{"id":7940,"date":"2023-03-08T06:00:20","date_gmt":"2023-03-08T04:00:20","guid":{"rendered":"http:\/\/www.glc.us.es\/~jalonso\/exercitium\/?p=7940"},"modified":"2023-02-22T20:05:13","modified_gmt":"2023-02-22T18:05:13","slug":"08-mar-23","status":"publish","type":"post","link":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/08-mar-23\/","title":{"rendered":"TAD de los conjuntos: Uni\u00f3n de dos conjuntos"},"content":{"rendered":"<p>Utilizando el <a href=\"https:\/\/bit.ly\/3HbB7fo\">tipo abstracto de datos de los conjuntos<\/a> definir la funci\u00f3n<\/p>\n<pre lang=\"text\">\n   union :: Ord a => Conj a -> Conj a -> Conj a\n<\/pre>\n<p>tal <code>union c1 c2<\/code> es la uni\u00f3n de ambos conjuntos. Por ejemplo,<\/p>\n<pre lang=\"text\">\n   \u03bb> ej1 = inserta 3 (inserta 5 vacio)\n   \u03bb> ej2 = inserta 4 (inserta 3 vacio)\n   \u03bb> union ej1 ej2\n   {3, 4, 5}\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.Conjunto (Conj, vacio, inserta, menor, elimina, esVacio)\nimport TAD_Transformaciones_conjuntos_listas (conjuntoAlista, listaAconjunto)\nimport qualified Data.List as L (union)\nimport Test.QuickCheck\n\n-- 1\u00aa soluci\u00f3n\n-- ===========\n\nunion :: Ord a => Conj a -> Conj a -> Conj a\nunion c1 c2\n  | esVacio c1 = c2\n  | otherwise  = inserta mc1 (rc1 `union` c2)\n  where mc1 = menor c1\n        rc1 = elimina mc1 c1\n\n-- 2\u00aa soluci\u00f3n\n-- ===========\n\nunion2 :: Ord a => Conj a -> Conj a -> Conj a\nunion2 c1 c2 =\n  foldr inserta c2 (conjuntoAlista c1)\n\n-- La funci\u00f3n conjuntoAlista est\u00e1 definida en el ejercicio\n-- \"Transformaciones entre conjuntos y listas\" que se encuentra en\n-- https:\/\/bit.ly\/3RexzxH\n\n-- 3\u00aa soluci\u00f3n\n-- ===========\n\nunion3 :: Ord a => Conj a -> Conj a -> Conj a\nunion3 c1 c2 =\n  listaAconjunto (conjuntoAlista c1 `L.union` conjuntoAlista c2)\n\n-- La funci\u00f3n listaAconjunto est\u00e1 definida en el ejercicio\n-- \"Transformaciones entre conjuntos y listas\" que se encuentra en\n-- https:\/\/bit.ly\/3RexzxH\n\n-- Comprobaci\u00f3n de equivalencia\n-- ============================\n\n-- La propiedad es\nprop_union :: Conj Int -> Conj Int -> Bool\nprop_union c1 c2 =\n  all (== union c1 c2)\n      [union2 c1 c2,\n       union3 c1 c2]\n\n-- La comprobaci\u00f3n es\n--    \u03bb> quickCheck prop_union\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 __future__ import annotations\n\nfrom abc import abstractmethod\nfrom copy import deepcopy\nfrom functools import reduce\nfrom typing import Protocol, TypeVar\n\nfrom hypothesis import given\n\nfrom src.TAD.conjunto import (Conj, conjuntoAleatorio, elimina, esVacio,\n                              inserta, menor, vacio)\nfrom src.TAD_Transformaciones_conjuntos_listas import conjuntoAlista\n\nclass Comparable(Protocol):\n    @abstractmethod\n    def __lt__(self: A, otro: A) -> bool:\n        pass\n\nA = TypeVar('A', bound=Comparable)\n\n# 1\u00aa soluci\u00f3n\n# ===========\n\ndef union(c1: Conj[A], c2: Conj[A]) -> Conj[A]:\n    if esVacio(c1):\n        return c2\n    mc1 = menor(c1)\n    rc1 = elimina(mc1, c1)\n    return inserta(mc1, union(rc1, c2))\n\n# 2\u00aa soluci\u00f3n\n# ===========\n\ndef union2(c1: Conj[A], c2: Conj[A]) -> Conj[A]:\n    return reduce(lambda c, x: inserta(x, c), conjuntoAlista(c1), c2)\n\n# La funci\u00f3n conjuntoAlista est\u00e1 definida en el ejercicio\n# \"Transformaciones entre conjuntos y listas\" que se encuentra en\n# https:\/\/bit.ly\/3RexzxH\n\n# 3\u00aa soluci\u00f3n\n# ===========\n\ndef union3(c1: Conj[A], c2: Conj[A]) -> Conj[A]:\n    r = c2\n    while not esVacio(c1):\n        mc1 = menor(c1)\n        r = inserta(mc1, r)\n        c1 = elimina(mc1, c1)\n    return r\n\n# 4\u00aa soluci\u00f3n\n# ===========\n\ndef union4Aux(c1: Conj[A], c2: Conj[A]) -> Conj[A]:\n    while not c1.esVacio():\n        mc1 = menor(c1)\n        c2.inserta(mc1)\n        c1.elimina(mc1)\n    return c2\n\ndef union4(c1: Conj[A], c2: Conj[A]) -> Conj[A]:\n    _c1 = deepcopy(c1)\n    _c2 = deepcopy(c2)\n    return union4Aux(_c1, _c2)\n\n# Comprobaci\u00f3n de equivalencia\n# ============================\n\n# La propiedad es\n@given(c1=conjuntoAleatorio(), c2=conjuntoAleatorio())\ndef test_union(c1: Conj[int], c2: Conj[int]) -> None:\n    r = union(c1, c2)\n    assert union2(c1, c2) == r\n    assert union3(c1, c2) == r\n    assert union4(c1, c2) == r\n\n# La comprobaci\u00f3n de las propiedades es\n#    > poetry run pytest -q TAD_Union_de_dos_conjuntos.py\n#    1 passed in 0.35s\n<\/pre>\n","protected":false},"excerpt":{"rendered":"<p>Utilizando el tipo abstracto de datos de los conjuntos definir la funci\u00f3n union :: Ord a => Conj a -> Conj a -> Conj a tal union c1 c2 es la uni\u00f3n de ambos conjuntos. Por ejemplo, \u03bb> ej1 = inserta 3 (inserta 5 vacio) \u03bb> ej2 = inserta 4 (inserta 3 vacio) \u03bb> union&#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":[331,585],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/7940"}],"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=7940"}],"version-history":[{"count":2,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/7940\/revisions"}],"predecessor-version":[{"id":7975,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/7940\/revisions\/7975"}],"wp:attachment":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/media?parent=7940"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/categories?post=7940"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/tags?post=7940"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}