{"id":2554,"date":"2016-11-10T06:00:57","date_gmt":"2016-11-10T04:00:57","guid":{"rendered":"http:\/\/www.glc.us.es\/~jalonso\/exercitium\/?p=2554"},"modified":"2016-11-17T08:16:59","modified_gmt":"2016-11-17T06:16:59","slug":"subconjuntos-acotados","status":"publish","type":"post","link":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/subconjuntos-acotados\/","title":{"rendered":"Subconjuntos acotados"},"content":{"rendered":"<p>Definir la funci\u00f3n<\/p>\n<pre lang=\"text\">\n   subconjuntosAcotados :: [a] -> Int -> [[a]]\n<\/pre>\n<p>tal que (subconjuntosAcotados xs k) es la lista de los subconjuntos de xs con k elementos como m\u00e1ximo. Por ejemplo,<\/p>\n<pre lang=\"text\">\n   \u03bb> subconjuntosAcotados \"abcd\" 1\n   [\"a\",\"b\",\"c\",\"d\",\"\"]\n   \u03bb> subconjuntosAcotados \"abcd\" 2\n   [\"ab\",\"ac\",\"ad\",\"a\",\"bc\",\"bd\",\"b\",\"cd\",\"c\",\"d\",\"\"]\n   \u03bb> subconjuntosAcotados \"abcd\" 3\n   [\"abc\",\"abd\",\"ab\",\"acd\",\"ac\",\"ad\",\"a\",\n    \"bcd\",\"bc\",\"bd\",\"b\",\"cd\",\"c\",\"d\",\"\"]\n   \u03bb> length (subconjuntosAcotados [1..1000] 2)\n   500501\n   \u03bb> length (subconjuntosAcotados2 [1..2000] 2)\n   2001001\n<\/pre>\n<h4>Soluciones<\/h4>\n<pre lang=\"haskell\">\nimport Data.List (subsequences)\n\n-- 1\u00aa definici\u00f3n\nsubconjuntosAcotados1 :: [a] -> Int -> [[a]]\nsubconjuntosAcotados1 xs k =\n  [ys | ys <- subsequences xs\n      , length ys <= k]\n\n-- 2\u00aa definici\u00f3n\nsubconjuntosAcotados2 :: [a] -> Int -> [[a]]\nsubconjuntosAcotados2 _ 0  = [[]]\nsubconjuntosAcotados2 [] _ = [[]]\nsubconjuntosAcotados2 (x:xs) k =\n  [x:ys | ys <- subconjuntosAcotados2 xs (k-1)]\n  ++ subconjuntosAcotados2 xs k\n\n-- Comparaci\u00f3n de eficiencia\n--    \u03bb> length (subconjuntosAcotados1 [1..25] 2)\n--    326\n--    (10.48 secs, 6,968,637,480 bytes)\n--    \u03bb> length (subconjuntosAcotados2 [1..25] 2)\n--    326\n--    (0.00 secs, 0 bytes)\n<\/pre>\n","protected":false},"excerpt":{"rendered":"<p>Definir la funci\u00f3n subconjuntosAcotados :: [a] -> Int -> [[a]] tal que (subconjuntosAcotados xs k) es la lista de los subconjuntos de xs con k elementos como m\u00e1ximo. Por ejemplo, \u03bb> subconjuntosAcotados \u00ababcd\u00bb 1 [\u00aba\u00bb,\u00bbb\u00bb,\u00bbc\u00bb,\u00bbd\u00bb,\u00bb\u00bb] \u03bb> subconjuntosAcotados \u00ababcd\u00bb 2 [\u00abab\u00bb,\u00bbac\u00bb,\u00bbad\u00bb,\u00bba\u00bb,\u00bbbc\u00bb,\u00bbbd\u00bb,\u00bbb\u00bb,\u00bbcd\u00bb,\u00bbc\u00bb,\u00bbd\u00bb,\u00bb\u00bb] \u03bb> subconjuntosAcotados \u00ababcd\u00bb 3 [\u00ababc\u00bb,\u00bbabd\u00bb,\u00bbab\u00bb,\u00bbacd\u00bb,\u00bbac\u00bb,\u00bbad\u00bb,\u00bba\u00bb, \u00abbcd\u00bb,\u00bbbc\u00bb,\u00bbbd\u00bb,\u00bbb\u00bb,\u00bbcd\u00bb,\u00bbc\u00bb,\u00bbd\u00bb,\u00bb\u00bb] \u03bb> length (subconjuntosAcotados [1..1000] 2) 500501 \u03bb> length (subconjuntosAcotados2&#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":[4],"tags":[8,28,6,88],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/2554"}],"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=2554"}],"version-history":[{"count":3,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/2554\/revisions"}],"predecessor-version":[{"id":2593,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/2554\/revisions\/2593"}],"wp:attachment":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/media?parent=2554"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/categories?post=2554"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/tags?post=2554"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}