Soluciones<\/h4>\n\nimport Test.QuickCheck\nimport Data.Numbers.Primes (primeFactors, primes)\n\n-- 1\u00aa soluci\u00f3n\n-- ===========\n\nprimosOcuadradosDePrimos :: [Integer]\nprimosOcuadradosDePrimos =\n filter esPrimoOcuadradoDePrimo [2..]\n\nesPrimoOcuadradoDePrimo :: Integer -> Bool\nesPrimoOcuadradoDePrimo n = aux xs\n where xs = primeFactors n\n aux [_] = True\n aux [x,y] = x == y\n aux _ = False\n\n-- 2\u00aa soluci\u00f3n\n-- ===========\n \nprimosOcuadradosDePrimos2 :: [Integer]\nprimosOcuadradosDePrimos2 = mezcla primes (map (^2) primes)\n\nmezcla :: Ord a => [a] -> [a] -> [a]\nmezcla (x:xs) (y:ys) | x < y = x : mezcla xs (y:ys)\n | otherwise = y : mezcla (x:xs) ys\n\n-- Comparaci\u00f3n de eficiencia\n-- =========================\n\n-- \u03bb> primosOcuadradosDePrimos !! (2*10^4)\n-- 223589\n-- (3.08 secs, 9,829,725,096 bytes)\n-- \u03bb> primosOcuadradosDePrimos2 !! (2*10^4)\n-- 223589\n-- (0.04 secs, 73,751,888 bytes)\n--\n-- \u03bb> primosOcuadradosDePrimos2 !! (5*10^5)\n-- 7362497\n-- (1.29 secs, 3,192,803,040 bytes)\n\n-- Propiedad de equivalencia\n-- =========================\n\n-- La propiedad es\nprop_equivalencia :: Int -> Property\nprop_equivalencia n =\n n >= 0 ==> primosOcuadradosDePrimos2 !! n == unifactorizables !! n\n\n-- unifactorizables es la l\u00edsta de los n\u00fameros enteros mayores que 1\n-- que se pueden escribir s\u00f3lo de una forma \u00fanica como producto de\n-- enteros distintos mayores que uno. Por ejemplo,\n-- \u03bb> take 20 unifactorizables\n-- [2,3,4,5,7,9,11,13,17,19,23,25,29,31,37,41,43,47,49,53]\n-- \u03bb> unifactorizables !! 300\n-- 1873\nunifactorizables :: [Integer]\nunifactorizables =\n [n | n <- [2..]\n , length (sublistasConProducto n [2..n]) == 1]\n\n-- (sublistasConProducto n xs) es la lista de las sublistas de la\n-- lista ordenada estrictamente creciente xs (cuyos elementos son\n-- enteros mayores que 1) cuyo producto es el n\u00famero entero n (con n\n-- mayor que 1). Por ejemplo, \n-- \u03bb> sublistasConProducto 72 [2,3,4,5,6,7,9,10,16]\n-- [[2,4,9],[3,4,6]]\n-- \u03bb> sublistasConProducto 720 [2,3,4,5,6,7,9,10,16]\n-- [[2,3,4,5,6],[2,4,9,10],[3,4,6,10],[5,9,16]]\n-- \u03bb> sublistasConProducto 2 [4,7]\n-- []\nsublistasConProducto :: Integer -> [Integer] -> [[Integer]]\nsublistasConProducto _ [] = []\nsublistasConProducto n (x:xs)\n | x > n = []\n | x == n = [[x]]\n | r == 0 = map (x:) (sublistasConProducto q xs)\n ++ sublistasConProducto n xs\n | otherwise = sublistasConProducto n xs\n where (q,r) = quotRem n x\n\n-- La comprobaci\u00f3n es\n-- \u03bb> quickCheck prop_equivalencia\n-- +++ OK, passed 100 tests.\n<\/pre>\nPensamiento<\/h4>\n\nDespacito y buena letra: el hacer las cosas bien importa m\u00e1s que el hacerlas.<\/p>\n
Antonio Machado\n<\/p><\/blockquote>\n","protected":false},"excerpt":{"rendered":"
Definir la constante primosOcuadradosDePrimos :: [Integer] cuyos elementos son los n\u00famero primos o cuadrados de primos. Por ejemplo, \u03bb> take 20 primosOcuadradosDePrimos [2,3,4,5,7,9,11,13,17,19,23,25,29,31,37,41,43,47,49,53] \u03bb> primosOcuadradosDePrimos !! (10^6) 15476729 Comprobar con QuickCheck que las lista primosOcuadradosDePrimos y unifactorizables (definida en el ejercicio anterior) son iguales. Soluciones import Test.QuickCheck import Data.Numbers.Primes (primeFactors, primes) — 1\u00aa soluci\u00f3n –…<\/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":[8,38,28,10,11,247,173,6,146],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/5208"}],"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=5208"}],"version-history":[{"count":5,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/5208\/revisions"}],"predecessor-version":[{"id":5249,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/5208\/revisions\/5249"}],"wp:attachment":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/media?parent=5208"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/categories?post=5208"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/tags?post=5208"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}