{"id":7371,"date":"2022-09-19T06:00:59","date_gmt":"2022-09-19T04:00:59","guid":{"rendered":"http:\/\/www.glc.us.es\/~jalonso\/exercitium\/?p=7371"},"modified":"2022-12-14T14:28:53","modified_gmt":"2022-12-14T12:28:53","slug":"igualdad-de-conjuntos","status":"publish","type":"post","link":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/igualdad-de-conjuntos\/","title":{"rendered":"Igualdad de conjuntos"},"content":{"rendered":"<p>Definir la funci\u00f3n<\/p>\n<pre lang=\"text\">\n   iguales :: Ord a => [a] -> [a] -> Bool\n<\/pre>\n<p>tal que <code>iguales xs ys<\/code> se verifica si <code>xs<\/code> e <code>ys<\/code> son iguales como conjuntos. Por ejemplo,<\/p>\n<pre lang=\"text\">\n   iguales [3,2,3] [2,3]    ==  True\n   iguales [3,2,3] [2,3,2]  ==  True\n   iguales [3,2,3] [2,3,4]  ==  False\n   iguales [2,3] [4,5]      ==  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 Data.List (nub, sort)\nimport Data.Set (fromList)\nimport Test.QuickCheck\n\n-- 1\u00aa soluci\u00f3n\n-- ===========\n\niguales1 :: Ord a => [a] -> [a] -> Bool\niguales1 xs ys =\n  subconjunto xs ys && subconjunto ys xs\n\n-- (subconjunto xs ys) se verifica si xs es un subconjunto de ys. Por\n-- ejemplo,\n--    subconjunto [3,2,3] [2,5,3,5]  ==  True\n--    subconjunto [3,2,3] [2,5,6,5]  ==  False\nsubconjunto :: Ord a => [a] -> [a] -> Bool\nsubconjunto xs ys =\n  [x | x <- xs, x `elem` ys] == xs\n\n-- 2\u00aa soluci\u00f3n\n-- ===========\n\niguales2 :: Ord a => [a] -> [a] -> Bool\niguales2 xs ys =\n  nub (sort xs) == nub (sort ys)\n\n-- 3\u00aa soluci\u00f3n\n-- ===========\n\niguales3 :: Ord a => [a] -> [a] -> Bool\niguales3 xs ys =\n  fromList xs == fromList ys\n\n-- Comprobaci\u00f3n de equivalencia\n-- ============================\n\n-- La propiedad es\nprop_iguales :: [Int] -> [Int] -> Bool\nprop_iguales xs ys =\n  all (== iguales1 xs ys)\n      [iguales2 xs ys,\n       iguales3 xs ys]\n\n-- La comprobaci\u00f3n es\n--    \u03bb> quickCheck prop_iguales\n--    +++ OK, passed 100 tests.\n\n-- Comparaci\u00f3n de eficiencia\n-- =========================\n\n-- La comparaci\u00f3n es\n--    \u03bb> iguales1 [1..2*10^4] [1..2*10^4]\n--    True\n--    (4.05 secs, 8,553,104 bytes)\n--    \u03bb> iguales2 [1..2*10^4] [1..2*10^4]\n--    True\n--    (4.14 secs, 9,192,768 bytes)\n--    \u03bb> iguales3 [1..2*10^4] [1..2*10^4]\n--    True\n--    (0.01 secs, 8,552,232 bytes)\n<\/pre>\n<p>El c\u00f3digo se encuentra en <a href=\"https:\/\/github.com\/jaalonso\/Exercitium\/blob\/main\/src\/Igualdad_de_conjuntos.hs\">GitHub<\/a>.<\/p>\n<p><a name=\"python\"><\/a><br \/>\n<b>Soluciones en Python<\/b><\/p>\n<pre lang=\"python\">\nfrom typing import Any\nfrom timeit import Timer, default_timer\nfrom hypothesis import given, strategies as st\n\n# 1\u00aa soluci\u00f3n\n# ===========\n\ndef subconjunto(xs: list[Any],\n                ys: list[Any]) -> bool:\n    return [x for x in xs if x in ys] == xs\n\ndef iguales1(xs: list[Any],\n             ys: list[Any]) -> bool:\n    return subconjunto(xs, ys) and subconjunto(ys, xs)\n\n# 2\u00aa soluci\u00f3n\n# ===========\n\ndef iguales2(xs: list[Any],\n             ys: list[Any]) -> bool:\n    return set(xs) == set(ys)\n\n# Equivalencia de las definiciones\n# ================================\n\n# La propiedad es\n@given(st.lists(st.integers()),\n       st.lists(st.integers()))\ndef test_iguales(xs, ys):\n    assert iguales1(xs, ys) == iguales2(xs, ys)\n\n# La comprobaci\u00f3n es\n#    src> poetry run pytest -q igualdad_de_conjuntos.py\n#    1 passed in 0.28s\n\n# Comparaci\u00f3n de eficiencia\n# =========================\n\ndef tiempo(e):\n    \"\"\"Tiempo medio (en segundos) de 10 evaluaciones de la expresi\u00f3n e.\n    \"\"\"\n    t = Timer(e, \"\", default_timer, globals()).timeit(1)\n    print(f\"{t:0.2f} segundos\")\n\n# La comparaci\u00f3n es\n#    >>> xs = list(range(20000))\n#    >>> tiempo('iguales1(xs, xs)')\n#    2.71 segundos\n#    >>> tiempo('iguales2(xs, xs)')\n#    0.01 segundos\n<\/pre>\n<p>El c\u00f3digo se encuentra en <a href=\"https:\/\/github.com\/jaalonso\/Exercitium-Python\/blob\/main\/src\/igualdad_de_conjuntos.py\">GitHub<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Definir la funci\u00f3n iguales :: Ord a => [a] -> [a] -> Bool tal que iguales xs ys se verifica si xs e ys son iguales como conjuntos. Por ejemplo, iguales [3,2,3] [2,3] == True iguales [3,2,3] [2,3,2] == True iguales [3,2,3] [2,3,4] == False iguales [2,3] [4,5] == False Soluciones A continuaci\u00f3n se muestran&#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":[],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/7371"}],"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=7371"}],"version-history":[{"count":4,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/7371\/revisions"}],"predecessor-version":[{"id":7689,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/7371\/revisions\/7689"}],"wp:attachment":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/media?parent=7371"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/categories?post=7371"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/tags?post=7371"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}