{"id":1894,"date":"2015-12-22T06:00:20","date_gmt":"2015-12-22T04:00:20","guid":{"rendered":"http:\/\/www.glc.us.es\/~jalonso\/exercitium\/?p=1894"},"modified":"2022-03-25T20:21:27","modified_gmt":"2022-03-25T18:21:27","slug":"producto-infinito","status":"publish","type":"post","link":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/producto-infinito\/","title":{"rendered":"Producto infinito"},"content":{"rendered":"<p>Definir la funci\u00f3n<\/p>\n<pre lang=\"text\">\n   productoInfinito :: [Int] -> [Int]\n<\/pre>\n<p>tal que (productoInfinito xs) es la lista infinita que en la posici\u00f3n N tiene el producto de los N primeros elementos de la lista infinita xs. Por ejemplo,<\/p>\n<pre lang=\"text\">\n   take 5 (productoInfinito [1..])    ==  [1,2,6,24,120]\n   take 5 (productoInfinito [2,4..])  ==  [2,8,48,384,3840]\n   take 5 (productoInfinito [1,3..])  ==  [1,3,15,105,945]\n<\/pre>\n<p><strong>Nota<\/strong>: Este ejercicio es parte del examen del grupo 3 del 2 de diciembre.<\/p>\n<h4>Soluciones<\/h4>\n<pre lang=\"haskell\">\n-- 1\u00aa definici\u00f3n (por comprensi\u00f3n):\nproductoInfinito1 :: [Integer] -> [Integer]\nproductoInfinito1 xs = [product (take n xs) | n <- [1..]]\n\n-- 2\u00aa definici\u00f3n (por recursi\u00f3n)\nproductoInfinito2 :: [Integer] -> [Integer]\nproductoInfinito2 (x:y:zs) = x : productoInfinito2 (x*y:zs)\n\n-- 2\u00aa definici\u00f3n (por recursi\u00f3n y map)\nproductoInfinito3 :: [Integer] -> [Integer]\nproductoInfinito3 []     = [1]\nproductoInfinito3 (x:xs) = map (x*) (1 : productoInfinito3 xs)\n\n-- 4\u00aa definici\u00f3n (con scanl1)\nproductoInfinito4 :: [Integer] -> [Integer]\nproductoInfinito4 = scanl1 (*)\n\n-- Comparaci\u00f3n de eficiencia\n--    \u03bb> take 20 (show (productoInfinito1 [2,4..] !! 10000))\n--    \"11358071114466915693\"\n--    (0.35 secs, 98,287,328 bytes)\n--    \u03bb> take 20 (show (productoInfinito2 [2,4..] !! 10000))\n--    \"11358071114466915693\"\n--    (0.35 secs, 98,840,440 bytes)\n--    \u03bb> take 20 (show (productoInfinito3 [2,4..] !! 10000))\n--    \"11358071114466915693\"\n--    (7.36 secs, 6,006,360,472 bytes)\n--    \u03bb> take 20 (show (productoInfinito4 [2,4..] !! 10000))\n--    \"11358071114466915693\"\n--    (0.34 secs, 96,367,000 bytes)\n<\/pre>\n","protected":false},"excerpt":{"rendered":"<p>Definir la funci\u00f3n productoInfinito :: [Int] -> [Int] tal que (productoInfinito xs) es la lista infinita que en la posici\u00f3n N tiene el producto de los N primeros elementos de la lista infinita xs. Por ejemplo, take 5 (productoInfinito [1..]) == [1,2,6,24,120] take 5 (productoInfinito [2,4..]) == [2,8,48,384,3840] take 5 (productoInfinito [1,3..]) == [1,3,15,105,945] Nota:&#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":[8,415,10,11,157,6,252,47],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/1894"}],"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=1894"}],"version-history":[{"count":3,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/1894\/revisions"}],"predecessor-version":[{"id":1935,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/1894\/revisions\/1935"}],"wp:attachment":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/media?parent=1894"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/categories?post=1894"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/tags?post=1894"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}