Los \u00e1rboles binarios con datos en los nodos se definen por<\/p>\n
\n data Arbol a = H\n | N a (Arbol a) (Arbol a)\n deriving (Eq, Show)\n<\/pre>\nPor ejemplo, el \u00e1rbol<\/p>\n
\n 3\n \/ \\\n \/ \\\n 0 5\n \/ \\ \/ \\\n 5 0 0 3\n \/ \\\n 2 4 \n<\/pre>\nse representa por<\/p>\n
\n ejArbol :: Arbol Int\n ejArbol = N 3\n (N 0\n (N 5\n (N 2 H H)\n (N 4 H H))\n (N 0 H H))\n (N 5\n (N 0 H H)\n (N 3 H H))\n<\/pre>\nCada posici\u00f3n de un elemento de un \u00e1rbol es una lista de movimientos hacia la izquierda o hacia la derecha. Por ejemplo, la posici\u00f3n de 4 en al \u00e1rbol anterior es [I,I,D].<\/p>\n
Los tipos de los movimientos y de las posiciones se definen por<\/p>\n
\n data Movimiento = I | D deriving (Show, Eq)\n type Posicion = [Movimiento]\n<\/pre>\nDefinir la funci\u00f3n<\/p>\n
\n posiciones :: Eq b => b -> Arbol b -> [Posicion]\n<\/pre>\ntal que (posiciones n a) es la lista de las posiciones del elemento n en el \u00e1rbol a. Por ejemplo,<\/p>\n
\n posiciones 0 ejArbol == [[I],[I,D],[D,I]]\n posiciones 2 ejArbol == [[I,I,I]]\n posiciones 3 ejArbol == [[],[D,D]]\n posiciones 4 ejArbol == [[I,I,D]]\n posiciones 5 ejArbol == [[I,I],[D]]\n posiciones 1 ejArbol == []\n<\/pre>\nSoluciones<\/h4>\n\ndata Arbol a = H\n | N a (Arbol a) (Arbol a)\n deriving (Eq, Show)\n\nejArbol :: Arbol Int\nejArbol = N 3\n (N 0\n (N 5\n (N 2 H H)\n (N 4 H H))\n (N 0 H H))\n (N 5\n (N 0 H H)\n (N 3 H H))\n\ndata Movimiento = I | D deriving (Show, Eq)\n\ntype Posicion = [Movimiento]\n\n-- 1\u00aa soluci\u00f3n\n-- ===========\n\nposiciones :: Eq b => b -> Arbol b -> [Posicion]\nposiciones n a = aux n a [[]]\n where aux _ H _ = []\n aux n (N x i d) cs | x == n = cs ++\n [I:xs | xs <- aux n i cs] ++\n [D:xs | xs <- aux n d cs]\n | otherwise = [I:xs | xs <- aux n i cs] ++\n [D:xs | xs <- aux n d cs]\n \n-- 2\u00aa soluci\u00f3n\n-- ===========\n\nposiciones2 :: Eq b => b -> Arbol b -> [Posicion]\nposiciones2 n a = aux n a [[]]\n where aux _ H _ = []\n aux n (N x i d) cs | x == n = cs ++ ps\n | otherwise = ps\n where ps = [I:xs | xs <- aux n i cs] ++\n [D:xs | xs <- aux n d cs]\n\n-- 3\u00aa soluci\u00f3n\n-- ===========\n\nposiciones3 :: Eq b => b -> Arbol b -> [Posicion]\nposiciones3 n a = aux n a [[]]\n where aux _ H _ = []\n aux n (N x i d) cs | x == n = cs ++ ps\n | otherwise = ps\n where ps = map (I:) (aux n i cs) ++\n map (D:) (aux n d cs)\n\n-- Equivalencia\n-- ============\n\n-- Generador de \u00e1rboles\ninstance Arbitrary a => Arbitrary (Arbol a) where\n arbitrary = sized genArbol\n\ngenArbol :: (Arbitrary a, Integral a1) => a1 -> Gen (Arbol a)\ngenArbol 0 = return H \ngenArbol n | n > 0 = N <$> arbitrary <*> subarbol <*> subarbol\n where subarbol = genArbol (div n 2)\n\n-- La propiedad es\nprop_posiciones_equiv :: Arbol Int -> Bool\nprop_posiciones_equiv a =\n and [posiciones n a == posiciones2 n a | n <- xs] &&\n and [posiciones n a == posiciones3 n a | n <- xs] \n where xs = take 3 (elementos a)\n\n-- (elementos a) son los elementos del \u00e1rbol a. Por ejemplo,\n-- elementos ejArbol == [3,0,5,2,4]\nelementos :: Eq b => Arbol b -> [b]\nelementos H = []\nelementos (N x i d) = nub (x : elementos i ++ elementos d)\n\n-- La comprobaci\u00f3n es\n-- \u03bb> quickCheck prop_posiciones_equiv\n-- +++ OK, passed 100 tests.\n<\/pre>\nPensamiento<\/h4>\n\nNunca traces tu frontera,
\nni cuides de tu perfil;
\ntodo eso es cosa de fuera.<\/p>\n
Antonio Machado\n<\/p><\/blockquote>\n","protected":false},"excerpt":{"rendered":"
Los \u00e1rboles binarios con datos en los nodos se definen por data Arbol a = H | N a (Arbol a) (Arbol a) deriving (Eq, Show) Por ejemplo, el \u00e1rbol 3 \/ \\ \/ \\ 0 5 \/ \\ \/ \\ 5 0 0 3 \/ \\ 2 4 se representa por ejArbol :: Arbol…<\/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":[269,8,10,11,6],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/4370"}],"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=4370"}],"version-history":[{"count":7,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/4370\/revisions"}],"predecessor-version":[{"id":4585,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/4370\/revisions\/4585"}],"wp:attachment":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/media?parent=4370"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/categories?post=4370"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/tags?post=4370"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}