{"id":3950,"date":"2018-04-09T06:00:04","date_gmt":"2018-04-09T04:00:04","guid":{"rendered":"http:\/\/www.glc.us.es\/~jalonso\/exercitium\/?p=3950"},"modified":"2018-04-16T12:41:30","modified_gmt":"2018-04-16T10:41:30","slug":"ampliacion-de-arboles-binarios","status":"publish","type":"post","link":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/ampliacion-de-arboles-binarios\/","title":{"rendered":"Ampliaci\u00f3n de \u00e1rboles binarios"},"content":{"rendered":"<p>Representamos los \u00e1rboles binarios mediante el tipo de dato<\/p>\n<pre lang=\"text\">\n   data Arbol a = H a\n                | N a (Arbol a) (Arbol a)\n     deriving Show\n<\/pre>\n<p>Una forma de ampliar un \u00e1rbol binario es a\u00f1adiendo un nuevo nivel donde<br \/>\nlas nuevas hojas sean iguales a la suma de los valores de los nodos<br \/>\ndesde el padre hasta llegar a la ra\u00edz (inclusives). Por ejemplo:<\/p>\n<pre lang=\"text\">\n      5               5       |         3                3\n     \/ \\             \/ \\      |        \/ \\             \/   \\\n    2   0    ==>    2   0     |       2   4    ==>    2     4\n                   \/ \\ \/ \\    |      \/ \\             \/ \\   \/ \\\n                  7  7 5  5   |     0   1           0   1 7   7\n                              |                    \/\\   \/\\\n                              |                   5  5 6  6\n<\/pre>\n<p>Definir la funci\u00f3n<\/p>\n<pre lang=\"text\">\n   ampliaArbol:: Num a => Arbol a -> Arbol a\n<\/pre>\n<p>tal que (ampliaArbol a) es el \u00e1rbol a ampliado en un nivel. Por<br \/>\nejemplo,<\/p>\n<pre lang=\"text\">\n   \u03bb> ampliaArbol (N 5 (H 2)(H 0))\n   N 5 (N 2 (H 7) (H 7)) (N 0 (H 5) (H 5))\n   \u03bb> ampliaArbol (N 3 (N 2 (H 0) (H 1)) (H 4))\n   N 3 (N 2 (N 0 (H 5) (H 5)) (N 1 (H 6) (H 6))) (N 4 (H 7) (H 7))\n   \u03bb> ampliaArbol (H 1)\n   N 1 (H 1) (H 1)\n   \u03bb> ampliaArbol N 1 (H 1) (H 1)\n   N 1 (N 1 (H 2) (H 2)) (N 1 (H 2) (H 2))\n<\/pre>\n<h4>Soluciones<\/h4>\n<pre lang=\"haskell\">\ndata Arbol a = H a\n             | N a (Arbol a) (Arbol a)\n  deriving Show\n\nampliaArbol :: Num a => Arbol a -> Arbol a\nampliaArbol a = aux 0 a\n  where aux n (H x)     = N x (H (n+x)) (H (n+x))\n        aux n (N x i d) = N x (aux (n+x) i) (aux (n+x) d)\n<\/pre>\n","protected":false},"excerpt":{"rendered":"<p>Representamos los \u00e1rboles binarios mediante el tipo de dato data Arbol a = H a | N a (Arbol a) (Arbol a) deriving Show Una forma de ampliar un \u00e1rbol binario es a\u00f1adiendo un nuevo nivel donde las nuevas hojas sean iguales a la suma de los valores de los nodos desde el padre hasta&#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":[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\/3950"}],"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=3950"}],"version-history":[{"count":4,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/3950\/revisions"}],"predecessor-version":[{"id":3979,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/3950\/revisions\/3979"}],"wp:attachment":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/media?parent=3950"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/categories?post=3950"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/tags?post=3950"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}