Definir la funci\u00f3n<\/p>\n
\n mayorProducto :: Int -> Integer -> Integer\n<\/pre>\ntal que (mayorProducto n x) es el mayor producto de n d\u00edgitos consecutivos del n\u00famero x (suponiendo que x tiene al menos n d\u00edgitos). Por ejemplo,<\/p>\n
\n mayorProducto 2 325 == 10\n mayorProducto 5 11111 == 1\n mayorProducto 5 113111 == 3\n mayorProducto 5 110111 == 0\n mayorProducto 5 10151112 == 10\n mayorProducto 5 101511124 == 10\n mayorProducto 5 (product [1..1000]) == 41472\n<\/pre>\nNota<\/strong>: Este ejercicio est\u00e1 basado en el problema 8<\/a> del Proyecto Euler<\/a><\/p>\nSoluciones<\/h4>\n\nimport Data.List (inits, tails)\nimport Data.Char (digitToInt)\n\n-- 1\u00aa soluci\u00f3n\n-- ===========\n\nmayorProducto :: Int -> Integer -> Integer\nmayorProducto n x =\n maximum [product xs | xs <- segmentos n (digitos x)]\n\n-- (digitos x) es la lista de las digitos del n\u00famero x. Por ejemplo, \n-- digitos 325 == [3,2,5]\ndigitos :: Integer -> [Integer]\ndigitos x = map (toInteger . digitToInt) (show x)\n\n-- (segmentos n xs) es la lista de los segmentos de longitud n de la\n-- lista xs. Por ejemplo,\n-- segmentos 2 [3,5,4,6] == [[3,5],[5,4],[4,6]]\nsegmentos :: Int -> [Integer] -> [[Integer]]\nsegmentos n xs = take (length xs - n + 1) (map (take n) (tails xs))\n\n-- 2\u00aa soluci\u00f3n\n-- ===========\n\nmayorProducto2 :: Int -> Integer -> Integer\nmayorProducto2 n x = maximum (aux ns)\n where ns = [read [d] | d <- show x]\n aux xs | length xs < n = []\n | otherwise = product (take n xs) : aux (tail xs)\n\n-- 3\u00aa soluci\u00f3n\n-- ===========\n\nmayorProducto3 :: Int -> Integer -> Integer\nmayorProducto3 n = maximum\n . map (product . take n)\n . filter ((>=n) . length) \n . tails\n . digitos\n\n-- 4\u00aa soluci\u00f3n\n-- ===========\n\nmayorProducto4 :: Int -> Integer -> Integer\nmayorProducto4 n = maximum \n . map (product . map (fromIntegral . digitToInt)) \n . filter ((==n) . length) \n . concatMap inits\n . tails \n . show\n\n-- Comparaci\u00f3n de eficiencia\n-- =========================\n\n-- \u03bb> mayorProducto 5 (product [1..500])\n-- 28224\n-- (0.01 secs, 1,645,256 bytes)\n-- \u03bb> mayorProducto2 5 (product [1..500])\n-- 28224\n-- (0.03 secs, 5,848,416 bytes)\n-- \u03bb> mayorProducto3 5 (product [1..500])\n-- 28224\n-- (0.03 secs, 1,510,640 bytes)\n-- \u03bb> mayorProducto4 5 (product [1..500])\n-- 28224\n-- (1.85 secs, 10,932,551,216 bytes)\n-- \n-- \u03bb> mayorProducto 5 (product [1..7000])\n-- 46656\n-- (0.10 secs, 68,590,808 bytes)\n-- \u03bb> mayorProducto2 5 (product [1..7000])\n-- 46656\n-- (1.63 secs, 157,031,432 bytes)\n-- \u03bb> mayorProducto3 5 (product [1..7000])\n-- 46656\n-- (1.55 secs, 65,727,176 bytes)\n<\/pre>\nPensamiento<\/h4>\n\n\u00abEl control de la complejidad es la esencia de la programaci\u00f3n.\u00bb ~ B.W. Kernigan\n<\/p><\/blockquote>\n","protected":false},"excerpt":{"rendered":"
Definir la funci\u00f3n mayorProducto :: Int -> Integer -> Integer tal que (mayorProducto n x) es el mayor producto de n d\u00edgitos consecutivos del n\u00famero x (suponiendo que x tiene al menos n d\u00edgitos). Por ejemplo, mayorProducto 2 325 == 10 mayorProducto 5 11111 == 1 mayorProducto 5 113111 == 3 mayorProducto 5 110111 ==…<\/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":[8,58,248,481,38,183,28,10,15,11,157,95,33,45,75,47,410],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/5185"}],"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=5185"}],"version-history":[{"count":3,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/5185\/revisions"}],"predecessor-version":[{"id":5222,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/5185\/revisions\/5222"}],"wp:attachment":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/media?parent=5185"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/categories?post=5185"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/tags?post=5185"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}