{"id":7749,"date":"2022-12-27T06:00:08","date_gmt":"2022-12-27T04:00:08","guid":{"rendered":"http:\/\/www.glc.us.es\/~jalonso\/exercitium\/?p=7749"},"modified":"2022-12-26T10:45:00","modified_gmt":"2022-12-26T08:45:00","slug":"27-dic-22","status":"publish","type":"post","link":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/27-dic-22\/","title":{"rendered":"\u00c1rboles balanceados"},"content":{"rendered":"

Los \u00e1rboles binarios con valores en los nodos se pueden definir por<\/p>\n

\n   data Arbol a = H\n                | N a (Arbol a) (Arbol a)\n     deriving (Show, Eq)\n<\/pre>\n
Por ejemplo, el \u00e1rbol<\/p>\n
\n        9\n       \/ \\\n      \/   \\\n     8     6\n    \/ \\   \/ \\\n   3   2 4   5\n<\/pre>\n
se puede representar por<\/p>\n
\n   N 9 (N 8 (N 3 H H) (N 2 H H)) (N 6 (N 4 H H) (N 5 H H))\n<\/pre>\n
Diremos que un \u00e1rbol est\u00e1 balanceado si para cada nodo la diferencia entre el n\u00famero de nodos de sus sub\u00e1rboles izquierdo y derecho es menor o igual que uno.<\/p>\n
Definir la funci\u00f3n<\/p>\n
\n   balanceado :: Arbol a -> Bool\n<\/pre>\n
tal que (balanceado a) se verifica si el \u00e1rbol a est\u00e1 balanceado. Por ejemplo,<\/p>\n
\n   \u03bb> balanceado (N 5 H (N 3 H H))\n   True\n   \u03bb> balanceado (N 4 (N 3 (N 2 H H) H) (N 5 H (N 6 H (N 7 H H))))\n   False\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
\ndata Arbol a = H\n             | N a (Arbol a) (Arbol a)\n  deriving (Show, Eq)\n\nbalanceado :: Arbol a -> Bool\nbalanceado H         = True\nbalanceado (N _ i d) = abs (numeroNodos i - numeroNodos d) <= 1\n                       && balanceado i\n                       && balanceado d\n\n-- (numeroNodos a) es el n\u00famero de nodos del \u00e1rbol a. Por ejemplo,\n--    numeroNodos (N 5 H (N 3 H H)) ==  2\nnumeroNodos :: Arbol a -> Int\nnumeroNodos H         = 0\nnumeroNodos (N _ i d) = 1 + numeroNodos i + numeroNodos d\n<\/pre>\n
<\/a>
\nSoluciones en Python<\/b><\/p>\n
\nfrom dataclasses import dataclass\nfrom typing import Generic, TypeVar\n\nA = TypeVar(\"A\")\n\n@dataclass\nclass Arbol(Generic[A]):\n    pass\n\n@dataclass\nclass H(Arbol[A]):\n    pass\n\n@dataclass\nclass N(Arbol[A]):\n    x: A\n    i: Arbol[A]\n    d: Arbol[A]\n\ndef numeroNodos(a: Arbol[A]) -> int:\n    match a:\n        case H():\n            return 0\n        case N(_, i, d):\n            return 1 + numeroNodos(i) + numeroNodos(d)\n    assert False\n\ndef balanceado(a: Arbol[A]) -> bool:\n    match a:\n        case H():\n            return True\n        case N(_, i, d):\n            return abs(numeroNodos(i) - numeroNodos(d)) <= 1 \\\n                and balanceado(i) and balanceado(d)\n    assert False\n<\/pre>\n","protected":false},"excerpt":{"rendered":"
Los \u00e1rboles binarios con valores en los nodos se pueden definir por data Arbol a = H | N a (Arbol a) (Arbol a) deriving (Show, Eq) Por ejemplo, el \u00e1rbol 9 \/ \\ \/ \\ 8 6 \/ \\ \/ \\ 3 2 4 5 se puede representar por N 9 (N 8 (N…<\/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\/7749"}],"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=7749"}],"version-history":[{"count":1,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/7749\/revisions"}],"predecessor-version":[{"id":7750,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/7749\/revisions\/7750"}],"wp:attachment":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/media?parent=7749"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/categories?post=7749"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/tags?post=7749"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}