{"id":7954,"date":"2023-03-17T06:00:22","date_gmt":"2023-03-17T04:00:22","guid":{"rendered":"http:\/\/www.glc.us.es\/~jalonso\/exercitium\/?p=7954"},"modified":"2023-02-22T20:40:12","modified_gmt":"2023-02-22T18:40:12","slug":"17-mar-23","status":"publish","type":"post","link":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/17-mar-23\/","title":{"rendered":"TAD de los conjuntos: Subconjunto determinado por una propiedad"},"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   filtra :: Ord a => (a -> Bool) -> Conj a -> Conj a\n<\/pre>\n<p>tal <code>filtra p c<\/code> es el conjunto de elementos de <code>c<\/code> que verifican el predicado <code>p<\/code>. Por ejemplo,<\/p>\n<pre lang=\"text\">\n   \u03bb> filtra even (inserta 5 (inserta 4 (inserta 7 (inserta 2 vacio))))\n   {2, 4}\n   \u03bb> filtra odd (inserta 5 (inserta 4 (inserta 7 (inserta 2 vacio))))\n   {5, 7}\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, esVacio, menor, elimina)\nimport TAD_Transformaciones_conjuntos_listas (conjuntoAlista, listaAconjunto)\nimport Test.QuickCheck.HigherOrder\n\n-- 1\u00aa soluci\u00f3n\n-- ===========\n\nfiltra :: Ord a => (a -> Bool) -> Conj a -> Conj a\nfiltra p c\n  | esVacio c = vacio\n  | p mc      = inserta mc (filtra p rc)\n  | otherwise = filtra p rc\n  where mc = menor c\n        rc = elimina mc c\n\n-- 2\u00aa soluci\u00f3n\n-- ===========\n\nfiltra2 :: Ord a => (a -> Bool) -> Conj a -> Conj a\nfiltra2 p c =\n  listaAconjunto (filter p (conjuntoAlista c))\n\n-- Comprobaci\u00f3n de equivalencia\n-- ============================\n\n-- La propiedad es\nprop_filtra :: (Int -> Bool) -> [Int] -> Bool\nprop_filtra p xs =\n  filtra p c == filtra2 p c\n  where c = listaAconjunto xs\n\n-- La comprobaci\u00f3n es\n--    \u03bb> quickCheck' prop_filtra\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 Callable, Protocol, TypeVar\n\nfrom hypothesis import given\n\nfrom src.TAD.conjunto import (Conj, conjuntoAleatorio, elimina, esVacio,\n                              inserta, menor, pertenece, vacio)\nfrom src.TAD_Transformaciones_conjuntos_listas import (conjuntoAlista,\n                                                       listaAconjunto)\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 filtra(p: Callable[[A], bool], c: Conj[A]) -> Conj[A]:\n    if esVacio(c):\n        return vacio()\n    mc = menor(c)\n    rc = elimina(mc, c)\n    if p(mc):\n        return inserta(mc, filtra(p, rc))\n    return filtra(p, rc)\n\n# 2\u00aa soluci\u00f3n\n# ===========\n\ndef filtra2(p: Callable[[A], bool], c: Conj[A]) -> Conj[A]:\n    return listaAconjunto(list(filter(p, conjuntoAlista(c))))\n\n# 3\u00aa soluci\u00f3n\n# ===========\n\ndef filtra3Aux(p: Callable[[A], bool], c: Conj[A]) -> Conj[A]:\n    r: Conj[A] = vacio()\n    while not esVacio(c):\n        mc = menor(c)\n        c = elimina(mc, c)\n        if p(mc):\n            r = inserta(mc, r)\n    return r\n\ndef filtra3(p: Callable[[A], bool], c: Conj[A]) -> Conj[A]:\n    _c = deepcopy(c)\n    return filtra3Aux(p, _c)\n\n# 4\u00aa soluci\u00f3n\n# ===========\n\ndef filtra4Aux(p: Callable[[A], bool], c: Conj[A]) -> Conj[A]:\n    r: Conj[A] = Conj()\n    while not c.esVacio():\n        mc = c.menor()\n        c.elimina(mc)\n        if p(mc):\n            r.inserta(mc)\n    return r\n\ndef filtra4(p: Callable[[A], bool], c: Conj[A]) -> Conj[A]:\n    _c = deepcopy(c)\n    return filtra4Aux(p, _c)\n\n# Comprobaci\u00f3n de equivalencia de las definiciones\n# ================================================\n\n# La propiedad es\n@given(c=conjuntoAleatorio())\ndef test_filtra(c: Conj[int]) -> None:\n    r = filtra(lambda x: x % 2 == 0, c)\n    assert filtra2(lambda x: x % 2 == 0, c) == r\n    assert filtra3(lambda x: x % 2 == 0, c) == r\n    assert filtra4(lambda x: x % 2 == 0, c) == r\n\n# La comprobaci\u00f3n es\n#    src> poetry run pytest -q TAD_Subconjunto_por_propiedad.py\n#    1 passed in 0.28s\n<\/pre>\n","protected":false},"excerpt":{"rendered":"<p>Utilizando el tipo abstracto de datos de los conjuntos definir la funci\u00f3n filtra :: Ord a => (a -> Bool) -> Conj a -> Conj a tal filtra p c es el conjunto de elementos de c que verifican el predicado p. Por ejemplo, \u03bb> filtra even (inserta 5 (inserta 4 (inserta 7 (inserta 2&#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\/7954"}],"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=7954"}],"version-history":[{"count":2,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/7954\/revisions"}],"predecessor-version":[{"id":7983,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/7954\/revisions\/7983"}],"wp:attachment":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/media?parent=7954"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/categories?post=7954"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/tags?post=7954"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}