{"id":8010,"date":"2023-04-04T06:00:43","date_gmt":"2023-04-04T04:00:43","guid":{"rendered":"http:\/\/www.glc.us.es\/~jalonso\/exercitium\/?p=8010"},"modified":"2023-03-12T12:10:33","modified_gmt":"2023-03-12T10:10:33","slug":"04-abr-23","status":"publish","type":"post","link":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/04-abr-23\/","title":{"rendered":"Reconocimiento de subconjunto"},"content":{"rendered":"<p>Definir la funci\u00f3n<\/p>\n<pre lang=\"text\">\n   subconjunto :: Ord a => [a] -> [a] -> Bool\n<\/pre>\n<p>tal que <code>subconjunto xs ys<\/code> se verifica si <code>xs<\/code> es un subconjunto de <code>ys<\/code>. Por ejemplo,<\/p>\n<pre lang=\"text\">\n   subconjunto [3,2,3] [2,5,3,5]  ==  True\n   subconjunto [3,2,3] [2,5,6,5]  ==  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\">\nmodule Reconocimiento_de_subconjunto where\n\nimport Data.List (nub, sort)\nimport Data.Set (fromList, isSubsetOf)\nimport Test.QuickCheck\n\n-- 1\u00aa soluci\u00f3n\n-- ===========\n\nsubconjunto1 :: Ord a => [a] -> [a] -> Bool\nsubconjunto1 xs ys =\n  [x | x <- xs, x `elem` ys] == xs\n\n-- 2\u00aa soluci\u00f3n\n-- ===========\n\nsubconjunto2 :: Ord a => [a] -> [a] -> Bool\nsubconjunto2 []     _  = True\nsubconjunto2 (x:xs) ys = x `elem` ys && subconjunto2 xs ys\n\n-- 3\u00aa soluci\u00f3n\n-- ===========\n\nsubconjunto3 :: Ord a => [a] -> [a] -> Bool\nsubconjunto3 xs ys =\n  all (`elem` ys) xs\n\n-- 4\u00aa soluci\u00f3n\n-- ===========\n\nsubconjunto4 :: Ord a => [a] -> [a] -> Bool\nsubconjunto4 xs ys =\n  fromList xs `isSubsetOf` fromList ys\n\n-- Comprobaci\u00f3n de equivalencia\n-- ============================\n\n-- La propiedad es\nprop_subconjunto :: [Int] -> [Int] -> Bool\nprop_subconjunto xs ys =\n  all (== subconjunto1 xs ys)\n      [subconjunto2 xs ys,\n       subconjunto3 xs ys,\n       subconjunto4 xs ys]\n\n-- La comprobaci\u00f3n es\n--    \u03bb> quickCheck prop_subconjunto\n--    +++ OK, passed 100 tests.\n\n-- Comparaci\u00f3n de eficiencia\n-- =========================\n\n-- La comparaci\u00f3n es\n--    \u03bb> subconjunto1 [1..2*10^4] [1..2*10^4]\n--    True\n--    (1.81 secs, 5,992,448 bytes)\n--    \u03bb> subconjunto2 [1..2*10^4] [1..2*10^4]\n--    True\n--    (1.83 secs, 6,952,200 bytes)\n--    \u03bb> subconjunto3 [1..2*10^4] [1..2*10^4]\n--    True\n--    (1.75 secs, 4,712,304 bytes)\n--    \u03bb> subconjunto4 [1..2*10^4] [1..2*10^4]\n--    True\n--    (0.04 secs, 6,312,056 bytes)\n\n-- En lo sucesivo, usaremos la 4\u00aa definici\u00f3n\nsubconjunto :: Ord a => [a] -> [a] -> Bool\nsubconjunto = subconjunto4\n<\/pre>\n<p><a name=\"python\"><\/a><br \/>\n<b>Soluciones en Python<\/b><\/p>\n<pre lang=\"python\">\nfrom sys import setrecursionlimit\nfrom timeit import Timer, default_timer\nfrom typing import TypeVar\n\nfrom hypothesis import given\nfrom hypothesis import strategies as st\n\nsetrecursionlimit(10**6)\n\nA = TypeVar('A')\n\n# 1\u00aa soluci\u00f3n\n# ===========\n\ndef subconjunto1(xs: list[A], ys: list[A]) -> bool:\n    return [x for x in xs if x in ys] == xs\n\n# 2\u00aa soluci\u00f3n\n# ===========\n\ndef subconjunto2(xs: list[A], ys: list[A]) -> bool:\n    if not xs:\n        return True\n    return xs[0] in ys and subconjunto2(xs[1:], ys)\n\n# 3\u00aa soluci\u00f3n\n# ===========\n\ndef subconjunto3(xs: list[A], ys: list[A]) -> bool:\n    return all(elem in ys for elem in xs)\n\n# 4\u00aa soluci\u00f3n\n# ===========\n\ndef subconjunto4(xs: list[A], ys: list[A]) -> bool:\n    return set(xs) <= set(ys)\n\n# Comprobaci\u00f3n de equivalencia\n# ============================\n\n# La propiedad es\n@given(st.lists(st.integers()),\n       st.lists(st.integers()))\ndef test_filtraAplica(xs: list[int], ys: list[int]) -> None:\n    r = subconjunto1(xs, ys)\n    assert subconjunto2(xs, ys) == r\n    assert subconjunto3(xs, ys) == r\n    assert subconjunto4(xs, ys) == r\n\n# La comprobaci\u00f3n es\n#    src> poetry run pytest -q Reconocimiento_de_subconjunto.py\n#    1 passed in 0.31s\n\n# Comparaci\u00f3n de eficiencia\n# =========================\n\ndef tiempo(e: str) -> None:\n    \"\"\"Tiempo (en segundos) de evaluar la expresi\u00f3n e.\"\"\"\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(2*10**4))\n#    >>> tiempo(\"subconjunto1(xs, xs)\")\n#    1.15 segundos\n#    >>> tiempo(\"subconjunto2(xs, xs)\")\n#    2.27 segundos\n#    >>> tiempo(\"subconjunto3(xs, xs)\")\n#    1.14 segundos\n#    >>> tiempo(\"subconjunto4(xs, xs)\")\n#    0.00 segundos\n\n# En lo sucesivo usaremos la cuarta definici\u00f3n\nsubconjunto = subconjunto4\n<\/pre>\n","protected":false},"excerpt":{"rendered":"<p>Definir la funci\u00f3n subconjunto :: Ord a => [a] -> [a] -> Bool tal que subconjunto xs ys se verifica si xs es un subconjunto de ys. Por ejemplo, subconjunto [3,2,3] [2,5,3,5] == True subconjunto [3,2,3] [2,5,6,5] == False Soluciones A continuaci\u00f3n se muestran las soluciones en Haskell y las soluciones en Python. Soluciones en&#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\/8010"}],"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=8010"}],"version-history":[{"count":1,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/8010\/revisions"}],"predecessor-version":[{"id":8011,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/8010\/revisions\/8011"}],"wp:attachment":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/media?parent=8010"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/categories?post=8010"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/tags?post=8010"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}