{"id":3233,"date":"2017-04-18T06:00:01","date_gmt":"2017-04-18T04:00:01","guid":{"rendered":"http:\/\/www.glc.us.es\/~jalonso\/exercitium\/?p=3233"},"modified":"2017-04-25T18:54:33","modified_gmt":"2017-04-25T16:54:33","slug":"subnumeros-pares","status":"publish","type":"post","link":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/subnumeros-pares\/","title":{"rendered":"Subn\u00fameros pares"},"content":{"rendered":"<p>Los subn\u00fameros de un n\u00famero x son los n\u00fameros que se pueden formar con d\u00edgitos de x en posiciones consecutivas. Por ejemplo, el n\u00famero 254 tiene 6 subn\u00fameros: 2, 5, 4, 25, 54 y 254.<\/p>\n<p>Definir las funciones<\/p>\n<pre lang=\"text\">\n   subnumeros       :: Integer -> [Integer]\n   nSubnumerosPares :: Integer -> Integer\n<\/pre>\n<p>tales que<\/p>\n<ul>\n<li>(subnumerosPares x) es la lista de los subn\u00fameros pares de x. Por ejemplo, <\/li>\n<\/ul>\n<pre lang=\"text\">\n     subnumerosPares 254   ==  [2,254,54,4]\n     subnumerosPares 154   ==  [154,54,4]\n     subnumerosPares 15    ==  []\n<\/pre>\n<ul>\n<li>(nSubnumerosPares x) es la cantidad de subn\u00fameros pares de x. Por ejemplo, <\/li>\n<\/ul>\n<pre lang=\"text\">\n     nSubnumerosPares 254   ==  4\n     nSubnumerosPares2 (4^(10^6))  ==  90625258498\n<\/pre>\n<h4>Soluciones<\/h4>\n<pre lang=\"haskell\">\nimport Data.List ( genericLength\n                 , inits\n                 , tails\n                 )\n\nsubnumerosPares :: Integer -> [Integer]\nsubnumerosPares n =\n  filter even (subnumeros n)\n\n-- (subnumeros n) es la lista de los subn\u00fameros de n. Por ejemplo,\n--    subnumeros 254  ==  [2,25,5,254,54,4]\nsubnumeros :: Integer -> [Integer]\nsubnumeros n =\n  [read x | x <- sublistas (show n)]\n\n-- (sublistas xs) es la lista de las sublistas de xs. Por ejemplo, \n--    sublistas \"abc\"  ==  [\"a\",\"ab\",\"b\",\"abc\",\"bc\",\"c\"]\nsublistas :: [a] -> [[a]]\nsublistas xs =\n  concat [init (tails ys) | ys <- tail (inits xs)]\n\n-- 1\u00aa definici\u00f3n\n-- =============\n\nnSubnumerosPares :: Integer -> Integer\nnSubnumerosPares =\n  genericLength . subnumerosPares\n\n-- 2\u00aa definici\u00f3n\n-- =============\n\nnSubnumerosPares2 :: Integer -> Integer\nnSubnumerosPares2 =\n  sum . posicionesDigitosPares \n\n-- (posicionesDigitosPares x) es la lista de las posiciones de los\n-- d\u00edgitos pares de x. Por ejemplo,\n--    posicionesDigitosPares 254  ==  [1,3]\nposicionesDigitosPares :: Integer -> [Integer]\nposicionesDigitosPares x =\n  [n | (n,y) <- zip [1..] (show x)\n     , y `elem` \"02468\"]\n\n-- Comparaci\u00f3n de eficiencia\n--    \u03bb> nSubnumerosPares (2^(10^3))\n--    22934\n--    (2.83 secs, 3,413,414,872 bytes)\n--    \u03bb> nSubnumerosPares2 (2^(10^3))\n--    22934\n--    (0.01 secs, 0 bytes)\n<\/pre>\n","protected":false},"excerpt":{"rendered":"<p>Los subn\u00fameros de un n\u00famero x son los n\u00fameros que se pueden formar con d\u00edgitos de x en posiciones consecutivas. Por ejemplo, el n\u00famero 254 tiene 6 subn\u00fameros: 2, 5, 4, 25, 54 y 254. Definir las funciones subnumeros :: Integer -> [Integer] nSubnumerosPares :: Integer -> Integer tales que (subnumerosPares x) es la lista&#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":[8,12,26,91,38,258,285,74,11,95,33,40,45,75,9],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/3233"}],"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=3233"}],"version-history":[{"count":3,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/3233\/revisions"}],"predecessor-version":[{"id":3271,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/3233\/revisions\/3271"}],"wp:attachment":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/media?parent=3233"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/categories?post=3233"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/tags?post=3233"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}