{"id":2334,"date":"2016-04-18T06:00:02","date_gmt":"2016-04-18T04:00:02","guid":{"rendered":"http:\/\/www.glc.us.es\/~jalonso\/exercitium\/?p=2334"},"modified":"2016-04-25T06:46:11","modified_gmt":"2016-04-25T04:46:11","slug":"minima-diferencia-entre-elementos-de-una-lista","status":"publish","type":"post","link":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/minima-diferencia-entre-elementos-de-una-lista\/","title":{"rendered":"M\u00ednima diferencia entre elementos de una lista"},"content":{"rendered":"<p>Definir la funci\u00f3n<\/p>\n<pre lang=\"text\">\n   minimaDiferencia :: (Num a, Ord a) => [a] -> a\n<\/pre>\n<p>tal que (minimaDiferencia xs) es el menor valor absoluto de las diferencias entre todos los pares de elementos de xs (que se supone que tiene al menos 2 elementos). Por ejemplo,<\/p>\n<pre lang=\"text\">\n   minimaDiferencia [1,5,3,19,18,25]  ==  1\n   minimaDiferencia [30,5,20,9]       ==  4\n   minimaDiferencia [30,5,20,9,5]     ==  0\n   minimaDiferencia [1..10^6]         ==  1\n<\/pre>\n<p>En el primer ejemplo la menor diferencia es 1 y se da entre los elementos 19 y 18; en el 2\u00aa es 4 entre los elementos 5 y 9 y en la 3\u00aa es 0 porque el elemento 5 est\u00e1 repetido.<\/p>\n<h4>Soluciones<\/h4>\n<pre lang=\"haskell\">\nimport Data.List (delete, sort)\n\n-- 1\u00aa definici\u00f3n    \nminimaDiferencia1 :: (Num a, Ord a) => [a] -> a\nminimaDiferencia1 xs =\n    minimum [abs (x - y) | x <- xs, y <- delete x xs]\n\n-- 2\u00aa definici\u00f3n    \nminimaDiferencia2 :: (Num a, Ord a) => [a] -> a\nminimaDiferencia2 [x,y]  = abs (x - y)\nminimaDiferencia2 (x:xs) = min (minimum [abs (x - y) | y <- xs])\n                               (minimaDiferencia2 xs)      \n\n-- 3\u00aa definici\u00f3n    \nminimaDiferencia3 :: (Num a, Ord a) => [a] -> a\nminimaDiferencia3 xs =\n    minimum [y - x | (x,y) <- zip ys (tail ys)]\n    where ys = sort xs\n\n-- Comparaci\u00f3n de eficiencia\n--    \u03bb> minimaDiferencia1 [1..2*10^3]\n--    1\n--    (3.47 secs, 1,419,790,688 bytes)\n--    \u03bb> minimaDiferencia2 [1..2*10^3]\n--    1\n--    (0.78 secs, 684,030,712 bytes)\n--    \u03bb> minimaDiferencia3 [1..2*10^3]\n--    1\n--    (0.02 secs, 0 bytes)\n--    \n--    \u03bb> minimaDiferencia2 [1..5*10^3]\n--    1\n--    (5.14 secs, 4,233,952,776 bytes)\n--    \u03bb> minimaDiferencia3 [1..5*10^3]\n--    1\n--    (0.02 secs, 0 bytes)\n<\/pre>\n","protected":false},"excerpt":{"rendered":"<p>Definir la funci\u00f3n minimaDiferencia :: (Num a, Ord a) => [a] -> a tal que (minimaDiferencia xs) es el menor valor absoluto de las diferencias entre todos los pares de elementos de xs (que se supone que tiene al menos 2 elementos). Por ejemplo, minimaDiferencia [1,5,3,19,18,25] == 1 minimaDiferencia [30,5,20,9] == 4 minimaDiferencia [30,5,20,9,5] ==&#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":[130,8,25,84,340,6,14,45,9],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/2334"}],"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=2334"}],"version-history":[{"count":3,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/2334\/revisions"}],"predecessor-version":[{"id":2362,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/2334\/revisions\/2362"}],"wp:attachment":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/media?parent=2334"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/categories?post=2334"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/tags?post=2334"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}