{"id":3563,"date":"2017-12-27T06:00:45","date_gmt":"2017-12-27T04:00:45","guid":{"rendered":"http:\/\/www.glc.us.es\/~jalonso\/exercitium\/?p=3563"},"modified":"2018-02-19T08:41:37","modified_gmt":"2018-02-19T06:41:37","slug":"recorrido-por-niveles-de-arboles-binarios","status":"publish","type":"post","link":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/recorrido-por-niveles-de-arboles-binarios\/","title":{"rendered":"Recorrido por niveles de \u00e1rboles binarios"},"content":{"rendered":"<p>Los \u00e1rboles binarios con valores en las hojas y en los nodos se definen por<\/p>\n<pre lang=\"text\">\n   data Arbol a = H a\n                | N a (Arbol a) (Arbol a) \n     deriving (Eq, Show)\n<\/pre>\n<p>Por ejemplo, el \u00e1rbol<\/p>\n<pre lang=\"text\">\n         1 \n       \/   \\\n      2     3\n     \/ \\   \/ \\\n    4   5 6   7\n       \/ \\\n      8   9 \n<\/pre>\n<p>se pueden representar por<\/p>\n<pre lang=\"text\">\n   ejArbol :: Arbol Int\n   ejArbol = N 1 (N 2 (H 4)\n                      (N 5 (H 8) (H 9)))\n                 (N 3 (H 6) (H 7))\n<\/pre>\n<p>Definir la funci\u00f3n<\/p>\n<pre lang=\"text\">\n   recorrido :: Arbol t -> [t]\n<\/pre>\n<p>tal que (recorrido a) es el recorrido del \u00e1rbol a por niveles desde la ra\u00edz a las hojas y de izquierda a derecha. Por ejemplo,<\/p>\n<pre lang=\"text\">\n   \u03bb> recorrido (N 1 (N 2 (H 4) (N 5 (H 8) (H 9))) (N 3 (H 6) (H 7)))\n   [1,2,3,4,5,6,7,8,9]\n   \u03bb> recorrido (N 1 (N 3 (H 6) (H 7)) (N 2 (H 4) (N 5 (H 8) (H 9))))\n   [1,3,2,6,7,4,5,8,9]\n   \u03bb> recorrido (N 1 (N 3 (H 6) (H 7)) (N 2 (H 4) (H 5)))\n   [1,3,2,6,7,4,5]\n   \u03bb> recorrido (N 1 (N 2 (H 4) (H 5)) (N 3 (H 6) (H 7)))\n   [1,2,3,4,5,6,7]\n   \u03bb> recorrido (N 1 (N 2 (H 4) (H 5)) (H 3))\n   [1,2,3,4,5]\n   \u03bb> recorrido (N 1 (H 4) (H 3))\n   [1,4,3]\n   \u03bb> recorrido (H 3)\n   [3]\n<\/pre>\n<h4>Soluciones<\/h4>\n<pre lang=\"haskell\">\ndata Arbol a = H a\n             | N a (Arbol a) (Arbol a) \n  deriving (Eq, Show)\n\nejArbol :: Arbol Int\nejArbol = N 1 (N 2 (H 4)\n                   (N 5 (H 8) (H 9)))\n              (N 3 (H 6) (H 7))\n\n-- 1\u00aa definici\u00f3n\n-- =============\n\nrecorrido :: Arbol t -> [t]\nrecorrido = concat . niveles\n\n-- (niveles a) es la lista de los niveles del \u00e1rbol a. Por ejemplo,\n--    \u03bb> niveles (N 1 (N 2 (H 4) (N 5 (H 8) (H 9))) (N 3 (H 6) (H 7)))\n--    [[1],[2,3],[4,5,6,7],[8,9]]\nniveles :: Arbol t -> [[t]]\nniveles (H x)     = [[x]]\nniveles (N x i d) = [x] : mezcla (niveles i) (niveles d)\n\n-- (mezcla xss yss) es la lista obtenida concatenando los\n-- correspondientes elementos de xss e yss. Por ejemplo,\n--    \u03bb> mezcla [[1,3],[2,5,7]] [[4],[1,9],[0,14]]\n--    [[1,3,4],[2,5,7,1,9],[0,14]]\n--    \u03bb> mezcla [[1,3],[2,5,7]] [[4]]\n--    [[1,3,4],[2,5,7]]\nmezcla :: [[a]] -> [[a]] -> [[a]]\nmezcla [] yss            = yss\nmezcla xss []            = xss\nmezcla (xs:xss) (ys:yss) = (xs ++ ys) : mezcla xss yss\n\n-- 2\u00aa definici\u00f3n\n-- =============\n\nrecorrido2 :: Arbol t -> [t]\nrecorrido2 = concat . niveles2\n\n-- (niveles2 a) es la lista de los niveles del \u00e1rbol a. Por ejemplo,\n--    \u03bb> niveles2 (N 1 (N 2 (H 4) (N 5 (H 8) (H 9))) (N 3 (H 6) (H 7)))\n--    [[1],[2,3],[4,5,6,7],[8,9]]\nniveles2 :: Arbol t -> [[t]]\nniveles2 a = takeWhile (not . null) [nivel n a | n <- [0..]]\n\n-- (nivel n a) es el nivel i\u00e9simo del \u00e1rbol a. Por ejemplo,\n--    \u03bb> nivel 2 (N 1 (N 2 (H 4) (N 5 (H 8) (H 9))) (N 3 (H 6) (H 7)))\n--    [4,5,6,7]\n--    \u03bb> nivel 5 (N 1 (N 2 (H 4) (N 5 (H 8) (H 9))) (N 3 (H 6) (H 7)))\n--    []\nnivel :: Int -> Arbol t -> [t]\nnivel 0 (H x)      = [x]\nnivel n (H _)      = []\nnivel 0 (N x _ _)  = [x]\nnivel n (N x i d)  = nivel (n-1) i ++ nivel (n-1) d\n<\/pre>\n","protected":false},"excerpt":{"rendered":"<p>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) deriving (Eq, Show) Por ejemplo, el \u00e1rbol 1 \/ \\ 2 3 \/ \\ \/ \\ 4 5 6 7 \/ \\ 8 9 se pueden representar&#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":[269,8,12,181,141,11,6,34],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/3563"}],"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=3563"}],"version-history":[{"count":4,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/3563\/revisions"}],"predecessor-version":[{"id":3795,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/3563\/revisions\/3795"}],"wp:attachment":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/media?parent=3563"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/categories?post=3563"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/tags?post=3563"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}