{"id":5206,"date":"2019-12-05T05:30:20","date_gmt":"2019-12-05T03:30:20","guid":{"rendered":"http:\/\/www.glc.us.es\/~jalonso\/exercitium\/?p=5206"},"modified":"2019-12-17T08:07:25","modified_gmt":"2019-12-17T06:07:25","slug":"sublistas-con-producto-dado","status":"publish","type":"post","link":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/sublistas-con-producto-dado\/","title":{"rendered":"Sublistas con producto dado"},"content":{"rendered":"<p>Definir las funciones<\/p>\n<pre lang=\"text\">\n   sublistasConProducto :: Integer -> [Integer] -> [[Integer]]\n   unifactorizables :: [Integer]\n<\/pre>\n<p>tales que<\/p>\n<ul>\n<li>(sublistasConProducto n xs) es la lista de las sublistas de la lista ordenada estrictamente creciente xs (cuyos elementos son enteros mayores que 1) cuyo producto es el n\u00famero entero n (con n mayor que 1). Por ejemplo,<\/li>\n<\/ul>\n<pre lang=\"text\"> \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     []\n     \u03bb> length (sublistasConProducto 1234567 [1..1234567])\n     4\n<\/pre>\n<ul>\n<li>unifactorizables es la l\u00edsta de los n\u00fameros enteros mayores que 1 que se pueden escribir s\u00f3lo de una forma \u00fanica como producto de enteros distintos mayores que uno. Por ejemplo,<\/li>\n<\/ul>\n<pre lang=\"text\"> \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\n<\/pre>\n<h4>Soluciones<\/h4>\n<pre lang=\"haskell\">\nimport Test.QuickCheck\nimport Data.List (nub, sort, subsequences)\n\n-- 1\u00aa soluci\u00f3n\n-- ===========\n\nsublistasConProducto :: Integer -> [Integer] -> [[Integer]]\nsublistasConProducto n xs =\n  [ys | ys <- subsequences xs\n      , product ys == n]\n\n-- 2\u00aa soluci\u00f3n\n-- ===========\n\nsublistasConProducto2 :: Integer -> [Integer] -> [[Integer]]\nsublistasConProducto2 _ [] = []\nsublistasConProducto2 n (x:xs)\n  | x > n     = []\n  | x == n    = [[x]]\n  | r == 0    = map (x:) (sublistasConProducto2 q xs)\n                ++ sublistasConProducto2 n xs\n  | otherwise = sublistasConProducto2 n xs\n  where (q,r) = quotRem n x\n\n-- Comprobaci\u00f3n de equivalencia\n-- ============================\n\n-- La propiedad es\nprop_sublistasConProducto :: Integer -> [Integer] -> Bool\nprop_sublistasConProducto n xs =\n  sort (sublistasConProducto n' xs') == sublistasConProducto2 n' xs'\n  where n'  = 2 + abs n\n        xs' = (nub . sort . map ((+2) . abs)) xs\n\n-- La comprobaci\u00f3n es\n--    \u03bb> quickCheckWith (stdArgs {maxSize=30}) prop_sublistasConProducto\n--    +++ OK, passed 100 tests.\n\n-- Comparaci\u00f3n de eficiencia\n-- =========================\n\n--    \u03bb> sublistasConProducto 15 [1..23]\n--    [[3,5],[1,3,5],[15],[1,15]]\n--    (3.44 secs, 7,885,411,472 bytes)\n--    \u03bb> sublistasConProducto2 15 [1..23]\n--    [[1,3,5],[1,15],[3,5],[15]]\n--    (0.01 secs, 135,056 bytes)\n--\n--    \u03bb> length (sublistasConProducto2 1234567 [1..1234567])\n--    4\n--    (1.49 secs, 1,054,380,480 bytes)\n\n-- Definici\u00f3n de unifactorizables\n-- ==============================\n\nunifactorizables :: [Integer]\nunifactorizables =\n  [n | n <- [2..]\n     , length (sublistasConProducto2 n [2..n]) == 1]\n<\/pre>\n<h4>Pensamiento<\/h4>\n<blockquote><p>\nY en el encinar,<br \/>\n\u00a1luna redonda y beata,<br \/>\nsiempre conmigo a la par!<br \/>\nCerca de \u00dabeda la grande,<br \/>\ncuyos cerros nadie ver\u00e1,<br \/>\nme iba siguiendo la luna<br \/>\nsobre el olivar.<br \/>\nUna luna jadeante,<br \/>\nsiempre conmigo a la par.<\/p>\n<p>Antonio Machado\n<\/p><\/blockquote>\n","protected":false},"excerpt":{"rendered":"<p>Definir las funciones sublistasConProducto :: Integer -> [Integer] -> [[Integer]] unifactorizables :: [Integer] tales que (sublistasConProducto n xs) es la lista de las sublistas de la lista ordenada estrictamente creciente xs (cuyos elementos son enteros mayores que 1) cuyo producto es el n\u00famero entero n (con n mayor que 1). Por ejemplo, \u03bb> sublistasConProducto 72&#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":[8,28,10,24,11,157,254,6,14,88,146],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/5206"}],"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=5206"}],"version-history":[{"count":2,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/5206\/revisions"}],"predecessor-version":[{"id":5250,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/5206\/revisions\/5250"}],"wp:attachment":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/media?parent=5206"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/categories?post=5206"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/tags?post=5206"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}