{"id":2855,"date":"2017-01-25T06:00:47","date_gmt":"2017-01-25T04:00:47","guid":{"rendered":"http:\/\/www.glc.us.es\/~jalonso\/exercitium\/?p=2855"},"modified":"2017-02-01T08:34:01","modified_gmt":"2017-02-01T06:34:01","slug":"arboles-continuos","status":"publish","type":"post","link":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/arboles-continuos\/","title":{"rendered":"\u00c1rboles continuos"},"content":{"rendered":"<p>Los \u00e1rboles binarios se pueden representar con el de tipo de dato algebraico<\/p>\n<pre lang=\"text\">\n   data Arbol a = H\n                | N a (Arbol a) (Arbol a)\n     deriving Show\n<\/pre>\n<p>Por ejemplo, los \u00e1rboles<\/p>\n<pre lang=\"text\">\n       3                7     \n      \/ \\              \/ \\    \n     2   4            5   8   \n    \/ \\   \\          \/ \\   \\  \n   1   3   5        6   4   10\n<\/pre>\n<p>se representan por<\/p>\n<pre lang=\"text\">\n   ej1, ej2 :: Arbol Int\n   ej1 = N 3 (N 2 (N 1 H H) (N 3 H H)) (N 4 H (N 5 H H))\n   ej2 = N 7 (N 5 (N 6 H H) (N 4 H H)) (N 8 H (N 10 H H))\n<\/pre>\n<p>Un \u00e1rbol binario es <strong>continuo<\/strong> si el valor absoluto de la diferencia de los elementos adyacentes es 1. Por ejemplo, el \u00e1rbol ej1 es continuo ya que el valor absoluto de sus pares de elementos adyacentes son<\/p>\n<pre lang=\"text\">\n   |3-2| = |2-1| = |2-3| = |3-4| = |4-5| = 1\n<\/pre>\n<p>En cambio, el ej2 no lo es ya que |8-10| \u2260 1.<\/p>\n<p>Definir la funci\u00f3n<\/p>\n<pre lang=\"text\">\n   esContinuo :: (Num a, Eq a) => Arbol a -> Bool\n<\/pre>\n<p>tal que (esContinuo x) se verifica si el \u00e1rbol x es continuo. Por ejemplo,<\/p>\n<pre lang=\"text\">\n   esContinuo ej1  ==  True\n   esContinuo ej2  ==  False\n<\/pre>\n<h4>Soluciones<\/h4>\n<pre lang=\"haskell\">\ndata Arbol a = H\n             | N a (Arbol a) (Arbol a)\n  deriving Show\n\nej1, ej2 :: Arbol Int\nej1 = N 3 (N 2 (N 1 H H) (N 3 H H)) (N 4 H (N 5 H H))\nej2 = N 7 (N 5 (N 6 H H) (N 4 H H)) (N 8 H (N 10 H H))\n\n-- 1\u00aa soluci\u00f3n\n-- ===========\n\nesContinuo :: (Num a, Eq a) => Arbol a -> Bool\nesContinuo H         = True\nesContinuo (N _ H H) = True\nesContinuo (N x i@(N y _ _) H) =\n  abs (x - y) == 1 && esContinuo i\nesContinuo (N x H d@(N y _ _)) =\n  abs (x - y) == 1 && esContinuo d\nesContinuo (N x i@(N y _ _) d@(N z _ _)) =\n  abs (x - y) == 1 && esContinuo i && abs (x - z) == 1 && esContinuo d \n\n-- 2\u00aa soluci\u00f3n\n-- ===========\n\nesContinuo2 :: (Num a, Eq a) => Arbol a -> Bool\nesContinuo2 x =\n  all esContinua (ramas x)\n\n-- (ramas x) es la lista de las ramas del \u00e1rbol x. Por ejemplo,\n--    ramas ej1  ==  [[3,2,1],[3,2,3],[3,4,5]]\n--    ramas ej2  ==  [[7,5,6],[7,5,4],[7,8,10]]\nramas :: Arbol a -> [[a]]\nramas H         = []\nramas (N x H H) = [[x]]\nramas (N x i d) = [x : xs | xs <- ramas i ++ ramas d]\n\n-- (esContinua xs) se verifica si el valor absoluto de la diferencia de\n-- los elementos adyacentes de xs es 1. Por ejemplo, \n--    esContinua [3,2,3]   ==  True\n--    esContinua [7,8,10]  ==  False\nesContinua :: (Num a, Eq a) => [a] -> Bool\nesContinua xs =\n  and [abs (x - y) == 1 | (x, y) <- zip xs (tail xs)]\n<\/pre>\n<h4>Referencias<\/h4>\n<ul>\n<li>Basado en <a href=\"http:\/\/bit.ly\/2jWxOjl\">Continuous tree<\/a> de GeeksforGeeks.<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>Los \u00e1rboles binarios se pueden representar con el de tipo de dato algebraico data Arbol a = H | N a (Arbol a) (Arbol a) deriving Show Por ejemplo, los \u00e1rboles 3 7 \/ \\ \/ \\ 2 4 5 8 \/ \\ \\ \/ \\ \\ 1 3 5 6 4 10 se representan&#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":[4],"tags":[130,41,100,8,11,6,45,9],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/2855"}],"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=2855"}],"version-history":[{"count":4,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/2855\/revisions"}],"predecessor-version":[{"id":2887,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/2855\/revisions\/2887"}],"wp:attachment":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/media?parent=2855"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/categories?post=2855"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/tags?post=2855"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}