{"id":5592,"date":"2020-02-24T05:30:40","date_gmt":"2020-02-24T03:30:40","guid":{"rendered":"http:\/\/www.glc.us.es\/~jalonso\/exercitium\/?p=5592"},"modified":"2020-03-02T09:42:09","modified_gmt":"2020-03-02T07:42:09","slug":"subconjuntos-de-orden-k","status":"publish","type":"post","link":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/subconjuntos-de-orden-k\/","title":{"rendered":"Subconjuntos de orden k"},"content":{"rendered":"<p>Definir la funci\u00f3n<\/p>\n<pre lang=\"text\">\n   kSubconjuntos :: [a] -> Int -> [[a]]\n<\/pre>\n<p>tal que (kSubconjuntos xs k) es la lista de los subconjuntos de xs con k elementos. Por ejemplo,<\/p>\n<pre lang=\"text\">\n   ghci> kSubconjuntos \"bcde\" 2\n   [\"bc\",\"bd\",\"be\",\"cd\",\"ce\",\"de\"]\n   ghci> kSubconjuntos \"bcde\" 3\n   [\"bcd\",\"bce\",\"bde\",\"cde\"]\n   ghci> kSubconjuntos \"abcde\" 3\n   [\"abc\",\"abd\",\"abe\",\"acd\",\"ace\",\"ade\",\"bcd\",\"bce\",\"bde\",\"cde\"]\n<\/pre>\n<h4>Soluciones<\/h4>\n<pre lang=\"haskell\">\nimport Data.List (subsequences)\n\n-- 1\u00aa definici\u00f3n\nkSubconjuntos1 :: [a] -> Int -> [[a]]\nkSubconjuntos1 xs k =\n  [ys | ys <- subsequences xs\n      , length ys == k]\n\n-- 2\u00aa definici\u00f3n\nkSubconjuntos :: [a] -> Int -> [[a]]\nkSubconjuntos _ 0      = [[]]\nkSubconjuntos [] _     = []\nkSubconjuntos (x:xs) k = \n  [x:ys | ys <- kSubconjuntos xs (k-1)] ++ kSubconjuntos xs k  \n\n-- Comparaci\u00f3n de eficiencia\n--    \u03bb> length (kSubconjuntos1 [1..24] 3)\n--    2024\n--    (4.70 secs, 3,489,911,856 bytes)\n--    \u03bb> length (kSubconjuntos [1..24] 3)\n--    2024\n--    (0.03 secs, 2,039,488 bytes)\n<\/pre>\n<h4>Otras soluciones<\/h4>\n<ul>\n<li>Se pueden escribir otras soluciones en los comentarios.\n<li>El c\u00f3digo se debe escribir entre una l\u00ednea con &#60;pre lang=\u00bbhaskell\u00bb&#62; y otra con &#60;\/pre&#62;\n<\/ul>\n<h4>Pensamiento<\/h4>\n<blockquote><p>\n\u00abLa belleza en las matem\u00e1ticas es ver la verdad sin esfuerzo.\u00bb <\/p>\n<p><a href=\"https:\/\/en.wikipedia.org\/wiki\/George_P%C3%B3lya\">George P\u00f3lya<\/a>.\n<\/p><\/blockquote>\n","protected":false},"excerpt":{"rendered":"<p>Definir la funci\u00f3n kSubconjuntos :: [a] -> Int -> [[a]] tal que (kSubconjuntos xs k) es la lista de los subconjuntos de xs con k elementos. Por ejemplo, ghci> kSubconjuntos \u00abbcde\u00bb 2 [\u00abbc\u00bb,\u00bbbd\u00bb,\u00bbbe\u00bb,\u00bbcd\u00bb,\u00bbce\u00bb,\u00bbde\u00bb] ghci> kSubconjuntos \u00abbcde\u00bb 3 [\u00abbcd\u00bb,\u00bbbce\u00bb,\u00bbbde\u00bb,\u00bbcde\u00bb] ghci> kSubconjuntos \u00ababcde\u00bb 3 [\u00ababc\u00bb,\u00bbabd\u00bb,\u00bbabe\u00bb,\u00bbacd\u00bb,\u00bbace\u00bb,\u00bbade\u00bb,\u00bbbcd\u00bb,\u00bbbce\u00bb,\u00bbbde\u00bb,\u00bbcde\u00bb] Soluciones import Data.List (subsequences) &#8212; 1\u00aa definici\u00f3n kSubconjuntos1 :: [a] -> Int&#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":[8,6,88],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/5592"}],"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=5592"}],"version-history":[{"count":3,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/5592\/revisions"}],"predecessor-version":[{"id":5652,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/5592\/revisions\/5652"}],"wp:attachment":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/media?parent=5592"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/categories?post=5592"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/tags?post=5592"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}