{"id":850,"date":"2014-12-23T06:00:04","date_gmt":"2014-12-23T04:00:04","guid":{"rendered":"http:\/\/www.glc.us.es\/~jalonso\/exercitium\/?p=850"},"modified":"2014-12-30T08:24:59","modified_gmt":"2014-12-30T06:24:59","slug":"desemparejamiento-de-listas","status":"publish","type":"post","link":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/desemparejamiento-de-listas\/","title":{"rendered":"Desemparejamiento de listas"},"content":{"rendered":"<p>Definir la funci\u00f3n<\/p>\n<pre lang=\"haskell\">\n   desemparejada :: [(a,b)] -> ([a],[b])\n<\/pre>\n<p>tal que (desemparejada ps) es el par de lista (xs,ys) tal que al emparejar (con zip) xs e ys devuelve ps. Por ejemplo,<\/p>\n<pre lang=\"text\">\n   ghci> desemparejada [(3,'l'),(2,'u'),(5,'i'),(9,'s')]\n   ([3,2,5,9],\"luis\")\n<\/pre>\n<p>Comprobar con QuickCheck que<\/p>\n<ul>\n<li>desemparejada es equivalente a la funci\u00f3n predefinida unzip.<\/li>\n<li>si el valor de (desemparejada ps) es (xs,ys), entonces (zip xs ys) es igual a ps. <\/li>\n<\/ul>\n<h4>Soluciones<\/h4>\n<pre lang=\"haskell\">\nimport Test.QuickCheck\n\n-- 1\u00aa definici\u00f3n (por comprensi\u00f3n):\ndesemparejada1 :: [(a,b)] -> ([a],[b])\ndesemparejada1 ps = ([x | (x,_) <- ps], [y | (_,y) <- ps])\n\n-- 2\u00aa definici\u00f3n (con map):\ndesemparejada2 :: [(a,b)] -> ([a],[b])\ndesemparejada2 ps = (map fst ps, map snd ps)\n\n-- 3\u00aa definici\u00f3n (por recursi\u00f3n):\ndesemparejada3 :: [(a,b)] -> ([a],[b])\ndesemparejada3 []         = ([],[])\ndesemparejada3 ((x,y):ps) = (x:xs,y:ys)\n    where (xs,ys) = desemparejada3 ps \n\n-- 4\u00aa definici\u00f3n (por plegado):\ndesemparejada4 :: [(a,b)] -> ([a],[b])\ndesemparejada4 = foldr f ([],[])\n    where f (x,y) (xs,ys) = (x:xs, y:ys)\n\n-- 5\u00aa definici\u00f3n (por plegado por la izquierda):\ndesemparejada5 :: [(a,b)] -> ([a],[b])\ndesemparejada5 ps = (reverse us, reverse vs)\n    where (us,vs) = foldl f ([],[]) ps\n          f (xs,ys) (x,y) = (x:xs,y:ys)\n\n-- Comparaci\u00f3n de eficiencia-\n--    ghci> let ps = zip [1..10^7] [1..10^7]\n--    \n--    ghci> length (fst (desemparejada1 ps))\n--    10000000\n--    (3.67 secs, 360441524 bytes)\n--    \n--    ghci> length (fst (desemparejada2 ps))\n--    10000000\n--    (0.38 secs, 440476764 bytes)\n--    \n--    ghci> length (fst (desemparejada3 ps))\n--    10000000\n--    (14.11 secs, 2160188668 bytes)\n--    \n--    ghci> length (fst (desemparejada4 ps))\n--    10000000\n--    (19.08 secs, 1658689692 bytes)\n--    \n--    ghci> length (fst (desemparejada5 ps))\n--    10000000\n--    (20.98 secs, 1610061796 bytes)\n\n-- En lo que sigue, usaremos la  2\u00ba definici\u00f3n\ndesemparejada :: [(a,b)] -> ([a],[b])\ndesemparejada = desemparejada2\n\n-- La primera propiedad es\nprop_desemparejada_1 :: (Eq a, Eq b) => [(a,b)] -> Bool\nprop_desemparejada_1 ps =\n    desemparejada ps == unzip ps\n\n-- Su comprobaci\u00f3n es\n--    ghci> quickCheck prop_desemparejada_1\n--    +++ OK, passed 100 tests.\n\n-- La segunda propiedad es\nprop_desemparejada_2 :: (Eq a, Eq b) => [(a,b)] -> Bool\nprop_desemparejada_2 ps = zip xs ys == ps\n    where (xs,ys) = desemparejada ps\n\n-- Su comprobaci\u00f3n es\n--    ghci> quickCheck prop_desemparejada_2\n--    +++ OK, passed 100 tests.\n<\/pre>\n","protected":false},"excerpt":{"rendered":"<p>Definir la funci\u00f3n desemparejada :: [(a,b)] -> ([a],[b]) tal que (desemparejada ps) es el par de lista (xs,ys) tal que al emparejar (con zip) xs e ys devuelve ps. Por ejemplo, ghci> desemparejada [(3,&#8217;l&#8217;),(2,&#8217;u&#8217;),(5,&#8217;i&#8217;),(9,&#8217;s&#8217;)] ([3,2,5,9],\u00bbluis\u00bb) Comprobar con QuickCheck que desemparejada es equivalente a la funci\u00f3n predefinida unzip. si el valor de (desemparejada ps) es (xs,ys),&#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":[5],"tags":[8,185,94,80,10,11,90,6,32,16,146],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/850"}],"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=850"}],"version-history":[{"count":7,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/850\/revisions"}],"predecessor-version":[{"id":894,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/850\/revisions\/894"}],"wp:attachment":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/media?parent=850"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/categories?post=850"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/tags?post=850"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}