{"id":6229,"date":"2021-03-31T06:00:16","date_gmt":"2021-03-31T04:00:16","guid":{"rendered":"http:\/\/www.glc.us.es\/~jalonso\/exercitium\/?p=6229"},"modified":"2021-04-07T11:47:15","modified_gmt":"2021-04-07T09:47:15","slug":"lista-muy-decreciente","status":"publish","type":"post","link":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/lista-muy-decreciente\/","title":{"rendered":"Lista muy decreciente"},"content":{"rendered":"<p>Una lista de n\u00fameros es muy decreciente si cada elemento es mayor que la suma de los restantes. Por ejemplo, [19,9,6,2] es muy decreciente ya que<\/p>\n<ul>\n<li>19 > 9 + 6 + 2,<\/li>\n<li>9 > 6 + 2 y<\/li>\n<li>6 > 2<\/li>\n<\/ul>\n<p>En cambio, [19,8,6,2] no lo es ya que 8 = 6 + 2.<\/p>\n<p>Definir la funci\u00f3n<\/p>\n<pre lang=\"text\">\n   muyDecreciente :: [Integer] -> Bool\n<\/pre>\n<p>tal que (muyDecreciente xs) se verifica si xs es muy decreciente. Por ejemplo,<\/p>\n<pre lang=\"text\">\n   muyDecreciente [19,9,6,2]  ==  True\n   muyDecreciente [19,8,6,2]  ==  False\n   muyDecreciente [2^k | k <- [60000,59999..0]]  ==  True\n<\/pre>\n<h4>Soluciones<\/h4>\n<pre lang=\"haskell\">\n-- 1\u00aa soluci\u00f3n\n-- ===========\n\nmuyDecreciente :: [Integer] -> Bool\nmuyDecreciente []     = True\nmuyDecreciente (x:xs) = x > sum xs && muyDecreciente xs\n\n-- 2\u00aa soluci\u00f3n\n-- ===========\n\nmuyDecreciente2 :: [Integer] -> Bool\nmuyDecreciente2 = snd . aux\n  where aux []     = (0,True)\n        aux (x:xs) = (x + s, x > s && b)\n          where (s,b) = aux xs\n\n-- 3\u00aa soluci\u00f3n\n-- ===========\n\nmuyDecreciente3 :: [Integer] -> Bool\nmuyDecreciente3 xs =\n  and (zipWith (>) xs (tail (scanr1 (+) xs)))\n\n-- Comparaci\u00f3n de eficiencia\n-- =========================\n\n-- La comparaci\u00f3n es\n--    \u03bb> muyDecreciente [2^k | k <- [10000,9999..0]]\n--    True\n--    (6.72 secs, 48,095,728,720 bytes)\n--    \u03bb> muyDecreciente2 [2^k | k <- [10000,9999..0]]\n--    True\n--    (0.08 secs, 67,222,960 bytes)\n--    \u03bb> muyDecreciente3 [2^k | k <- [10000,9999..0]]\n--    True\n--    (0.10 secs, 66,664,928 bytes)\n--\n--    \u03bb> muyDecreciente2 [2^k | k <- [50000,49999..0]]\n--    True\n--    (1.88 secs, 857,128,312 bytes)\n--    \u03bb> muyDecreciente3 [2^k | k <- [50000,49999..0]]\n--    True\n--    (1.67 secs, 854,326,736 bytes)\n<\/pre>\n<h4>Nuevas soluciones<\/h4>\n<ul>\n<li>En los comentarios se pueden escribir nuevas soluciones.\n<li>El c\u00f3digo se debe escribir entre una l\u00ednea con &#60;pre lang=&quot;haskell&quot;&#62; y otra con &#60;\/pre&#62;\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>Una lista de n\u00fameros es muy decreciente si cada elemento es mayor que la suma de los restantes. Por ejemplo, [19,9,6,2] es muy decreciente ya que 19 > 9 + 6 + 2, 9 > 6 + 2 y 6 > 2 En cambio, [19,8,6,2] no lo es ya que 8 = 6 + 2&#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":[2],"tags":[],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/6229"}],"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=6229"}],"version-history":[{"count":4,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/6229\/revisions"}],"predecessor-version":[{"id":6261,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/6229\/revisions\/6261"}],"wp:attachment":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/media?parent=6229"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/categories?post=6229"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/tags?post=6229"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}