{"id":8089,"date":"2022-12-06T05:00:40","date_gmt":"2022-12-06T03:00:40","guid":{"rendered":"http:\/\/www.glc.us.es\/~jalonso\/exercitium\/?p=8089"},"modified":"2023-04-23T19:17:48","modified_gmt":"2023-04-23T17:17:48","slug":"06-dic-22a","status":"publish","type":"post","link":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/06-dic-22a\/","title":{"rendered":"El tipo de los \u00e1rboles binarios con valores en las hojas"},"content":{"rendered":"<h3>1. El tipo de los \u00e1rboles binarios con valores en las hojas en Haskell<\/h3>\n<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>usando el tipo de los \u00e1rboles binarios con valores en las hojas definido como se muestra a continuaci\u00f3n.<\/p>\n<pre lang=\"haskell\">\ndata Arbol a = Hoja a\n             | Nodo (Arbol a) (Arbol a)\n  deriving (Eq, Show)\n\n-- (arbolArbitrario n) es un \u00e1rbol aleatorio de altura n. Por ejemplo,\n--    \u03bb> sample (arbolArbitrario 3 :: Gen (Arbol Int))\n--    Nodo (Nodo (Nodo (Hoja 0) (Hoja 0)) (Hoja 0)) (Hoja 0)\n--    Nodo (Nodo (Hoja 4) (Hoja 8)) (Hoja (-4))\n--    Nodo (Nodo (Nodo (Hoja 4) (Hoja 10)) (Hoja (-6))) (Hoja (-1))\n--    Nodo (Nodo (Hoja 3) (Hoja 6)) (Hoja (-5))\n--    Nodo (Nodo (Hoja (-11)) (Hoja (-13))) (Hoja 14)\n--    Nodo (Nodo (Hoja (-7)) (Hoja 15)) (Hoja (-2))\n--    Nodo (Nodo (Hoja (-9)) (Hoja (-2))) (Hoja (-6))\n--    Nodo (Nodo (Hoja (-15)) (Hoja (-16))) (Hoja (-20))\narbolArbitrario :: Arbitrary a => Int -> Gen (Arbol a)\narbolArbitrario n\n  | n <= 1    = Hoja <$> arbitrary\n  | otherwise = do\n      k <- choose (2, n - 1)\n      Nodo <$> arbolArbitrario k <*> arbolArbitrario (n - k)\n\n-- Arbol es subclase de Arbitraria\ninstance Arbitrary a => Arbitrary (Arbol a) where\n  arbitrary = sized arbolArbitrario\n  shrink (Hoja x)   = Hoja <$> shrink x\n  shrink (Nodo l r) = l :\n                      r :\n                      [Nodo l' r | l' <- shrink l] ++\n                      [Nodo l r' | r' <- shrink r]\n<\/pre>\n<h3>2. El tipo de los \u00e1rboles binarios con valores en las hojas en Python<\/h3>\n<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>usando el tipo de los \u00e1rboles binarios con valores en las hojas definido como se muestra a continuaci\u00f3n.<\/p>\n<pre lang=\"python\">\nfrom dataclasses import dataclass\nfrom typing import Generic, TypeVar\nfrom random import randint\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\n# Generador\n# =========\n\n# arbolArbitrario(n) es un \u00e1rbol aleatorio de orden n. Por ejemplo,\n#    >>> arbolArbitrario(2)\n#    Nodo(i=Nodo(i=Hoja(x=6), d=Hoja(x=3)), d=Nodo(i=Hoja(x=4), d=Hoja(x=4)))\n#    >>> arbolArbitrario(2)\n#    Nodo(i=Nodo(i=Hoja(x=9), d=Hoja(x=6)), d=Nodo(i=Hoja(x=9), d=Hoja(x=8)))\ndef arbolArbitrario(n: int) -> Arbol[int]:\n    if n == 0:\n        return Hoja(randint(1, 10))\n    if n == 1:\n        return Nodo(arbolArbitrario(0), arbolArbitrario(0))\n    k = min(randint(1, n + 1), n - 1)\n    return Nodo(arbolArbitrario(k), arbolArbitrario(n - k))\n<\/pre>\n","protected":false},"excerpt":{"rendered":"<p>1. El tipo de los \u00e1rboles binarios con valores en las hojas en Haskell 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)) usando el tipo de los \u00e1rboles&#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":[269],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/8089"}],"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=8089"}],"version-history":[{"count":4,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/8089\/revisions"}],"predecessor-version":[{"id":8093,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/8089\/revisions\/8093"}],"wp:attachment":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/media?parent=8089"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/categories?post=8089"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/tags?post=8089"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}