{"id":3045,"date":"2017-03-03T06:00:22","date_gmt":"2017-03-03T04:00:22","guid":{"rendered":"http:\/\/www.glc.us.es\/~jalonso\/exercitium\/?p=3045"},"modified":"2022-03-25T20:17:35","modified_gmt":"2022-03-25T18:17:35","slug":"numeros-construibles-como-sumas-de-dos-dados","status":"publish","type":"post","link":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/numeros-construibles-como-sumas-de-dos-dados\/","title":{"rendered":"N\u00fameros construibles como sumas de dos dados"},"content":{"rendered":"<p>Un n\u00famero x es <strong>construible<\/strong> a partir de de los n\u00fameros enteros positivos a y b si se puede escribir como una suma cuyos sumandos son a o b. Por ejemplo, 7 y 9 son construibles a partir de 2 y 3 ya que 7 = 2+2+3 y 9 = 3+3+3.<\/p>\n<p>Definir las funciones<\/p>\n<pre lang=\"text\">\n   construibles  :: Integer -> Integer -> [Integer]\n   esConstruible :: Integer -> Integer -> Integer -> Bool\n<\/pre>\n<p>tales que<\/p>\n<ul>\n<li>(construibles a b) es la lista de los n\u00fameros construibles a partir de a y b. Por ejemplo,<\/li>\n<\/ul>\n<pre lang=\"text\">\n     take 5 (construibles 2 9)  ==  [2,4,6,8,9]\n     take 5 (construibles 6 4)  ==  [4,6,8,10,12]\n     take 5 (construibles 9 7)  ==  [7,9,14,16,18]\n<\/pre>\n<ul>\n<li>(esConstruible a b x) se verifica si x es construible a partir de a y b. Por ejemplo,<\/li>\n<\/ul>\n<pre lang=\"text\">\n     esConstruible 2 3 7   ==  True\n     esConstruible 9 7 15  ==  False\n<\/pre>\n<h4>Soluciones<\/h4>\n<pre lang=\"haskell\">\nimport Data.List (nub)\n\nconstruibles :: Integer -> Integer -> [Integer]\nconstruibles a b = tail aux\n  where aux = 0 : mezcla [a + x | x <- aux]\n                         [b + x | x <- aux]\n\nmezcla :: [Integer] -> [Integer] -> [Integer]\nmezcla p@(x:xs) q@(y:ys) | x < y     = x : mezcla xs q\n                         | x > y     = y : mezcla p  ys  \n                         | otherwise = x : mezcla xs ys\nmezcla []       ys                   = ys\nmezcla xs       []                   = xs\n              \nesConstruible :: Integer -> Integer -> Integer -> Bool\nesConstruible a b x = x == y\n  where (y:_) = dropWhile (<x) (construibles a b)\n<\/pre>\n","protected":false},"excerpt":{"rendered":"<p>Un n\u00famero x es construible a partir de de los n\u00fameros enteros positivos a y b si se puede escribir como una suma cuyos sumandos son a o b. Por ejemplo, 7 y 9 son construibles a partir de 2 y 3 ya que 7 = 2+2+3 y 9 = 3+3+3. Definir las funciones construibles&#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":[8,59,415,11,6,45],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/3045"}],"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=3045"}],"version-history":[{"count":5,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/3045\/revisions"}],"predecessor-version":[{"id":3077,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/3045\/revisions\/3077"}],"wp:attachment":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/media?parent=3045"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/categories?post=3045"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/tags?post=3045"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}