{"id":3106,"date":"2017-03-17T06:00:27","date_gmt":"2017-03-17T04:00:27","guid":{"rendered":"http:\/\/www.glc.us.es\/~jalonso\/exercitium\/?p=3106"},"modified":"2017-03-24T08:06:44","modified_gmt":"2017-03-24T06:06:44","slug":"suma-de-subconjuntos","status":"publish","type":"post","link":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/suma-de-subconjuntos\/","title":{"rendered":"Suma de subconjuntos"},"content":{"rendered":"<p>Los subconjuntos de [1, 4, 2] son<\/p>\n<pre lang=\"text\">\n   [], [1], [4], [1, 4], [2], [1, 2], [4, 2], [1, 4, 2]\n<\/pre>\n<p>Las sumas de sus elementos son<\/p>\n<pre lang=\"text\">\n   0, 1, 4, 5, 2, 3, 6, 7\n<\/pre>\n<p>Y la suma de las sumas es 28.<\/p>\n<p>Definir la funci\u00f3n<\/p>\n<pre lang=\"text\">\n   sumaSubconjuntos :: [Integer] -> Integer\n<\/pre>\n<p>tal que (sumaSubconjuntos xs) es la suma de las sumas de  los<br \/>\nsubconjuntos de xs. Por ejemplo,<\/p>\n<pre lang=\"text\">\n   sumaSubconjuntos [1,2]                     == 6\n   sumaSubconjuntos [1,4,2]                   == 28\n   length (show (sumaSubconjuntos [1..10^6])) == 301042\n<\/pre>\n<h4>Soluciones<\/h4>\n<pre lang=\"haskell\">\nimport Data.List (subsequences)\n\n-- 1\u00aa definici\u00f3n\nsumaSubconjuntos :: [Integer] -> Integer\nsumaSubconjuntos xs =\n  sum [sum ys | ys <- subsequences xs]\n\n-- 2\u00aa definici\u00f3n\nsumaSubconjuntos2 :: [Integer] -> Integer\nsumaSubconjuntos2 =\n  sum . map sum . subsequences\n\n-- 3\u00aa definici\u00f3n\nsumaSubconjuntos3 :: [Integer] -> Integer\nsumaSubconjuntos3 xs =\n  2^(n-1) * sum xs\n  where n = length xs\n<\/pre>\n","protected":false},"excerpt":{"rendered":"<p>Los subconjuntos de [1, 4, 2] son [], [1], [4], [1, 4], [2], [1, 2], [4, 2], [1, 4, 2] Las sumas de sus elementos son 0, 1, 4, 5, 2, 3, 6, 7 Y la suma de las sumas es 28. Definir la funci\u00f3n sumaSubconjuntos :: [Integer] -> Integer tal que (sumaSubconjuntos xs) es&#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":[8,10,11,88,40],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/3106"}],"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=3106"}],"version-history":[{"count":3,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/3106\/revisions"}],"predecessor-version":[{"id":3132,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/3106\/revisions\/3132"}],"wp:attachment":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/media?parent=3106"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/categories?post=3106"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/tags?post=3106"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}