Definir la funci\u00f3n<\/p>\n
\n inflexion :: Ord a => [a] -> Maybe a\n<\/pre>\ntal que (inflexion xs) es el primer elemento de la lista en donde se cambia de creciente a decreciente o de decreciente a creciente y Nothing si no se cambia. Por ejemplo,<\/p>\n
\n inflexion [2,2,3,5,4,6] == Just 4\n inflexion [9,8,6,7,10,10] == Just 7\n inflexion [2,2,3,5] == Nothing\n inflexion [5,3,2,2] == Nothing\n<\/pre>\nSoluciones<\/h4>\n\nimport Data.List (find) \nimport Data.Maybe (isJust, fromJust) \n\n-- 1\u00aa soluci\u00f3n\n-- ===========\n\ninflexion :: Ord a => [a] -> Maybe a\ninflexion (x:y:zs) \n | x == y = inflexion (y:zs)\n | x < y = decreciente (y:zs)\n | otherwise = creciente (y:zs)\ninflexion _ = Nothing\n\n-- (creciente xs) es el segundo elemento de la primera parte creciente\n-- de xs y Nothing, en caso contrario. Por ejemplo,\n-- creciente [4,3,5,6] == Just 5\n-- creciente [4,3,5,2,7] == Just 5\n-- creciente [4,3,2] == Nothing\ncreciente (x:y:zs) \n | x >= y = creciente (y:zs)\n | otherwise = Just y\ncreciente _ = Nothing\n\n-- (decreciente xs) es el segundo elemento de la primera parte\n-- decreciente de xs y Nothing, en caso contrario. Por ejemplo,\n-- decreciente [4,2,3,1,0] == Just 2\n-- decreciente [4,5,3,1,0] == Just 3\n-- decreciente [4,5,7] == Nothing\ndecreciente (x:y:zs) \n | x <= y = decreciente (y:zs)\n | otherwise = Just y\ndecreciente _ = Nothing\n\n-- 2\u00aa soluci\u00f3n\n-- ===========\n\ninflexion2 :: Ord a => [a] -> Maybe a\ninflexion2 = aux . signos \n where aux [] = Nothing\n aux ((s,_):ys) | null zs = Nothing\n | otherwise = Just (snd (head zs))\n where zs = dropWhile (\\(p,_) -> p == s) ys\n\n-- (signos xs) es la lista de los pares dormado por el signo de\n-- crecimiento o decrecimiento de cada elemento de xs respecto de su\n-- anterior. Por ejemplo, \n-- \u03bb> signos [2,2,2,3,5,5,4,5,2]\n-- [(1,3),(1,5),(-1,4),(1,5),(-1,2)]\nsignos :: Ord a => [a] -> [(Int,a)]\nsignos xs = [(signo x y,y) | (x,y) <- zip xs (tail xs), x \/= y] \n\n-- (signo x y) es el signo de crecimiento o decrecimiento de y respecto\n-- de x. \nsigno :: Ord a => a -> a -> Int\nsigno x y | x > y = 1\n | x < y = -1\n | otherwise = 0\n\n-- 3\u00aa soluci\u00f3n\n-- ===========\n\ninflexion3 :: Ord a => [a] -> Maybe a\ninflexion3 (x:y:xs)\n | x == y = inflexion3 $ y:xs\n | x < y = buscaMenor $ y:xs\n | otherwise = buscaMayor $ y:xs\ninflexion3 _ = Nothing\n \nbuscaMenor :: Ord a => [a] -> Maybe a\nbuscaMenor (y:xs)\n | isJust busca = Just (snd (fromJust busca))\n | otherwise = Nothing\n where busca = find parDecreciente (zip (y:xs) xs)\n \nbuscaMayor :: Ord a => [a] -> Maybe a\nbuscaMayor (y:xs)\n | isJust busca = Just (snd (fromJust busca))\n | otherwise = Nothing\n where busca = find parCreciente (zip (y:xs) xs)\n \nparCreciente :: Ord a => (a,a) -> Bool\nparCreciente (a,b) = a < b\n \nparDecreciente :: Ord a => (a,a) -> Bool\nparDecreciente (a,b) = a > b\n\n-- Comparaci\u00f3n de eficiencia\n-- =========================\n\n-- \u03bb> inflexion (replicate (10^7) 5 ++ [0,1])\n-- Just 1\n-- (4.73 secs, 3,360,141,912 bytes)\n-- \u03bb> inflexion2 (replicate (10^7) 5 ++ [0,1])\n-- Just 1\n-- (2.71 secs, 2,480,144,352 bytes)\n-- \u03bb> inflexion3 (replicate (10^7) 5 ++ [0,1])\n-- Just 1\n-- (5.06 secs, 3,360,143,680 bytes)\n-- \n-- \u03bb> inflexion ([1..10^7] ++ [0,1])\n-- Just 0\n-- (3.60 secs, 3,120,146,728 bytes)\n-- \u03bb> inflexion2 ([1..10^7] ++ [0,1])\n-- Just 0\n-- (11.33 secs, 6,480,143,376 bytes)\n-- \u03bb> inflexion3 ([1..10^7] ++ [0,1])\n-- Just 0\n-- (3.28 secs, 3,280,140,784 bytes)\n-- \n-- \u03bb> inflexion ([10^7,10^7-1..1] ++ [2,1])\n-- Just 2\n-- (3.62 secs, 3,200,141,784 bytes)\n-- \u03bb> inflexion2 ([10^7,10^7-1..1] ++ [2,1])\n-- Just 2\n-- (10.01 secs, 5,840,144,200 bytes)\n-- \u03bb> inflexion3 ([10^7,10^7-1..1] ++ [2,1])\n-- Just 2\n-- (3.56 secs, 3,360,145,728 bytes)\n<\/pre>\n","protected":false},"excerpt":{"rendered":"Definir la funci\u00f3n inflexion :: Ord a => [a] -> Maybe a tal que (inflexion xs) es el primer elemento de la lista en donde se cambia de creciente a decreciente o de decreciente a creciente y Nothing si no se cambia. Por ejemplo, inflexion [2,2,3,5,4,6] == Just 4 inflexion [9,8,6,7,10,10] == Just 7 inflexion…<\/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":[500,411,6],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/3431"}],"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=3431"}],"version-history":[{"count":4,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/3431\/revisions"}],"predecessor-version":[{"id":3466,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/3431\/revisions\/3466"}],"wp:attachment":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/media?parent=3431"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/categories?post=3431"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/tags?post=3431"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}