{"id":4520,"date":"2019-01-10T06:00:29","date_gmt":"2019-01-10T04:00:29","guid":{"rendered":"http:\/\/www.glc.us.es\/~jalonso\/exercitium\/?p=4520"},"modified":"2019-01-17T09:37:52","modified_gmt":"2019-01-17T07:37:52","slug":"subarboles-monovalorados","status":"publish","type":"post","link":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/subarboles-monovalorados\/","title":{"rendered":"Sub\u00e1rboles monovalorados"},"content":{"rendered":"<p>Los \u00e1rboles binarios con valores enteros se pueden representar mediante el tipo Arbol definido por<\/p>\n<pre lang=\"text\"> \n   data Arbol = H Int \n              | N Int Arbol Arbol\n              deriving Show\n<\/pre>\n<p>Por ejemplo, el \u00e1rbol<\/p>\n<pre lang=\"text\"> \n         7\n        \/ \\ \n       \/   \\\n      \/     \\\n     4       9\n    \/ \\     \/ \\\n   1   3   5   6 \n<\/pre>\n<p>se puede representar por<\/p>\n<pre lang=\"text\"> \n   N 7 (N 4 (H 1) (H 3)) (N 9 (H 5) (H 6))\n<\/pre>\n<p>Un \u00e1rbol es monovalorado si todos sus elementos son iguales. Por ejemplo, de los siguientes \u00e1rboles s\u00f3lo son monovalorados los dos primeros<\/p>\n<pre lang=\"text\"> \n    5          9           5          9    \n   \/ \\        \/ \\         \/ \\        \/ \\   \n  5   5      9   9       5   6      9   7  \n                \/ \\                    \/ \\ \n               9   9                  9   9\n<\/pre>\n<p>Definir la funci\u00f3n<\/p>\n<pre lang=\"text\"> \n   monovalorados :: Arbol -> [Arbol]\n<\/pre>\n<p>tal que (monovalorados a) es la lista de los sub\u00e1rboles monovalorados de a. Por ejemplo,<\/p>\n<pre lang=\"text\"> \n   \u03bb> monovalorados (N 5 (H 5) (H 5))\n   [N 5 (H 5) (H 5),H 5,H 5]\n   \u03bb> monovalorados (N 5 (H 5) (H 6))\n   [H 5,H 6]\n   \u03bb> monovalorados (N 9 (H 9) (N 9 (H 9) (H 9)))\n   [N 9 (H 9) (N 9 (H 9) (H 9)),H 9,N 9 (H 9) (H 9),H 9,H 9]\n   \u03bb> monovalorados (N 9 (H 9) (N 7 (H 9) (H 9)))\n   [H 9,H 9,H 9]\n   \u03bb> monovalorados (N 9 (H 9) (N 9 (H 7) (H 9)))\n   [H 9,H 7,H 9]\n<\/pre>\n<h4>Soluciones<\/h4>\n<pre lang=\"haskell\">\ndata Arbol = H Int \n           | N Int Arbol Arbol\n           deriving (Show, Eq)\n\nmonovalorados :: Arbol -> [Arbol]\nmonovalorados (H x) = [H x]\nmonovalorados (N x i d) \n    | todosIguales i x && todosIguales d x =\n        (N x i d) : (subarboles i ++ subarboles d)\n    | otherwise = monovalorados i ++ monovalorados d\n\n-- (todosIguales a x) se verifica si todos los valores de los nodos y\n-- las hojas del \u00e1rbol a son iguales a x.\ntodosIguales :: Arbol -> Int -> Bool\ntodosIguales (H y) x     = y == x\ntodosIguales (N y i d) x = y == x && todosIguales i x && todosIguales d x\n\n-- (subarboles a) es la lista de los sub\u00e1rboles de a.\nsubarboles :: Arbol -> [Arbol]\nsubarboles (H x)     = [H x]\nsubarboles (N x i d) = (N x i d) : (subarboles i ++ subarboles d)\n<\/pre>\n<h4>Pensamiento<\/h4>\n<blockquote><p>\nY nadie pregunta<br \/>\nni nadie contesta,<br \/>\ntodos hablan solos.<\/p>\n<p>Antonio Machado\n<\/p><\/blockquote>\n","protected":false},"excerpt":{"rendered":"<p>Los \u00e1rboles binarios con valores enteros se pueden representar mediante el tipo Arbol definido por data Arbol = H Int | N Int Arbol Arbol deriving Show Por ejemplo, el \u00e1rbol 7 \/ \\ \/ \\ \/ \\ 4 9 \/ \\ \/ \\ 1 3 5 6 se puede representar por N 7 (N&#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":[269,6],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/4520"}],"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=4520"}],"version-history":[{"count":4,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/4520\/revisions"}],"predecessor-version":[{"id":4567,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/4520\/revisions\/4567"}],"wp:attachment":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/media?parent=4520"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/categories?post=4520"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/tags?post=4520"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}