{"id":7560,"date":"2022-12-08T06:00:42","date_gmt":"2022-12-08T04:00:42","guid":{"rendered":"http:\/\/www.glc.us.es\/~jalonso\/exercitium\/?p=7560"},"modified":"2022-12-14T10:17:33","modified_gmt":"2022-12-14T08:17:33","slug":"08-dic-22","status":"publish","type":"post","link":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/08-dic-22\/","title":{"rendered":"\u00c1rboles con la misma forma"},"content":{"rendered":"<p>El \u00e1rbol binario<\/p>\n<pre lang=\"text\">\n        \u00b7\n       \/ \\\n      \/   \\\n     \u00b7     \u00b7\n    \/ \\   \/ \\\n   1   4 6   9\n<\/pre>\n<p>se puede representar por<\/p>\n<pre lang=\"text\">\n   ejArbol = Nodo (Nodo (Hoja 1) (Hoja 4))\n                  (Nodo (Hoja 6) (Hoja 9))\n<\/pre>\n<p>El tipo de los \u00e1rboles binarios se puede definir por<\/p>\n<pre lang=\"text\">\n   data Arbol a = Hoja a\n                | Nodo (Arbol a) (Arbol a)\n     deriving (Show, Eq)\n<\/pre>\n<p>Definir la funci\u00f3n<\/p>\n<pre lang=\"text\">\n   mismaForma :: Arbol a -> Arbol b -> Bool\n<\/pre>\n<p>tal que <code>mismaForma t1 t2<\/code> se verifica si <code>t1<\/code> y <code>t2<\/code> tienen la misma estructura. Por ejemplo,<\/p>\n<pre lang=\"text\">\n   \u03bb> arbol1 = Hoja 5\n   \u03bb> arbol2 = Hoja 3\n   \u03bb> mismaForma arbol1 arbol2\n   True\n   \u03bb> arbol3 = Nodo (Hoja 6) (Hoja 7)\n   \u03bb> mismaForma arbol1 arbol3\n   False\n   \u03bb> arbol4 = Nodo (Hoja 9) (Hoja 5)\n   \u03bb> mismaForma arbol3 arbol4\n   True\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 Test.QuickCheck\n\ndata Arbol a = Hoja a\n             | Nodo (Arbol a) (Arbol a)\n  deriving (Show, Eq)\n\n-- 1\u00aa soluci\u00f3n\n-- ===========\n\nmismaForma1 :: Arbol a -> Arbol b -> Bool\nmismaForma1 (Hoja _)   (Hoja _)     = True\nmismaForma1 (Nodo l r) (Nodo l' r') = mismaForma1 l l' && mismaForma1 r r'\nmismaForma1 _          _            = False\n\n-- 2\u00aa soluci\u00f3n\n-- ===========\n\nmismaForma2 :: Arbol a -> Arbol b -> Bool\nmismaForma2 x y = f x == f y\n  where\n    f = mapArbol (const ())\n\n-- (mapArbol f t) es el \u00e1rbol obtenido aplicando la funci\u00f3n f a los\n-- elementos del \u00e1rbol t. Por ejemplo,\n--    \u03bb> mapArbol (+ 1) (Nodo (Hoja 2) (Hoja 4))\n--    Nodo (Hoja 3) (Hoja 5)\nmapArbol :: (a -> b) -> Arbol a -> Arbol b\nmapArbol f (Hoja a)   = Hoja (f a)\nmapArbol f (Nodo i d) = Nodo (mapArbol f i) (mapArbol f d)\n\n-- Comprobaci\u00f3n de equivalencia\n-- ============================\n\n-- (arbolArbitrario n) es un \u00e1rbol aleatorio de altura n. Por ejemplo,\n--    \u03bb> sample (arbolArbitrario 3 :: Gen (Arbol Int))\n--    Nodo (Nodo (Nodo (Hoja 0) (Hoja 0)) (Hoja 0)) (Hoja 0)\n--    Nodo (Nodo (Hoja 4) (Hoja 8)) (Hoja (-4))\n--    Nodo (Nodo (Nodo (Hoja 4) (Hoja 10)) (Hoja (-6))) (Hoja (-1))\n--    Nodo (Nodo (Hoja 3) (Hoja 6)) (Hoja (-5))\n--    Nodo (Nodo (Hoja (-11)) (Hoja (-13))) (Hoja 14)\n--    Nodo (Nodo (Hoja (-7)) (Hoja 15)) (Hoja (-2))\n--    Nodo (Nodo (Hoja (-9)) (Hoja (-2))) (Hoja (-6))\n--    Nodo (Nodo (Hoja (-15)) (Hoja (-16))) (Hoja (-20))\narbolArbitrario :: Arbitrary a => Int -> Gen (Arbol a)\narbolArbitrario n\n  | n <= 1    = Hoja <$> arbitrary\n  | otherwise = do\n      k <- choose (2, n - 1)\n      Nodo <$> arbolArbitrario k <*> arbolArbitrario (n - k)\n\n-- Arbol es subclase de Arbitraria\ninstance Arbitrary a => Arbitrary (Arbol a) where\n  arbitrary = sized arbolArbitrario\n  shrink (Hoja x)   = Hoja <$> shrink x\n  shrink (Nodo l r) = l :\n                      r :\n                      [Nodo l' r | l' <- shrink l] ++\n                      [Nodo l r' | r' <- shrink r]\n\n-- La propiedad es\nprop_mismaForma :: Arbol Int -> Arbol Int -> Property\nprop_mismaForma a1 a2 =\n  mismaForma1 a1 a2 === mismaForma2 a1 a2\n\n-- La comprobaci\u00f3n es\n--    \u03bb> quickCheck prop_mismaForma\n--    +++ OK, passed 100 tests.\n<\/pre>\n<p><a name=\"python\"><\/a><br \/>\n<b>Soluciones en Python<\/b><\/p>\n<pre lang=\"python\">\nfrom dataclasses import dataclass\nfrom random import randint\nfrom typing import Callable, Generic, TypeVar\n\nfrom hypothesis import given\nfrom hypothesis import strategies as st\n\nA = TypeVar(\"A\")\nB = TypeVar(\"B\")\n\n@dataclass\nclass Arbol(Generic[A]):\n    pass\n\n@dataclass\nclass Hoja(Arbol[A]):\n    x: A\n\n@dataclass\nclass Nodo(Arbol[A]):\n    i: Arbol[A]\n    d: Arbol[A]\n\n# -- 1\u00aa soluci\u00f3n\n# -- ===========\n\ndef mismaForma1(a: Arbol[A], b: Arbol[B]) -> bool:\n    match (a, b):\n        case (Hoja(_), Hoja(_)):\n            return True\n        case (Nodo(i1, d1), Nodo(i2, d2)):\n            return mismaForma1(i1, i2) and mismaForma1(d1, d2)\n        case (_, _):\n            return False\n    assert False\n\n# -- 2\u00aa soluci\u00f3n\n# -- ===========\n\n# mapArbol(f, t) es el \u00e1rbolo obtenido aplicando la funci\u00f3n f a\n# los elementos del \u00e1rbol t. Por ejemplo,\n#    >>> mapArbol(lambda x: 1 + x, Nodo(Hoja(2), Hoja(4)))\n#    Nodo(i=Hoja(x=3), d=Hoja(x=5))\ndef mapArbol(f: Callable[[A], B], a: Arbol[A]) -> Arbol[B]:\n    match a:\n        case Hoja(x):\n            return Hoja(f(x))\n        case Nodo(i, d):\n            return Nodo(mapArbol(f, i), mapArbol(f, d))\n    assert False\n\ndef mismaForma2(a: Arbol[A], b: Arbol[B]) -> bool:\n    return mapArbol(lambda x: 0, a) == mapArbol(lambda x: 0, b)\n\n# Comprobaci\u00f3n de equivalencia\n# ============================\n\n# arbolArbitrario(n) es un \u00e1rbol aleatorio de altura n. Por ejemplo,\n#    >>> arbolArbitrario(3)\n#    Nodo(i=Hoja(x=2), d=Nodo(i=Hoja(x=5), d=Hoja(x=2)))\n#    >>> arbolArbitrario(3)\n#    Nodo(i=Nodo(i=Hoja(x=6), d=Hoja(x=9)), d=Hoja(x=1))\ndef arbolArbitrario(n: int) -> Arbol[int]:\n    if n <= 1:\n        return Hoja(randint(1, 10 * n))\n    k = min(randint(1, n), n - 1)\n    return Nodo(arbolArbitrario(k), arbolArbitrario(n - k))\n\n# La propiedad es\n@given(st.integers(min_value=1, max_value=10),\n       st.integers(min_value=1, max_value=10))\ndef test_mismaForma(n1: int, n2: int) -> None:\n    a1 = arbolArbitrario(n1)\n    a2 = arbolArbitrario(n2)\n    assert mismaForma1(a1, a2) == mismaForma2(a1, a2)\n\n# La comprobaci\u00f3n es\n#    src> poetry run pytest -q arboles_con_la_misma_forma.py\n#    1 passed in 0.22s\n<\/pre>\n","protected":false},"excerpt":{"rendered":"<p>El \u00e1rbol binario \u00b7 \/ \\ \/ \\ \u00b7 \u00b7 \/ \\ \/ \\ 1 4 6 9 se puede representar por ejArbol = Nodo (Nodo (Hoja 1) (Hoja 4)) (Nodo (Hoja 6) (Hoja 9)) El tipo de los \u00e1rboles binarios se puede definir por data Arbol a = Hoja a | Nodo (Arbol 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":"","_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":[269],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/7560"}],"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=7560"}],"version-history":[{"count":6,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/7560\/revisions"}],"predecessor-version":[{"id":7631,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/7560\/revisions\/7631"}],"wp:attachment":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/media?parent=7560"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/categories?post=7560"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/tags?post=7560"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}