{"id":7543,"date":"2022-11-29T06:00:29","date_gmt":"2022-11-29T04:00:29","guid":{"rendered":"http:\/\/www.glc.us.es\/~jalonso\/exercitium\/?p=7543"},"modified":"2022-12-14T10:24:09","modified_gmt":"2022-12-14T08:24:09","slug":"29-nov-22","status":"publish","type":"post","link":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/29-nov-22\/","title":{"rendered":"El tipo de los \u00e1rboles binarios"},"content":{"rendered":"<p>El \u00e1rbol binario<\/p>\n<pre lang=\"text\">\n        5\n       \/ \\\n      \/   \\\n     3     7\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) 3 (Hoja 4))\n                  5\n                  (Nodo (Hoja 6) 7 (Hoja 9))\n<\/pre>\n<p>El tipo de los \u00e1rboles binarios se puede definir por<\/p>\n<pre lang=\"text\">\n   data Arbol = Hoja Int\n              | Nodo Arbol Int Arbol\n<\/pre>\n<p>Definir las funciones<\/p>\n<pre lang=\"text\">\n   ocurre :: Int -> Arbol -> Bool\n   aplana :: Arbol -> [Int]\n<\/pre>\n<p>tales que<\/p>\n<ul>\n<li><code>ocurre m a<\/code> se verifica si <code>m<\/code> ocurre en el \u00e1rbol <code>a<\/code>. Por ejemplo,<\/li>\n<\/ul>\n<pre lang=\"text\">\n     ocurre 4  ejArbol  ==  True\n     ocurre 10 ejArbol  ==  False\n<\/pre>\n<ul>\n<li><code>aplana a<\/code> es la lista obtenida aplanando el \u00e1rbol <code>a<\/code>. Por ejemplo,<\/li>\n<\/ul>\n<pre lang=\"text\">\n     aplana ejArbol  ==  [1,3,4,5,6,7,9]\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 = Hoja Int\n           | Nodo Arbol Int Arbol\n\nejArbol :: Arbol\nejArbol = Nodo (Nodo (Hoja 1) 3 (Hoja 4))\n               5\n               (Nodo (Hoja 6) 7 (Hoja 9))\n\nocurre :: Int -> Arbol -> Bool\nocurre m (Hoja n)     = m == n\nocurre m (Nodo i n d) = m == n || ocurre m i || ocurre m d\n\naplana :: Arbol -> [Int]\naplana (Hoja n)     = [n]\naplana (Nodo i n d) = aplana i ++ [n] ++ aplana d\n<\/pre>\n<p><a name=\"python\"><\/a><br \/>\n<b>Soluciones en Python<\/b><\/p>\n<pre lang=\"python\">\nfrom dataclasses import dataclass\n\n@dataclass\nclass Arbol:\n    pass\n\n@dataclass\nclass Hoja(Arbol):\n    x: int\n\n@dataclass\nclass Nodo(Arbol):\n    i: Arbol\n    x: int\n    d: Arbol\n\nejArbol = Nodo(Nodo(Hoja(1), 3, Hoja(4)),\n               5,\n               Nodo(Hoja(6), 7, Hoja(9)))\n\ndef ocurre(m: int, a: Arbol) -> bool:\n    match a:\n        case Hoja(n):\n            return m == n\n        case Nodo(i, n, d):\n            return m == n or ocurre(m, i) or ocurre(m, d)\n    assert False\n\ndef aplana(a: Arbol) -> list[int]:\n    match a:\n        case Hoja(n):\n            return [n]\n        case Nodo(i, n, d):\n            return aplana(i) + [n] + aplana(d)\n    assert False\n<\/pre>\n","protected":false},"excerpt":{"rendered":"<p>El \u00e1rbol binario 5 \/ \\ \/ \\ 3 7 \/ \\ \/ \\ 1 4 6 9 se puede representar por ejArbol = Nodo (Nodo (Hoja 1) 3 (Hoja 4)) 5 (Nodo (Hoja 6) 7 (Hoja 9)) El tipo de los \u00e1rboles binarios se puede definir por data Arbol = Hoja Int | Nodo&#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\/7543"}],"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=7543"}],"version-history":[{"count":3,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/7543\/revisions"}],"predecessor-version":[{"id":7638,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/7543\/revisions\/7638"}],"wp:attachment":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/media?parent=7543"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/categories?post=7543"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/tags?post=7543"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}