{"id":2745,"date":"2016-12-27T06:00:22","date_gmt":"2016-12-27T04:00:22","guid":{"rendered":"http:\/\/www.glc.us.es\/~jalonso\/exercitium\/?p=2745"},"modified":"2017-01-03T08:12:17","modified_gmt":"2017-01-03T06:12:17","slug":"numeros-super-pandigitales","status":"publish","type":"post","link":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/numeros-super-pandigitales\/","title":{"rendered":"N\u00fameros super pandigitales"},"content":{"rendered":"<p>Un entero positivo n es <a href=\"http:\/\/bit.ly\/2ir1HrQ\">pandigital<\/a> en base b si su expresi\u00f3n en base b contiene todos los d\u00edgitos de 0 a b-1 al menos una vez. Por ejemplo,<\/p>\n<ul>\n<li>el  2 es pandigital en base 2 porque  2 en base 2 es 10,<\/li>\n<li>el 11 es pandigital en base 3 porque 11 en base 3 es 102 y<\/li>\n<li>el 75 es pandigital en base 4 porque 75 en base 4 es 1023.<\/li>\n<\/ul>\n<p>Un n\u00famero n es super pandigital de orden m si es pandigital en todas las bases<br \/>\ndesde 2 hasta m. Por ejemplo, 978 es super pandigital de orden 5 pues<\/p>\n<ul>\n<li>en base 2 es: 1111010010<\/li>\n<li>en base 3 es: 1100020<\/li>\n<li>en base 4 es: 33102<\/li>\n<li>en base 5 es: 12403<\/li>\n<\/ul>\n<p>Definir la funci\u00f3n<\/p>\n<pre lang=\"text\">\n   superPandigitales :: Integer -> [Integer]\n<\/pre>\n<p>tal que (superPandigitales m) es la lista de los n\u00fameros super pandigitales de orden m. Por ejemplo,<\/p>\n<pre lang=\"text\">\n   take 3 (superPandigitales 3) == [11,19,21]\n   take 3 (superPandigitales 4) == [75,99,114]\n   take 3 (superPandigitales 5) == [978,1070,1138]\n<\/pre>\n<h4>Soluciones<\/h4>\n<pre lang=\"haskell\">\nsuperPandigitales :: Integer -> [Integer]\nsuperPandigitales m =\n  [n | n <- [1..]\n     , and [pandigitalBase b n | b <- [2..m]]]\n\n-- (pandigitalBase b n) se verifica si n es pandigital en base la base\n-- b. Por ejemplo,\n--    pandigitalBase 4 75  ==  True\n--    pandigitalBase 4 76  ==  False\npandigitalBase :: Integer -> Integer -> Bool\npandigitalBase b n = [0..b-1] `esSubconjunto` enBase b n\n\n-- (enBase b n) es la lista de los d\u00edgitos de n en base b. Por ejemplo,\n--    enBase 4 75  ==  [3,2,0,1]\n--    enBase 4 76  ==  [0,3,0,1]\nenBase :: Integer -> Integer -> [Integer]\nenBase b n | n < b     = [n]\n           | otherwise = n `mod` b : enBase b (n `div` b)\n\n-- (esSubconjunto xs ys) se verifica si xs es un subconjunto de ys. Por\n-- ejemplo,\n--    esSubconjunto [1,5] [5,2,1]  ==  True\n--    esSubconjunto [1,5] [5,2,3]  ==  False\nesSubconjunto :: Eq a => [a] -> [a] -> Bool\nesSubconjunto xs ys = all (`elem` ys) xs\n<\/pre>\n","protected":false},"excerpt":{"rendered":"<p>Un entero positivo n es pandigital en base b si su expresi\u00f3n en base b contiene todos los d\u00edgitos de 0 a b-1 al menos una vez. Por ejemplo, el 2 es pandigital en base 2 porque 2 en base 2 es 10, el 11 es pandigital en base 3 porque 11 en base 3&#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":[41,8,30,26,89,11,6],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/2745"}],"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=2745"}],"version-history":[{"count":5,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/2745\/revisions"}],"predecessor-version":[{"id":2779,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/2745\/revisions\/2779"}],"wp:attachment":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/media?parent=2745"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/categories?post=2745"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/tags?post=2745"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}