{"id":1860,"date":"2015-12-14T06:00:07","date_gmt":"2015-12-14T04:00:07","guid":{"rendered":"http:\/\/www.glc.us.es\/~jalonso\/exercitium\/?p=1860"},"modified":"2022-03-25T20:22:01","modified_gmt":"2022-03-25T18:22:01","slug":"ano-cubico","status":"publish","type":"post","link":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/ano-cubico\/","title":{"rendered":"A\u00f1o c\u00fabico"},"content":{"rendered":"<p>El a\u00f1o 2016 ser\u00e1 un a\u00f1o c\u00fabico porque se puede escribir como la suma de los cubos de 7 n\u00fameros consecutivos; en efecto,<\/p>\n<pre lang=\"text\">\n   2016 = 3\u00b3+ 4\u00b3 +...+ 9\u00b3\n<\/pre>\n<p>Definir la funci\u00f3n<\/p>\n<pre lang=\"text\">\n   esCubico :: Integer -> Bool\n<\/pre>\n<p>tal que (esCubico x) se verifica si x se puede escribir como la suma  de los cubos de 7 n\u00fameros consecutivos. Por ejemplo,<\/p>\n<pre lang=\"text\">\n   esCubico 2016                ==  True\n   esCubico 2017                ==  False\n   esCubico 189005670081900441  ==  True\n   esCubico 189005670081900442  ==  False\n<\/pre>\n<h4>Soluciones<\/h4>\n<pre lang=\"haskell\">\n-- 1\u00aa definici\u00f3n\n-- =============\n\nesCubico1 :: Integer -> Bool\nesCubico1 x = pertenece x cubicos\n\n-- cubicos es la lista de los n\u00fameros que se pueden escribir como la\n-- suma de los cubos de 7 n\u00fameros consecutivos. Por ejemplo,\n--    take 5 cubicos  ==  [784,1295,2016,2989,4256]\ncubicos :: [Integer]\ncubicos = [sum [x^3 | x <- [y..y+6]] | y <- [1..]]\n\n-- (pertenece x ys) se verifica si x pertenece a la lista ordenada\n-- ys. Por ejemplo,\n--    pertenece 25 [0,3..]  ==  False\n--    pertenece 27 [0,3..]  ==  True\npertenece :: Integer -> [Integer] ->  Bool\npertenece x ys = x == head (dropWhile (<x) ys)\n\n-- 2\u00aa definici\u00f3n\n-- =============\n\nesCubico2 :: Integer -> Bool\nesCubico2 x = pertenece x (cubicosDesde k)\n    where k = floor ((fromIntegral x\/7)**(1\/3))\n\ncubicosDesde :: Integer -> [Integer]\ncubicosDesde k = [sum [x^3 | x <- [y..y+6]] | y <- [k..]]\n\n-- Comparaci\u00f3n de eficiencia\n-- =========================\n\n--    \u03bb> esCubico1 189005670081900441\n--    True\n--    (7.49 secs, 1,917,868,024 bytes)\n--    \u03bb> esCubico2 189005670081900441\n--    True\n--    (0.01 secs, 0 bytes)\n<\/pre>\n","protected":false},"excerpt":{"rendered":"<p>El a\u00f1o 2016 ser\u00e1 un a\u00f1o c\u00fabico porque se puede escribir como la suma de los cubos de 7 n\u00fameros consecutivos; en efecto, 2016 = 3\u00b3+ 4\u00b3 +&#8230;+ 9\u00b3 Definir la funci\u00f3n esCubico :: Integer -> Bool tal que (esCubico x) se verifica si x se puede escribir como la suma de los cubos 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":[8,282,183,71,415,11,40],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/1860"}],"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=1860"}],"version-history":[{"count":6,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/1860\/revisions"}],"predecessor-version":[{"id":1893,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/1860\/revisions\/1893"}],"wp:attachment":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/media?parent=1860"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/categories?post=1860"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/tags?post=1860"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}