{"id":1483,"date":"2015-05-25T06:30:59","date_gmt":"2015-05-25T04:30:59","guid":{"rendered":"http:\/\/www.glc.us.es\/~jalonso\/exercitium\/?p=1483"},"modified":"2015-11-30T18:45:33","modified_gmt":"2015-11-30T16:45:33","slug":"inversiones-de-un-numero","status":"publish","type":"post","link":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/inversiones-de-un-numero\/","title":{"rendered":"Inversiones de un n\u00famero"},"content":{"rendered":"<p>Un n\u00famero tiene una inversi\u00f3n cuando existe un d\u00edgito x a la derecha de otro d\u00edgito de forma que x es menor que y. Por ejemplo, en el n\u00famero 1745 hay dos inversiones ya que 4 es menor que 7 y 5 es menor que 7 y est\u00e1n a la derecha de 7.<\/p>\n<p>Definir la funci\u00f3n<\/p>\n<pre lang=\"text\">\n   nInversiones :: Integer -> Int\n<\/pre>\n<p>tal que (nInversiones n) es el n\u00famero de inversiones de n. Por ejemplo,<\/p>\n<pre lang=\"text\">\n   nInversiones 1745  ==  2\n<\/pre>\n<h4>Soluciones<\/h4>\n<pre lang=\"haskell\">\nimport Data.List (tails)\n\n-- 1\u00aa definici\u00f3n\n-- =============\n\nnInversiones1 :: Integer -> Int\nnInversiones1 = length . inversiones . show\n\n-- (inversiones xs) es la lista de las inversiones de xs. Por ejemplo, \n--    inversiones \"1745\"   ==  [('7','4'),('7','5')]\n--    inversiones \"cbafd\"  ==  [('c','b'),('c','a'),('b','a'),('f','d')]\ninversiones :: Ord a => [a] -> [(a,a)]\ninversiones []     = []\ninversiones (x:xs) = [(x,y) | y <- xs, y < x] ++ inversiones xs\n\n-- 2\u00aa definici\u00f3n\n-- =============\n\nnInversiones2 :: Integer -> Int\nnInversiones2 = aux . show\n    where aux [] = 0\n          aux (y:ys) | null xs   = aux ys\n                     | otherwise = length xs + aux ys\n                     where xs = [x | x <- ys, x < y]  \n\n-- 3\u00aa soluci\u00f3n\n-- ===========\n\nnInversiones3 :: Integer -> Int\nnInversiones3 x = sum $ map f xss\n    where xss = init $ tails (show x)\n          f (x:xs) = length $ filter (<x) xs\n\n-- Comparaci\u00f3n de eficiencia\n-- =========================\n\n-- La comparaci\u00f3n es\n--    ghci> let f1000 = product [1..1000] \n--    ghci> nInversiones1 f1000\n--    1751225\n--    (2.81 secs, 452526504 bytes)\n--    ghci> nInversiones2 f1000\n--    1751225\n--    (2.45 secs, 312752672 bytes)\n--    ghci> nInversiones3 f1000\n--    1751225\n--    (0.71 secs, 100315896 bytes)\n<\/pre>\n","protected":false},"excerpt":{"rendered":"<p>Un n\u00famero tiene una inversi\u00f3n cuando existe un d\u00edgito x a la derecha de otro d\u00edgito de forma que x es menor que y. Por ejemplo, en el n\u00famero 1745 hay dos inversiones ya que 4 es menor que 7 y 5 es menor que 7 y est\u00e1n a la derecha de 7. Definir la&#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":[],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/1483"}],"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=1483"}],"version-history":[{"count":4,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/1483\/revisions"}],"predecessor-version":[{"id":1797,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/1483\/revisions\/1797"}],"wp:attachment":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/media?parent=1483"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/categories?post=1483"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/tags?post=1483"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}