{"id":2786,"date":"2017-01-06T06:00:20","date_gmt":"2017-01-06T04:00:20","guid":{"rendered":"http:\/\/www.glc.us.es\/~jalonso\/exercitium\/?p=2786"},"modified":"2017-01-13T07:13:16","modified_gmt":"2017-01-13T05:13:16","slug":"numeros-dorados","status":"publish","type":"post","link":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/numeros-dorados\/","title":{"rendered":"N\u00fameros dorados"},"content":{"rendered":"<p>Los d\u00edgitos del n\u00famero 2375 se pueden separar en dos grupos de igual tama\u00f1o ([7,2] y [5,3]) tales que para los correspondientes n\u00fameros (72 y 53) se verifique que la diferencia de sus cuadrados sea el n\u00famero original (es decir, 72^2 &#8211; 53^2 = 2375).<\/p>\n<p>Un n\u00famero x es dorado si sus d\u00edgitos se pueden separar en dos grupos de igual tama\u00f1o tales que para los correspondientes n\u00fameros (a y b) se verifique que la diferencia de sus cuadrados sea el n\u00famero  original (es decir, b^2 &#8211; a^2 = x).<\/p>\n<p>Definir la funci\u00f3n<\/p>\n<pre lang=\"text\">\n   esDorado :: Integer -> Bool\n<\/pre>\n<p>tales que (esDorado x) se verifica si x es un n\u00famero dorado. Por<br \/>\nejemplo,<\/p>\n<pre lang=\"text\">\n   \u03bb> esDorado 2375\n   True\n   \u03bb> take 5 [x | x <- [1..], esDorado x]\n   [48,1023,1404,2325,2375]\n<\/pre>\n<h4>Soluciones<\/h4>\n<pre lang=\"haskell\">\n\nimport Data.List (permutations)\n\nesDorado :: Integer -> Bool\nesDorado x =\n  even (length (show x)) &&\n  or [b^2 - a^2 == x | (a,b) <- particionesNumero x]\n\n-- (particiones xs) es la lista de las formas de dividir xs en dos\n-- partes de igual longitud (se supone que xs tiene un n\u00famero par de\n-- elementos). Por ejemplo,\n--    \u03bb> particiones \"abcd\"\n--    [(\"ab\",\"cd\"),(\"ba\",\"cd\"),(\"cb\",\"ad\"),(\"bc\",\"ad\"),(\"ca\",\"bd\"),\n--     (\"ac\",\"bd\"),(\"dc\",\"ba\"),(\"cd\",\"ba\"),(\"cb\",\"da\"),(\"db\",\"ca\"),\n--     (\"bd\",\"ca\"),(\"bc\",\"da\"),(\"da\",\"bc\"),(\"ad\",\"bc\"),(\"ab\",\"dc\"),\n--     (\"db\",\"ac\"),(\"bd\",\"ac\"),(\"ba\",\"dc\"),(\"da\",\"cb\"),(\"ad\",\"cb\"),\n--     (\"ac\",\"db\"),(\"dc\",\"ab\"),(\"cd\",\"ab\"),(\"ca\",\"db\")]\nparticiones :: [a] -> [([a],[a])]\nparticiones xs =\n  [splitAt m ys | ys <- permutations xs]\n  where m = length xs `div` 2\n\n-- (particionesNumero n) es la lista de las formas de dividir n en dos\n-- partes de igual longitud (se supone que n tiene un n\u00famero par de\n-- d\u00edgitos). Por ejemplo,\n--    \u03bb> particionesNumero 1234\n--    [(12,34),(21,34),(32,14),(23,14),(31,24),(13,24),(43,21),(34,21),\n--     (32,41),(42,31),(24,31),(23,41),(41,23),(14,23),(12,43),(42,13),\n--     (24,13),(21,43),(41,32),(14,32),(13,42),(43,12),(34,12),(31,42)]\nparticionesNumero :: Integer -> [(Integer,Integer)]\nparticionesNumero n =\n  [(read xs,read ys) | (xs,ys) <- particiones (show n)]\n<\/pre>\n","protected":false},"excerpt":{"rendered":"<p>Los d\u00edgitos del n\u00famero 2375 se pueden separar en dos grupos de igual tama\u00f1o ([7,2] y [5,3]) tales que para los correspondientes n\u00fameros (72 y 53) se verifique que la diferencia de sus cuadrados sea el n\u00famero original (es decir, 72^2 &#8211; 53^2 = 2375). Un n\u00famero x es dorado si sus d\u00edgitos se pueden&#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":[7],"tags":[8,30,91,28,169,228,95,33,73],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/2786"}],"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=2786"}],"version-history":[{"count":6,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/2786\/revisions"}],"predecessor-version":[{"id":2816,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/2786\/revisions\/2816"}],"wp:attachment":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/media?parent=2786"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/categories?post=2786"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/tags?post=2786"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}