{"id":2206,"date":"2016-03-08T06:00:01","date_gmt":"2016-03-08T04:00:01","guid":{"rendered":"http:\/\/www.glc.us.es\/~jalonso\/exercitium\/?p=2206"},"modified":"2016-05-02T09:02:46","modified_gmt":"2016-05-02T07:02:46","slug":"elemento-ausente","status":"publish","type":"post","link":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/elemento-ausente\/","title":{"rendered":"Elemento ausente"},"content":{"rendered":"<p>Sea xs una lista y n su longitud. Se dice que xs es casi completa si sus elementos son los n\u00fameros enteros entre 0 y n excepto uno. Por ejemplo, la lista [3,0,1] es casi completa.<\/p>\n<p>Definir la funci\u00f3n<\/p>\n<pre lang=\"text\">\n   ausente :: [Integer] -> Integer\n<\/pre>\n<p>tal que (ausente xs) es el \u00fanico entero (entre 0 y la longitud de xs) que no pertenece a la lista casi completa xs. Por ejemplo,<\/p>\n<pre lang=\"text\">\n   ausente [3,0,1]               ==  2\n   ausente [1,2,0]               ==  3\n   ausente (1+10^7:[0..10^7-1])  ==  10000000\n<\/pre>\n<h4>Soluciones<\/h4>\n<pre lang=\"haskell\">\nimport Data.List (foldl', genericLength)\nimport Data.Set (fromList, notMember)\n    \n-- 1\u00aa definici\u00f3n\nausente1 :: [Integer] -> Integer\nausente1 xs =\n    head [n | n <- [0..], n `notElem` xs]\n\n-- 2\u00aa definici\u00f3n\nausente2 :: [Integer] -> Integer\nausente2 xs =\n    head [n | n <- [0..], n `notMember` ys]\n    where ys = fromList xs\n         \n-- 3\u00aa definici\u00f3n (lineal)\nausente3 :: [Integer] -> Integer\nausente3 xs =\n    ((n * (n+1)) `div` 2) - sum xs\n    where n = genericLength xs  \n\n-- 4\u00aa definici\u00f3n\nausente4 :: [Integer] -> Integer\nausente4 xs =\n    ((n * (n+1)) `div` 2) - foldl' (+) 0 xs\n    where n = genericLength xs  \n\n-- Comparaci\u00f3n de eficiencia\n-- =========================\n\n--    \u03bb> let n = 10^5 in ausente1 (n+1:[0..n-1])\n--    100000\n--    (68.51 secs, 25,967,840 bytes)\n--    \u03bb> let n = 10^5 in ausente2 (n+1:[0..n-1])\n--    100000\n--    (0.12 secs, 123,488,144 bytes)\n--    \u03bb> let n = 10^5 in ausente3 (n+1:[0..n-1])\n--    100000\n--    (0.07 secs, 30,928,384 bytes)\n--    \u03bb> let n = 10^5 in ausente4 (n+1:[0..n-1])\n--    100000\n--    (0.02 secs, 23,039,904 bytes)\n--    \n--    \u03bb> let n = 10^7 in ausente2 (n+1:[0..n-1])\n--    10000000\n--    (14.32 secs, 15,358,509,280 bytes)\n--    \u03bb> let n = 10^7 in ausente3 (n+1:[0..n-1])\n--    10000000\n--    (5.57 secs, 2,670,214,936 bytes)\n--    \u03bb> let n = 10^7 in ausente4 (n+1:[0..n-1])\n--    10000000\n--    (3.36 secs, 2,074,919,184 bytes)\n<\/pre>\n","protected":false},"excerpt":{"rendered":"<p>Sea xs una lista y n su longitud. Se dice que xs es casi completa si sus elementos son los n\u00fameros enteros entre 0 y n excepto uno. Por ejemplo, la lista [3,0,1] es casi completa. Definir la funci\u00f3n ausente :: [Integer] -> Integer tal que (ausente xs) es el \u00fanico entero (entre 0 y&#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":[8,331,185,344,258,71,27,345,11,40],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/2206"}],"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=2206"}],"version-history":[{"count":4,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/2206\/revisions"}],"predecessor-version":[{"id":2236,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/2206\/revisions\/2236"}],"wp:attachment":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/media?parent=2206"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/categories?post=2206"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/tags?post=2206"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}