Un n\u00famero x es un cubo si existe un y tal que x = y^3. Por ejemplo, 8 es un cubo porque 8 = 2^3.<\/p>\n
Definir la funci\u00f3n<\/p>\n
\n raizCubicaEntera :: Integer -> Maybe Integer.\n<\/pre>\ntal que (raizCubicaEntera x n) es justo la ra\u00edz c\u00fabica del n\u00famero natural x, si x es un cubo y Nothing en caso contrario. Por ejemplo,<\/p>\n
\n raizCubicaEntera 8 == Just 2\n raizCubicaEntera 9 == Nothing\n raizCubicaEntera 27 == Just 3\n raizCubicaEntera 64 == Just 4\n raizCubicaEntera (2^30) == Just 1024\n raizCubicaEntera (10^9000) == Just (10^3000)\n raizCubicaEntera (5 + 10^9000) == Nothing\n<\/pre>\nSoluciones<\/h4>\n\nimport Test.QuickCheck\n\n-- 1\u00aa definici\u00f3n\n-- =============\n\nraizCubicaEntera :: Integer -> Maybe Integer\nraizCubicaEntera x = aux 0\n where aux y | y^3 > x = Nothing\n | y^3 == x = Just y\n | otherwise = aux (y+1)\n\n-- 2\u00aa definici\u00f3n\n-- =============\n\nraizCubicaEntera2 :: Integer -> Maybe Integer\nraizCubicaEntera2 x \n | y^3 == x = Just y\n | otherwise = Nothing\n where (y:_) = dropWhile (\\y -> y^3 < x) [0..]\n\n-- 3\u00aa definici\u00f3n\n-- =============\n\nraizCubicaEntera3 :: Integer -> Maybe Integer \nraizCubicaEntera3 1 = Just 1\nraizCubicaEntera3 x = aux (0,x)\n where aux (a,b) | d == x = Just c\n | c == a = Nothing\n | d < x = aux (c,b)\n | otherwise = aux (a,c) \n where c = (a+b) `div` 2\n d = c^3\n\n-- 4\u00aa definici\u00f3n\n-- =============\n\nraizCubicaEntera4 :: Integer -> Maybe Integer\nraizCubicaEntera4 x \n | y^3 == x = Just y\n | otherwise = Nothing\n where y = floor ((fromIntegral x)**(1 \/ 3))\n\n-- Nota. La definici\u00f3n anterior falla para n\u00fameros grandes. Por ejemplo,\n-- \u03bb> raizCubicaEntera4 (2^30)\n-- Nothing\n-- \u03bb> raizCubicaEntera (2^30)\n-- Just 1024\n\n-- Equivalencia\n-- ============\n\n-- La propiedad es \nprop_raizCubicaEntera :: Integer -> Property\nprop_raizCubicaEntera x =\n x >= 0 ==>\n and [raizCubicaEntera x == f x | f <- [ raizCubicaEntera2\n , raizCubicaEntera3]]\n\n-- La comprobaci\u00f3n es \n-- \u03bb> quickCheck prop_raizCubicaEntera\n-- +++ OK, passed 100 tests.\n\n-- Comparaci\u00f3n de eficiencia\n-- =========================\n \n-- \u03bb> raizCubicaEntera (10^18)\n-- Just 1000000\n-- (1.80 secs, 1,496,137,192 bytes)\n-- \u03bb> raizCubicaEntera2 (10^18)\n-- Just 1000000\n-- (0.71 secs, 712,134,128 bytes)\n-- \u03bb> raizCubicaEntera3 (10^18)\n-- Just 1000000\n-- (0.01 secs, 196,424 bytes)\n--\n-- \u03bb> raizCubicaEntera2 (5^27)\n-- Just 1953125\n-- (1.42 secs, 1,390,760,920 bytes)\n-- \u03bb> raizCubicaEntera3 (5^27)\n-- Just 1953125\n-- (0.00 secs, 195,888 bytes)\n--\n-- \u03bb> raizCubicaEntera3 (10^9000) == Just (10^3000)\n-- True\n-- (2.05 secs, 420,941,368 bytes)\n-- \u03bb> raizCubicaEntera3 (5 + 10^9000) == Nothing\n-- True\n-- (2.08 secs, 420,957,576 bytes)\n<\/pre>\nPensamiento<\/h4>\n\nTras el vivir y el so\u00f1ar,
\nest\u00e1 lo que m\u00e1s importa:
\ndespertar.<\/p>\n
Antonio Machado\n<\/p><\/blockquote>\n","protected":false},"excerpt":{"rendered":"
Un n\u00famero x es un cubo si existe un y tal que x = y^3. Por ejemplo, 8 es un cubo porque 8 = 2^3. Definir la funci\u00f3n raizCubicaEntera :: Integer -> Maybe Integer. tal que (raizCubicaEntera x n) es justo la ra\u00edz c\u00fabica del n\u00famero natural x, si x es un cubo y Nothing…<\/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":[7],"tags":[500,30,59,11,6],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/4348"}],"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=4348"}],"version-history":[{"count":6,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/4348\/revisions"}],"predecessor-version":[{"id":4589,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/4348\/revisions\/4589"}],"wp:attachment":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/media?parent=4348"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/categories?post=4348"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/tags?post=4348"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}