{"id":4083,"date":"2018-05-17T06:00:01","date_gmt":"2018-05-17T04:00:01","guid":{"rendered":"http:\/\/www.glc.us.es\/~jalonso\/exercitium\/?p=4083"},"modified":"2018-05-27T11:03:12","modified_gmt":"2018-05-27T09:03:12","slug":"sustitucion-de-pares-de-elementos-consecutivos-iguales","status":"publish","type":"post","link":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/sustitucion-de-pares-de-elementos-consecutivos-iguales\/","title":{"rendered":"Sustituci\u00f3n de pares de elementos consecutivos iguales"},"content":{"rendered":"<p>Dada una lista xs se reemplaza el primer par de elementos consecutivos iguales x por x+1 y se repite el proceso con las listas obtenidas hasta que no haya ning\u00fan par de elementos consecutivos iguales. Por ejemplo, para [5,2,1,1,2,2] se tiene el siguiente proceso<\/p>\n<pre lang=\"text\">\n       [5,2,1,1,2,2] \n   ==> [5,2,2,  2,2]\n   ==> [5,3,    2,2]\n   ==> [5,3,    3]\n   ==> [5,4]\n<\/pre>\n<p>Definir la funci\u00f3n<\/p>\n<pre lang=\"text\">\n   sustitucion :: [Int] -> [Int]\n<\/pre>\n<p>tal que (sustitucion xs) es la lista obtenida aplic\u00e1ndole a xs el proceso anterior. Por ejemplo,<\/p>\n<pre lang=\"text\">\n   sustitucion [5,2,1,1,2,2]         ==  [5,4]\n   sustitucion [4,2,1,1,2,2]         ==  [5]\n   sustitucion [4,5,11,2,5,7,2]      ==  [4,5,11,2,5,7,2]\n   sustitucion (1:[1..2*10^6])       ==  [2000001]\n   length (sustitucion [1..2*10^6])  ==  2000000\n<\/pre>\n<h4>Soluciones<\/h4>\n<pre lang=\"haskell\">\n-- 1\u00aa soluci\u00f3n\n-- ===========\n\nsustitucion :: [Int] -> [Int]\nsustitucion xs\n  | xs == ys  = xs\n  | otherwise = sustitucion ys\n  where ys = sustitucionElemental xs\n\nsustitucionElemental :: [Int] -> [Int]\nsustitucionElemental []  = []\nsustitucionElemental [x] = [x]\nsustitucionElemental (x:y:zs)\n  | x == y = x+1:zs\n  | otherwise = x : sustitucionElemental (y:zs)\n\n-- 2\u00aa soluci\u00f3n\n-- ===========\n\nsustitucion2 :: [Int] -> [Int]\nsustitucion2 xs = until esPuntoFijo sustitucionElemental xs\n  where esPuntoFijo ys = sustitucionElemental ys == ys\n\n-- Comparaci\u00f3n de eficiencia\n-- =========================\n\n--    \u03bb> sustitucion (1:[1..2*10^6])\n--    [2000001]\n--    (1.54 secs, 800,143,448 bytes)\n--    \u03bb> sustitucion2 (1:[1..2*10^6])\n--    [2000001]\n--    (2.21 secs, 1,072,143,584 bytes)\n<\/pre>\n","protected":false},"excerpt":{"rendered":"<p>Dada una lista xs se reemplaza el primer par de elementos consecutivos iguales x por x+1 y se repite el proceso con las listas obtenidas hasta que no haya ning\u00fan par de elementos consecutivos iguales. Por ejemplo, para [5,2,1,1,2,2] se tiene el siguiente proceso [5,2,1,1,2,2] ==> [5,2,2, 2,2] ==> [5,3, 2,2] ==> [5,3, 3] ==>&#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":[11,6,367],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/4083"}],"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=4083"}],"version-history":[{"count":2,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/4083\/revisions"}],"predecessor-version":[{"id":4109,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/4083\/revisions\/4109"}],"wp:attachment":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/media?parent=4083"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/categories?post=4083"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/tags?post=4083"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}