{"id":7458,"date":"2022-10-25T06:00:42","date_gmt":"2022-10-25T04:00:42","guid":{"rendered":"http:\/\/www.glc.us.es\/~jalonso\/exercitium\/?p=7458"},"modified":"2022-12-14T12:25:13","modified_gmt":"2022-12-14T10:25:13","slug":"potencia-entera","status":"publish","type":"post","link":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/potencia-entera\/","title":{"rendered":"Potencia entera"},"content":{"rendered":"

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

\n   potencia :: Integer -> Integer -> Integer\n<\/pre>\n
tal que potencia x n<\/code> es x<\/code> elevado al n\u00famero natural n<\/code>. Por ejemplo,<\/p>\n
\n   potencia 2 3  ==  8\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 Control.Arrow ((***))\nimport Test.QuickCheck\n\n-- 1\u00aa soluci\u00f3n\n-- ===========\n\npotencia1 :: Integer -> Integer -> Integer\npotencia1 _ 0 = 1\npotencia1 m n = m * potencia1 m (n-1)\n\n-- 2\u00aa soluci\u00f3n\n-- ===========\n\npotencia2 :: Integer -> Integer -> Integer\npotencia2 m = aux\n  where aux 0 = 1\n        aux n = m * aux (n-1)\n\n-- 3\u00aa soluci\u00f3n\n-- ===========\n\npotencia3 :: Integer -> Integer -> Integer\npotencia3 m = aux 1\n  where aux r 0 = r\n        aux r n = aux (r*m) (n-1)\n\n-- 4\u00aa soluci\u00f3n\n-- ===========\n\npotencia4 :: Integer -> Integer -> Integer\npotencia4 m = aux 1\n  where aux r 0 = r\n        aux r n = (aux $! (r*m)) $! (n-1)\n\n-- 5\u00aa soluci\u00f3n\n-- ===========\n\npotencia5 :: Integer -> Integer -> Integer\npotencia5 m n = product [m | _ <- [1..n]]\n\n-- 6\u00aa soluci\u00f3n\n-- ===========\n\npotencia6 :: Integer -> Integer -> Integer\npotencia6 m n = foldl' (*) 1 [m | _ <- [1..n]]\n\n-- 7\u00aa soluci\u00f3n\n-- ===========\n\npotencia7 :: Integer -> Integer -> Integer\npotencia7 m n =\n  fst (until (\\ (_,k) -> k == n)\n             (\\ (r,k) -> (r*m, k+1))\n             (1,0))\n\n-- 8\u00aa soluci\u00f3n\n-- ===========\n\npotencia8 :: Integer -> Integer -> Integer\npotencia8 m n =\n  fst (until ((== n) . snd)\n             ((m *) *** (1 +))\n             (1,0))\n\n-- 9\u00aa soluci\u00f3n\n-- ===========\n\npotencia9 :: Integer -> Integer -> Integer\npotencia9 m n = m^n\n\n-- Comprobaci\u00f3n de equivalencia\n-- ============================\n\n-- La propiedad es\nprop_potencia :: Integer -> NonNegative Integer -> Bool\nprop_potencia m (NonNegative n) =\n  all (== potencia1 m n)\n      [potencia2 m n,\n       potencia3 m n,\n       potencia4 m n,\n       potencia5 m n,\n       potencia6 m n,\n       potencia7 m n,\n       potencia8 m n,\n       potencia9 m n]\n\n-- La comprobaci\u00f3n es\n--    \u03bb> quickCheck prop_potencia\n--    +++ OK, passed 100 tests.\n\n-- Comparaci\u00f3n de eficiencia\n-- =========================\n\n-- La comparaci\u00f3n es\n--    \u03bb> length (show (potencia1 2 (2*10^5)))\n--    60206\n--    (2.97 secs, 2,602,252,408 bytes)\n--    \u03bb> length (show (potencia2 2 (2*10^5)))\n--    60206\n--    (2.63 secs, 2,624,652,624 bytes)\n--    \u03bb> length (show (potencia3 2 (2*10^5)))\n--    60206\n--    (3.41 secs, 2,619,606,368 bytes)\n--    \u03bb> length (show (potencia4 2 (2*10^5)))\n--    60206\n--    (0.64 secs, 2,636,888,928 bytes)\n--    \u03bb> length (show (potencia5 2 (2*10^5)))\n--    60206\n--    (2.47 secs, 2,597,108,000 bytes)\n--    \u03bb> length (show (potencia6 2 (2*10^5)))\n--    60206\n--    (0.35 secs, 2,582,488,824 bytes)\n--    \u03bb> length (show (potencia7 2 (2*10^5)))\n--    60206\n--    (2.48 secs, 2,616,406,272 bytes)\n--    \u03bb> length (show (potencia8 2 (2*10^5)))\n--    60206\n--    (2.40 secs, 2,608,652,736 bytes)\n--    \u03bb> length (show (potencia9 2 (2*10^5)))\n--    60206\n--    (0.01 secs, 4,212,968 bytes)\n--\n--    \u03bb> length (show (potencia4 2 (10^6)))\n--    301030\n--    (10.39 secs, 63,963,999,656 bytes)\n--    \u03bb> length (show (potencia6 2 (10^6)))\n--    301030\n--    (8.90 secs, 63,691,999,552 bytes)\n--    \u03bb> length (show (potencia9 2 (10^6)))\n--    301030\n--    (0.04 secs, 19,362,032 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 operator import mul\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 potencia1(m: int, n: int) -> int:\n    if n == 0:\n        return 1\n    return m * potencia1(m, n-1)\n\n# 2\u00aa soluci\u00f3n\n# ===========\n\ndef potencia2(m: int, n: int) -> int:\n    def aux(k: int) -> int:\n        if k == 0:\n            return 1\n        return m * aux(k-1)\n    return aux(n)\n\n# 3\u00aa soluci\u00f3n\n# ===========\n\ndef potencia3(m: int, n: int) -> int:\n    def aux(r: int, k: int) -> int:\n        if k == 0:\n            return r\n        return aux(r*m, k-1)\n    return aux(1, n)\n\n# 4\u00aa soluci\u00f3n\n# ===========\n\n# producto(xs) es el producto de los elementos de xs. Por ejemplo,\n#    producto([2, 3, 5])  ==  30\ndef producto(xs: list[int]) -> int:\n    return reduce(mul, xs, 1)\n\ndef potencia4(m: int, n: int) -> int:\n    return producto([m]*n)\n\n# 5\u00aa soluci\u00f3n\n# ===========\n\ndef potencia5(m: int, n: int) -> int:\n    r = 1\n    for _ in range(0, n):\n        r = r * m\n    return r\n\n# 6\u00aa soluci\u00f3n\n# ===========\n\ndef potencia6(m: int, n: int) -> int:\n    return m**n\n\n# Comprobaci\u00f3n de equivalencia\n# ============================\n\n# La propiedad es\n@given(st.integers(),\n       st.integers(min_value=0, max_value=100))\ndef test_potencia(m: int, n: int) -> None:\n    r = potencia1(m, n)\n    assert potencia2(m, n) == r\n    assert potencia3(m, n) == r\n    assert potencia4(m, n) == r\n    assert potencia5(m, n) == r\n    assert potencia6(m, n) == r\n\n# La comprobaci\u00f3n es\n#    src> poetry run pytest -q potencia_entera.py\n#    1 passed in 0.17s\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('potencia1(2, 2*10**4)')\n#    0.01 segundos\n#    >>> tiempo('potencia2(2, 2*10**4)')\n#    0.01 segundos\n#    >>> tiempo('potencia3(2, 2*10**4)')\n#    0.02 segundos\n#    >>> tiempo('potencia4(2, 2*10**4)')\n#    0.01 segundos\n#    >>> tiempo('potencia5(2, 2*10**4)')\n#    0.01 segundos\n#    >>> tiempo('potencia6(2, 2*10**4)')\n#    0.00 segundos\n#\n#    >>> tiempo('potencia4(2, 5*10**5)')\n#    2.87 segundos\n#    >>> tiempo('potencia5(2, 5*10**5)')\n#    3.17 segundos\n#    >>> tiempo('potencia6(2, 5*10**5)')\n#    0.00 segundos\n<\/pre>\n
El c\u00f3digo se encuentra en GitHub<\/a>.<\/p>\n","protected":false},"excerpt":{"rendered":"
Definir la funci\u00f3n potencia :: Integer -> Integer -> Integer tal que potencia x n es x elevado al n\u00famero natural n. Por ejemplo, potencia 2 3 == 8 Soluciones A continuaci\u00f3n se muestran las soluciones en Haskell y las soluciones en Python. Soluciones en Haskell import Data.List (foldl’) import Control.Arrow ((***)) import Test.QuickCheck –…<\/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\/7458"}],"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=7458"}],"version-history":[{"count":3,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/7458\/revisions"}],"predecessor-version":[{"id":7663,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/7458\/revisions\/7663"}],"wp:attachment":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/media?parent=7458"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/categories?post=7458"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/tags?post=7458"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}