{"id":6282,"date":"2021-04-19T06:00:21","date_gmt":"2021-04-19T04:00:21","guid":{"rendered":"http:\/\/www.glc.us.es\/~jalonso\/exercitium\/?p=6282"},"modified":"2021-04-26T07:42:50","modified_gmt":"2021-04-26T05:42:50","slug":"arbol-de-cadenas","status":"publish","type":"post","link":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/arbol-de-cadenas\/","title":{"rendered":"\u00c1rbol de cadenas"},"content":{"rendered":"<p>En la librer\u00eda <a href=\"http:\/\/bit.ly\/2mLEVg4\">Data.Tree<\/a> se definen los \u00e1rboles y los bosques como sigue<\/p>\n<pre lang=\"text\">\n   data Tree a   = Node a (Forest a)\n   type Forest a = [Tree a]\n<\/pre>\n<p>Se pueden definir \u00e1rboles. Por ejemplo,<\/p>\n<pre lang=\"text\">\n   ej = Node 3 [Node 5 [Node 9 []], Node 7 []]\n<\/pre>\n<p>Y se pueden dibujar con la funci\u00f3n drawTree. Por ejemplo,<\/p>\n<pre lang=\"text\">\n   \u03bb> putStrLn (drawTree (fmap show ej))\n   3\n   |\n   +- 5\n   |  |\n   |  `- 9\n   |\n   `- 7\n<\/pre>\n<p>Una cadena con un conjunto de pares ps es una lista xs de elementos distintos de ps tales que la segunda componente de cada elemento de xs es igual a la primera componente de su siguiente elemento. Por ejemplo, si ps = [(1,6),(2,5),(3,6),(4,9),(6,4),(8,1)] entonces [(6,4)], [(8,1),(1,6)] y [(8,1),(1,6),(6,4),(4,9)] son cadenas con ps.<\/p>\n<p>Definir la funci\u00f3n<\/p>\n<pre lang=\"text\">\n   arbolCadenas :: Eq a => [(a,a)] -> Tree [(a,a)]\n<\/pre>\n<p>tal que (arbolCadenas ps) es el \u00e1rbol de las cadenas formadas con los elementos de ps. Por ejemplo,<\/p>\n<pre lang=\"text\">\n   \u03bb> putStrLn (drawTree (fmap show (arbolCadenas [(1,2),(2,3),(3,1)])))\n   []\n   |\n   +- [(1,2)]\n   |  |\n   |  `- [(3,1),(1,2)]\n   |     |\n   |     `- [(2,3),(3,1),(1,2)]\n   |\n   +- [(2,3)]\n   |  |\n   |  `- [(1,2),(2,3)]\n   |     |\n   |     `- [(3,1),(1,2),(2,3)]\n   |\n   `- [(3,1)]\n      |\n      `- [(2,3),(3,1)]\n         |\n         `- [(1,2),(2,3),(3,1)]\n\n   \u03bb> putStrLn (drawTree (fmap show (arbolCadenas [(1,6),(2,5),(3,6),(4,9),(6,4),(8,1)])))\n   []\n   |\n   +- [(1,6)]\n   |  |\n   |  `- [(8,1),(1,6)]\n   |\n   +- [(2,5)]\n   |\n   +- [(3,6)]\n   |\n   +- [(4,9)]\n   |  |\n   |  `- [(6,4),(4,9)]\n   |     |\n   |     +- [(1,6),(6,4),(4,9)]\n   |     |  |\n   |     |  `- [(8,1),(1,6),(6,4),(4,9)]\n   |     |\n   |     `- [(3,6),(6,4),(4,9)]\n   |\n   +- [(6,4)]\n   |  |\n   |  +- [(1,6),(6,4)]\n   |  |  |\n   |  |  `- [(8,1),(1,6),(6,4)]\n   |  |\n   |  `- [(3,6),(6,4)]\n   |\n   `- [(8,1)]\n<\/pre>\n<h4>Soluciones<\/h4>\n<pre lang=\"haskell\">\nimport Data.Tree (Tree (Node), drawTree)\n\narbolCadenas :: Eq a => [(a,a)] -> Tree [(a,a)]\narbolCadenas ps = aux []\n  where\n    aux xs = Node xs (map aux (extensiones xs))\n    extensiones [] =\n      [[p] | p <- ps]\n    extensiones ((x,y):rs) =\n      [(a,b):(x,y):rs | (a,b) <- ps,\n                        b == x,\n                        (a,b) `notElem` ((x,y):rs)]\n<\/pre>\n<h4>Nuevas soluciones<\/h4>\n<ul>\n<li>En los comentarios se pueden escribir nuevas soluciones.\n<li>El c\u00f3digo se debe escribir entre una l\u00ednea con &#60;pre lang=&quot;haskell&quot;&#62; y otra con &#60;\/pre&#62;\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>En la librer\u00eda Data.Tree se definen los \u00e1rboles y los bosques como sigue data Tree a = Node a (Forest a) type Forest a = [Tree a] Se pueden definir \u00e1rboles. Por ejemplo, ej = Node 3 [Node 5 [Node 9 []], Node 7 []] Y se pueden dibujar con la funci\u00f3n drawTree. Por ejemplo,&#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":[2],"tags":[],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/6282"}],"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=6282"}],"version-history":[{"count":2,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/6282\/revisions"}],"predecessor-version":[{"id":6363,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/6282\/revisions\/6363"}],"wp:attachment":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/media?parent=6282"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/categories?post=6282"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/tags?post=6282"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}