{"id":7554,"date":"2022-12-06T09:37:22","date_gmt":"2022-12-06T07:37:22","guid":{"rendered":"http:\/\/www.glc.us.es\/~jalonso\/exercitium\/?p=7554"},"modified":"2022-12-14T10:18:38","modified_gmt":"2022-12-14T08:18:38","slug":"06-dic-22","status":"publish","type":"post","link":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/06-dic-22\/","title":{"rendered":"Altura de un \u00e1rbol binario"},"content":{"rendered":"

El \u00e1rbol binario<\/p>\n

\n        \u00b7\n       \/ \\\n      \/   \\\n     \u00b7     \u00b7\n    \/ \\   \/ \\\n   1   4 6   9\n<\/pre>\n
se puede representar por<\/p>\n
\n   ejArbol = Nodo (Nodo (Hoja 1) (Hoja 4))\n                  (Nodo (Hoja 6) (Hoja 9))\n<\/pre>\n
El tipo de los \u00e1rboles binarios se puede definir por<\/p>\n
   data Arbol a = Hoja a
\n                | Nodo (Arbol a) (Arbol a)<\/p>\n
Definir la funci\u00f3n<\/p>\n
\n   altura :: Arbol a -> Int\n<\/pre>\n
tal que altura t<\/code> es la altura del \u00e1rbol t<\/code>. Por ejemplo,<\/p>\n
\n   \u03bb> altura (Hoja 1)\n   0\n   \u03bb> altura (Nodo (Hoja 1) (Hoja 6))\n   1\n   \u03bb> altura (Nodo (Nodo (Hoja 1) (Hoja 6)) (Hoja 2))\n   2\n   \u03bb> altura (Nodo (Nodo (Hoja 1) (Hoja 6)) (Nodo (Hoja 2) (Hoja 7)))\n   2\n<\/pre>\n
Soluciones<\/b><\/p>\n
A continuaci\u00f3n se muestran las soluciones en Haskell<\/a> y las soluciones en Python<\/a>.<\/p>\n
<\/a>
\nSoluciones en Haskell<\/b><\/p>\n
\ndata Arbol a = Hoja a\n             | Nodo (Arbol a) (Arbol a)\n\naltura :: Arbol a -> Int\naltura (Hoja _)   = 0\naltura (Nodo i d) = 1 + max (altura i) (altura d)\n<\/pre>\n
<\/a>
\nSoluciones en Python<\/b><\/p>\n
\nfrom dataclasses import dataclass\nfrom typing import Generic, TypeVar\n\nA = TypeVar(\"A\")\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 altura(a: Arbol[A]) -> int:\n    match a:\n        case Hoja(_):\n            return 0\n        case Nodo(i, d):\n            return 1 + max(altura(i), altura(d))\n    assert False\n<\/pre>\n","protected":false},"excerpt":{"rendered":"
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)…<\/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\/7554"}],"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=7554"}],"version-history":[{"count":4,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/7554\/revisions"}],"predecessor-version":[{"id":7633,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/7554\/revisions\/7633"}],"wp:attachment":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/media?parent=7554"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/categories?post=7554"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/tags?post=7554"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}