{"id":8529,"date":"2024-03-29T06:00:18","date_gmt":"2024-03-29T04:00:18","guid":{"rendered":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/?p=8529"},"modified":"2024-04-02T14:13:27","modified_gmt":"2024-04-02T12:13:27","slug":"29-mar-24","status":"publish","type":"post","link":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/29-mar-24\/","title":{"rendered":"M\u00e1ximos locales"},"content":{"rendered":"<p>Un m\u00e1ximo local de una lista es un elemento de la lista que es mayor que su predecesor y que su sucesor en la lista. Por ejemplo, 5 es un m\u00e1ximo local de [3,2,5,3,7,7,1,6,2] ya que es mayor que 2 (su predecesor) y que 3 (su sucesor).<\/p>\n<p>Definir la funci\u00f3n<\/p>\n<pre lang=\"haskell\">\n   maximosLocales :: Ord a => [a] -> [a]\n<\/pre>\n<p>tal que (maximosLocales xs) es la lista de los m\u00e1ximos locales de la lista xs. Por ejemplo,<\/p>\n<pre lang=\"haskell\">\n   maximosLocales [3,2,5,3,7,7,1,6,2]  ==  [5,6]\n   maximosLocales [1..100]             ==  []\n   maximosLocales \"adbpmqexyz\"         ==  \"dpq\"\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 Maximos_locales where\n\nimport Test.Hspec (Spec, describe, hspec, it, shouldBe)\nimport Test.QuickCheck\n\n-- 1\u00aa soluci\u00f3n\n-- ===========\n\nmaximosLocales1 :: Ord a => [a] -> [a]\nmaximosLocales1 (x:y:z:xs)\n  | y > x && y > z = y : maximosLocales1 (z:xs)\n  | otherwise      = maximosLocales1 (y:z:xs)\nmaximosLocales1 _ = []\n\n-- 2\u00aa soluci\u00f3n\n-- ===========\n\nmaximosLocales2 :: Ord a => [a] -> [a]\nmaximosLocales2 xs =\n  [y | (x,y,z) <- zip3 xs (tail xs) (drop 2 xs), y > x, y > z]\n\n-- Verificaci\u00f3n\n-- ============\n\nverifica :: IO ()\nverifica = hspec spec\n\nspecG :: ([Int] -> [Int]) -> Spec\nspecG maximosLocales = do\n  it \"e1\" $\n    maximosLocales [3,2,5,3,7,7,1,6,2]  `shouldBe`  [5,6]\n  it \"e2\" $\n    maximosLocales [1..100]             `shouldBe`  []\n\nspec :: Spec\nspec = do\n  describe \"def. 1\" $ specG maximosLocales1\n  describe \"def. 2\" $ specG maximosLocales2\n\n-- La verificaci\u00f3n es\n--    \u03bb> verifica\n--\n--    4 examples, 0 failures\n\n\n-- Comprobaci\u00f3n de equivalencia\n-- ============================\n\n-- La propiedad es\nprop_maximosLocales :: [Int] -> Property\nprop_maximosLocales xs =\n  maximosLocales1 xs === maximosLocales2 xs\n\n-- La comprobaci\u00f3n es\n--    \u03bb> quickCheck prop_maximosLocales\n--    +++ OK, passed 100 tests.\n\n-- Comparaci\u00f3n de eficiencia\n-- =========================\n\n-- La comparaci\u00f3n es\n--    \u03bb> last (maximosLocales1 (take (6*10^6) (cycle \"abc\")))\n--    'c'\n--    (3.26 secs, 1,904,464,984 bytes)\n--    \u03bb> last (maximosLocales2 (take (6*10^6) (cycle \"abc\")))\n--    'c'\n--    (2.79 secs, 1,616,465,088 bytes)\n<\/pre>\n<p><a name=\"python\"><\/a><\/p>\n<h2>2. Soluciones en Python<\/h2>\n<pre lang=\"python\">\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 maximosLocales1(xs: list[int]) -> list[int]:\n    if len(xs) < 3:\n        return []\n    x, y, z, *ys = xs\n    if y > x and y > z:\n        return [y] + maximosLocales1([z] + ys)\n    return maximosLocales1([y, z] + ys)\n\n# 2\u00aa soluci\u00f3n\n# ===========\n\ndef maximosLocales2(xs: list[int]) -> list[int]:\n    ys: list[int] = []\n    if len(xs) < 3:\n        return ys\n    for i in range(1, len(xs) - 1):\n        if xs[i] > xs[i - 1] and xs[i] > xs[i + 1]:\n            ys.append(xs[i])\n    return ys\n\n# 3\u00aa soluci\u00f3n\n# ===========\n\ndef maximosLocales3(xs: list[int]) -> list[int]:\n    return [y for x, y, z in zip(xs, xs[1:], xs[2:]) if y > x and y > z]\n\n# Verificaci\u00f3n\n# ============\n\ndef test_maximosLocales() -> None:\n    for maximosLocales in [maximosLocales1,\n                           maximosLocales2,\n                           maximosLocales3]:\n        assert maximosLocales([3,2,5,3,7,7,1,6,2]) == [5,6]\n        assert maximosLocales(list(range(0, 100))) == []\n    print(\"Verificado\")\n\n# La verificaci\u00f3n es\n#    >>> test_maximosLocales()\n#    Verificado\n\n# Comprobaci\u00f3n de equivalencia\n# ============================\n\n# La propiedad es\n@given(st.lists(st.integers()))\ndef test_maximosLocales_equiv(xs: list[int]) -> None:\n    r = maximosLocales1(xs)\n    assert maximosLocales2(xs) == r\n    assert maximosLocales3(xs) == r\n\n# La comprobaci\u00f3n es\n#    >>> test_maximosLocales_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('maximosLocales1([1,2,3]*(10**4))')\n#    3.19 segundos\n#    >>> tiempo('maximosLocales2([1,2,3]*(10**4))')\n#    0.01 segundos\n#    >>> tiempo('maximosLocales3([1,2,3]*(10**4))')\n#    0.01 segundos\n#\n#    >>> tiempo('maximosLocales2([1,2,3]*(10**7))')\n#    3.95 segundos\n#    >>> tiempo('maximosLocales3([1,2,3]*(10**7))')\n#    1.85 segundos\n<\/pre>\n","protected":false},"excerpt":{"rendered":"<p>Un m\u00e1ximo local de una lista es un elemento de la lista que es mayor que su predecesor y que su sucesor en la lista. Por ejemplo, 5 es un m\u00e1ximo local de [3,2,5,3,7,7,1,6,2] ya que es mayor que 2 (su predecesor) y que 3 (su sucesor). Definir la funci\u00f3n maximosLocales :: Ord a =>&#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\/8529"}],"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=8529"}],"version-history":[{"count":1,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/8529\/revisions"}],"predecessor-version":[{"id":8530,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/8529\/revisions\/8530"}],"wp:attachment":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/media?parent=8529"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/categories?post=8529"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/tags?post=8529"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}