{"id":296,"date":"2014-06-12T07:00:26","date_gmt":"2014-06-12T05:00:26","guid":{"rendered":"http:\/\/www.glc.us.es\/~jalonso\/exercitium\/?p=296"},"modified":"2022-04-21T12:55:34","modified_gmt":"2022-04-21T10:55:34","slug":"ordenada-ciclicamente-2014","status":"publish","type":"post","link":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/ordenada-ciclicamente-2014\/","title":{"rendered":"Ordenada c\u00edclicamente"},"content":{"rendered":"<h4>Enunciado<\/h4>\n<pre lang=\"text\">\n-- Se dice que una sucesi\u00f3n x(1), ..., x(n) est\u00e1 ordenada c\u00edclicamente\n-- si existe un \u00edndice i tal que la sucesi\u00f3n  \n--    x(i), x(i+1), ..., x(n), x(1), ..., x(i-1)\n-- est\u00e1 ordenada crecientemente. \n-- \n-- Definir la funci\u00f3n \n--    ordenadaCiclicamente :: Ord a => [a] -> Int\n-- tal que (ordenadaCiclicamente xs) es el \u00edndice (empezando en 1) a\n-- partir del cual est\u00e1 ordenada, si el la lista est\u00e1 ordenado c\u00edclicamente\n-- y 0 en caso contrario. Por ejemplo,\n--    ordenadaCiclicamente [1,2,3,4]      ==  1  \n--    ordenadaCiclicamente [5,8,2,3]      ==  3 \n--    ordenadaCiclicamente [4,6,7,5,4,3]  ==  0 \n--    ordenadaCiclicamente [1,0,1,2]      ==  0\n--    ordenadaCiclicamente [0,2,0]        ==  3\n--    ordenadaCiclicamente \"cdeab\"        ==  4\n<\/pre>\n<h4>Soluciones<\/h4>\n<pre lang=\"haskell\">\n-- 1\u00aa definici\u00f3n (por comprensi\u00f3n)\n-- ===============================\n\nordenadaCiclicamente1 :: Ord a => [a] -> Int\nordenadaCiclicamente1 xs = \n    primero [n+1 | n <- [0..length xs-1], \n                   ordenada (drop n xs ++ take n xs)]\n    where primero []     = 0\n          primero (x:xs) = x\n\n-- (ordenada xs) se verifica si la lista xs est\u00e1 ordenada\n-- crecientemente. Por ejemplo,\n--   ordenada \"acd\"   ==  True\n--   ordenada \"acdb\"  ==  False\nordenada :: Ord a => [a] -> Bool \nordenada (x:y:zs) = x <= y &#038;&#038; ordenada (y:zs) \nordenada _        = True \n \n-- 2\u00aa definici\u00f3n (por recursi\u00f3n)\n-- =============================\n\nordenadaCiclicamente2 :: Ord a => [a] -> Int\nordenadaCiclicamente2 xs = aux xs 1 (length xs)  \n    where aux xs i k \n              | i > k       = 0 \n              | ordenada xs = i \n              | otherwise   = aux (siguienteCiclo xs) (i+1) k \n\n-- (siguienteCiclo xs) es la lista obtenida a\u00f1adiendo el primer elemento\n-- de xs al final del resto de xs. Por ejemplo,\n--   siguienteCiclo [3,2,5]  =>  [2,5,3]\nsiguienteCiclo [] = [] \nsiguienteCiclo (x:xs) = xs ++ [x] \n<\/pre>\n","protected":false},"excerpt":{"rendered":"<p>Enunciado &#8212; Se dice que una sucesi\u00f3n x(1), &#8230;, x(n) est\u00e1 ordenada c\u00edclicamente &#8212; si existe un \u00edndice i tal que la sucesi\u00f3n &#8212; x(i), x(i+1), &#8230;, x(n), x(1), &#8230;, x(i-1) &#8212; est\u00e1 ordenada crecientemente. &#8212; &#8212; Definir la funci\u00f3n &#8212; ordenadaCiclicamente :: Ord a => [a] -> Int &#8212; tal que (ordenadaCiclicamente xs) es&#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":[8,46,28,6,47],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/296"}],"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=296"}],"version-history":[{"count":5,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/296\/revisions"}],"predecessor-version":[{"id":691,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/296\/revisions\/691"}],"wp:attachment":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/media?parent=296"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/categories?post=296"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/tags?post=296"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}