{"id":7938,"date":"2023-03-07T06:00:17","date_gmt":"2023-03-07T04:00:17","guid":{"rendered":"http:\/\/www.glc.us.es\/~jalonso\/exercitium\/?p=7938"},"modified":"2023-02-22T20:03:01","modified_gmt":"2023-02-22T18:03:01","slug":"07-mar-23","status":"publish","type":"post","link":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/07-mar-23\/","title":{"rendered":"TAD de los conjuntos: N\u00famero de elementos de un conjunto"},"content":{"rendered":"<p>Utilizando el <a href=\"https:\/\/bit.ly\/3HbB7fo\">tipo abstracto de datos de los conjuntos<\/a> definir la funci\u00f3n<\/p>\n<pre lang=\"text\">\n   cardinal :: Conj a -> Int\n<\/pre>\n<p>tal que <code>cardinal c<\/code> es el n\u00famero de elementos del conjunto <code>c<\/code>. Por ejemplo,<\/p>\n<pre lang=\"text\">\n   cardinal (inserta 4 (inserta 5 vacio))             == 2\n   cardinal (inserta 4 (inserta 5 (inserta 4 vacio))) == 2\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\">\nimport TAD.Conjunto (Conj, vacio, inserta, menor, elimina, esVacio)\nimport TAD_Transformaciones_conjuntos_listas (conjuntoAlista)\nimport Test.QuickCheck\n\n-- 1\u00aa soluci\u00f3n\n-- ===========\n\ncardinal :: Ord a => Conj a -> Int\ncardinal c\n  | esVacio c = 0\n  | otherwise = 1 + cardinal (elimina (menor c) c)\n\n-- 2\u00aa soluci\u00f3n\n-- ===========\n\ncardinal2 :: Ord a => Conj a -> Int\ncardinal2 = length . conjuntoAlista\n\n-- Comprobaci\u00f3n de equivalencia\n-- ============================\n\n-- La propiedad es\nprop_cardinal :: Conj Int -> Bool\nprop_cardinal c =\n  cardinal c == cardinal2 c\n\n-- La comprobaci\u00f3n es\n--    \u03bb> quickCheck prop_cardinal\n--    +++ OK, passed 100 tests.\n<\/pre>\n<p><a name=\"python\"><\/a><br \/>\n<b>Soluciones en Python<\/b><\/p>\n<pre lang=\"python\">\nfrom __future__ import annotations\n\nfrom abc import abstractmethod\nfrom copy import deepcopy\nfrom typing import Protocol, TypeVar\n\nfrom hypothesis import given\n\nfrom src.TAD.conjunto import (Conj, conjuntoAleatorio, elimina, esVacio,\n                              inserta, menor, vacio)\nfrom src.TAD_Transformaciones_conjuntos_listas import conjuntoAlista\n\nclass Comparable(Protocol):\n    @abstractmethod\n    def __lt__(self: A, otro: A) -> bool:\n        pass\n\nA = TypeVar('A', bound=Comparable)\n\n# 1\u00aa soluci\u00f3n\n# ===========\n\ndef cardinal(c: Conj[A]) -> int:\n    if esVacio(c):\n        return 0\n    return 1 + cardinal(elimina(menor(c), c))\n\n# 2\u00aa soluci\u00f3n\n# ===========\n\ndef cardinal2(c: Conj[A]) -> int:\n    return len(conjuntoAlista(c))\n\n# 3\u00aa soluci\u00f3n\n# ===========\n\ndef cardinal3(c: Conj[A]) -> int:\n    r = 0\n    while not esVacio(c):\n        r = r + 1\n        c = elimina(menor(c), c)\n    return r\n\n# 4\u00aa soluci\u00f3n\n# ===========\n\ndef cardinal4Aux(c: Conj[A]) -> int:\n    r = 0\n    while not c.esVacio():\n        r = r + 1\n        c.elimina(menor(c))\n    return r\n\ndef cardinal4(c: Conj[A]) -> int:\n    _c = deepcopy(c)\n    return cardinal4Aux(_c)\n\n# Comprobaci\u00f3n de equivalencia\n# ============================\n\n@given(c=conjuntoAleatorio())\ndef test_cardinal(c: Conj[int]) -> None:\n    r = cardinal(c)\n    assert cardinal2(c) == r\n    assert cardinal3(c) == r\n    assert cardinal3(c) == r\n\n# La comprobaci\u00f3n es\n#    src> poetry run pytest -q TAD_Numero_de_elementos_de_un_conjunto.py\n#    1 passed in 0.33s\n<\/pre>\n","protected":false},"excerpt":{"rendered":"<p>Utilizando el tipo abstracto de datos de los conjuntos definir la funci\u00f3n cardinal :: Conj a -> Int tal que cardinal c es el n\u00famero de elementos del conjunto c. Por ejemplo, cardinal (inserta 4 (inserta 5 vacio)) == 2 cardinal (inserta 4 (inserta 5 (inserta 4 vacio))) == 2 Soluciones A continuaci\u00f3n se muestran&#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":[331,585],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/7938"}],"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=7938"}],"version-history":[{"count":2,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/7938\/revisions"}],"predecessor-version":[{"id":7974,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/7938\/revisions\/7974"}],"wp:attachment":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/media?parent=7938"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/categories?post=7938"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/tags?post=7938"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}