Los \u00e1rboles se pueden representar mediante el siguiente tipo de datos<\/p>\n
\n data Arbol a = N a [Arbol a]\n deriving Show\n<\/pre>\nPor ejemplo, los \u00e1rboles<\/p>\n
\n 1 3 \n \/ \\ \/|\\ \n 2 3 \/ | \\ \n | 5 4 7 \n 4 | \/|\\ \n 6 2 8 6 \n<\/pre>\nse representan por<\/p>\n
\n ej1, ej2 :: Arbol Int\n ej1 = N 1 [N 2 [], N 3 [N 4 []]]\n ej2 = N 3 [N 5 [N 6 []], \n N 4 [], \n N 7 [N 2 [], N 8 [], N 6 []]]\n<\/pre>\nDefinir la funci\u00f3n<\/p>\n
\n nodosSumaMaxima :: (Num t, Ord t) => Arbol t -> [t]\n<\/pre>\ntal que (nodosSumaMaxima a) es la lista de los nodos del \u00e1rbol a cuyos hijos tienen m\u00e1xima suma. Por ejemplo,<\/p>\n
\n nodosSumaMaxima ej1 == [1]\n nodosSumaMaxima ej2 == [7,3]\n<\/pre>\nSoluciones<\/h4>\n\nimport Data.List (groupBy, sort)\nimport Data.Function (on)\n\ndata Arbol a = N a [Arbol a]\n deriving Show\n\nej1, ej2 :: Arbol Int\nej1 = N 1 [N 2 [], N 3 [N 4 []]]\nej2 = N 3 [N 5 [N 6 []], \n N 4 [], \n N 7 [N 2 [], N 8 [], N 6 []]]\n\n-- 1\u00aa soluci\u00f3n\n-- ===========\n\nnodosSumaMaxima :: (Num t, Ord t) => Arbol t -> [t]\nnodosSumaMaxima a =\n [x | (s,x) <- ns, s == m]\n where ns = reverse (sort (nodosSumas a))\n m = fst (head ns)\n\n-- (nodosSumas x) es la lista de los pares (s,n) donde n es un nodo del\n-- \u00e1rbol x y s es la suma de sus hijos. Por ejemplo, \n-- \u03bb> nodosSumas ej1\n-- [(5,1),(0,2),(4,3),(0,4)]\n-- \u03bb> nodosSumas ej2\n-- [(16,3),(6,5),(0,6),(0,4),(16,7),(0,2),(0,8),(0,6)]\nnodosSumas :: Num t => Arbol t -> [(t,t)]\nnodosSumas (N x []) = [(0,x)]\nnodosSumas (N x as) = (sum (raices as),x) : concatMap nodosSumas as\n\n-- (raices b) es la lista de las ra\u00edces del bosque b. Por ejemplo,\n-- raices [ej1,ej2] == [1,3]\nraices :: [Arbol t] -> [t]\nraices = map raiz\n\n-- (raiz a) es la ra\u00edz del \u00e1rbol a. Por ejemplo,\n-- raiz ej1 == 1\n-- raiz ej2 == 3\nraiz :: Arbol t -> t\nraiz (N x _) = x\n\n-- 2\u00aa soluci\u00f3n\n-- ===========\n\nnodosSumaMaxima2 :: (Num t, Ord t) => Arbol t -> [t]\nnodosSumaMaxima2 a =\n [x | (s,x) <- ns, s == m]\n where ns = sort (nodosOpSumas a)\n m = fst (head ns)\n\n-- (nodosOpSumas x) es la lista de los pares (s,n) donde n es un nodo del\n-- \u00e1rbol x y s es el opuesto de la suma de sus hijos. Por ejemplo, \n-- \u03bb> nodosOpSumas ej1\n-- [(-5,1),(0,2),(-4,3),(0,4)]\n-- \u03bb> nodosOpSumas ej2\n-- [(-16,3),(-6,5),(0,6),(0,4),(-16,7),(0,2),(0,8),(0,6)]\nnodosOpSumas :: Num t => Arbol t -> [(t,t)]\nnodosOpSumas (N x []) = [(0,x)]\nnodosOpSumas (N x as) = (-sum (raices as),x) : concatMap nodosOpSumas as\n\n\n-- 3\u00aa soluci\u00f3n\n-- ===========\n\nnodosSumaMaxima3 :: (Num t, Ord t) => Arbol t -> [t]\nnodosSumaMaxima3 a =\n [x | (s,x) <- ns, s == m]\n where ns = sort (nodosOpSumas a)\n m = fst (head ns)\n\n-- 4\u00aa soluci\u00f3n\n-- ===========\n\nnodosSumaMaxima4 :: (Num t, Ord t) => Arbol t -> [t]\nnodosSumaMaxima4 a =\n map snd (head (groupBy (\\p q -> fst p == fst q)\n (sort (nodosOpSumas a))))\n\n-- 5\u00aa soluci\u00f3n\n-- ===========\n\nnodosSumaMaxima5 :: (Num t, Ord t) => Arbol t -> [t]\nnodosSumaMaxima5 a =\n map snd (head (groupBy ((==) `on` fst)\n (sort (nodosOpSumas a))))\n\n-- 6\u00aa soluci\u00f3n\n-- ===========\n\nnodosSumaMaxima6 :: (Num t, Ord t) => Arbol t -> [t]\nnodosSumaMaxima6 =\n map snd\n . head\n . groupBy ((==) `on` fst)\n . sort\n . nodosOpSumas\n<\/pre>\n","protected":false},"excerpt":{"rendered":"Los \u00e1rboles se pueden representar mediante el siguiente tipo de datos data Arbol a = N a [Arbol a] deriving Show Por ejemplo, los \u00e1rboles 1 3 \/ \\ \/|\\ 2 3 \/ | \\ | 5 4 7 4 | \/|\\ 6 2 8 6 se representan por ej1, ej2 :: Arbol Int ej1…<\/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":[269,161,8,58,160,80,440,71,10,11,6,32,14,159,40],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/3819"}],"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=3819"}],"version-history":[{"count":2,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/3819\/revisions"}],"predecessor-version":[{"id":3853,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/3819\/revisions\/3853"}],"wp:attachment":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/media?parent=3819"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/categories?post=3819"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/tags?post=3819"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}