{"id":2823,"date":"2017-01-17T06:00:41","date_gmt":"2017-01-17T04:00:41","guid":{"rendered":"http:\/\/www.glc.us.es\/~jalonso\/exercitium\/?p=2823"},"modified":"2017-01-24T06:34:55","modified_gmt":"2017-01-24T04:34:55","slug":"sumas-de-dos-capicuas","status":"publish","type":"post","link":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/sumas-de-dos-capicuas\/","title":{"rendered":"Sumas de dos capic\u00faas"},"content":{"rendered":"<p>Definir las funciones<\/p>\n<pre lang=\"text\">\n   sumas2Capicuas  :: Integer -> [(Integer, Integer)]\n   noSuma2Capicuas :: [Integer]\n<\/pre>\n<p>tales que<\/p>\n<ul>\n<li>(sumas2Capicuas x) es la lista de las descomposiciones de x como suma de dos capic\u00faas (con el primer sumando menor o igual que el segundo). Por ejemplo, <\/li>\n<\/ul>\n<pre lang=\"text\">\n      sumas2Capicuas 17  == [(6,11),(8,9)]\n      sumas2Capicuas 187 == [(6,181),(66,121),(88,99)]\n      sumas2Capicuas 165 == [(4,161),(44,121),(66,99),(77,88)]\n      sumas2Capicuas 382 == [(9,373),(191,191)]\n      sumas2Capicuas 151 == [(0,151)]\n      sumas2Capicuas 201 == []\n<\/pre>\n<ul>\n<li>noSuma2Capicuas es la sucesi\u00f3n de los n\u00fameros que no se pueden escribir como suma de dos capic\u00faas. Por ejemplo,<\/li>\n<\/ul>\n<pre lang=\"text\">\n      \u03bb> take 15 noSuma2Capicuas\n      [21,32,43,54,65,76,87,98,201,1031,1041,1042,1051,1052,1053]\n      \u03bb> noSuma2Capicuas !! 3000\n      19941\n<\/pre>\n<h4>Soluciones<\/h4>\n<pre lang=\"haskell\">\nsumas2Capicuas :: Integer -> [(Integer, Integer)]\nsumas2Capicuas x =\n  [(y,z) | y <- takeWhile (<= (x `div` 2)) capicuas\n         , let z = x - y\n         , esCapicua z]\n\n-- capicuas es la sucesi\u00f3n de los n\u00fameros capic\u00faas. Por ejemplo,\n--    \u03bb> take 45 capicuas\n--    [0,1,2,3,4,5,6,7,8,9,11,22,33,44,55,66,77,88,99,101,111,121,131,\n--     141,151,161,171,181,191,202,212,222,232,242,252,262,272,282,292,\n--     303,313,323,333,343,353]\n-- Se usar\u00e1 la 2\u00aa definici\u00f3n del ejercicio \"Sucesi\u00f3n de capic\u00faas\".\ncapicuas :: [Integer]\ncapicuas = capicuasImpares `mezcla` capicuasPares\n\n-- capicuasPares es la sucesi\u00f3n del cero y las capic\u00faas con un n\u00famero\n-- par de d\u00edgitos. Por ejemplo,  \n--    \u03bb> take 17 capicuasPares\n--    [0,11,22,33,44,55,66,77,88,99,1001,1111,1221,1331,1441,1551,1661]\ncapicuasPares :: [Integer]\ncapicuasPares =\n  [read (ns ++ reverse ns) | n <- [0..]\n                           , let ns = show n]   \n\n-- capicuasImpares es la sucesi\u00f3n de las capic\u00faas con un n\u00famero\n-- impar de d\u00edgitos a partir de 1. Por ejemplo,  \n--    \u03bb> take 20 capicuasImpares\n--    [1,2,3,4,5,6,7,8,9,101,111,121,131,141,151,161,171,181,191,202]\ncapicuasImpares :: [Integer]\ncapicuasImpares =\n  [1..9] ++ [read (ns ++ [z] ++ reverse ns)\n            | n <- [1..]\n            , let ns = show n\n            , z <- \"0123456789\"]   \n\n-- (mezcla xs ys) es la lista ordenada obtenida mezclando las dos listas\n-- ordenadas xs e ys, suponiendo que ambas son infinitas y con elementos\n-- distintos. Por ejemplo,\n--    take 10 (mezcla [2,12..] [5,15..])  ==  [2,5,12,15,22,25,32,35,42,45]\n--    take 10 (mezcla [2,22..] [5,15..])  ==  [2,5,15,22,25,35,42,45,55,62]\nmezcla :: Ord a => [a] -> [a] -> [a]\nmezcla us@(x:xs) vs@(y:ys)\n  | x < y     = x : mezcla xs vs\n  | otherwise = y : mezcla us ys\n\n-- (esCapicua x) se verifica si x es capic\u00faa. Por ejemplo,\n--    esCapicua 353   ==  True\n--    esCapicua 3553  ==  True\n--    esCapicua 3535  ==  False\nesCapicua :: Integer -> Bool\nesCapicua x =\n  xs == reverse xs\n  where xs = show x\n\nnoSuma2Capicuas :: [Integer]\nnoSuma2Capicuas =\n  [x | x <- [0..]\n     , null (sumas2Capicuas x)]\n<\/pre>\n","protected":false},"excerpt":{"rendered":"<p>Definir las funciones sumas2Capicuas :: Integer -> [(Integer, Integer)] noSuma2Capicuas :: [Integer] tales que (sumas2Capicuas x) es la lista de las descomposiciones de x como suma de dos capic\u00faas (con el primer sumando menor o igual que el segundo). Por ejemplo, sumas2Capicuas 17 == [(6,11),(8,9)] sumas2Capicuas 187 == [(6,181),(66,121),(88,99)] sumas2Capicuas 165 == [(4,161),(44,121),(66,99),(77,88)] sumas2Capicuas 382&#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":[8,30,141,11,95,6,32,33,34],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/2823"}],"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=2823"}],"version-history":[{"count":3,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/2823\/revisions"}],"predecessor-version":[{"id":2854,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/2823\/revisions\/2854"}],"wp:attachment":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/media?parent=2823"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/categories?post=2823"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/tags?post=2823"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}