{"id":7882,"date":"2023-02-08T06:00:14","date_gmt":"2023-02-08T04:00:14","guid":{"rendered":"http:\/\/www.glc.us.es\/~jalonso\/exercitium\/?p=7882"},"modified":"2023-01-23T09:20:23","modified_gmt":"2023-01-23T07:20:23","slug":"08-feb-23","status":"publish","type":"post","link":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/08-feb-23\/","title":{"rendered":"TAD de las colas: Transformaciones entre colas y listas"},"content":{"rendered":"<p>Utilizando el <a href=\"https:\/\/bit.ly\/3QWTsRL\">tipo abstracto de datos de las colas<\/a>, definir las funciones<\/p>\n<pre lang=\"text\">\n   listaAcola :: [a] -> Cola a\n   colaAlista :: Cola a -> [a]\n<\/pre>\n<p>tales que<\/p>\n<ul>\n<li><code>listaAcola xs<\/code> es la cola formada por los elementos de <code>xs<\/code>. Por ejemplo,<\/li>\n<\/ul>\n<pre lang=\"text\">\n     \u03bb> listaAcola [3, 2, 5]\n     3 | 2 | 5\n<\/pre>\n<ul>\n<li><code>colaAlista c<\/code> es la lista formada por los elementos de la cola <code>c<\/code>. Por ejemplo,<\/li>\n<\/ul>\n<pre lang=\"text\">\n     \u03bb> colaAlista (inserta 5 (inserta 2 (inserta 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   colaAlista (listaAcola xs) = xs\n   listaAcola (colaAlista c)  = c\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.Cola (Cola, vacia, inserta, esVacia, primero, resto)\nimport Test.QuickCheck\n\n-- 1\u00aa definici\u00f3n de listaAcola\n-- ===========================\n\nlistaAcola :: [a] -> Cola a\nlistaAcola ys = aux (reverse ys)\n  where aux []     = vacia\n        aux (x:xs) = inserta x (aux xs)\n\n-- 2\u00aa definici\u00f3n de listaAcola\n-- ===========================\n\nlistaAcola2 :: [a] -> Cola a\nlistaAcola2 = aux . reverse\n  where aux [] = vacia\n        aux (x:xs) = inserta x (aux xs)\n\n-- 3\u00aa definici\u00f3n de listaAcola\n-- ===========================\n\nlistaAcola3 :: [a] -> Cola a\nlistaAcola3 = aux . reverse\n  where aux = foldr inserta vacia\n\n-- 4\u00aa definici\u00f3n de listaAcola\n-- ===========================\n\nlistaAcola4 :: [a] -> Cola a\nlistaAcola4 xs = foldr inserta vacia (reverse xs)\n\n-- 5\u00aa definici\u00f3n de listaAcola\n-- ===========================\n\nlistaAcola5 :: [a] -> Cola a\nlistaAcola5 = foldr inserta vacia . reverse\n\n-- Comprobaci\u00f3n de equivalencia de las definiciones de listaAcola\n-- ==============================================================\n\n-- La propiedad es\nprop_listaAcola :: [Int] -> Bool\nprop_listaAcola xs =\n  all (== listaAcola xs)\n      [listaAcola2 xs,\n       listaAcola3 xs,\n       listaAcola4 xs,\n       listaAcola5 xs]\n\n-- La comprobaci\u00f3n es\n--    \u03bb> quickCheck prop_listaAcola\n--    +++ OK, passed 100 tests.\n\n-- Definici\u00f3n de colaAlista\n-- ========================\n\ncolaAlista :: Cola a -> [a]\ncolaAlista c\n  | esVacia c = []\n  | otherwise = pc : colaAlista rc\n  where pc = primero c\n        rc = resto c\n\n-- Comprobaci\u00f3n de las propiedades\n-- ===============================\n\n-- La primera propiedad es\nprop_1_listaAcola :: [Int] -> Bool\nprop_1_listaAcola xs =\n  colaAlista (listaAcola xs) == xs\n\n-- La comprobaci\u00f3n es\n--    \u03bb> quickCheck prop_1_listaAcola\n--    +++ OK, passed 100 tests.\n\n-- La segunda propiedad es\nprop_2_listaAcola :: Cola Int -> Bool\nprop_2_listaAcola c =\n  listaAcola (colaAlista c) == c\n\n-- La comprobaci\u00f3n es\n--    \u03bb> quickCheck prop_2_listaAcola\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.cola import (Cola, inserta, primero, resto, esVacia, vacia,\n                          colaAleatoria)\n\nA = TypeVar('A')\n\n# 1\u00aa definici\u00f3n de listaAcola\n# ===========================\n\ndef listaAcola(ys: list[A]) -> Cola[A]:\n    def aux(xs: list[A]) -> Cola[A]:\n        if not xs:\n            return vacia()\n        return inserta(xs[0], aux(xs[1:]))\n\n    return aux(list(reversed(ys)))\n\n# 2\u00aa soluci\u00f3n de listaAcola\n# =========================\n\ndef listaAcola2(xs: list[A]) -> Cola[A]:\n    p: Cola[A] = Cola()\n    for x in xs:\n        p.inserta(x)\n    return p\n\n# Comprobaci\u00f3n de equivalencia de las definiciones de listaAcola\n# ==============================================================\n\n# La propiedad es\n@given(st.lists(st.integers()))\ndef test_listaAcola(xs: list[int]) -> None:\n    assert listaAcola(xs) == listaAcola2(xs)\n\n# 1\u00aa definici\u00f3n de colaAlista\n# ===========================\n\ndef colaAlista(c: Cola[A]) -> list[A]:\n    if esVacia(c):\n        return []\n    pc = primero(c)\n    rc = resto(c)\n    return [pc] + colaAlista(rc)\n\n# 2\u00aa definici\u00f3n de colaAlista\n# ===========================\n\ndef colaAlista2Aux(c: Cola[A]) -> list[A]:\n    if c.esVacia():\n        return []\n    pc = c.primero()\n    c.resto()\n    return [pc] + colaAlista2Aux(c)\n\ndef colaAlista2(c: Cola[A]) -> list[A]:\n    c1 = deepcopy(c)\n    return colaAlista2Aux(c1)\n\n# 3\u00aa definici\u00f3n de colaAlista\n# ===========================\n\ndef colaAlista3Aux(c: Cola[A]) -> list[A]:\n    r = []\n    while not c.esVacia():\n        r.append(c.primero())\n        c.resto()\n    return r\n\ndef colaAlista3(c: Cola[A]) -> list[A]:\n    c1 = deepcopy(c)\n    return colaAlista3Aux(c1)\n\n# Comprobaci\u00f3n de equivalencia de las definiciones de colaAlista\n# ==============================================================\n\n@given(p=colaAleatoria())\ndef test_colaAlista(p: Cola[int]) -> None:\n    assert colaAlista(p) == colaAlista2(p)\n    assert colaAlista(p) == colaAlista3(p)\n\n# Comprobaci\u00f3n de las propiedades\n# ===============================\n\n# La primera propiedad es\n@given(st.lists(st.integers()))\ndef test_1_listaAcola(xs: list[int]) -> None:\n    assert colaAlista(listaAcola(xs)) == xs\n\n# La segunda propiedad es\n@given(c=colaAleatoria())\ndef test_2_listaAcola(c: Cola[int]) -> None:\n    assert listaAcola(colaAlista(c)) == c\n\n# La comprobaci\u00f3n es\n#      src> poetry run pytest -v transformaciones_colas_listas.py\n#      test_listaAcola PASSED\n#      test_colaAlista PASSED\n#      test_1_listaAcola PASSED\n#      test_2_listaAcola PASSED\n<\/pre>\n","protected":false},"excerpt":{"rendered":"<p>Utilizando el tipo abstracto de datos de las colas, definir las funciones listaAcola :: [a] -> Cola a colaAlista :: Cola a -> [a] tales que listaAcola xs es la cola formada por los elementos de xs. Por ejemplo, \u03bb> listaAcola [3, 2, 5] 3 | 2 | 5 colaAlista c 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":[515,585],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/7882"}],"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=7882"}],"version-history":[{"count":1,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/7882\/revisions"}],"predecessor-version":[{"id":7883,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/7882\/revisions\/7883"}],"wp:attachment":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/media?parent=7882"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/categories?post=7882"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/tags?post=7882"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}