El orden de divisibilidad de un n\u00famero x es el mayor n tal que para todo i menor o igual que n, los i primeros d\u00edgitos de n es divisible por i. Por ejemplo, el orden de divisibilidad de 74156 es 3 porque<\/p>\n
\n 7 es divisible por 1\n 74 es divisible por 2\n 741 es divisible por 3\n 7415 no es divisible por 4\n<\/pre>\nDefinir la funci\u00f3n<\/p>\n
\n ordenDeDivisibilidad :: Integer -> Int\n<\/pre>\ntal que (ordenDeDivisibilidad x) es el orden de divisibilidad de x. Por ejemplo,<\/p>\n
\n ordenDeDivisibilidad 74156 == 3\n ordenDeDivisibilidad 3608528850368400786036725 == 25\n<\/pre>\nSoluciones<\/h4>\n\nimport Data.List (inits)\n\n-- 1\u00aa definici\u00f3n de ordenDeDivisibilidad\n-- =====================================\n\nordenDeDivisibilidad :: Integer -> Int\nordenDeDivisibilidad n = \n length (takeWhile (\\(x,k) -> x `mod` k == 0) (zip (sucDigitos n) [1..]))\n\n-- (sucDigitos x) es la sucesi\u00f3n de los d\u00edgitos de x. Por ejemplo,\n-- sucDigitos 325 == [3,32,325]\n-- sucDigitos 32050 == [3,32,320,3205,32050]\nsucDigitos :: Integer -> [Integer]\nsucDigitos n = \n [n `div` (10^i) | i <- [k-1,k-2..0]]\n where k = length (show n)\n\n-- 2\u00aa definici\u00f3n de sucDigitos\nsucDigitos2 :: Integer -> [Integer]\nsucDigitos2 n = [read xs | xs <- aux (show n)]\n where aux [] = []\n aux (d:ds) = [d] : map (d:) (aux ds)\n\n-- 3\u00aa definici\u00f3n de sucDigitos\nsucDigitos3 :: Integer -> [Integer]\nsucDigitos3 n = \n [read (take k ds) | k <- [1..length ds]]\n where ds = show n\n\n-- 4\u00aa definici\u00f3n de sucDigitos\nsucDigitos4 :: Integer -> [Integer]\nsucDigitos4 n = [read xs | xs <- tail (inits (show n))]\n\n-- 5\u00aa definici\u00f3n de sucDigitos\nsucDigitos5 :: Integer -> [Integer]\nsucDigitos5 n = map read (tail (inits (show n)))\n\n-- 6\u00aa definici\u00f3n de sucDigitos\nsucDigitos6 :: Integer -> [Integer]\nsucDigitos6 = map read . (tail . inits . show)\n\n-- Eficiencia de las definiciones de sucDigitos\n-- ghci> length (sucDigitos (10^5000))\n-- 5001\n-- (0.01 secs, 1550688 bytes)\n-- ghci> length (sucDigitos2 (10^5000))\n-- 5001\n-- (1.25 secs, 729411872 bytes)\n-- ghci> length (sucDigitos3 (10^5000))\n-- 5001\n-- (0.02 secs, 2265120 bytes)\n-- ghci> length (sucDigitos4 (10^5000))\n-- 5001\n-- (1.10 secs, 728366872 bytes)\n-- ghci> length (sucDigitos5 (10^5000))\n-- 5001\n-- (1.12 secs, 728393864 bytes)\n-- ghci> length (sucDigitos6 (10^5000))\n-- 5001\n-- (1.20 secs, 728403052 bytes)\n-- \n-- ghci> length (sucDigitos (10^3000000))\n-- 3000001\n-- (2.73 secs, 820042696 bytes)\n-- ghci> length (sucDigitos3 (10^3000000))\n-- 3000001\n-- (3.69 secs, 820043688 bytes)\n\n-- 2\u00aa definici\u00f3n de ordenDeDivisibilidad\n-- =====================================\n\nordenDeDivisibilidad :: Integer -> Int\nordenDeDivisibilidad x =\n length $ takeWhile (==0) $ zipWith (mod . read) (tail $ inits $ show x) [1..]\n<\/pre>\n","protected":false},"excerpt":{"rendered":"El orden de divisibilidad de un n\u00famero x es el mayor n tal que para todo i menor o igual que n, los i primeros d\u00edgitos de n es divisible por i. Por ejemplo, el orden de divisibilidad de 74156 es 3 porque 7 es divisible por 1 74 es divisible por 2 741 es…<\/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":[5],"tags":[8,30,74,28,10,89,11,95,6,33,45,47,34,9],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/1175"}],"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=1175"}],"version-history":[{"count":5,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/1175\/revisions"}],"predecessor-version":[{"id":1212,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/1175\/revisions\/1212"}],"wp:attachment":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/media?parent=1175"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/categories?post=1175"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/tags?post=1175"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}