{"id":2368,"date":"2016-04-27T06:01:19","date_gmt":"2016-04-27T04:01:19","guid":{"rendered":"http:\/\/www.glc.us.es\/~jalonso\/exercitium\/?p=2368"},"modified":"2016-05-04T06:06:07","modified_gmt":"2016-05-04T04:06:07","slug":"minimo-numero-de-cambios-para-igualar-una-lista","status":"publish","type":"post","link":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/minimo-numero-de-cambios-para-igualar-una-lista\/","title":{"rendered":"M\u00ednimo n\u00famero de cambios para igualar una lista"},"content":{"rendered":"<p>Definir la funci\u00f3n<\/p>\n<pre lang=\"text\">\n   nMinimoCambios :: Ord a => [a] -> Int\n<\/pre>\n<p>tal que (nMinimoCambios xs) es el menor n\u00famero de elementos de xs que hay que cambiar para que todos sean iguales. Por ejemplo,<\/p>\n<pre lang=\"text\">\n   nMinimoCambios [3,5,3,7,9,6]      ==  4\n   nMinimoCambios [3,5,3,7,3,3]      ==  2\n   nMinimoCambios \"Salamanca\"        ==  5\n   nMinimoCambios (4 : [1..500000])  ==  499999\n<\/pre>\n<p>En el primer ejemplo, los elementos que hay que cambiar son 5, 7, 9 y 6.<\/p>\n<h4>Soluciones<\/h4>\n<pre lang=\"haskell\">\nimport Data.List (group, nub, sort)\n\n-- 1\u00aa definici\u00f3n\n-- =============\n\nnMinimoCambios1 :: Ord a => [a] -> Int\nnMinimoCambios1 xs = \n    length xs - fst (last (sort (frecuencias xs)))\n\n-- (frecuencias xs) es la lista de los pares de los elementos de xs y el\n-- n\u00famero de veces que ocurren en xs. Por ejemplo,\n--    frecuencias [3,5,3,7,9,6]  ==  [(2,3),(1,5),(1,7),(1,9),(1,6)]\n--    frecuencias [3,5,3,7,5,5]  ==  [(2,3),(3,5),(1,7)]\nfrecuencias :: Ord a => [a] -> [(Int,a)]\nfrecuencias xs = [(cuenta x xs,x) | x <- nub xs]\n\n-- (cuenta x ys) es el n\u00famero de veces que ocurre x en ys. Por ejemplo,\n--    cuenta 3 [3,5,3,7,9,6]  ==  2\ncuenta :: Ord a => a -> [a] -> Int\ncuenta x ys = length [y | y <- ys, y == x]\n\n-- 2\u00aa definici\u00f3n\n-- =============\n\nnMinimoCambios2 :: Ord a => [a] -> Int\nnMinimoCambios2 xs = \n    length xs - fst (last (sort (frecuencias2 xs)))\n\n-- (frecuencias2 xs) es la lista de los pares de los elementos de xs y el\n-- n\u00famero de veces que ocurren en xs. Por ejemplo,\n--    frecuencias2 [3,5,3,7,9,6]  ==  [(2,3),(1,5),(1,7),(1,9),(1,6)]\n--    frecuencias2 [3,5,3,7,5,5]  ==  [(2,3),(3,5),(1,7)]\nfrecuencias2 :: Ord a  => [a] -> [(Int,a)]\nfrecuencias2 xs = \n    [(1 + length ys, y) | (y:ys) <- group (sort xs)] \n\n-- 3\u00aa definici\u00f3n\n-- =============\n\nnMinimoCambios3 :: Ord a => [a] -> Int\nnMinimoCambios3 xs = sum ys - maximum ys\n    where ys = [length ys | ys <- group (sort xs)] \n<\/pre>\n","protected":false},"excerpt":{"rendered":"<p>Definir la funci\u00f3n nMinimoCambios :: Ord a => [a] -> Int tal que (nMinimoCambios xs) es el menor n\u00famero de elementos de xs que hay que cambiar para que todos sean iguales. Por ejemplo, nMinimoCambios [3,5,3,7,9,6] == 4 nMinimoCambios [3,5,3,7,3,3] == 2 nMinimoCambios \u00abSalamanca\u00bb == 5 nMinimoCambios (4 : [1..500000]) == 499999 En el primer&#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":[8,80,13,134,28,15,24,14],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/2368"}],"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=2368"}],"version-history":[{"count":3,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/2368\/revisions"}],"predecessor-version":[{"id":2409,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/2368\/revisions\/2409"}],"wp:attachment":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/media?parent=2368"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/categories?post=2368"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/tags?post=2368"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}