{"id":4001,"date":"2018-04-24T06:00:37","date_gmt":"2018-04-24T04:00:37","guid":{"rendered":"http:\/\/www.glc.us.es\/~jalonso\/exercitium\/?p=4001"},"modified":"2018-05-01T12:03:41","modified_gmt":"2018-05-01T10:03:41","slug":"sumas-de-subconjuntos","status":"publish","type":"post","link":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/sumas-de-subconjuntos\/","title":{"rendered":"Sumas de subconjuntos"},"content":{"rendered":"<p>Definir la funci\u00f3n<\/p>\n<pre lang=\"text\">\n   sumasSubconjuntos :: Set Int -> Set Int\n<\/pre>\n<p>tal que (sumasSubconjuntos xs) es el conjunto de las sumas de cada uno de los subconjuntos de xs. Por ejemplo,<\/p>\n<pre lang=\"text\">\n   \u03bb> sumasSubconjuntos (fromList [3,2,5])\n   fromList [0,2,3,5,7,8,10]\n   \u03bb> length (sumasSubconjuntos (fromList [-40,-39..40]))\n   1641\n<\/pre>\n<h4>Soluciones<\/h4>\n<pre lang=\"haskell\">\nimport Data.List\nimport Data.Set ( Set\n                , deleteFindMin\n                , fromList\n                , singleton\n                , toList\n                )\nimport qualified Data.Set as S\n\n-- 1\u00aa definici\u00f3n\n-- =============\n\nsumasSubconjuntos :: Set Int -> Set Int\nsumasSubconjuntos xs =\n  fromList (map sum (subsequences (toList xs))) \n\n-- 2\u00aa definici\u00f3n\n-- =============\n\nsumasSubconjuntos2 :: Set Int -> Set Int\nsumasSubconjuntos2 =\n  fromList . sumasSubconjuntosL . toList  \n\nsumasSubconjuntosL :: [Int] -> [Int]\nsumasSubconjuntosL []     = [0]\nsumasSubconjuntosL (x:xs) = ys `union` map (+x) ys\n  where ys = sumasSubconjuntosL xs\n\n-- 3\u00aa soluci\u00f3n\n-- ===========\n\nsumasSubconjuntos3 :: Set Int -> Set Int\nsumasSubconjuntos3 xs\n  | S.null xs = singleton 0\n  | otherwise = zs `S.union` (S.map (+y) zs)\n  where (y,ys) = deleteFindMin xs\n        zs     = sumasSubconjuntos2 ys\n\n-- Comparaci\u00f3n de eficiencia\n-- =========================\n\n--    \u03bb> length (sumasSubconjuntos (fromList [1..22]))\n--    254\n--    (4.17 secs, 4,574,495,128 bytes)\n--    \u03bb> length (sumasSubconjuntos2 (fromList [1..22]))\n--    254\n--    (0.03 secs, 5,583,200 bytes)\n--    \u03bb> length (sumasSubconjuntos3 (fromList [1..22]))\n--    254\n--    (0.03 secs, 5,461,064 bytes)\n--\n--    \u03bb> length (sumasSubconjuntos2 (fromList [1..60]))\n--    1831\n--    (2.75 secs, 611,912,128 bytes)\n--    \u03bb> length (sumasSubconjuntos3 (fromList [1..60]))\n--    1831\n--    (2.81 secs, 610,476,992 bytes)\n<\/pre>\n","protected":false},"excerpt":{"rendered":"<p>Definir la funci\u00f3n sumasSubconjuntos :: Set Int -> Set Int tal que (sumasSubconjuntos xs) es el conjunto de las sumas de cada uno de los subconjuntos de xs. Por ejemplo, \u03bb> sumasSubconjuntos (fromList [3,2,5]) fromList [0,2,3,5,7,8,10] \u03bb> length (sumasSubconjuntos (fromList [-40,-39..40])) 1641 Soluciones import Data.List import Data.Set ( Set , deleteFindMin , fromList , singleton&#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":[331,450,392,10,390,404,11,6,350,88,40,349,242,405],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/4001"}],"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=4001"}],"version-history":[{"count":2,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/4001\/revisions"}],"predecessor-version":[{"id":4029,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/4001\/revisions\/4029"}],"wp:attachment":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/media?parent=4001"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/categories?post=4001"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/tags?post=4001"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}