{"id":7759,"date":"2023-01-02T06:00:18","date_gmt":"2023-01-02T04:00:18","guid":{"rendered":"http:\/\/www.glc.us.es\/~jalonso\/exercitium\/?p=7759"},"modified":"2023-01-02T10:23:43","modified_gmt":"2023-01-02T08:23:43","slug":"02-ene-23","status":"publish","type":"post","link":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/02-ene-23\/","title":{"rendered":"Elementos del nivel k de un \u00e1rbol"},"content":{"rendered":"

Los \u00e1rboles binarios con valores en las hojas y en los nodos se definen por<\/p>\n

\n   data Arbol a = H a\n                | N a (Arbol a) (Arbol a)\n<\/pre>\n
Por ejemplo, el \u00e1rbol<\/p>\n
\n        7\n       \/ \\\n      \/   \\\n     2     9\n    \/ \\\n   5   4\n<\/pre>\n
se representa por<\/p>\n
\n   N 7 (N 2 (H 5) (H 4)) (H 9)\n<\/pre>\n
Un elemento de un \u00e1rbol se dir\u00e1 de nivel k<\/code> si aparece en el \u00e1rbol a distancia k<\/code> de la ra\u00edz.<\/p>\n
Definir la funci\u00f3n<\/p>\n
\n   nivel :: Int -> Arbol a -> [a]\n<\/pre>\n
tal que nivel k a<\/code> es la lista de los elementos de nivel k<\/code> del \u00e1rbol a<\/code>. Por ejemplo,<\/p>\n
\n   nivel 0 (H 5)                          ==  [5]\n   nivel 1 (H 5)                          ==  []\n   nivel 0 (N 7 (N 2 (H 5) (H 4)) (H 9))  ==  [7]\n   nivel 1 (N 7 (N 2 (H 5) (H 4)) (H 9))  ==  [2,9]\n   nivel 2 (N 7 (N 2 (H 5) (H 4)) (H 9))  ==  [5,4]\n   nivel 3 (N 7 (N 2 (H 5) (H 4)) (H 9))  ==  []\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 a\n             | N a (Arbol a) (Arbol a)\n\nnivel :: Int -> Arbol a -> [a]\nnivel 0 (H x)      = [x]\nnivel 0 (N x _  _) = [x]\nnivel _ (H _ )     = []\nnivel k (N _ i d)  = nivel (k-1) i ++ nivel (k-1) 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    x: A\n\n@dataclass\nclass N(Arbol[A]):\n    x: A\n    i: Arbol[A]\n    d: Arbol[A]\n\ndef nivel(k: int, a: Arbol[A]) -> list[A]:\n    match (k, a):\n        case (0, H(x)):\n            return [x]\n        case (0, N(x, _, _)):\n            return [x]\n        case (_, H(_)):\n            return []\n        case (_, N(_, i, d)):\n            return nivel(k - 1, i) + nivel(k - 1, d)\n    assert False\n<\/pre>\n","protected":false},"excerpt":{"rendered":"
Los \u00e1rboles binarios con valores en las hojas y en los nodos se definen por data Arbol a = H a | N a (Arbol a) (Arbol a) Por ejemplo, el \u00e1rbol 7 \/ \\ \/ \\ 2 9 \/ \\ 5 4 se representa por N 7 (N 2 (H 5) (H 4)) (H…<\/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\/7759"}],"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=7759"}],"version-history":[{"count":2,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/7759\/revisions"}],"predecessor-version":[{"id":7795,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/7759\/revisions\/7795"}],"wp:attachment":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/media?parent=7759"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/categories?post=7759"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/tags?post=7759"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}