La descomposici\u00f3n prima de 600 es<\/p>\n
\n 600 = 2\u00b3 * 3 * 5\u00b2\n<\/pre>\nDefinir la funci\u00f3n<\/p>\n
\n factorizacion :: Integer -> [(Integer,Integer)]\n<\/pre>\ntal que (factorizacion x) ses la lista de las bases y exponentes de la descomposici\u00f3n prima de x. Por ejemplo,<\/p>\n
\n factorizacion 600 == [(2,3),(3,1),(5,2)]\n length (factorizacion (product [1..3*10^4])) == 3245\n<\/pre>\nSoluciones<\/h4>\n\nimport Data.List (genericLength, group, inits, nub, sort, subsequences)\nimport Data.Numbers.Primes (primes, primeFactors)\n\n-- 1\u00aa soluci\u00f3n\n-- ===========\n\nfactorizacion :: Integer -> [(Integer,Integer)]\nfactorizacion n =\n [(x,nOcurrencias x xs) | x <- elementos xs]\n where xs = factoresPrimos n\n\n-- (factores primos n) es la lista de los factores primos de n. Por\n-- ejemplo, \n-- factoresPrimos 600 == [2,2,2,3,5,5]\nfactoresPrimos :: Integer -> [Integer]\nfactoresPrimos 1 = []\nfactoresPrimos n = x : factoresPrimos (n `div` x)\n where x = menorFactor n\n\n-- (menorFactor n) es el menor factor primo de n. Por ejemplo,\n-- menorFactor 10 == 2\n-- menorFactor 11 == 11\nmenorFactor :: Integer -> Integer\nmenorFactor n = head [x | x <- [2..n], n `mod` x == 0]\n\n-- (elementos xs) es la lista de los elementos, sin repeticiones, de\n-- xs. Por ejemplo,\n-- elementos [3,2,3,5,2] == [3,2,5]\nelementos :: Eq a => [a] -> [a]\nelementos [] = []\nelementos (x:xs) = x : elementos (filter (\/=x) xs)\n\n-- (nOcurrencias x ys) es el n\u00famero de ocurrencias de x en ys. Por\n-- ejemplo, \n-- nOcurrencias 'a' \"Salamanca\" == 4\nnOcurrencias :: Eq a => a -> [a] -> Integer\nnOcurrencias x ys = genericLength (filter (==x) ys) \n\n-- 2\u00aa soluci\u00f3n\n-- ===========\n\nfactorizacion2 :: Integer -> [(Integer,Integer)]\nfactorizacion2 n =\n [(head xs,genericLength xs) | xs <- group (primeFactors n)]\n\n-- 3\u00aa soluci\u00f3n\n-- ===========\n\nfactorizacion3 :: Integer -> [(Integer,Integer)]\nfactorizacion3 = map primeroYlongitud\n . group\n . primeFactors\n\n-- (primeroYlongitud xs) es el par formado por el primer elemento de xs\n-- y la longitud de xs. Por ejemplo,\n-- primeroYlongitud [3,2,5,7] == (3,4)\nprimeroYlongitud :: [a] -> (a,Integer)\nprimeroYlongitud (x:xs) =\n (x, 1 + genericLength xs)\n\n-- Comparaci\u00f3n de eficiencia de sumaDivisores\n-- ==========================================\n\n-- \u03bb> length (factorizacion (product [1..10^4]))\n-- 1229\n-- (4.84 secs, 2,583,331,768 bytes)\n-- \u03bb> length (factorizacion2 (product [1..10^4]))\n-- 1229\n-- (0.24 secs, 452,543,360 bytes)\n-- \u03bb> length (factorizacion3 (product [1..10^4]))\n-- 1229\n-- (0.23 secs, 452,433,504 bytes)\n-- \n-- \u03bb> length (factorizacion (product (take (2*10^3) primes)))\n-- 2000\n-- (6.58 secs, 3,415,098,552 bytes)\n-- \u03bb> length (factorizacion2 (product (take (2*10^3) primes)))\n-- 2000\n-- (0.02 secs, 23,060,512 bytes)\n-- \u03bb> length (factorizacion3 (product (take (2*10^3) primes)))\n-- 2000\n-- (0.02 secs, 22,882,080 bytes)\n<\/pre>\nPensamiento<\/h4>\n\n\u00bfTodo para los dem\u00e1s?
\nMancebo, llena tu jarro,
\nque ya te lo beber\u00e1n.<\/p>\n
Antonio Machado\n<\/p><\/blockquote>\n","protected":false},"excerpt":{"rendered":"
La descomposici\u00f3n prima de 600 es 600 = 2\u00b3 * 3 * 5\u00b2 Definir la funci\u00f3n factorizacion :: Integer -> [(Integer,Integer)] tal que (factorizacion x) ses la lista de las bases y exponentes de la descomposici\u00f3n prima de x. Por ejemplo, factorizacion 600 == [(2,3),(3,1),(5,2)] length (factorizacion (product [1..3*10^4])) == 3245 Soluciones import Data.List (genericLength,…<\/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":[8,30,38,258,13,71,89,11,247,6],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/5135"}],"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=5135"}],"version-history":[{"count":6,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/5135\/revisions"}],"predecessor-version":[{"id":5196,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/5135\/revisions\/5196"}],"wp:attachment":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/media?parent=5135"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/categories?post=5135"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/tags?post=5135"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}