{"id":7482,"date":"2022-10-28T06:00:31","date_gmt":"2022-10-28T04:00:31","guid":{"rendered":"http:\/\/www.glc.us.es\/~jalonso\/exercitium\/?p=7482"},"modified":"2022-12-14T12:22:00","modified_gmt":"2022-12-14T10:22:00","slug":"suma-de-los-digitos-de-un-numero","status":"publish","type":"post","link":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/suma-de-los-digitos-de-un-numero\/","title":{"rendered":"Suma de los d\u00edgitos de un n\u00famero"},"content":{"rendered":"

Definir la funci\u00f3n<\/p>\n

\n   sumaDigitos :: Integer -> Integer\n<\/pre>\n
tal que sumaDigitos n<\/code> es la suma de los d\u00edgitos de n<\/code>. Por ejemplo,<\/p>\n
\n   sumaDigitos 3     ==  3\n   sumaDigitos 2454  == 15\n   sumaDigitos 20045 == 11\n<\/pre>\n
Soluciones<\/b><\/p>\n
A continuaci\u00f3n se muestran las soluciones en Haskell<\/a> y las soluciones en Python<\/a>.<\/p>\n
<\/a>
\nSoluciones en Haskell<\/b><\/p>\n
\nimport Data.List (foldl')\nimport Test.QuickCheck\n\n-- 1\u00aa soluci\u00f3n\n-- ===========\n\nsumaDigitos1 :: Integer -> Integer\nsumaDigitos1 n = sum (digitos n)\n\n-- (digitos n) es la lista de los d\u00edgitos del n\u00famero n. Por ejemplo,\n--    digitos 320274  ==  [3,2,0,2,7,4]\ndigitos :: Integer -> [Integer]\ndigitos n = [read [x] | x <- show n]\n\n-- Nota. En lugar de la definici\u00f3n anterior de digitos se puede usar\n-- cualquiera del ejercicio \"D\u00edgitos de un n\u00famero\" https:\/\/bit.ly\/3Tkhc2T\n\n-- 2\u00aa soluci\u00f3n\n-- ===========\n\nsumaDigitos2 :: Integer -> Integer\nsumaDigitos2 n = foldl' (+) 0 (digitos n)\n\n-- 3\u00aa soluci\u00f3n\n-- ===========\n\nsumaDigitos3 :: Integer -> Integer\nsumaDigitos3 n\n  | n < 10    = n\n  | otherwise = n `rem` 10 + sumaDigitos3 (n `div` 10)\n\n-- 4\u00aa soluci\u00f3n\n-- ===========\n\nsumaDigitos4 :: Integer -> Integer\nsumaDigitos4 = aux 0\n  where aux r n\n          | n < 10    = r + n\n          | otherwise = aux (r + n `rem` 10) (n `div` 10)\n\n-- Comprobaci\u00f3n de equivalencia\n-- ============================\n\n-- La propiedad es\nprop_sumaDigitos :: NonNegative Integer -> Bool\nprop_sumaDigitos (NonNegative n) =\n  all (== sumaDigitos1 n)\n      [sumaDigitos2 n,\n       sumaDigitos3 n,\n       sumaDigitos4 n]\n\n-- La comprobaci\u00f3n es\n--    \u03bb> quickCheck prop_sumaDigitos\n--    +++ OK, passed 100 tests.\n\n-- Comparaci\u00f3n de eficiencia\n-- =========================\n\n-- La comparaci\u00f3n es\n--    \u03bb> sumaDigitos1 (product [1..2*10^4])\n--    325494\n--    (0.64 secs, 665,965,832 bytes)\n--    \u03bb> sumaDigitos2 (product [1..2*10^4])\n--    325494\n--    (0.41 secs, 660,579,064 bytes)\n--    \u03bb> sumaDigitos3 (product [1..2*10^4])\n--    325494\n--    (1.58 secs, 1,647,082,224 bytes)\n--    \u03bb> sumaDigitos4 (product [1..2*10^4])\n--    325494\n--    (1.72 secs, 1,662,177,792 bytes)\n--\n--    \u03bb> sumaDigitos1 (product [1..5*10^4])\n--    903555\n--    (2.51 secs, 3,411,722,136 bytes)\n--    \u03bb> sumaDigitos2 (product [1..5*10^4])\n--    903555\n--    (2.30 secs, 3,396,802,856 bytes)\n<\/pre>\n
El c\u00f3digo se encuentra en GitHub<\/a>.<\/p>\n
<\/a>
\nSoluciones en Python<\/b><\/p>\n
\nfrom functools import reduce\nfrom math import factorial\nfrom operator import add\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\n# digitos(n) es la lista de los d\u00edgitos del n\u00famero n. Por ejemplo,\n#    digitos(320274)  ==  [3, 2, 0, 2, 7, 4]\ndef digitos(n: int) -> list[int]:\n    return list(map(int, list(str(n))))\n\ndef sumaDigitos1(n: int) -> int:\n    return sum(digitos(n))\n\n# Nota. En lugar de la definici\u00f3n anterior de digitos se puede usar\n# cualquiera del ejercicio \"D\u00edgitos de un n\u00famero\" https:\/\/bit.ly\/3Tkhc2T\n\n# 2\u00aa soluci\u00f3n\n# ===========\n\ndef sumaDigitos2(n: int) -> int:\n    return reduce(add, digitos(n))\n\n# 3\u00aa soluci\u00f3n\n# ===========\n\ndef sumaDigitos3(n: int) -> int:\n    if n < 10:\n        return n\n    return n % 10 + sumaDigitos3(n \/\/ 10)\n\n# 4\u00aa soluci\u00f3n\n# ===========\n\ndef sumaDigitos4(n: int) -> int:\n    def aux(r: int, m: int) -> int:\n        if m < 10:\n            return r + m\n        return aux(r + m % 10, m \/\/ 10)\n    return aux(0, n)\n\n# 5\u00aa soluci\u00f3n\n# ===========\n\ndef sumaDigitos5(n: int) -> int:\n    r = 0\n    for x in digitos(n):\n        r = r + x\n    return r\n\n# Comprobaci\u00f3n de equivalencia\n# ============================\n\n# La propiedad es\n@given(st.integers(min_value=0, max_value=1000))\ndef test_sumaDigitos(n: int) -> None:\n    r = sumaDigitos1(n)\n    assert sumaDigitos2(n) == r\n    assert sumaDigitos3(n) == r\n    assert sumaDigitos4(n) == r\n    assert sumaDigitos5(n) == r\n\n# La comprobaci\u00f3n es\n#    src> poetry run pytest -q suma_de_los_digitos_de_un_numero.py\n#    1 passed in 0.35s\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('sumaDigitos1(factorial(6*10**3))')\n#    0.01 segundos\n#    >>> tiempo('sumaDigitos2(factorial(6*10**3))')\n#    0.01 segundos\n#    >>> tiempo('sumaDigitos3(factorial(6*10**3))')\n#    0.13 segundos\n#    >>> tiempo('sumaDigitos4(factorial(6*10**3))')\n#    0.13 segundos\n#    >>> tiempo('sumaDigitos5(factorial(6*10**3))')\n#    0.01 segundos\n#\n#    >>> tiempo('sumaDigitos1(factorial(10**5))')\n#    2.20 segundos\n#    >>> tiempo('sumaDigitos2(factorial(10**5))')\n#    2.22 segundos\n#    >>> tiempo('sumaDigitos5(factorial(10**5))')\n#    2.19 segundos\n<\/pre>\n
El c\u00f3digo se encuentra en GitHub<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"
Definir la funci\u00f3n sumaDigitos :: Integer -> Integer tal que sumaDigitos n es la suma de los d\u00edgitos de n. Por ejemplo, sumaDigitos 3 == 3 sumaDigitos 2454 == 15 sumaDigitos 20045 == 11 Soluciones A continuaci\u00f3n se muestran las soluciones en Haskell y las soluciones en Python. Soluciones en Haskell import Data.List (foldl’) import…<\/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\/7482"}],"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=7482"}],"version-history":[{"count":2,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/7482\/revisions"}],"predecessor-version":[{"id":7660,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/7482\/revisions\/7660"}],"wp:attachment":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/media?parent=7482"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/categories?post=7482"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/tags?post=7482"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}