{"id":3567,"date":"2017-12-28T06:00:40","date_gmt":"2017-12-28T04:00:40","guid":{"rendered":"http:\/\/www.glc.us.es\/~jalonso\/exercitium\/?p=3567"},"modified":"2018-02-19T08:40:13","modified_gmt":"2018-02-19T06:40:13","slug":"factorial-modulo","status":"publish","type":"post","link":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/factorial-modulo\/","title":{"rendered":"Factorial m\u00f3dulo"},"content":{"rendered":"<p>Definir la funci\u00f3n<\/p>\n<pre lang=\"text\">\n   factorialMod :: Integer -> Integer -> Integer\n<\/pre>\n<p>tal que (factorialMod n x) es el factorial de x m\u00f3dulo n. Por ejemplo,<\/p>\n<pre lang=\"text\">\n   factorialMod (7+10^9) 100       ==  437918130\n   factorialMod (7+10^9) (5*10^6)  ==  974067448\n<\/pre>\n<h4>Soluciones<\/h4>\n<pre lang=\"haskell\">\nimport Data.List (foldl')\n\n-- 1\u00aa definici\u00f3n\n-- =============\n\nfactorialMod :: Integer -> Integer -> Integer\nfactorialMod n x =\n  factorial x `mod` n\n\n-- (factorial x) es el factorial de x. Por ejemplo,\n--    factorial 3  ==  6\nfactorial :: Integer -> Integer\nfactorial x = product [1..x]\n\n-- 2\u00aa definici\u00f3n\n-- =============\n\nfactorialMod2 :: Integer -> Integer -> Integer\nfactorialMod2 n x =\n  foldl' (prodMod n) 1 [1..x]\n\n-- (prodMod n x y) es el producto de x e y m\u00f3dulo n. Por ejemplo,\n--    prodMod 3 4 7  ==  1\n--    prodMod 5 4 7  ==  -- 3\nprodMod :: Integer -> Integer -> Integer -> Integer\nprodMod n x y =\n  ((x `mod` n) * (y `mod` n)) `mod` n\n  \n-- Comparaci\u00f3n de eficiencia\n-- =========================\n\n--    \u03bb> factorialMod (7+10^9) (5*10^4)\n--    737935835\n--    (2.62 secs, 2,601,358,640 bytes)\n--    \u03bb> factorialMod2 (7+10^9) (5*10^4)\n--    737935835\n--    (0.07 secs, 23,471,880 bytes)\n<\/pre>\n","protected":false},"excerpt":{"rendered":"<p>Definir la funci\u00f3n factorialMod :: Integer -> Integer -> Integer tal que (factorialMod n x) es el factorial de x m\u00f3dulo n. Por ejemplo, factorialMod (7+10^9) 100 == 437918130 factorialMod (7+10^9) (5*10^6) == 974067448 Soluciones import Data.List (foldl&#8217;) &#8212; 1\u00aa definici\u00f3n &#8212; ============= factorialMod :: Integer -> Integer -> Integer factorialMod n x = factorial&#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":[185,89,11,157],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/3567"}],"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=3567"}],"version-history":[{"count":2,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/3567\/revisions"}],"predecessor-version":[{"id":3794,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/3567\/revisions\/3794"}],"wp:attachment":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/media?parent=3567"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/categories?post=3567"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/tags?post=3567"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}