{"id":7558,"date":"2022-12-07T06:00:10","date_gmt":"2022-12-07T04:00:10","guid":{"rendered":"http:\/\/www.glc.us.es\/~jalonso\/exercitium\/?p=7558"},"modified":"2022-12-14T10:18:12","modified_gmt":"2022-12-14T08:18:12","slug":"07-dic-22","status":"publish","type":"post","link":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/07-dic-22\/","title":{"rendered":"Aplicaci\u00f3n de una funci\u00f3n a un \u00e1rbol"},"content":{"rendered":"<p>El \u00e1rbol binario<\/p>\n<pre lang=\"text\">\n        \u00b7\n       \/ \\\n      \/   \\\n     \u00b7     \u00b7\n    \/ \\   \/ \\\n   1   4 6   9\n<\/pre>\n<p>se puede representar por<\/p>\n<pre lang=\"text\">\n   ejArbol = Nodo (Nodo (Hoja 1) (Hoja 4))\n                  (Nodo (Hoja 6) (Hoja 9))\n<\/pre>\n<p>El tipo de los \u00e1rboles binarios se puede definir por<\/p>\n<pre lang=\"text\">\n   data Arbol a = Hoja a\n                | Nodo (Arbol a) (Arbol a)\n     deriving (Show, Eq)\n<\/pre>\n<p>Definir la funci\u00f3n<\/p>\n<pre lang=\"text\">\n   mapArbol :: (a -> b) -> Arbol a -> Arbol b\n<\/pre>\n<p>tal que <code>mapArbol f t<\/code> es el \u00e1rbolo obtenido aplicando la funci\u00f3n <code>f<\/code> a los elementos del \u00e1rbol <code>t<\/code>. Por ejemplo,<\/p>\n<pre lang=\"text\">\n   \u03bb> mapArbol (+ 1) (Nodo (Hoja 2) (Hoja 4))\n   Nodo (Hoja 3) (Hoja 5)\n<\/pre>\n<p><b>Soluciones<\/b><\/p>\n<p>A continuaci\u00f3n se muestran las <a href=\"#haskell\">soluciones en Haskell<\/a> y las <a href=\"#python\">soluciones en Python<\/a>.<\/p>\n<p><a name=\"haskell\"><\/a><br \/>\n<b>Soluciones en Haskell<\/b><\/p>\n<pre lang=\"haskell\">\ndata Arbol a = Hoja a\n             | Nodo (Arbol a) (Arbol a)\n  deriving (Show, Eq)\n\nmapArbol :: (a -> b) -> Arbol a -> Arbol b\nmapArbol f (Hoja a)   = Hoja (f a)\nmapArbol f (Nodo l r) = Nodo (mapArbol f l) (mapArbol f r)\n<\/pre>\n<p><a name=\"python\"><\/a><br \/>\n<b>Soluciones en Python<\/b><\/p>\n<pre lang=\"python\">\nfrom dataclasses import dataclass\nfrom typing import Callable, Generic, TypeVar\n\nA = TypeVar(\"A\")\nB = TypeVar(\"B\")\n\n@dataclass\nclass Arbol(Generic[A]):\n    pass\n\n@dataclass\nclass Hoja(Arbol[A]):\n    x: A\n\n@dataclass\nclass Nodo(Arbol[A]):\n    i: Arbol[A]\n    d: Arbol[A]\n\ndef mapArbol(f: Callable[[A], B], a: Arbol[A]) -> Arbol[B]:\n    match a:\n        case Hoja(x):\n            return Hoja(f(x))\n        case Nodo(i, d):\n            return Nodo(mapArbol(f, i), mapArbol(f, d))\n    assert False\n<\/pre>\n","protected":false},"excerpt":{"rendered":"<p>El \u00e1rbol binario \u00b7 \/ \\ \/ \\ \u00b7 \u00b7 \/ \\ \/ \\ 1 4 6 9 se puede representar por ejArbol = Nodo (Nodo (Hoja 1) (Hoja 4)) (Nodo (Hoja 6) (Hoja 9)) El tipo de los \u00e1rboles binarios se puede definir por data Arbol a = Hoja a | Nodo (Arbol a)&#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":[581],"tags":[],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/7558"}],"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=7558"}],"version-history":[{"count":3,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/7558\/revisions"}],"predecessor-version":[{"id":7632,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/7558\/revisions\/7632"}],"wp:attachment":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/media?parent=7558"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/categories?post=7558"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/tags?post=7558"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}