{"id":1221,"date":"2015-03-23T06:00:12","date_gmt":"2015-03-23T04:00:12","guid":{"rendered":"http:\/\/www.glc.us.es\/~jalonso\/exercitium\/?p=1221"},"modified":"2015-05-01T08:57:58","modified_gmt":"2015-05-01T06:57:58","slug":"caminos-maximales-en-arboles-binarios","status":"publish","type":"post","link":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/caminos-maximales-en-arboles-binarios\/","title":{"rendered":"Caminos maximales en \u00e1rboles binarios"},"content":{"rendered":"<p>Consideremos los \u00e1rboles binarios con etiquetas en las hojas y en los nodos. Por ejemplo,<\/p>\n<pre lang=\"text\">\n         5 \n        \/ \\ \n       2   4 \n          \/ \\ \n         7   1\n            \/ \\\n           2   3\n<\/pre>\n<p>Un camino es una sucesi\u00f3n de nodos desde la raiz hasta una hoja. Por ejemplo, [5,2] y [5,4,1,2] son caminos que llevan a 2, mientras que [5,4,1] no es un camino, pues no lleva a una hoja.<\/p>\n<p>Definimos el tipo de dato Arbol y el ejemplo por<\/p>\n<pre lang=\"text\">\n   data Arbol = H Int | N Arbol Int Arbol \n                deriving Show\n   \n   arb1:: Arbol \n   arb1 = N (H 2) 5 (N (H 7) 4 (N (H 2) 1 (H 3)))\n<\/pre>\n<p>Definir la funci\u00f3n<\/p>\n<pre lang=\"text\">\n   maxLong :: Int -> Arbol -> Int\n<\/pre>\n<p>tal que (maxLong x a) es la longitud m\u00e1xima de los caminos que terminan en x. Por ejemplo,<\/p>\n<pre lang=\"text\">\n   maxLong 3 arb1 == 4\n   maxLong 2 arb1 == 4\n   maxLong 7 arb1 == 3\n<\/pre>\n<h4>Soluciones<\/h4>\n<pre lang=\"haskell\">\ndata Arbol = H Int | N Arbol Int Arbol \n             deriving Show\n\narb1:: Arbol \narb1 = N (H 2) 5 (N (H 7) 4 (N (H 2) 1 (H 3)))\n\n-- 1\u00aa soluci\u00f3n (calculando los caminos)\n-- ------------------------------------\n\n-- (caminos x a) es la lista de los caminos en el \u00e1rbol a desde la ra\u00edz\n-- hasta las hojas x. Por ejemplo,\n--    caminos 2 arb1 == [[5,2],[5,4,1,2]]\n--    caminos 3 arb1 == [[5,4,1,3]]\n--    caminos 1 arb1 == []\ncaminos :: Int -> Arbol -> [[Int]]\ncaminos x (H y) | x == y    = [[x]]\n                | otherwise = []\ncaminos x (N i r d) = map (r:) (caminos x i ++ caminos x d)\n\nmaxLong1 :: Int -> Arbol -> Int\nmaxLong1 x a = maximum (0: map length (caminos x a))\n\n-- 2\u00aa soluci\u00f3n\n-- -----------\n\nmaxLong2 :: Int -> Arbol -> Int\nmaxLong2 x a = maximum (0 : aux x a)\n    where aux x (H y) | x == y    = [1]\n                      | otherwise = []\n          aux x (N i r d) = map (+1) (aux x i ++ aux x d)\n<\/pre>\n","protected":false},"excerpt":{"rendered":"<p>Consideremos los \u00e1rboles binarios con etiquetas en las hojas y en los nodos. Por ejemplo, 5 \/ \\ 2 4 \/ \\ 7 1 \/ \\ 2 3 Un camino es una sucesi\u00f3n de nodos desde la raiz hasta una hoja. Por ejemplo, [5,2] y [5,4,1,2] son caminos que llevan a 2, mientras que [5,4,1]&#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":[269,28,10,15,11,6],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/1221"}],"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=1221"}],"version-history":[{"count":3,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/1221\/revisions"}],"predecessor-version":[{"id":1276,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/1221\/revisions\/1276"}],"wp:attachment":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/media?parent=1221"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/categories?post=1221"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/tags?post=1221"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}