{"id":8085,"date":"2022-12-15T05:00:29","date_gmt":"2022-12-15T03:00:29","guid":{"rendered":"http:\/\/www.glc.us.es\/~jalonso\/exercitium\/?p=8085"},"modified":"2023-04-22T11:40:49","modified_gmt":"2023-04-22T09:40:49","slug":"15-dic-22a","status":"publish","type":"post","link":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/15-dic-22a\/","title":{"rendered":"El tipo de los \u00e1rboles binarios"},"content":{"rendered":"<h3>1. El tipo de los \u00e1rboles binarios en Haskell<\/h3>\n<p>El \u00e1rbol binario<\/p>\n<pre lang=\"text\">\n        9\n       \/ \\\n      \/   \\\n     3     7\n    \/ \\\n   2   4\n<\/pre>\n<p>se puede representar por<\/p>\n<pre lang=\"text\">\n   N 9 (N 3 (H 2) (H 4)) (H 7)\n<\/pre>\n<p>usando el tipo de los \u00e1rboles binarios definido como se muestra a continuaci\u00f3n.<\/p>\n<pre lang=\"haskell\">\nimport Test.QuickCheck\n\ndata Arbol a = H a\n             | N a (Arbol a) (Arbol a)\n  deriving (Show, Eq)\n\n-- Generador de \u00e1rboles binarios\n-- =============================\n\n-- (arbolArbitrario n) es un \u00e1rbol aleatorio de altura n. Por ejemplo,\n--    \u03bb> sample (arbolArbitrario 3 :: Gen (Arbol Int))\n--    N 0 (H 0) (H 0)\n--    N 1 (N (-2) (H (-1)) (H 1)) (H 2)\n--    N 3 (H 1) (H 2)\n--    N 6 (N 0 (H 5) (H (-5))) (N (-5) (H (-5)) (H 4))\n--    H 7\n--    N (-8) (H (-8)) (H 9)\n--    H 2\n--    N (-1) (H 7) (N 9 (H (-2)) (H (-8)))\n--    H (-3)\n--    N 0 (N 16 (H (-14)) (H (-18))) (H 7)\n--    N (-16) (H 18) (N (-19) (H (-15)) (H (-18)))\narbolArbitrario :: Arbitrary a => Int -> Gen (Arbol a)\narbolArbitrario 0 = H <$> arbitrary\narbolArbitrario n =\n  oneof [H <$> arbitrary,\n         N <$> arbitrary <*> arbolArbitrario (div n 2) <*> arbolArbitrario (div n 2)]\n\n-- Arbol es subclase de Arbitrary\ninstance Arbitrary a => Arbitrary (Arbol a) where\n  arbitrary = sized arbolArbitrario\n<\/pre>\n<h3>2. El tipo de los \u00e1rboles binarios en Python<\/h3>\n<p>El \u00e1rbol binario<\/p>\n<pre lang=\"text\">\n        9\n       \/ \\\n      \/   \\\n     3     7\n    \/ \\\n   2   4\n<\/pre>\n<p>se puede representar por<\/p>\n<pre lang=\"text\">\n   N(9, N(3, H(2), H(4)), H(7))\n<\/pre>\n<p>usando la definici\u00f3n de los \u00e1rboles binarios que se muestra a continuaci\u00f3n.<\/p>\n<pre lang=\"python\">\n\nfrom dataclasses import dataclass\nfrom random import choice, randint\nfrom typing import Generic, TypeVar\n\nA = TypeVar(\"A\")\n\n@dataclass\nclass Arbol(Generic[A]):\n    pass\n\n@dataclass\nclass H(Arbol[A]):\n    x: A\n\n@dataclass\nclass N(Arbol[A]):\n    x: A\n    i: Arbol[A]\n    d: Arbol[A]\n\ndef nHojas(a: Arbol[A]) -> int:\n    match a:\n        case H(_):\n            return 1\n        case N(_, i, d):\n            return nHojas(i) + nHojas(d)\n    assert False\n\ndef nNodos(a: Arbol[A]) -> int:\n    match a:\n        case H(_):\n            return 0\n        case N(_, i, d):\n            return 1 + nNodos(i) + nNodos(d)\n    assert False\n\n# Generador de \u00e1rboles\n# ====================\n\n# (arbolArbitrario n) es un \u00e1rbol aleatorio de orden n. Por ejemplo,\n#    >>> arbolArbitrario(4)\n#    N(x=2, i=H(x=1), d=H(x=9))\n#    >>> arbolArbitrario(4)\n#    H(x=10)\n#    >>> arbolArbitrario(4)\n#    N(x=4, i=N(x=7, i=H(x=4), d=H(x=0)), d=H(x=6))\ndef arbolArbitrario(n: int) -> Arbol[int]:\n    if n <= 1:\n        return H(randint(0, 10))\n    m = n \/\/ 2\n    return choice([H(randint(0, 10)),\n                   N(randint(0, 10),\n                     arbolArbitrario(m),\n                     arbolArbitrario(m))])\n<\/pre>\n","protected":false},"excerpt":{"rendered":"<p>1. El tipo de los \u00e1rboles binarios en Haskell El \u00e1rbol binario 9 \/ \\ \/ \\ 3 7 \/ \\ 2 4 se puede representar por N 9 (N 3 (H 2) (H 4)) (H 7) usando el tipo de los \u00e1rboles binarios definido como se muestra a continuaci\u00f3n. import Test.QuickCheck data 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":[269],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/8085"}],"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=8085"}],"version-history":[{"count":1,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/8085\/revisions"}],"predecessor-version":[{"id":8086,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/8085\/revisions\/8086"}],"wp:attachment":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/media?parent=8085"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/categories?post=8085"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/tags?post=8085"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}