{"id":2280,"date":"2016-04-04T06:00:57","date_gmt":"2016-04-04T04:00:57","guid":{"rendered":"http:\/\/www.glc.us.es\/~jalonso\/exercitium\/?p=2280"},"modified":"2016-04-11T08:56:07","modified_gmt":"2016-04-11T06:56:07","slug":"factorial-generalizado","status":"publish","type":"post","link":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/factorial-generalizado\/","title":{"rendered":"Factorial generalizado"},"content":{"rendered":"<p>El factorial generalizado de x respecto de y y z es el producto x(x-z)(x-2z) &#8230; (x-(y-1)z). Por ejemplo, el factorial generalizado de 7 respecto de 3 y 2 es 7x5x3 = 105 y el de 7 respecto de 2 y 3 es 7&#215;4 = 28<\/p>\n<p>Definir la funci\u00f3n<\/p>\n<pre lang=\"text\">\n   factGen :: Integer -> Integer -> Integer -> Integer\n<\/pre>\n<p>tal que (factGen x y z) es el factorial generalizado de x respecto de y y z. Por ejemplo,<\/p>\n<pre lang=\"text\">\n   factGen 7 3 2  ==  105\n   factGen 7 2 3  ==  28\n<\/pre>\n<p>Nota: Se supone que x, y y z son positivos y z &lt; x.<\/p>\n<p>Comprobar con QuickCheck que (factGen x x 1) es el factorial de x.<\/p>\n<h4>Soluciones<\/h4>\n<pre lang=\"haskell\">\nimport Test.QuickCheck\n\n-- 1\u00aa definici\u00f3n (por comprensi\u00f3n):\nfactGen :: Integer -> Integer -> Integer -> Integer\nfactGen x y z = product [x,x-z..x-(y-1)*z]\n\n-- 2\u00aa definici\u00f3n (por recursi\u00f3n):\nfactGen2 :: Integer -> Integer -> Integer -> Integer\nfactGen2 x 1 _ = x\nfactGen2 x y z = x * factGen2 (x-z) (y-1) z\n\n-- Propiedad de equivalencia\nprop_equiv :: Positive Integer\n           -> Positive Integer -> Positive Integer -> Property\nprop_equiv (Positive x) (Positive y) (Positive z) =\n    z < x ==> factGen x y z == factGen2 x y z\n\n-- La comprobaci\u00f3n es\n--    \u03bb> quickCheck prop_equiv\n--    +++ OK, passed 100 tests.\n      \n-- La propiedad es       \nprop_factGen :: Positive Integer -> Bool\nprop_factGen (Positive x) =\n    factGen x x 1 == product [1..x]\n\n-- La comprobaci\u00f3n es      \n--    \u03bb> quickCheck prop_factGen\n--    +++ OK, passed 100 tests.\n<\/pre>\n<h4>Soluci\u00f3n en Maxima<\/h4>\n<pre lang=\"text\">\nfactGen (x,y,z) := genfact (x,y,z)$\n<\/pre>\n","protected":false},"excerpt":{"rendered":"<p>El factorial generalizado de x respecto de y y z es el producto x(x-z)(x-2z) &#8230; (x-(y-1)z). Por ejemplo, el factorial generalizado de 7 respecto de 3 y 2 es 7x5x3 = 105 y el de 7 respecto de 2 y 3 es 7&#215;4 = 28 Definir la funci\u00f3n factGen :: Integer -> Integer -> Integer&#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":[8,157,6,146],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/2280"}],"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=2280"}],"version-history":[{"count":3,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/2280\/revisions"}],"predecessor-version":[{"id":2306,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/2280\/revisions\/2306"}],"wp:attachment":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/media?parent=2280"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/categories?post=2280"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/tags?post=2280"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}