{"id":7915,"date":"2023-02-24T06:00:48","date_gmt":"2023-02-24T04:00:48","guid":{"rendered":"http:\/\/www.glc.us.es\/~jalonso\/exercitium\/?p=7915"},"modified":"2023-01-27T19:10:52","modified_gmt":"2023-01-27T17:10:52","slug":"24-feb-23","status":"publish","type":"post","link":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/24-feb-23\/","title":{"rendered":"TAD de las colas: Reconocimiento de ordenaci\u00f3n de colas"},"content":{"rendered":"<p>Utilizando el <a href=\"https:\/\/bit.ly\/3QWTsRL\">tipo abstracto de datos de las colas<\/a>, definir la funci\u00f3n<\/p>\n<pre lang=\"text\">\n   ordenadaCola :: Ord a => Cola a -> Bool\n<\/pre>\n<p>tal que <code>ordenadaCola c<\/code> se verifica si los elementos de la cola <code>c<\/code> est\u00e1n ordenados en orden creciente. Por ejemplo,<\/p>\n<pre lang=\"text\">\n   ordenadaCola (inserta 6 (inserta 5 (inserta 1 vacia))) == True\n   ordenadaCola (inserta 1 (inserta 0 (inserta 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.Cola (Cola, vacia, inserta, esVacia, primero, resto)\nimport Transformaciones_colas_listas (colaAlista)\nimport Test.QuickCheck\n\n-- 1\u00aa soluci\u00f3n\n-- ===========\n\nordenadaCola :: Ord a => Cola a -> Bool\nordenadaCola c\n  | esVacia c  = True\n  | esVacia rc = True\n  | otherwise  = pc <= prc &#038;&#038; ordenadaCola rc\n  where pc  = primero c\n        rc  = resto c\n        prc = primero rc\n\n-- 2\u00aa soluci\u00f3n\n-- ===========\n\nordenadaCola2 :: Ord a => Cola a -> Bool\nordenadaCola2 =\n  ordenadaLista . colaAlista\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-- La funci\u00f3n colaAlista est\u00e1 definida en el ejercicio\n-- \"Transformaciones entre colas y listas\" que se encuentra en\n-- https:\/\/bit.ly\/3Xv0oIt\n\n-- Comprobaci\u00f3n de equivalencia\n-- ============================\n\n-- La propiedad es\nprop_ordenadaCola :: Cola Int -> Bool\nprop_ordenadaCola c =\n  ordenadaCola c == ordenadaCola2 c\n\n-- La comprobaci\u00f3n es\n--    \u03bb> quickCheck prop_ordenadaCola\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.cola import (Cola, colaAleatoria, esVacia, inserta, primero,\n                          resto, vacia)\nfrom src.transformaciones_colas_listas import colaAlista\n\nA = TypeVar('A', int, float, str)\n\n# 1\u00aa soluci\u00f3n\n# ===========\n\ndef ordenadaCola(c: Cola[A]) -> bool:\n    if esVacia(c):\n        return True\n    pc = primero(c)\n    rc = resto(c)\n    if esVacia(rc):\n        return True\n    prc = primero(rc)\n    return pc <= prc and ordenadaCola(rc)\n\n# 2\u00aa soluci\u00f3n\n# ===========\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 ordenadaCola2(p: Cola[A]) -> bool:\n    return ordenadaLista(colaAlista(p))\n\n# La funci\u00f3n colaAlista  est\u00e1 definida en el ejercicio\n# \"Transformaciones entre colas y listas\" que se encuentra en\n# https:\/\/bit.ly\/3Xv0oIt\n\n# 3\u00aa soluci\u00f3n\n# ===========\n\ndef ordenadaCola3Aux(c: Cola[A]) -> bool:\n    if c.esVacia():\n        return True\n    pc = c.primero()\n    c.resto()\n    if c.esVacia():\n        return True\n    return pc <= c.primero() and ordenadaCola3Aux(c)\n\ndef ordenadaCola3(c: Cola[A]) -> bool:\n    _c = deepcopy(c)\n    return ordenadaCola3Aux(_c)\n\n# 4\u00aa soluci\u00f3n\n# ===========\n\ndef ordenadaCola4Aux(c: Cola[A]) -> bool:\n    while not c.esVacia():\n        pc = c.primero()\n        c.resto()\n        if not c.esVacia() and pc > c.primero():\n            return False\n    return True\n\ndef ordenadaCola4(c: Cola[A]) -> bool:\n    _c = deepcopy(c)\n    return ordenadaCola4Aux(_c)\n\n# Comprobaci\u00f3n de equivalencia de las definiciones\n# ================================================\n\n# La propiedad es\n@given(p=colaAleatoria())\ndef test_ordenadaCola(p: Cola[int]) -> None:\n    r = ordenadaCola(p)\n    assert ordenadaCola2(p) == r\n    assert ordenadaCola3(p) == r\n    assert ordenadaCola4(p) == r\n\n# La comprobaci\u00f3n es\n#    src> poetry run pytest -q ordenadaCola.py\n#    1 passed in 0.27s\n<\/pre>\n","protected":false},"excerpt":{"rendered":"<p>Utilizando el tipo abstracto de datos de las colas, definir la funci\u00f3n ordenadaCola :: Ord a => Cola a -> Bool tal que ordenadaCola c se verifica si los elementos de la cola c est\u00e1n ordenados en orden creciente. Por ejemplo, ordenadaCola (inserta 6 (inserta 5 (inserta 1 vacia))) == True ordenadaCola (inserta 1 (inserta&#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\/7915"}],"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=7915"}],"version-history":[{"count":1,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/7915\/revisions"}],"predecessor-version":[{"id":7916,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/7915\/revisions\/7916"}],"wp:attachment":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/media?parent=7915"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/categories?post=7915"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/tags?post=7915"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}