{"id":7942,"date":"2023-03-09T06:00:24","date_gmt":"2023-03-09T04:00:24","guid":{"rendered":"http:\/\/www.glc.us.es\/~jalonso\/exercitium\/?p=7942"},"modified":"2023-02-22T20:06:15","modified_gmt":"2023-02-22T18:06:15","slug":"09-mar-23","status":"publish","type":"post","link":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/09-mar-23\/","title":{"rendered":"TAD de los conjuntos: Uni\u00f3n de varios 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   unionG:: Ord a => [Conj a] -> Conj a\n<\/pre>\n<p>tal <code>unionG cs<\/code> calcule la uni\u00f3n de la lista de conjuntos <code>cs<\/code>. Por ejemplo,<\/p>\n<pre lang=\"text\">\n   \u03bb> ej1 = inserta 3 (inserta 5 vacio)\n   \u03bb> ej2 = inserta 5 (inserta 6 vacio)\n   \u03bb> ej3 = inserta 3 (inserta 6 vacio)\n   \u03bb> unionG [ej1, ej2, ej3]\n   {3, 5, 6}\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)\nimport TAD_Union_de_dos_conjuntos (union)\nimport Test.QuickCheck\n\n-- 1\u00aa soluci\u00f3n\n-- ===========\n\nunionG :: Ord a => [Conj a] -> Conj a\nunionG []          = vacio\nunionG (c:cs) = c `union` unionG cs\n\n-- La funci\u00f3n union est\u00e1 definida en el ejercicio\n-- \"Uni\u00f3n de dos conjuntos\" que se encuentra en\n-- https:\/\/bit.ly\/3Y1jBl8\n\n-- 2\u00aa soluci\u00f3n\n-- ===========\n\nunionG2 :: Ord a => [Conj a] -> Conj a\nunionG2 = foldr union vacio\n\n-- Comprobaci\u00f3n de equivalencia\n-- ============================\n\n-- La propiedad es\nprop_unionG :: [Conj Int] -> Bool\nprop_unionG cs =\n  unionG cs == unionG2 cs\n\n-- La comprobaci\u00f3n es\n--    \u03bb> quickCheck prop_unionG\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 functools import reduce\nfrom typing import Protocol, TypeVar\n\nfrom hypothesis import given\nfrom hypothesis import strategies as st\n\nfrom src.TAD.conjunto import Conj, conjuntoAleatorio, inserta, vacio\nfrom src.TAD_Union_de_dos_conjuntos import union\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 unionG(cs: list[Conj[A]]) -> Conj[A]:\n    if not cs:\n        return vacio()\n    return union(cs[0], unionG(cs[1:]))\n\n# La funci\u00f3n union est\u00e1 definida en el ejercicio\n# \"Uni\u00f3n de dos conjuntos\" que se encuentra en\n# https:\/\/bit.ly\/3Y1jBl8\n\n# 2\u00aa soluci\u00f3n\n# ===========\n\ndef unionG2(cs: list[Conj[A]]) -> Conj[A]:\n    return reduce(union, cs, vacio())\n\n# 3\u00aa soluci\u00f3n\n# ===========\n\ndef unionG3(cs: list[Conj[A]]) -> Conj[A]:\n    r: Conj[A] = vacio()\n    for c in cs:\n        r = union(c, r)\n    return r\n\n# Comprobaci\u00f3n de equivalencia\n# ============================\n\n# La propiedad es\n@given(st.lists(conjuntoAleatorio(), max_size=10))\ndef test_union(cs: list[Conj[int]]) -> None:\n    r = unionG(cs)\n    assert unionG2(cs) == r\n    assert unionG3(cs) == r\n\n# La comprobaci\u00f3n de las propiedades es\n#    > poetry run pytest -q TAD_Union_de_varios_conjuntos.py\n#    1 passed in 0.75s\n<\/pre>\n","protected":false},"excerpt":{"rendered":"<p>Utilizando el tipo abstracto de datos de los conjuntos definir la funci\u00f3n unionG:: Ord a => [Conj a] -> Conj a tal unionG cs calcule la uni\u00f3n de la lista de conjuntos cs. Por ejemplo, \u03bb> ej1 = inserta 3 (inserta 5 vacio) \u03bb> ej2 = inserta 5 (inserta 6 vacio) \u03bb> ej3 = 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":[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\/7942"}],"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=7942"}],"version-history":[{"count":2,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/7942\/revisions"}],"predecessor-version":[{"id":7976,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/7942\/revisions\/7976"}],"wp:attachment":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/media?parent=7942"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/categories?post=7942"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/tags?post=7942"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}