{"id":2484,"date":"2016-05-25T06:00:02","date_gmt":"2016-05-25T04:00:02","guid":{"rendered":"http:\/\/www.glc.us.es\/~jalonso\/exercitium\/?p=2484"},"modified":"2022-03-26T12:11:49","modified_gmt":"2022-03-26T10:11:49","slug":"centro-de-gravedad-de-una-lista","status":"publish","type":"post","link":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/centro-de-gravedad-de-una-lista\/","title":{"rendered":"Centro de gravedad de una lista"},"content":{"rendered":"<p>Se dice que una lista de n\u00fameros xs es <strong>equilibrada<\/strong> si existe una posici\u00f3n k tal que la suma de los elementos de xs en las posiciones menores que k es igual a la de los elementos de xs en las posiciones mayores que k. La posici\u00f3n k se llama el <strong>centro de gravedad<\/strong> de xs. Por ejemplo, la lista [1,3,4,5,-2,1] es equilibrada, y su centro de gravedad es 2, ya que la suma de [1,3] es igual a la de [5,-2,1]. En cambio, la lista [1,6,4,5,-2,1] no tiene centro de gravedad.<\/p>\n<p>Definir la funci\u00f3n<\/p>\n<pre lang=\"text\">\n   centro :: (Num a, Eq a) => [a] -> Maybe Int\n<\/pre>\n<p>tal que (centro xs) es justo el centro e gravedad de xs, si la lista xs es equilibrada y Nothing en caso contrario. Por ejemplo,<\/p>\n<pre lang=\"text\">\n   centro [1,3,4,5,-2,1]           ==  Just 2\n   centro [1,6,4,5,-2,1]           ==  Nothing\n   centro [1,2,3,4,3,2,1]          ==  Just 3\n   centro [1,100,50,-51,1,1]       ==  Just 1\n   centro [1,2,3,4,5,6]            ==  Nothing\n   centro [20,10,30,10,10,15,35]   ==  Just 3\n   centro [20,10,-80,10,10,15,35]  ==  Just 0\n   centro [10,-80,10,10,15,35,20]  ==  Just 6\n   centro [0,0,0,0,0]              ==  Just 0\n   centro [-1,-2,-3,-4,-3,-2,-1]   ==  Just 3\n<\/pre>\n<h4>Soluciones<\/h4>\n<pre lang=\"haskell\">\nimport Data.List (inits, tails)\nimport Data.Maybe (listToMaybe)\n\n-- 1\u00aa soluci\u00f3n\n-- ===========\n\ncentro1 :: (Num a, Eq a) => [a] -> Maybe Int\ncentro1 xs \n    | null ns   = Nothing\n    | otherwise = Just (head ns)\n    where ns = [n | n <- [0..length xs - 1],\n                    let (ys,_:zs) = splitAt n xs,\n                    sum ys == sum zs]\n\n-- 2\u00aa soluci\u00f3n\n-- ===========\n\ncentro2 :: (Num a, Eq a) => [a] -> Maybe Int\ncentro2 xs = aux 0 0 (sum xs) xs where\n    aux _ _ _ [] = Nothing\n    aux k i d (z:zs) | i == d - z = Just k\n                     | otherwise  = aux (k + 1) (i + z) (d - z) zs\n\n-- 3\u00aa soluci\u00f3n\n-- ===========\n\ncentro3 :: (Num a, Eq a) => [a] -> Maybe Int\ncentro3 xs =\n  listToMaybe [ k | (k,ys,_:zs) <- zip3 [0..] (inits xs) (tails xs)\n                  , sum ys == sum zs]\n\n-- Comparaci\u00f3n de eficiencia\n-- =========================\n\n--    \u03bb> let xs = [1..3000] in centro1 (xs ++ (0:xs))\n--    Just 3000\n--    (2.70 secs, 2,088,881,728 bytes)\n--    \u03bb> let xs = [1..3000] in centro2 (xs ++ (0:xs))\n--    Just 3000\n--    (0.03 secs, 0 bytes)\n--    \u03bb> let xs = [1..3000] in centro3 (xs ++ (0:xs))\n--    Just 3000\n--    (2.34 secs, 1,727,569,688 bytes)\n<\/pre>\n","protected":false},"excerpt":{"rendered":"<p>Se dice que una lista de n\u00fameros xs es equilibrada si existe una posici\u00f3n k tal que la suma de los elementos de xs en las posiciones menores que k es igual a la de los elementos de xs en las posiciones mayores que k. La posici\u00f3n k se llama el centro de gravedad de&#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":[500,71,74,28,246,141,6,73,40,75,44],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/2484"}],"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=2484"}],"version-history":[{"count":4,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/2484\/revisions"}],"predecessor-version":[{"id":2518,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/2484\/revisions\/2518"}],"wp:attachment":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/media?parent=2484"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/categories?post=2484"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/tags?post=2484"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}