{"id":8003,"date":"2023-03-31T06:00:43","date_gmt":"2023-03-31T04:00:43","guid":{"rendered":"http:\/\/www.glc.us.es\/~jalonso\/exercitium\/?p=8003"},"modified":"2023-03-10T11:35:38","modified_gmt":"2023-03-10T09:35:38","slug":"31-mar-23","status":"publish","type":"post","link":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/31-mar-23\/","title":{"rendered":"Relaciones sim\u00e9tricas"},"content":{"rendered":"<p>Usando el <a href=\"https:\/\/bit.ly\/3IVVqOT\">tipo de las relaciones binarias<\/a>, definir la funci\u00f3n<\/p>\n<pre lang=\"text\">\n   simetrica :: Eq a => Rel a -> Bool\n<\/pre>\n<p>tal que <code>simetrica r<\/code> se verifica si la relaci\u00f3n <code>r<\/code> es sim\u00e9trica. Por ejemplo,<\/p>\n<pre lang=\"text\">\n   simetrica (R ([1,3],[(1,1),(1,3),(3,1)]))  ==  True\n   simetrica (R ([1,3],[(1,1),(1,3),(3,2)]))  ==  False\n   simetrica (R ([1,3],[]))                   ==  True\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 Relaciones_binarias (Rel(R))\nimport Test.QuickCheck\n\n-- 1\u00aa soluci\u00f3n\n-- ===========\n\nsimetrica :: Eq a => Rel a -> Bool\nsimetrica (R (_,g)) = and [(y,x) `elem` g | (x,y) <- g]\n\n-- 2\u00aa soluci\u00f3n\n-- ===========\n\nsimetrica2 :: Eq a => Rel a -> Bool\nsimetrica2 (R (_,g)) = all (\\(x,y) -> (y,x) `elem` g) g\n\n-- 3\u00aa soluci\u00f3n\n-- ===========\n\nsimetrica3 :: Eq a => Rel a -> Bool\nsimetrica3 (R (_,g)) = aux g\n  where aux [] = True\n        aux ((x,y):ps) = (y,x) `elem` g && aux ps\n\n-- Comprobaci\u00f3n de equivalencia\n-- ============================\n\n-- La propiedad es\nprop_simetrica :: Rel Int -> Bool\nprop_simetrica r =\n  all (== simetrica r)\n      [simetrica2 r,\n       simetrica3 r]\n\n-- La comprobaci\u00f3n es\n--    \u03bb> quickCheck prop_simetrica\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 typing import TypeVar\n\nfrom hypothesis import given\nfrom hypothesis import strategies as st\n\nfrom src.Relaciones_binarias import Rel, relacionArbitraria\n\nA = TypeVar('A')\n\n# 1\u00aa soluci\u00f3n\n# ===========\n\ndef simetrica(r: Rel[A]) -> bool:\n    (_, g) = r\n    return all(((y, x) in g for (x, y) in g))\n\n# 2\u00aa soluci\u00f3n\n# ===========\n\ndef simetrica2(r: Rel[A]) -> bool:\n    (_, g) = r\n    def aux(ps: list[tuple[A, A]]) -> bool:\n        if not ps:\n            return True\n        (x, y) = ps[0]\n        return (y, x) in g and aux(ps[1:])\n\n    return aux(g)\n\n# 3\u00aa soluci\u00f3n\n# ===========\n\ndef simetrica3(r: Rel[A]) -> bool:\n    (_, g) = r\n    for (x, y) in g:\n        if (y, x) not in g:\n            return False\n    return True\n\n# Comprobaci\u00f3n de equivalencia\n# ============================\n\n# La propiedad es\n@given(st.integers(min_value=0, max_value=10))\ndef test_simetrica(n: int) -> None:\n    r = relacionArbitraria(n)\n    res = simetrica(r)\n    assert simetrica2(r) == res\n    assert simetrica3(r) == res\n\n# La comprobaci\u00f3n es\n#    > poetry run pytest -q Relaciones_simetricas.py\n#    1 passed in 0.11s\n<\/pre>\n","protected":false},"excerpt":{"rendered":"<p>Usando el tipo de las relaciones binarias, definir la funci\u00f3n simetrica :: Eq a => Rel a -> Bool tal que simetrica r se verifica si la relaci\u00f3n r es sim\u00e9trica. Por ejemplo, simetrica (R ([1,3],[(1,1),(1,3),(3,1)])) == True simetrica (R ([1,3],[(1,1),(1,3),(3,2)])) == False simetrica (R ([1,3],[])) == True Soluciones A continuaci\u00f3n se muestran las soluciones&#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":[576],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/8003"}],"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=8003"}],"version-history":[{"count":1,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/8003\/revisions"}],"predecessor-version":[{"id":8004,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/8003\/revisions\/8004"}],"wp:attachment":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/media?parent=8003"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/categories?post=8003"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/tags?post=8003"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}