{"id":2796,"date":"2017-01-09T06:00:29","date_gmt":"2017-01-09T04:00:29","guid":{"rendered":"http:\/\/www.glc.us.es\/~jalonso\/exercitium\/?p=2796"},"modified":"2017-01-16T08:46:19","modified_gmt":"2017-01-16T06:46:19","slug":"sumas-y-restas-alternativas","status":"publish","type":"post","link":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/sumas-y-restas-alternativas\/","title":{"rendered":"Sumas y restas alternativas"},"content":{"rendered":"<p>Definir la funci\u00f3n<\/p>\n<pre lang=\"text\">\n   sumasYrestas :: Num a => [a] -> a\n<\/pre>\n<p>tal que (sumasYrestas xs) es el resultado de alternativamente los elementos de xs. Por ejemplo,<\/p>\n<pre lang=\"text\">\n   sumasYrestas [3,2,4,1,7] = 3 - 2 + 4 - 1 + 7\n                            = 11\n<\/pre>\n<p>Otros ejemplos,<\/p>\n<pre lang=\"text\">\n   sumasYrestas [3,2,4]              ==  5\n   sumasYrestas [3,2,4,1]            ==  4\n   sumasYrestas [3,2,4,1,7]          ==  11\n   sumasYrestas (replicate (10^6) 1) ==  0\n<\/pre>\n<h4>Soluciones<\/h4>\n<pre lang=\"haskell\">\n-- 1\u00aa definici\u00f3n\nsumasYrestas1 :: Num a => [a] -> a\nsumasYrestas1 []       = 0\nsumasYrestas1 [x]      = x\nsumasYrestas1 (x:y:xs) = x - y + sumasYrestas1 xs\n\n-- 2\u00aa definici\u00f3n\nsumasYrestas2 :: Num a => [a] -> a\nsumasYrestas2 xs = aux 1 xs\n  where aux _ []     = 0\n        aux n (y:ys) = n * y + aux (-n) ys\n\n-- 3\u00aa definici\u00f3n\nsumasYrestas3 :: Num a => [a] -> a\nsumasYrestas3 xs = auxS 0 xs\n  where auxS v []       = v\n        auxS v [x]      = v + x\n        auxS v (x:y:xs) = auxS (v+x-y) xs\n\n-- 4\u00aa definici\u00f3n\nsumasYrestas4 :: Num a => [a] -> a\nsumasYrestas4 xs =\n  sum (zipWith (*) xs [(-1)^n | n <- [0..]])\n\n-- 5\u00aa definici\u00f3n\nsumasYrestas5 :: Num a => [a] -> a\nsumasYrestas5 = sum . zipWith (*) (cycle [1,-1])\n\n-- 6\u00aa definici\u00f3n\nsumasYrestas6 :: Num a => [a] -> a\nsumasYrestas6 = foldr (-) 0\n\n-- Comparaci\u00f3n de eficiencia\n--    \u03bb> sumasYrestas1 (replicate (10^6) 1)\n--    0\n--    (1.50 secs, 171,623,648 bytes)\n--    \u03bb> sumasYrestas2 (replicate (10^6) 1)\n--    0\n--    (3.78 secs, 382,691,856 bytes)\n--    \u03bb> sumasYrestas3 (replicate (10^6) 1)\n--    0\n--    (1.39 secs, 204,404,024 bytes)\n--    \u03bb> sumasYrestas4 (replicate (10^6) 1)\n--    0\n--    (16.04 secs, 5,727,351,024 bytes)\n--    \u03bb> sumasYrestas5 (replicate (10^6) 1)\n--    0\n--    (1.39 secs, 235,770,344 bytes)\n--    \u03bb> sumasYrestas6 (replicate (10^6) 1)\n--    0\n--    (0.53 secs, 142,802,656 bytes)\n<\/pre>\n","protected":false},"excerpt":{"rendered":"<p>Definir la funci\u00f3n sumasYrestas :: Num a => [a] -> a tal que (sumasYrestas xs) es el resultado de alternativamente los elementos de xs. Por ejemplo, sumasYrestas [3,2,4,1,7] = 3 &#8211; 2 + 4 &#8211; 1 + 7 = 11 Otros ejemplos, sumasYrestas [3,2,4] == 5 sumasYrestas [3,2,4,1] == 4 sumasYrestas [3,2,4,1,7] == 11 sumasYrestas&#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":[166,94,11,6,40,76],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/2796"}],"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=2796"}],"version-history":[{"count":4,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/2796\/revisions"}],"predecessor-version":[{"id":2822,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/2796\/revisions\/2822"}],"wp:attachment":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/media?parent=2796"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/categories?post=2796"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/tags?post=2796"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}