{"id":2734,"date":"2016-12-23T06:00:00","date_gmt":"2016-12-23T04:00:00","guid":{"rendered":"http:\/\/www.glc.us.es\/~jalonso\/exercitium\/?p=2734"},"modified":"2016-12-30T08:36:41","modified_gmt":"2016-12-30T06:36:41","slug":"listas-duplicadas","status":"publish","type":"post","link":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/listas-duplicadas\/","title":{"rendered":"Listas duplicadas"},"content":{"rendered":"<p>Se observa que en la cadena \u00abaabbccddeffgg\u00bb todos los caracteres est\u00e1n duplicados excepto el &#8216;e&#8217;. Al a\u00f1adirlo obtenemos la lista \u00abaabbccddeeffgg\u00bb y se dice que esta \u00faltima est\u00e1 duplicada.<\/p>\n<p>Tambi\u00e9n se observa que \u00abaaaabbbccccdd\u00bb no est\u00e1 duplicada (porque hay un n\u00famero impar de &#8216;b&#8217; consecutivas). A\u00f1adiendo una &#8216;b&#8217; se obtiene \u00abaaaabbbbccccdd\u00bb que est\u00e1 duplicada.<\/p>\n<p>Definir las funciones<\/p>\n<pre lang=\"text\">\n   esDuplicada :: Eq a => [a] -> Bool\n   duplica     :: Eq a => [a] -> [a]\n<\/pre>\n<p>tales que<\/p>\n<ul>\n<li>(esDuplicada xs) se verifica si xs es una lista duplicada. Por ejemplo,  <\/li>\n<\/ul>\n<pre lang=\"text\">\n     esDuplicada \"aabbccddeffgg\"   ==  False\n     esDuplicada \"aabbccddeeffgg\"  ==  True\n     esDuplicada \"aaaabbbccccdd\"   ==  False\n     esDuplicada \"aaaabbbbccccdd\"  ==  True\n<\/pre>\n<ul>\n<li>(duplica xs) es la lista obtenida duplicando los elementos de xs que no lo est\u00e1n. Por ejemplo,<\/li>\n<\/ul>\n<pre lang=\"text\">\n     duplica \"b\"        ==  \"bb\"\n     duplica \"abba\"     ==  \"aabbaa\"\n     duplica \"Betis\"    ==  \"BBeettiiss\"\n     duplica [1,1,1]    ==  [1,1,1,1]\n     duplica [1,1,1,1]  ==  [1,1,1,1]\n<\/pre>\n<p>Comprobar con QuickCheck que, para cualquier lista de enteros xs, se verifica la siguiente propiedad:<\/p>\n<pre lang=\"text\">\n  esDuplicada (duplica xs)\n<\/pre>\n<h4>Soluciones<\/h4>\n<pre lang=\"haskell\">\nimport Data.List (group)\nimport Test.QuickCheck\n\n-- 1\u00aa definici\u00f3n de esDuplicada\nesDuplicada :: Eq a => [a] -> Bool\nesDuplicada []       = True\nesDuplicada [_]      = False\nesDuplicada (x:y:zs) = x == y && esDuplicada zs\n\n-- 2\u00aa definici\u00f3n de esDuplicada\nesDuplicada2 :: Eq a => [a] -> Bool\nesDuplicada2 = all (even . length) . group\n\n-- 1\u00aa definici\u00f3n de duplica\nduplica :: Eq a => [a] -> [a]\nduplica []       = []\nduplica [x]      = [x,x]\nduplica (x:y:zs) | x == y    = x : x : duplica zs\n                 | otherwise = x : x : duplica (y:zs)\n\n-- 2\u00aa definici\u00f3n de duplica\nduplica2 :: Eq a => [a] -> [a]\nduplica2 xs = concatMap dupl (group xs)\n  where dupl ys@(y:_) | (even.length) ys = ys\n                      | otherwise        = y : ys\n\n-- Propiedad\nprop_duplica_esDuplicada :: [Int] -> Bool\nprop_duplica_esDuplicada xs =\n  esDuplicada (duplica xs)\n\n-- La comprobaci\u00f3n es\n--    \u03bb> quickCheck prop_duplica_esDuplicada\n--    +++ OK, passed 100 tests.\n<\/pre>\n","protected":false},"excerpt":{"rendered":"<p>Se observa que en la cadena \u00abaabbccddeffgg\u00bb todos los caracteres est\u00e1n duplicados excepto el &#8216;e&#8217;. Al a\u00f1adirlo obtenemos la lista \u00abaabbccddeeffgg\u00bb y se dice que esta \u00faltima est\u00e1 duplicada. Tambi\u00e9n se observa que \u00abaaaabbbccccdd\u00bb no est\u00e1 duplicada (porque hay un n\u00famero impar de &#8216;b&#8217; consecutivas). A\u00f1adiendo una &#8216;b&#8217; se obtiene \u00abaaaabbbbccccdd\u00bb que est\u00e1 duplicada. Definir&#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":[6,146],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/2734"}],"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=2734"}],"version-history":[{"count":4,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/2734\/revisions"}],"predecessor-version":[{"id":2767,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/2734\/revisions\/2767"}],"wp:attachment":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/media?parent=2734"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/categories?post=2734"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/tags?post=2734"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}