{"id":7829,"date":"2023-02-01T06:00:04","date_gmt":"2023-02-01T04:00:04","guid":{"rendered":"http:\/\/www.glc.us.es\/~jalonso\/exercitium\/?p=7829"},"modified":"2023-01-22T17:30:51","modified_gmt":"2023-01-22T15:30:51","slug":"01-feb-23","status":"publish","type":"post","link":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/01-feb-23\/","title":{"rendered":"TAD de las pilas: Reconocimiento de ordenaci\u00f3n de pilas"},"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   ordenadaPila :: Ord a => Pila a -> Bool\n<\/pre>\n<p>tal que <code>ordenadaPila p<\/code> se verifica si los elementos de la pila <code>p<\/code> est\u00e1n ordenados en orden creciente. Por ejemplo,<\/p>\n<pre lang=\"text\">\n   ordenadaPila (apila 1 (apila 5 (apila 6 vacia))) == True\n   ordenadaPila (apila 1 (apila 0 (apila 6 vacia))) == False\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 (pilaAlista)\nimport Test.QuickCheck\n\n-- 1\u00aa soluci\u00f3n\n-- ===========\n\nordenadaPila :: Ord a => Pila a -> Bool\nordenadaPila p\n  | esVacia p  = True\n  | esVacia dp = True\n  | otherwise  = cp <= cdp &#038;&#038; ordenadaPila dp\n  where cp  = cima p\n        dp  = desapila p\n        cdp = cima dp\n\n-- 2\u00aa soluci\u00f3n\n-- ===========\n\nordenadaPila2 :: Ord a => Pila a -> Bool\nordenadaPila2 =\n  ordenadaLista . reverse . pilaAlista\n\n-- (ordenadaLista xs) se verifica si la lista xs est\u00e1 ordenada de menor\n-- a mayor. Por ejemplo,\nordenadaLista :: Ord a => [a] -> Bool\nordenadaLista xs =\n  and [x <= y | (x,y) <- zip xs (tail xs)]\n\n-- Se usar\u00e1 la funci\u00f3n pilaAlista del ejercicio\n-- \"Transformaciones entre pilas y listas\" que se encuentra en\n-- https:\/\/bit.ly\/3ZHewQ8\n\n-- Comprobaci\u00f3n de equivalencia\n-- ============================\n\n-- La propiedad es\nprop_ordenadaPila :: Pila Int -> Bool\nprop_ordenadaPila p =\n  ordenadaPila p == ordenadaPila2 p\n\n-- La comprobaci\u00f3n es\n--    \u03bb> quickCheck prop_ordenadaPila\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\n\nfrom src.TAD.pila import (Pila, apila, cima, desapila, esVacia, pilaAleatoria,\n                          vacia)\nfrom src.transformaciones_pilas_listas import pilaAlista\n\nA = TypeVar('A', int, float, str)\n\n# 1\u00aa soluci\u00f3n\n# ===========\n\ndef ordenadaPila(p: Pila[A]) -> bool:\n    if esVacia(p):\n        return True\n    cp = cima(p)\n    dp = desapila(p)\n    if esVacia(dp):\n        return True\n    cdp = cima(dp)\n    return cp <= cdp and ordenadaPila(dp)\n\n# 2\u00aa soluci\u00f3n\n# ===========\n\n# Se usar\u00e1 la funci\u00f3n pilaAlista del ejercicio\n# \"Transformaciones entre pilas y listas\" que se encuentra en\n# https:\/\/bit.ly\/3ZHewQ8\n\n# ordenadaLista(xs, ys) se verifica si xs es una lista ordenada. Por\n# ejemplo,\n#    >>> ordenadaLista([2, 5, 8])\n#    True\n#    >>> ordenadalista([2, 8, 5])\n#    False\ndef ordenadaLista(xs: list[A]) -> bool:\n    return all((x <= y for (x, y) in zip(xs, xs[1:])))\n\ndef ordenadaPila2(p: Pila[A]) -> bool:\n    return ordenadaLista(list(reversed(pilaAlista(p))))\n\n# 3\u00aa soluci\u00f3n\n# ===========\n\ndef ordenadaPila3Aux(p: Pila[A]) -> bool:\n    if p.esVacia():\n        return True\n    cp = p.cima()\n    p.desapila()\n    if p.esVacia():\n        return True\n    return cp <= p.cima() and ordenadaPila3Aux(p)\n\ndef ordenadaPila3(p: Pila[A]) -> bool:\n    q = deepcopy(p)\n    return ordenadaPila3Aux(q)\n\n# 4\u00aa soluci\u00f3n\n# ===========\n\ndef ordenadaPila4Aux(p: Pila[A]) -> bool:\n    while not p.esVacia():\n        cp = p.cima()\n        p.desapila()\n        if not p.esVacia() and cp > p.cima():\n            return False\n    return True\n\ndef ordenadaPila4(p: Pila[A]) -> bool:\n    q = deepcopy(p)\n    return ordenadaPila4Aux(q)\n\n# Comprobaci\u00f3n de equivalencia de las definiciones\n# ================================================\n\n# La propiedad es\n@given(p=pilaAleatoria())\ndef test_ordenadaPila(p: Pila[int]) -> None:\n    r = ordenadaPila(p)\n    assert ordenadaPila2(p) == r\n    assert ordenadaPila3(p) == r\n    assert ordenadaPila4(p) == r\n\n# La comprobaci\u00f3n es\n#    src> poetry run pytest -q ordenadaPila.py\n#    1 passed in 0.31s\n<\/pre>\n","protected":false},"excerpt":{"rendered":"<p>Utilizando el tipo abstracto de datos de las pilas, definir la funci\u00f3n ordenadaPila :: Ord a => Pila a -> Bool tal que ordenadaPila p se verifica si los elementos de la pila p est\u00e1n ordenados en orden creciente. Por ejemplo, ordenadaPila (apila 1 (apila 5 (apila 6 vacia))) == True ordenadaPila (apila 1 (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\/7829"}],"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=7829"}],"version-history":[{"count":4,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/7829\/revisions"}],"predecessor-version":[{"id":7873,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/7829\/revisions\/7873"}],"wp:attachment":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/media?parent=7829"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/categories?post=7829"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/tags?post=7829"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}