En una lista xs se produce un cambio de signo por cada elemento x de la lista junto el primero de los elementos de xs con signo opuesto al de x. Por ejemplo,en la lista [6,5,-4,0,-2,-7,0,-8,-1,4] hay 2 cambios de signo (entre (5,-4) y (-1,4)) y en la lista [6,5,-4,0, 2,-7,0,-8,-1,4] hay 4 cambios de signo (entre (5,-4), (-4,2), (2,-7) y(-1,4)).<\/p>\n
Definir la funci\u00f3n<\/p>\n
\n nCambios :: (Num a, Ord a) => [a] -> Int\n<\/pre>\ntal que (nCambios xs) es el n\u00famero de cambios de signos de la lista xs. Por ejemplo,<\/p>\n
\n nCambios [] == 0\n nCambios [6,5,-4,0,-2,-7,0,-8,-1,4] == 2\n nCambios [6,5,-4,0, 2,-7,0,-8,-1,4] == 4\n<\/pre>\nSoluciones<\/h4>\n\nimport Data.List (group)\n\n-- 1\u00aa definici\u00f3n\nnCambios1 :: (Num a, Ord a) => [a] -> Int\nnCambios1 = length . cambios\n\n-- (cambios xs) es la lista de los pares de elementos de xs entre los\n-- que se producen cambios de signo. Por ejemplo,\n-- cambios [6,5,-4,0,-2,-7,0,-8,-1,4] == [(5,-4),(-1,4)]\n-- cambios [6,5,-4,0, 2,-7,0,-8,-1,4] == [(5,-4),(-4,2),(2,-7),(-1,4)]\ncambios :: (Num a, Ord a) => [a] -> [(a,a)]\ncambios xs =\n [(x,y) | (x,y) <- zip ys (tail ys), x*y < 0]\n where ys = filter (\/=0) xs\n\n-- 2\u00aa definici\u00f3n\nnCambios2 :: (Num a, Ord a) => [a] -> Int\nnCambios2 [] = 0\nnCambios2 xs = length (group (filter (\/=0) (map signum xs))) - 1\n\n-- 3\u00aa definici\u00f3n\nnCambios3 :: (Num a, Ord a) => [a] -> Int\nnCambios3 = pred . length . group . filter (\/=0) . map signum\n\n-- Comparaci\u00f3n de eficiencia\n-- =========================\n\n-- \u03bb> nCambios1 (take (2*10^6) (cycle [3,0,-3]))\n-- 1333332\n-- (3.84 secs, 679,805,392 bytes)\n-- \u03bb> nCambios2 (take (2*10^6) (cycle [3,0,-3]))\n-- 1333332\n-- (0.98 secs, 694,247,368 bytes)\n-- \u03bb> nCambios3 (take (2*10^6) (cycle [3,0,-3]))\n-- 1333332\n-- (0.95 secs, 708,118,976 bytes)\n<\/pre>\n","protected":false},"excerpt":{"rendered":"En una lista xs se produce un cambio de signo por cada elemento x de la lista junto el primero de los elementos de xs con signo opuesto al de x. Por ejemplo,en la lista [6,5,-4,0,-2,-7,0,-8,-1,4] hay 2 cambios de signo (entre (5,-4) y (-1,4)) y en la lista [6,5,-4,0, 2,-7,0,-8,-1,4] hay 4 cambios de…<\/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":[8,38,13,28,10,11,151,45,9],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/1973"}],"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=1973"}],"version-history":[{"count":4,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/1973\/revisions"}],"predecessor-version":[{"id":2012,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/1973\/revisions\/2012"}],"wp:attachment":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/media?parent=1973"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/categories?post=1973"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/tags?post=1973"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}