{"id":7477,"date":"2022-10-31T06:00:23","date_gmt":"2022-10-31T04:00:23","guid":{"rendered":"http:\/\/www.glc.us.es\/~jalonso\/exercitium\/?p=7477"},"modified":"2022-12-14T12:20:58","modified_gmt":"2022-12-14T10:20:58","slug":"numero-a-partir-de-sus-digitos","status":"publish","type":"post","link":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/numero-a-partir-de-sus-digitos\/","title":{"rendered":"N\u00famero a partir de sus d\u00edgitos"},"content":{"rendered":"<p>Definir la funci\u00f3n<\/p>\n<pre lang=\"text\">\n   listaNumero :: [Integer] -> Integer\n<\/pre>\n<p>tal que <code>listaNumero xs<\/code> es el n\u00famero formado por los d\u00edgitos <code>xs<\/code>. Por ejemplo,<\/p>\n<pre lang=\"text\">\n   listaNumero [5]        == 5\n   listaNumero [1,3,4,7]  == 1347\n   listaNumero [0,0,1]    == 1\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 (foldl')\nimport Data.Digits (unDigits)\nimport Test.QuickCheck\n\n-- 1\u00aa soluci\u00f3n\n-- ===========\n\nlistaNumero1 :: [Integer] -> Integer\nlistaNumero1 = aux . reverse\n  where\n    aux :: [Integer] -> Integer\n    aux []     = 0\n    aux (x:xs) = x + 10 * aux xs\n\n-- 2\u00aa soluci\u00f3n\n-- ===========\n\nlistaNumero2 :: [Integer] -> Integer\nlistaNumero2 = aux 0\n  where\n    aux :: Integer -> [Integer] -> Integer\n    aux r []     = r\n    aux r (x:xs) = aux (x+10*r) xs\n\n-- 3\u00aa soluci\u00f3n\n-- ===========\n\nlistaNumero3 :: [Integer] -> Integer\nlistaNumero3 = aux 0\n  where\n    aux :: Integer -> [Integer] -> Integer\n    aux = foldl (\\ r x -> x + 10 * r)\n\n-- 4\u00aa soluci\u00f3n\n-- ===========\n\nlistaNumero4 :: [Integer] -> Integer\nlistaNumero4 = foldl' (\\ r x -> x + 10 * r) 0\n\n-- 5\u00aa soluci\u00f3n\n-- ===========\n\nlistaNumero5 :: [Integer] -> Integer\nlistaNumero5 xs = sum [y*10^n | (y,n) <- zip (reverse xs) [0..]]\n\n-- 6\u00aa soluci\u00f3n\n-- ===========\n\nlistaNumero6 :: [Integer] -> Integer\nlistaNumero6 xs = sum (zipWith (\\ y n -> y*10^n) (reverse xs) [0..])\n\n-- 7\u00aa soluci\u00f3n\n-- ===========\n\nlistaNumero7 :: [Integer] -> Integer\nlistaNumero7 = unDigits 10\n\n-- 7\u00aa soluci\u00f3n\n-- ===========\n\nlistaNumero8 :: [Integer] -> Integer\nlistaNumero8 = read . concatMap show\n\n-- Comprobaci\u00f3n de equivalencia\n-- ============================\n\n-- La propiedad es\nprop_listaNumero :: NonEmptyList Integer -> Bool\nprop_listaNumero (NonEmpty xs) =\n  all (== listaNumero1 ys)\n      [listaNumero2 ys,\n       listaNumero3 ys,\n       listaNumero4 ys,\n       listaNumero5 ys,\n       listaNumero6 ys,\n       listaNumero7 ys,\n       listaNumero8 ys]\n  where ys = map (`mod` 10) xs\n\n-- La comprobaci\u00f3n es\n--    \u03bb> quickCheck prop_listaNumero\n--    +++ OK, passed 100 tests.\n\n-- Comparaci\u00f3n de eficiencia\n-- =========================\n\n-- La comparaci\u00f3n es\n--    \u03bb> length (show (listaNumero1 (replicate (10^5) 9)))\n--    100000\n--    (4.01 secs, 4,309,740,064 bytes)\n--    \u03bb> length (show (listaNumero2 (replicate (10^5) 9)))\n--    100000\n--    (4.04 secs, 4,307,268,856 bytes)\n--    \u03bb> length (show (listaNumero3 (replicate (10^5) 9)))\n--    100000\n--    (4.08 secs, 4,300,868,816 bytes)\n--    \u03bb> length (show (listaNumero4 (replicate (10^5) 9)))\n--    100000\n--    (0.42 secs, 4,288,480,208 bytes)\n--    \u03bb> length (show (listaNumero4 (replicate (10^5) 9)))\n--    100000\n--    (0.41 secs, 4,288,480,208 bytes)\n--    \u03bb> length (show (listaNumero5 (replicate (10^5) 9)))\n--    100000\n--    (43.35 secs, 10,702,827,328 bytes)\n--    \u03bb> length (show (listaNumero6 (replicate (10^5) 9)))\n--    100000\n--    (46.89 secs, 10,693,227,280 bytes)\n--    \u03bb> length (show (listaNumero7 (replicate (10^5) 9)))\n--    100000\n--    (4.33 secs, 4,297,499,344 bytes)\n--    \u03bb> length (show (listaNumero8 (replicate (10^5) 9)))\n--    100000\n--    (0.03 secs, 60,760,360 bytes)\n<\/pre>\n<p>El c\u00f3digo se encuentra en <a href=\"https:\/\/github.com\/jaalonso\/Exercitium\/blob\/main\/src\/Numero_a_partir_de_sus_digitos.hs\">GitHub<\/a>.<\/p>\n<p><a name=\"python\"><\/a><br \/>\n<b>Soluciones en Python<\/b><\/p>\n<pre lang=\"python\">\nfrom functools import reduce\nfrom sys import setrecursionlimit\nfrom timeit import Timer, default_timer\n\nfrom hypothesis import given\nfrom hypothesis import strategies as st\n\nsetrecursionlimit(10**6)\n\n# 1\u00aa soluci\u00f3n\n# ===========\n\ndef listaNumero1(xs: list[int]) -> int:\n    def aux(ys: list[int]) -> int:\n        if ys:\n            return ys[0] + 10 * aux(ys[1:])\n        return 0\n    return aux(list(reversed(xs)))\n\n# 2\u00aa soluci\u00f3n\n# ===========\n\ndef listaNumero2(xs: list[int]) -> int:\n    def aux(r: int, ys: list[int]) -> int:\n        if ys:\n            return aux(ys[0] + 10 * r, ys[1:])\n        return r\n    return aux(0, xs)\n\n# 3\u00aa soluci\u00f3n\n# ===========\n\ndef listaNumero3(xs: list[int]) -> int:\n    return reduce((lambda r, x: x + 10 * r), xs)\n\n# 4\u00aa soluci\u00f3n\n# ===========\n\ndef listaNumero4(xs: list[int]) -> int:\n    r = 0\n    for x in xs:\n        r = x + 10 * r\n    return r\n\n# 5\u00aa soluci\u00f3n\n# ===========\n\ndef listaNumero5(xs: list[int]) -> int:\n    return sum((y * 10**n\n                for (y, n) in zip(list(reversed(xs)), range(0, len(xs)))))\n\n# 6\u00aa soluci\u00f3n\n# ===========\n\ndef listaNumero6(xs: list[int]) -> int:\n    return int(\"\".join(list(map(str, xs))))\n\n# Comprobaci\u00f3n de equivalencia\n# ============================\n\n# La propiedad es\n@given(st.lists(st.integers(min_value=0, max_value=9), min_size=1))\ndef test_listaNumero(xs: list[int]) -> None:\n    r = listaNumero1(xs)\n    assert listaNumero2(xs) == r\n    assert listaNumero3(xs) == r\n    assert listaNumero4(xs) == r\n    assert listaNumero5(xs) == r\n    assert listaNumero6(xs) == r\n\n# La comprobaci\u00f3n es\n#    src> poetry run pytest -q numero_a_partir_de_sus_digitos.py\n#    1 passed in 0.27s\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#    >>> tiempo('listaNumero1([9]*(10**4))')\n#    0.28 segundos\n#    >>> tiempo('listaNumero2([9]*(10**4))')\n#    0.16 segundos\n#    >>> tiempo('listaNumero3([9]*(10**4))')\n#    0.01 segundos\n#    >>> tiempo('listaNumero4([9]*(10**4))')\n#    0.01 segundos\n#    >>> tiempo('listaNumero5([9]*(10**4))')\n#    0.41 segundos\n#    >>> tiempo('listaNumero6([9]*(10**4))')\n#    0.00 segundos\n#\n#    >>> tiempo('listaNumero3([9]*(2*10**5))')\n#    3.45 segundos\n#    >>> tiempo('listaNumero4([9]*(2*10**5))')\n#    3.29 segundos\n#    >>> tiempo('listaNumero6([9]*(2*10**5))')\n#    0.19 segundos\n<\/pre>\n<p>El c\u00f3digo se encuentra en <a href=\"https:\/\/github.com\/jaalonso\/Exercitium-Python\/blob\/main\/src\/numero_a_partir_de_sus_digitos.py\">GitHub<\/a>.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Definir la funci\u00f3n listaNumero :: [Integer] -> Integer tal que listaNumero xs es el n\u00famero formado por los d\u00edgitos xs. Por ejemplo, listaNumero [5] == 5 listaNumero [1,3,4,7] == 1347 listaNumero [0,0,1] == 1 Soluciones A continuaci\u00f3n se muestran las soluciones en Haskell y las soluciones en Python. Soluciones en Haskell import Data.List (foldl&#8217;) import&#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\/7477"}],"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=7477"}],"version-history":[{"count":2,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/7477\/revisions"}],"predecessor-version":[{"id":7659,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/7477\/revisions\/7659"}],"wp:attachment":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/media?parent=7477"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/categories?post=7477"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/tags?post=7477"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}