{"id":3065,"date":"2017-03-09T06:00:52","date_gmt":"2017-03-09T04:00:52","guid":{"rendered":"http:\/\/www.glc.us.es\/~jalonso\/exercitium\/?p=3065"},"modified":"2017-03-20T07:34:48","modified_gmt":"2017-03-20T05:34:48","slug":"generadores-de-numeros-de-gabonacci","status":"publish","type":"post","link":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/generadores-de-numeros-de-gabonacci\/","title":{"rendered":"Generadores de n\u00fameros de Gabonacci"},"content":{"rendered":"<p>Los n\u00fameros de Gabonacci generados por (a,b) son los elementos de la sucesi\u00f3n de Gabonacci definida por<\/p>\n<pre lang=\"text\">\n   G(0) = a\n   G(1) = b\n   G(n) = G(n-2) + G(n-1), si n > 1\n<\/pre>\n<p>Por ejemplo, la sucesi\u00f3n de Gabonacci generada por (2,5) es 2, 5, 7, 12, 19, 31, 50, 81, 131, 212, &#8230;<\/p>\n<p>Un n\u00famero pertenece a  distintas sucesiones de Gabonacci. Por ejemplo, el 9 pertenece a las sucesiones de Gabonacci generados por (3,3), (1,4) y (4,5).<\/p>\n<p>El <strong>menor generador de Gabonacci<\/strong> de un n\u00famero x es el par (a,b), con 1 \u2264 a \u2264 b, tal que (a,b) es un generador de Gabonacci de x y no existe ning\u00fan generador de Gabonacci de x (a&#8217;,b&#8217;) tal que b&#8217; &lt; b \u00f3 b&#8217; = b y a&#8217; &lt; a.  Por ejemplo, el menor generador de Gabonacci de 9 es (3,3).<\/p>\n<p>Definir la funci\u00f3n<\/p>\n<pre lang=\"text\">\n   menorGenerador :: Integer -> (Integer,Integer)\n<\/pre>\n<p>tal que (menorGenerador x) es el menor generador de Gabonacci de x. Por ejemplo,<\/p>\n<pre lang=\"text\">\n   menorGenerador 9          ==  (3,3)\n   menorGenerador 7          ==  (1,3)\n   menorGenerador 5          ==  (1,1)\n   menorGenerador 27         ==  (3,7)\n   menorGenerador 57         ==  (4,9)\n   menorGenerador 218        ==  (10,21)\n   menorGenerador 1121       ==  (20,41)\n   menorGenerador 89         ==  (1,1)\n   menorGenerador 123        ==  (1,3)\n   menorGenerador 1000       ==  (2,10)\n   menorGenerador 842831057  ==  (2,7)\n   menorGenerador 1573655    ==  (985,1971)\n<\/pre>\n<h4>Soluciones<\/h4>\n<pre lang=\"haskell\">\nmenorGenerador :: Integer -> (Integer,Integer)\nmenorGenerador = head . generadores\n\ngeneradores :: Integer -> [(Integer,Integer)]\ngeneradores x = [(a,b) | b <- [1..x]\n                       , a <- [1..b]\n                       , pertenece x (gabonacci a b)]\n\ngabonacci :: Integer -> Integer -> [Integer]\ngabonacci a b = aux\n  where aux = a : scanl (+) b aux\n\npertenece :: Integer -> [Integer] -> Bool\npertenece x ys =\n  x == head (dropWhile (<x) ys)\n<\/pre>\n","protected":false},"excerpt":{"rendered":"<p>Los n\u00fameros de Gabonacci generados por (a,b) son los elementos de la sucesi\u00f3n de Gabonacci definida por G(0) = a G(1) = b G(n) = G(n-2) + G(n-1), si n > 1 Por ejemplo, la sucesi\u00f3n de Gabonacci generada por (2,5) es 2, 5, 7, 12, 19, 31, 50, 81, 131, 212, &#8230; Un n\u00famero&#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":[286,59,71,11,6,78],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/3065"}],"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=3065"}],"version-history":[{"count":6,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/3065\/revisions"}],"predecessor-version":[{"id":3114,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/3065\/revisions\/3114"}],"wp:attachment":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/media?parent=3065"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/categories?post=3065"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/tags?post=3065"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}