{"id":7396,"date":"2022-09-27T06:00:14","date_gmt":"2022-09-27T04:00:14","guid":{"rendered":"http:\/\/www.glc.us.es\/~jalonso\/exercitium\/?p=7396"},"modified":"2022-12-14T14:22:04","modified_gmt":"2022-12-14T12:22:04","slug":"suma-de-los-primeros-numeros-naturales","status":"publish","type":"post","link":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/suma-de-los-primeros-numeros-naturales\/","title":{"rendered":"Suma de los primeros n\u00fameros naturales"},"content":{"rendered":"<p>Definir la funci\u00f3n<\/p>\n<pre lang=\"text\">\n   suma :: Integer -> Integer\n<\/pre>\n<p>tal <code>suma n<\/code> es la suma de los <code>n<\/code> primeros n\u00fameros. Por ejemplo,<\/p>\n<pre lang=\"text\">\n   suma 3  ==  6\n   length (show (suma (10^100)))  ==  200\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 Test.QuickCheck\n\n-- 1\u00aa soluci\u00f3n\n-- ===========\n\nsuma1 :: Integer -> Integer\nsuma1 n = sum [1..n]\n\n-- 2\u00aa soluci\u00f3n\n-- ===========\n\nsuma2 :: Integer -> Integer\nsuma2 n = (1+n)*n `div` 2\n\n-- 3\u00aa soluci\u00f3n\n-- ===========\n\nsuma3 :: Integer -> Integer\nsuma3 1 = 1\nsuma3 n = n + suma3 (n-1)\n\n-- 4\u00aa soluci\u00f3n\n-- ===========\n\nsuma4 :: Integer -> Integer\nsuma4 n = foldl (+) 0 [0..n]\n\n-- 5\u00aa soluci\u00f3n\n-- ===========\n\nsuma5 :: Integer -> Integer\nsuma5 n = foldl' (+) 0 [0..n]\n\n-- Comprobaci\u00f3n de equivalencia\n-- ============================\n\n-- La propiedad es\nprop_suma :: Positive Integer -> Bool\nprop_suma (Positive n) =\n  all (== suma1 n)\n      [suma2 n,\n       suma3 n,\n       suma4 n,\n       suma5 n]\n\n-- La comprobaci\u00f3n es\n--    \u03bb> quickCheck prop_suma\n--    +++ OK, passed 100 tests.\n\n-- Comparaci\u00f3n de eficiencia\n-- =========================\n\n-- La comparaci\u00f3n es\n--    \u03bb> suma1 (5*10^6)\n--    12500002500000\n--    (1.23 secs, 806,692,792 bytes)\n--    \u03bb> suma2 (5*10^6)\n--    12500002500000\n--    (0.02 secs, 559,064 bytes)\n--    \u03bb> suma3 (5*10^6)\n--    12500002500000\n--    (3.06 secs, 1,214,684,352 bytes)\n--    \u03bb> suma4 (5*10^6)\n--    12500002500000\n--    (1.25 secs, 806,692,848 bytes)\n--    \u03bb> suma5 (5*10^6)\n--    12500002500000\n--    (0.26 secs, 440,559,048 bytes)\n<\/pre>\n<p>El c\u00f3digo se encuentra en <a href=\"https:\/\/github.com\/jaalonso\/Exercitium\/blob\/main\/src\/Suma_de_los_primeros_numeros_naturales.hs\">GitHub<\/a>.<\/p>\n<p><a name=\"python\"><\/a><br \/>\n<b>Soluciones en Python<\/b><\/p>\n<pre lang=\"python\">\nfrom operator import add\nfrom functools import reduce\nfrom sys import setrecursionlimit\nfrom timeit import Timer, default_timer\nfrom hypothesis import given, strategies as st\nsetrecursionlimit(10**8)\n\n# 1\u00aa soluci\u00f3n\n# ===========\n\ndef suma1(n: int) -> int:\n    return sum(range(1, n + 1))\n\n# 2\u00aa soluci\u00f3n\n# ===========\n\ndef suma2(n: int) -> int:\n    return (1 + n) * n \/\/ 2\n\n# 3\u00aa soluci\u00f3n\n# ===========\n\ndef suma3(n: int) -> int:\n    if n == 1:\n        return 1\n    return n + suma3(n - 1)\n\n# 4\u00aa soluci\u00f3n\n# ===========\n\ndef suma4(n: int) -> int:\n    return reduce(add, range(1, n + 1))\n\n# 5\u00aa soluci\u00f3n\n# ===========\n\ndef suma5(n: int) -> int:\n    x, r = 1, 0\n    while x <= n:\n        r = r + x\n        x = x + 1\n    return r\n\n# 6\u00aa soluci\u00f3n\n# ===========\n\ndef suma6(n: int) -> int:\n    r = 0\n    for x in range(1, n + 1):\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=1, max_value=1000))\ndef test_suma(n):\n    r = suma1(n)\n    assert suma2(n) == r\n    assert suma3(n) == r\n    assert suma4(n) == r\n    assert suma5(n) == r\n    assert suma6(n) == r\n\n# La comprobaci\u00f3n es\n#    src> poetry run pytest -q suma_de_los_primeros_numeros_naturales.py\n#    1 passed in 0.16s\n\n# Comparaci\u00f3n de eficiencia\n# =========================\n\ndef tiempo(e):\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('suma3(20000)')\n#    0.04 segundos\n#    >>> tiempo('suma1(20000)')\n#    0.00 segundos\n#    >>> tiempo('suma2(20000)')\n#    0.00 segundos\n#    >>> tiempo('suma3(20000)')\n#    0.02 segundos\n#    >>> tiempo('suma4(20000)')\n#    0.00 segundos\n#    >>> tiempo('suma5(20000)')\n#    0.01 segundos\n#    >>> tiempo('suma6(20000)')\n#    0.00 segundos\n#\n#    >>> tiempo('suma1(10**8)')\n#    1.55 segundos\n#    >>> tiempo('suma2(10**8)')\n#    0.00 segundos\n#    >>> tiempo('suma4(10**8)')\n#    3.69 segundos\n#    >>> tiempo('suma5(10**8)')\n#    7.04 segundos\n#    >>> tiempo('suma6(10**8)')\n#    4.23 segundos\n<\/pre>\n<p>El c\u00f3digo se encuentra en <a href=\"https:\/\/github.com\/jaalonso\/Exercitium-Python\/blob\/main\/src\/suma_de_los_primeros_numeros_naturales.py\">GitHub<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Definir la funci\u00f3n suma :: Integer -> Integer tal suma n es la suma de los n primeros n\u00fameros. Por ejemplo, suma 3 == 6 length (show (suma (10^100))) == 200 Soluciones A continuaci\u00f3n se muestran las soluciones en Haskell y las soluciones en Python. Soluciones en Haskell import Data.List (foldl&#8217;) import Test.QuickCheck &#8212; 1\u00aa&#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\/7396"}],"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=7396"}],"version-history":[{"count":2,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/7396\/revisions"}],"predecessor-version":[{"id":7683,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/7396\/revisions\/7683"}],"wp:attachment":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/media?parent=7396"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/categories?post=7396"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/tags?post=7396"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}