{"id":571,"date":"2014-11-14T07:17:05","date_gmt":"2014-11-14T05:17:05","guid":{"rendered":"http:\/\/www.glc.us.es\/~jalonso\/exercitium\/?p=571"},"modified":"2021-04-25T17:08:02","modified_gmt":"2021-04-25T15:08:02","slug":"ultimo-digito-no-nulo-del-factorial-2014","status":"publish","type":"post","link":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/ultimo-digito-no-nulo-del-factorial-2014\/","title":{"rendered":"\u00daltimo d\u00edgito no nulo del factorial"},"content":{"rendered":"<h4>Enunciado<\/h4>\n<pre lang=\"text\">\n-- El factorial de 7 es\n--    7! = 1 * 2 * 3 * 4 * 5 * 6 * 7 = 5040\n-- por tanto, el \u00faltimo d\u00edgito no nulo del factorial de 7 es 4.\n-- \n-- Definir la funci\u00f3n\n--    ultimoNoNuloFactorial :: Integer -> Integer\n-- tal que (ultimoNoNuloFactorial n) es el \u00faltimo d\u00edgito no nulo del\n-- factorial de n. Por ejemplo,\n--    ultimoNoNuloFactorial  7  == 4\n--    ultimoNoNuloFactorial 10  == 8\n--    ultimoNoNuloFactorial 12  == 6\n--    ultimoNoNuloFactorial 97  == 2\n--    ultimoNoNuloFactorial  0  == 1\n--\n-- Comprobar con QuickCheck que si n es mayor que 4, entonces el \u00faltimo\n-- d\u00edgito no nulo del factorial de n es par.\n<\/pre>\n<h4>Soluciones<\/h4>\n<pre lang=\"haskell\">\nimport Test.QuickCheck\n\nultimoNoNuloFactorial :: Integer -> Integer\nultimoNoNuloFactorial n = ultimoNoNulo (factorial n)\n\n-- (ultimoNoNulo n) es el \u00faltimo d\u00edgito no nulo de n. Por ejemplo,\n--    ultimoNoNulo 5040  ==  4\nultimoNoNulo :: Integer -> Integer\nultimoNoNulo n | m \/= 0    = m\n               | otherwise = ultimoNoNulo (n `div` 10)\n               where m = n `rem` 10\n\n-- 2\u00aa definici\u00f3n (por comprensi\u00f3n)\nultimoNoNulo2 :: Integer -> Integer\nultimoNoNulo2 n = read [head (dropWhile (=='0') (reverse (show n)))]\n\n-- (factorial n) es el factorial de n. Por ejemplo,\n--    factorial 7  ==  5040\nfactorial :: Integer -> Integer\nfactorial n = product [1..n]\n\n\n-- La propiedad es\nprop_ultimoNoNuloFactorial :: Integer -> Property\nprop_ultimoNoNuloFactorial n = \n    n > 4 ==> even (ultimoNoNuloFactorial n)\n                  \n-- La comprobaci\u00f3n es\n--    ghci> quickCheck prop_ultimoNoNuloFactorial\n--    +++ OK, passed 100 tests.\n<\/pre>\n","protected":false},"excerpt":{"rendered":"<p>Enunciado &#8212; El factorial de 7 es &#8212; 7! = 1 * 2 * 3 * 4 * 5 * 6 * 7 = 5040 &#8212; por tanto, el \u00faltimo d\u00edgito no nulo del factorial de 7 es 4. &#8212; &#8212; Definir la funci\u00f3n &#8212; ultimoNoNuloFactorial :: Integer -> Integer &#8212; tal que (ultimoNoNuloFactorial n)&#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":[8,30,59,91,71,11,157,6,31,32,146],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/571"}],"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=571"}],"version-history":[{"count":5,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/571\/revisions"}],"predecessor-version":[{"id":740,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/571\/revisions\/740"}],"wp:attachment":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/media?parent=571"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/categories?post=571"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/tags?post=571"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}