{"id":1063,"date":"2015-02-12T06:00:17","date_gmt":"2015-02-12T04:00:17","guid":{"rendered":"http:\/\/www.glc.us.es\/~jalonso\/exercitium\/?p=1063"},"modified":"2021-04-25T16:20:43","modified_gmt":"2021-04-25T14:20:43","slug":"mayor-producto-de-n-digitos-consecutivos-de-un-numero-2015","status":"publish","type":"post","link":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/mayor-producto-de-n-digitos-consecutivos-de-un-numero-2015\/","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 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, de derecha a\n-- izquierda. Por ejemplo, \n--    cifras 325  ==  [5,2,3]\ncifras :: Integer -> [Integer]\ncifras x \n    | x < 10    = [x]\n    | otherwise = r : cifras q\n    where (q,r) = quotRem x 10\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 (mayorProducto4 5 (product [1..]))\n-- \n--    | Def | 10   | 100  | 1000 | 5000  |\n--    |-----+------+------+------+-------|\n--    | 1   | 0.01 | 0.01 | 0.04 |  0.34 |\n--    | 2   | 0.01 | 0.01 | 0.07 |  2.86 |\n--    | 3   | 0.01 | 0.01 | 0.06 | 12.48 |\n--    | 4   | 0.00 | 0.12 |      |       |\n...\n<\/pre>\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":[4],"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\/1063"}],"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=1063"}],"version-history":[{"count":3,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/1063\/revisions"}],"predecessor-version":[{"id":1109,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/1063\/revisions\/1109"}],"wp:attachment":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/media?parent=1063"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/categories?post=1063"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/tags?post=1063"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}