{"id":4999,"date":"2019-05-14T06:00:55","date_gmt":"2019-05-14T04:00:55","guid":{"rendered":"http:\/\/www.glc.us.es\/~jalonso\/exercitium\/?p=4999"},"modified":"2021-04-25T12:40:06","modified_gmt":"2021-04-25T10:40:06","slug":"mayor-producto-de-n-digitos-consecutivos-de-un-numero-2019","status":"publish","type":"post","link":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/mayor-producto-de-n-digitos-consecutivos-de-un-numero-2019\/","title":{"rendered":"Mayor producto de n d\u00edgitos consecutivos de un n\u00famero"},"content":{"rendered":"<p>Definir la funci\u00f3n<\/p>\n<pre lang=\"text\">\n   mayorProducto :: Int -> Integer -> Integer\n<\/pre>\n<p>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,<\/p>\n<pre lang=\"text\">\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>\n<h4>Soluciones<\/h4>\n<pre lang=\"haskell\">\nimport Test.QuickCheck\nimport Data.List (inits, tails)\nimport Data.Char (digitToInt)\n\n-- 1\u00aa soluci\u00f3n\n-- ===========\n\nmayorProducto1 :: Int -> Integer -> Integer\nmayorProducto1 n x =\n  maximum [product xs | xs <- segmentos n (cifras x)]\n\n-- (cifras x) es la lista de las cifras del n\u00famero x. Por ejemplo, \n--    cifras 325  ==  [3,2,5]\ncifras :: Integer -> [Integer]\ncifras 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                 . cifras\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-- ---------------------------------------------------------------------\n-- Comparaci\u00f3n de soluciones                                          --\n-- ---------------------------------------------------------------------\n\n-- Tiempo (en segundos) del c\u00e1lculo de (mayorProducto 5 (product [1..n]))\n-- \n--    | Def | 500  | 1000 | 5000 | 10000 \n--    | 1   | 0.01 | 0.02 | 0.06 | 0.11\n--    | 2   | 0.01 | 0.03 | 0.80 | 3.98\n--    | 3   | 0.01 | 0.03 | 0.82 | 4.13\n--    | 4   | 2.77 |      |      |\n<\/pre>\n<h4>Pensamiento<\/h4>\n<blockquote><p>\nA las palabras de amor<br \/>\nles sienta bien su poquito<br \/>\nde exageraci\u00f3n.<\/p>\n<p>Antonio Machado\n<\/p><\/blockquote>\n","protected":false},"excerpt":{"rendered":"<p>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 ==&#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":[5],"tags":[58,248,38,74,28,10,15,11,157,6,33,45,75,47],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/4999"}],"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=4999"}],"version-history":[{"count":2,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/4999\/revisions"}],"predecessor-version":[{"id":5048,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/4999\/revisions\/5048"}],"wp:attachment":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/media?parent=4999"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/categories?post=4999"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/tags?post=4999"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}