{"id":7803,"date":"2023-01-23T06:00:43","date_gmt":"2023-01-23T04:00:43","guid":{"rendered":"http:\/\/www.glc.us.es\/~jalonso\/exercitium\/?p=7803"},"modified":"2023-01-22T20:19:43","modified_gmt":"2023-01-22T18:19:43","slug":"23-ene-23","status":"publish","type":"post","link":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/23-ene-23\/","title":{"rendered":"TAD de las pilas: Transformaciones entre pilas y listas"},"content":{"rendered":"<p>Utilizando el <a href=\"https:\/\/bit.ly\/3GTToyK\">tipo abstracto de datos de las pilas<\/a>, definir las funciones<\/p>\n<pre lang=\"text\">\n   listaApila :: [a] -> Pila a\n   pilaAlista :: Pila a -> [a]\n<\/pre>\n<p>tales que<\/p>\n<ul>\n<li><code>listaApila xs<\/code> es la pila formada por los elementos de <code>xs<\/code>. Por ejemplo,<\/li>\n<\/ul>\n<pre lang=\"text\">\n     \u03bb> listaApila [3, 2, 5]\n     5 | 2 | 3\n <\/pre>\n<ul>\n<li><code>pilaAlista p<\/code> es la lista formada por los elementos de la pila <code>p<\/code>. Por ejemplo,<\/li>\n<\/ul>\n<pre lang=\"text\">\n     \u03bb> pilaAlista (apila 5 (apila 2 (apila 3 vacia)))\n     [3, 2, 5]\n<\/pre>\n<p>Comprobar con QuickCheck que ambas funciones son inversa; es decir,<\/p>\n<pre lang=\"text\">\n   pilaAlista (listaApila xs) == xs\n   listaApila (pilaAlista p)  == p\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\">\nmodule Transformaciones_pilas_listas where\n\nimport TAD.Pila (Pila, vacia, apila, esVacia, cima, desapila)\nimport Test.QuickCheck\n\n-- 1\u00aa definici\u00f3n de listaApila\n-- ===========================\n\nlistaApila :: [a] -> Pila a\nlistaApila ys = aux (reverse ys)\n  where aux []     = vacia\n        aux (x:xs) = apila x (aux xs)\n\n-- 2\u00aa definici\u00f3n de listaApila\n-- ===========================\n\nlistaApila2 :: [a] -> Pila a\nlistaApila2 = aux . reverse\n  where aux [] = vacia\n        aux (x:xs) = apila x (aux xs)\n\n-- 3\u00aa definici\u00f3n de listaApila\n-- ===========================\n\nlistaApila3 :: [a] -> Pila a\nlistaApila3 = aux . reverse\n  where aux = foldr apila vacia\n\n-- 4\u00aa definici\u00f3n de listaApila\n-- ===========================\n\nlistaApila4 :: [a] -> Pila a\nlistaApila4 xs = foldr apila vacia (reverse xs)\n\n-- 5\u00aa definici\u00f3n de listaApila\n-- ===========================\n\nlistaApila5 :: [a] -> Pila a\nlistaApila5 = foldr apila vacia . reverse\n\n-- Comprobaci\u00f3n de equivalencia de las definiciones de listaApila\n-- ==============================================================\n\n-- La propiedad es\nprop_listaApila :: [Int] -> Bool\nprop_listaApila xs =\n  all (== listaApila xs)\n      [listaApila2 xs,\n       listaApila3 xs,\n       listaApila4 xs,\n       listaApila5 xs]\n\n-- La comprobaci\u00f3n es\n--    \u03bb> quickCheck prop_listaApila\n--    +++ OK, passed 100 tests.\n\n-- 1\u00aa definici\u00f3n de pilaAlista\n-- ===========================\n\npilaAlista :: Pila a -> [a]\npilaAlista p\n  | esVacia p = []\n  | otherwise = pilaAlista dp ++ [cp]\n  where cp = cima p\n        dp = desapila p\n\n-- 2\u00aa definici\u00f3n de pilaAlista\n-- ===========================\n\npilaAlista2 :: Pila a -> [a]\npilaAlista2 = reverse . aux\n  where aux p | esVacia p = []\n              | otherwise = cp : aux dp\n          where cp = cima p\n                dp = desapila p\n\n-- Comprobaci\u00f3n de equivalencia de las definiciones de pilaAlista\n-- ==============================================================\n\n-- La propiedad es\nprop_pilaAlista :: Pila Int -> Bool\nprop_pilaAlista p =\n  pilaAlista p == pilaAlista2 p\n\n-- La comprobaci\u00f3n es\n--    \u03bb> quickCheck prop_pilaAlista\n--    +++ OK, passed 100 tests.\n\n-- Comprobaci\u00f3n de las propiedades\n-- ===============================\n\n-- La primera propiedad es\nprop_1_listaApila :: [Int] -> Bool\nprop_1_listaApila xs =\n  pilaAlista (listaApila xs) == xs\n\n-- La comprobaci\u00f3n es\n--    \u03bb> quickCheck prop_1_listaApila\n--    +++ OK, passed 100 tests.\n\n-- La segunda propiedad es\nprop_2_listaApila :: Pila Int -> Bool\nprop_2_listaApila p =\n  listaApila (pilaAlista p) == p\n\n-- La comprobaci\u00f3n es\n--    \u03bb> quickCheck prop_2_listaApila\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 TypeVar\n\nfrom hypothesis import given\nfrom hypothesis import strategies as st\n\nfrom src.TAD.pila import (Pila, apila, cima, desapila, esVacia, pilaAleatoria,\n                          vacia)\n\nA = TypeVar('A')\n\n# 1\u00aa definici\u00f3n de listaApila\n# ===========================\n\ndef listaApila(ys: list[A]) -> Pila[A]:\n    def aux(xs: list[A]) -> Pila[A]:\n        if not xs:\n            return vacia()\n        return apila(xs[0], aux(xs[1:]))\n\n    return aux(list(reversed(ys)))\n\n# 2\u00aa soluci\u00f3n de listaApila\n# =========================\n\ndef listaApila2(xs: list[A]) -> Pila[A]:\n    p: Pila[A] = Pila()\n    for x in xs:\n        p.apila(x)\n    return p\n\n# Comprobaci\u00f3n de equivalencia de las definiciones de listaApila\n# ==============================================================\n\n# La propiedad es\n@given(st.lists(st.integers()))\ndef test_listaApila(xs: list[int]) -> None:\n    assert listaApila(xs) == listaApila2(xs)\n\n# 1\u00aa definici\u00f3n de pilaAlista\n# ===========================\n\ndef pilaAlista(p: Pila[A]) -> list[A]:\n    if esVacia(p):\n        return []\n    cp = cima(p)\n    dp = desapila(p)\n    return pilaAlista(dp) + [cp]\n\n# 2\u00aa definici\u00f3n de pilaAlista\n# ===========================\n\ndef pilaAlista2Aux(p: Pila[A]) -> list[A]:\n    if p.esVacia():\n        return []\n    cp = p.cima()\n    p.desapila()\n    return pilaAlista2Aux(p) + [cp]\n\ndef pilaAlista2(p: Pila[A]) -> list[A]:\n    p1 = deepcopy(p)\n    return pilaAlista2Aux(p1)\n\n# 3\u00aa definici\u00f3n de pilaAlista\n# ===========================\n\ndef pilaAlista3Aux(p: Pila[A]) -> list[A]:\n    r = []\n    while not p.esVacia():\n        r.append(p.cima())\n        p.desapila()\n    return r[::-1]\n\ndef pilaAlista3(p: Pila[A]) -> list[A]:\n    p1 = deepcopy(p)\n    return pilaAlista3Aux(p1)\n\n# Comprobaci\u00f3n de equivalencia de las definiciones de pilaAlista\n# ==============================================================\n\n@given(p=pilaAleatoria())\ndef test_pilaAlista(p: Pila[int]) -> None:\n    assert pilaAlista(p) == pilaAlista2(p)\n    assert pilaAlista(p) == pilaAlista3(p)\n\n# Comprobaci\u00f3n de las propiedades\n# ===============================\n\n# La primera propiedad es\n@given(st.lists(st.integers()))\ndef test_1_listaApila(xs: list[int]) -> None:\n    assert pilaAlista(listaApila(xs)) == xs\n\n# La segunda propiedad es\n@given(p=pilaAleatoria())\ndef test_2_listaApila(p: Pila[int]) -> None:\n    assert listaApila(pilaAlista(p)) == p\n\n# La comprobaci\u00f3n es\n#      src> poetry run pytest -v transformaciones_pilas_listas.py\n#      test_listaApila PASSED\n#      test_pilaAlista PASSED\n#      test_1_listaApila PASSED\n#      test_2_listaApila PASSED\n<\/pre>\n","protected":false},"excerpt":{"rendered":"<p>Utilizando el tipo abstracto de datos de las pilas, definir las funciones listaApila :: [a] -> Pila a pilaAlista :: Pila a -> [a] tales que listaApila xs es la pila formada por los elementos de xs. Por ejemplo, \u03bb> listaApila [3, 2, 5] 5 | 2 | 3 pilaAlista p es la lista formada&#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\/7803"}],"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=7803"}],"version-history":[{"count":12,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/7803\/revisions"}],"predecessor-version":[{"id":7879,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/7803\/revisions\/7879"}],"wp:attachment":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/media?parent=7803"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/categories?post=7803"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/tags?post=7803"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}