{"id":7810,"date":"2023-01-24T06:00:36","date_gmt":"2023-01-24T04:00:36","guid":{"rendered":"http:\/\/www.glc.us.es\/~jalonso\/exercitium\/?p=7810"},"modified":"2023-01-22T17:22:28","modified_gmt":"2023-01-22T15:22:28","slug":"24-ene-23","status":"publish","type":"post","link":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/24-ene-23\/","title":{"rendered":"TAD de las pilas: Filtrado de pilas seg\u00fan una propiedad"},"content":{"rendered":"<p>Utilizando el <a href=\"https:\/\/bit.ly\/3GTToyK\">tipo abstracto de datos de las pilas<\/a>, definir la funci\u00f3n<\/p>\n<pre lang=\"text\">\n   filtraPila :: (a -> Bool) -> Pila a -> Pila a\n<\/pre>\n<p>tal que <code>filtraPila p q<\/code> es la pila obtenida con los elementos de pila <code>q<\/code> que verifican el predicado <code>p<\/code>, en el mismo orden. Por ejemplo,<\/p>\n<pre lang=\"text\">\n   \u03bb> ejPila = apila 6 (apila 3 (apila 1 (apila 4 vacia)))\n   \u03bb> ejPila\n   6 | 3 | 1 | 4\n   \u03bb> filtraPila even ejPila\n   6 | 4\n   \u03bb> filtraPila odd ejPila\n   3 | 1\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.Pila (Pila, vacia, apila, esVacia, cima, desapila)\nimport Transformaciones_pilas_listas (listaApila, pilaAlista)\nimport Test.QuickCheck.HigherOrder\n\n-- 1\u00aa soluci\u00f3n\n-- ===========\n\nfiltraPila1 :: (a -> Bool) -> Pila a -> Pila a\nfiltraPila1 p q\n  | esVacia q = vacia\n  | p cq      = apila cq (filtraPila1 p dq)\n  | otherwise = filtraPila1 p dq\n  where cq = cima q\n        dq = desapila q\n\n-- 2\u00aa soluci\u00f3n\n-- ===========\n\n-- Se usar\u00e1n las funciones listaApila y pilaAlista del ejercicio\n-- \"Transformaciones entre pilas y listas\" que se encuentra en\n-- https:\/\/bit.ly\/3ZHewQ8\n\nfiltraPila2 :: (a -> Bool) -> Pila a -> Pila a\nfiltraPila2 p q =\n  listaApila (filter p (pilaAlista q))\n\n-- Comprobaci\u00f3n de equivalencia\n-- ============================\n\n-- La propiedad es\nprop_filtraPila :: (Int -> Bool) -> [Int] -> Bool\nprop_filtraPila p xs =\n  filtraPila1 p q == filtraPila2 p q\n  where q = listaApila xs\n\n-- La comprobaci\u00f3n es\n--    \u03bb> quickCheck' prop_filtraPila\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 copy import deepcopy\nfrom typing import Callable, TypeVar\n\nfrom hypothesis import given\n\nfrom src.TAD.pila import (Pila, apila, cima, desapila, esVacia, pilaAleatoria,\n                          vacia)\nfrom src.transformaciones_pilas_listas import listaApila, pilaAlista\n\nA = TypeVar('A')\n\n# 1\u00aa soluci\u00f3n\n# ===========\n\ndef filtraPila1(p: Callable[[A], bool], q: Pila[A]) -> Pila[A]:\n    if esVacia(q):\n        return q\n    cq = cima(q)\n    dq = desapila(q)\n    r = filtraPila1(p, dq)\n    if p(cq):\n        return apila(cq, r)\n    return r\n\n# 2\u00aa soluci\u00f3n\n# ===========\n\n# Se usar\u00e1n las funciones listaApila y pilaAlista del ejercicio\n# \"Transformaciones entre pilas y listas\" que se encuentra en\n# https:\/\/bit.ly\/3ZHewQ8\n\ndef filtraPila2(p: Callable[[A], bool], q: Pila[A]) -> Pila[A]:\n    return listaApila(list(filter(p, pilaAlista(q))))\n\n# 3\u00aa soluci\u00f3n\n# ===========\n\ndef filtraPila3Aux(p: Callable[[A], bool], q: Pila[A]) -> Pila[A]:\n    if q.esVacia():\n        return q\n    cq = q.cima()\n    q.desapila()\n    r = filtraPila3Aux(p, q)\n    if p(cq):\n        r.apila(cq)\n    return r\n\ndef filtraPila3(p: Callable[[A], bool], q: Pila[A]) -> Pila[A]:\n    q1 = deepcopy(q)\n    return filtraPila3Aux(p, q1)\n\n# 4\u00aa soluci\u00f3n\n# ===========\n\ndef filtraPila4Aux(p: Callable[[A], bool], q: Pila[A]) -> Pila[A]:\n    r: Pila[A] = Pila()\n    while not q.esVacia():\n        cq = q.cima()\n        q.desapila()\n        if p(cq):\n            r.apila(cq)\n    r1: Pila[A] = Pila()\n    while not r.esVacia():\n        r1.apila(r.cima())\n        r.desapila()\n    return r1\n\ndef filtraPila4(p: Callable[[A], bool], q: Pila[A]) -> Pila[A]:\n    q1 = deepcopy(q)\n    return filtraPila4Aux(p, q1)\n\n# Comprobaci\u00f3n de equivalencia de las definiciones\n# ================================================\n\n# La propiedad es\n@given(p=pilaAleatoria())\ndef test_filtraPila(p: Pila[int]) -> None:\n    r = filtraPila1(lambda x: x % 2 == 0, p)\n    assert filtraPila2(lambda x: x % 2 == 0, p) == r\n    assert filtraPila3(lambda x: x % 2 == 0, p) == r\n    assert filtraPila4(lambda x: x % 2 == 0, p) == r\n\n# La comprobaci\u00f3n es\n#    src> poetry run pytest -q filtraPila.py\n#    1 passed in 0.25s\n<\/pre>\n","protected":false},"excerpt":{"rendered":"<p>Utilizando el tipo abstracto de datos de las pilas, definir la funci\u00f3n filtraPila :: (a -> Bool) -> Pila a -> Pila a tal que filtraPila p q es la pila obtenida con los elementos de pila q que verifican el predicado p, en el mismo orden. Por ejemplo, \u03bb> ejPila = apila 6 (apila&#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":[586,585],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/7810"}],"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=7810"}],"version-history":[{"count":5,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/7810\/revisions"}],"predecessor-version":[{"id":7867,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/7810\/revisions\/7867"}],"wp:attachment":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/media?parent=7810"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/categories?post=7810"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/tags?post=7810"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}