{"id":8504,"date":"2024-02-29T06:00:10","date_gmt":"2024-02-29T04:00:10","guid":{"rendered":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/?p=8504"},"modified":"2024-02-28T14:22:55","modified_gmt":"2024-02-28T12:22:55","slug":"29-feb-24","status":"publish","type":"post","link":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/29-feb-24\/","title":{"rendered":"Suma fila del tri\u00e1ngulo de los impares"},"content":{"rendered":"<p>Se condidera el siguiente tri\u00e1ngulo de n\u00fameros impares<\/p>\n<pre lang=\"text\">\n             1\n          3     5\n       7     9    11\n   13    15    17    19\n21    23    25    27    29\n...\n<\/pre>\n<p>Definir la funci\u00f3n<\/p>\n<pre lang=\"haskell\">\n   sumaFilaTrianguloImpares :: Integer -> Integer\n<\/pre>\n<p>tal que (sumaFilaTrianguloImpares n) es la suma de la n-\u00e9sima fila del tri\u00e1ngulo de los n\u00fameros impares. Por ejemplo,<\/p>\n<pre lang=\"haskell\">\n   sumaFilaTrianguloImpares 1  ==  1\n   sumaFilaTrianguloImpares 2  ==  8\n   length (show (sumaFilaTrianguloImpares (10^500)))    ==  1501\n   length (show (sumaFilaTrianguloImpares (10^5000)))   ==  15001\n   length (show (sumaFilaTrianguloImpares (10^50000)))  ==  150001\n<\/pre>\n<p><!--more--><\/p>\n<p><a name=\"haskell\"><\/a><\/p>\n<h2>1. Soluciones en Haskell<\/h2>\n<pre lang=\"haskell\">\nmodule Suma_de_fila_del_triangulo_de_los_impares where\n\nimport Test.Hspec (Spec, describe, hspec, it, shouldBe)\nimport Test.QuickCheck\n\n-- 1\u00aa soluci\u00f3n\nsumaFilaTrianguloImpares1 :: Integer -> Integer\nsumaFilaTrianguloImpares1 n =\n  sum [n^2-n+1, n^2-n+3 .. n^2+n-1]\n\n-- 2\u00aa soluci\u00f3n\nsumaFilaTrianguloImpares2 :: Integer -> Integer\nsumaFilaTrianguloImpares2 = (^3)\n\n-- Verificaci\u00f3n\n-- ============\n\nverifica :: IO ()\nverifica = hspec spec\n\nspecG :: (Integer -> Integer) -> Spec\nspecG sumaFilaTrianguloImpares = do\n  it \"e1\" $\n    sumaFilaTrianguloImpares 1  `shouldBe`  1\n  it \"e2\" $\n    sumaFilaTrianguloImpares 2  `shouldBe`  8\n\nspec :: Spec\nspec = do\n  describe \"def. 1\" $ specG sumaFilaTrianguloImpares1\n  describe \"def. 2\" $ specG sumaFilaTrianguloImpares2\n\n-- La verificaci\u00f3n es\n--    \u03bb> verifica\n--\n--    4 examples, 0 failures\n\n-- Equivalencia de las definiciones\n-- ================================\n\n-- La propiedad es\nprop_sumaFilaTrianguloImpares :: Positive Integer -> Bool\nprop_sumaFilaTrianguloImpares (Positive n) =\n  sumaFilaTrianguloImpares1 n == sumaFilaTrianguloImpares2 n\n\n-- La comprobaci\u00f3n es\n--    \u03bb> quickCheck prop_sumaFilaTrianguloImpares\n--    +++ OK, passed 100 tests.\n\n-- Comparaci\u00f3n de eficiencia\n-- =========================\n\n-- La comparaci\u00f3n es\n--    \u03bb> length (show (sumaFilaTrianguloImpares1 (10^7)))\n--    22\n--    (2.91 secs, 2,167,239,232 bytes)\n--    \u03bb> length (show (sumaFilaTrianguloImpares2 (10^7)))\n--    22\n--    (0.01 secs, 102,584 bytes)\n<\/pre>\n<p><a name=\"python\"><\/a><\/p>\n<h2>2. Soluciones en Python<\/h2>\n<pre lang=\"python\">\nfrom sys import set_int_max_str_digits\nfrom timeit import Timer, default_timer\n\nfrom hypothesis import given\nfrom hypothesis import strategies as st\n\nset_int_max_str_digits(10**6)\n\n# 1\u00aa soluci\u00f3n\n# ===========\n\ndef sumaFilaTrianguloImpares1(n: int) -> int:\n    return sum(range(n**2-n+1, n**2+n, 2))\n\n# 2\u00aa soluci\u00f3n\n# ===========\n\ndef sumaFilaTrianguloImpares2(n: int) -> int:\n    return n**3\n\n# Verificaci\u00f3n\n# ============\n\ndef test_sumaFilaTrianguloImpares() -> None:\n    for sumaFilaTrianguloImpares in [sumaFilaTrianguloImpares1,\n                                     sumaFilaTrianguloImpares2]:\n        assert sumaFilaTrianguloImpares(1) == 1\n        assert sumaFilaTrianguloImpares(2) == 8\n    print(\"Verificado\")\n\n# La verificaci\u00f3n es\n#    >>> test_sumaFilaTrianguloImpares()\n#    Verificado\n\n# Equivalencia de las definiciones\n# ================================\n\n# La propiedad es\n@given(st.integers(min_value=1, max_value=1000))\ndef test_sumaFilaTrianguloImpares_equiv(n: int) -> None:\n    assert sumaFilaTrianguloImpares1(n) == sumaFilaTrianguloImpares2(n)\n\n# La comprobaci\u00f3n es\n#    >>> test_sumaFilaTrianguloImpares_equiv()\n#    >>>\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('len(str(sumaFilaTrianguloImpares1(6*10**7)))')\n#    2.04 segundos\n#    >>> tiempo('len(str(sumaFilaTrianguloImpares2(6*10**7)))')\n#    0.00 segundos\n<\/pre>\n","protected":false},"excerpt":{"rendered":"<p>Se condidera el siguiente tri\u00e1ngulo de n\u00fameros impares 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 &#8230; Definir la funci\u00f3n sumaFilaTrianguloImpares :: Integer -> Integer tal que (sumaFilaTrianguloImpares n) es la suma de la n-\u00e9sima fila del tri\u00e1ngulo de los n\u00fameros impares. Por ejemplo, sumaFilaTrianguloImpares 1 == 1&#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":"default","_kad_post_title":"default","_kad_post_layout":"default","_kad_post_sidebar_id":"","_kad_post_content_style":"default","_kad_post_vertical_padding":"default","_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\/8504"}],"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=8504"}],"version-history":[{"count":3,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/8504\/revisions"}],"predecessor-version":[{"id":8508,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/8504\/revisions\/8508"}],"wp:attachment":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/media?parent=8504"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/categories?post=8504"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/tags?post=8504"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}