n\n--    reiteracion4 f n x = flip ((!!) . (iterate f)) n x\n--    reiteracion4 f = flip ((!!) . (iterate f))\n--    reiteracion4 f = flip (((!!) .) (iterate f))\n--    reiteracion4 f = flip (((!!) .) . iterate) f\n--    reiteracion4 f = (flip . ((!!) .) . iterate) f\n--    reiteracion4   = flip . ((!!) .) . iterate\n\nreiteracion6 :: (a -> a) -> Int -> a -> a\nreiteracion6 = flip . ((!!) .) . iterate\n\n-- Comprobaci\u00f3n de equivalencia\n-- ============================\n\n-- La propiedad es\nprop_reiteracion :: Fun Int Int -> Positive Int -> Int -> Bool\nprop_reiteracion (Fun _ f) (Positive n) x =\n  all (== reiteracion1 f n x)\n      [reiteracion2 f n x,\n       reiteracion3 f n x,\n       reiteracion4 f n x,\n       reiteracion5 f n x,\n       reiteracion6 f n x]\n\n-- La comprobaci\u00f3n es\n--    \u03bb> quickCheck prop_reiteracion\n--    +++ OK, passed 100 tests.\n\n-- Comparaci\u00f3n de eficiencia\n-- =========================\n\n-- La comparaci\u00f3n es\n--    \u03bb> reiteracion1 (+1) (10^7) 0\n--    10000000\n--    (5.09 secs, 2,505,392,792 bytes)\n--    \u03bb> reiteracion2 (+1) (10^7) 0\n--    10000000\n--    (5.45 secs, 2,896,899,728 bytes)\n--    \u03bb> reiteracion3 (+1) (10^7) 0\n--    10000000\n--    (2.14 secs, 816,909,416 bytes)\n--    \u03bb> reiteracion4 (+1) (10^7) 0\n--    10000000\n--    (4.24 secs, 1,696,899,816 bytes)\n--    \u03bb> reiteracion5 (+1) (10^7) 0\n--    10000000\n--    (2.53 secs, 1,376,899,800 bytes)\n--    \u03bb> reiteracion6 (+1) (10^7) 0\n--    10000000\n--    (2.34 secs, 1,376,899,984 bytes)\n<\/pre>\n<p>El c\u00f3digo se encuentra en <a href=\"https:\/\/github.com\/jaalonso\/Exercitium\/blob\/main\/src\/Reiteracion_de_funciones.hs\">GitHub<\/a>.<\/p>\n<p>La elaboraci\u00f3n de las soluciones se describe en el siguiente v\u00eddeo<\/p>\n<p><iframe loading=\"lazy\" width=\"560\" height=\"315\" src=\"https:\/\/www.youtube.com\/embed\/1Kig_ipFIu0\" title=\"YouTube video player\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen><\/iframe><\/p>\n<h4>Nuevas soluciones<\/h4>\n<ul>\n<li>En los comentarios se pueden escribir nuevas soluciones.\n<li>El c\u00f3digo se debe escribir entre una l\u00ednea con &#60;pre lang=&quot;haskell&quot;&#62; y otra con &#60;\/pre&#62;\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>Definir la funci\u00f3n reiteracion :: (a -> a) -> Int -> a -> a tal que (reiteracion f n x) es el resultado de aplicar n veces la funci\u00f3n f a x. Por ejemplo, reiteracion (+1) 10 5 == 15 reiteracion (+5) 10 0 == 50 reiteracion (*2) 4 1 == 16 reiteracion (5:) 4&#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":[2],"tags":[41,30,91,160,63,50,11,6,519,146],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/6887"}],"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=6887"}],"version-history":[{"count":5,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/6887\/revisions"}],"predecessor-version":[{"id":6958,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/6887\/revisions\/6958"}],"wp:attachment":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/media?parent=6887"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/categories?post=6887"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/tags?post=6887"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}