El conjunto de todas las palabras se puede ordenar como en los diccionarios:<\/p>\n
\n a, b, ..., z, A, B, ..., Z,\n aa, ab, ..., az, aA, aB, ..., aZ,\n ba, bb, ..., bz, bA, bB, ..., bZ,\n ...\n za, zb, ..., zz, zA, zB, ..., zZ,\n aaa, aab, ..., aaz, aaA, aaB, ..., aaZ,\n baa, bab, ..., baz, baA, baB, ..., baZ,\n ...\n<\/pre>\nDefinir las funciones<\/p>\n
\n palabras :: [String]\n posicion :: String -> Integer\n<\/pre>\ntales que<\/p>\n
\n \u03bb> take 10 (drop 100 palabras)\n [\"aW\",\"aX\",\"aY\",\"aZ\",\"ba\",\"bb\",\"bc\",\"bd\",\"be\",\"bf\"]\n \u03bb> take 10 (drop 2750 palabras)\n [\"ZU\",\"ZV\",\"ZW\",\"ZX\",\"ZY\",\"ZZ\",\"aaa\",\"aab\",\"aac\",\"aad\"]\n \u03bb> palabras !! (10^6)\n \"gePO\"\n<\/pre>\n \n posicion \"c\" == 2\n posicion \"ab\" == 53\n posicion \"ba\" == 104\n posicion \"eva\" == 14664\n posicion \"adan\" == 151489\n posicion \"HoyEsMartes\" == 4957940944437977046\n posicion \"EnUnLugarDeLaMancha\" == 241779893912461058861484239910864\n<\/pre>\nComprobar con QuickCheck que para todo entero positivo n se verifica que<\/p>\n
\n posicion (palabras `genericIndex` n) == n\n<\/pre>\nSoluciones<\/h4>\n
[schedule expon=’2016-06-07′ expat=\u00bb06:00″]<\/p>\n
[\/schedule]<\/p>\n
[schedule on=’2016-06-07′ at=\u00bb06:00″]<\/p>\n
\r\nimport Data.List (genericIndex, genericLength)\r\nimport Test.QuickCheck\r\n\r\n-- 1\u00aa definici\u00f3n de palabras\r\n-- =========================\r\n \r\npalabras1 :: [String]\r\npalabras1 = concatMap palabrasDeLongitud [1..]\r\n\r\n-- (palabrasDeLongitud n) es la lista ordenada de palabras longitud\r\n-- n. Por ejemplo,\r\n-- take 3 (palabrasDeLongitud 2) == [\"aa\",\"ab\",\"ac\"]\r\n-- take 3 (palabrasDeLongitud 3) == [\"aaa\",\"aab\",\"aac\"]\r\npalabrasDeLongitud :: Integer -> [String]\r\npalabrasDeLongitud 1 = [[x] | x <- letras]\r\npalabrasDeLongitud n = [x:ys | x <- letras,\r\n ys <- palabrasDeLongitud (n-1)]\r\n\r\n-- letras es la lista ordenada de las letras. \r\nletras :: [Char]\r\nletras = ['a'..'z'] ++ ['A'..'Z']\r\n\r\n-- 2\u00aa definici\u00f3n de palabras\r\n-- =========================\r\n\r\npalabras2 :: [String]\r\npalabras2 = concat (iterate f elementales)\r\n where f = concatMap (\\x -> map (x++) elementales)\r\n\r\n-- elementales es la lista de las palabras de una letra. \r\nelementales :: [String] \r\nelementales = map (:[]) letras\r\n\r\n-- 3\u00aa definici\u00f3n de palabras\r\n-- =========================\r\n\r\npalabras3 :: [String]\r\npalabras3 = tail $ map reverse aux\r\n where aux = \"\" : [c:cs | cs <- aux, c <- letras]\r\n\r\n-- Comparaci\u00f3n\r\n-- ===========\r\n\r\n-- \u03bb> palabras1 !! (10^6)\r\n-- \"gePO\"\r\n-- (0.87 secs, 480,927,648 bytes)\r\n-- \u03bb> palabras2 !! (10^6)\r\n-- \"gePO\"\r\n-- (0.11 secs, 146,879,840 bytes)\r\n-- \u03bb> palabras3 !! (10^6)\r\n-- \"gePO\"\r\n-- (0.25 secs, 203,584,608 bytes)\r\n\r\n-- 1\u00aa definici\u00f3n de posicion\r\n-- =========================\r\n\r\nposicion1 :: String -> Integer\r\nposicion1 cs = genericLength (takeWhile (\/=cs) palabras1)\r\n\r\n-- 1\u00aa definici\u00f3n de posicion\r\n-- =========================\r\n\r\nposicion2 :: String -> Integer\r\nposicion2 \"\" = -1\r\nposicion2 (c:cs) = (1 + posicionLetra c) * 52^(length cs) + posicion2 cs\r\n\r\nposicionLetra :: Char -> Integer\r\nposicionLetra c = genericLength (takeWhile (\/=c) letras)\r\n\r\n-- La propiedad es\r\nprop_palabras :: (Positive Integer) -> Bool\r\nprop_palabras (Positive n) =\r\n posicion2 (palabras3 `genericIndex` n) == n\r\n\r\n-- La comprobaci\u00f3n es \r\n-- \u03bb> quickCheck prop_palabras\r\n-- +++ OK, passed 100 tests.\r\n<\/pre>\n[\/schedule]<\/p>\n","protected":false},"excerpt":{"rendered":"
El conjunto de todas las palabras se puede ordenar como en los diccionarios: a, b, …, z, A, B, …, Z, aa, ab, …, az, aA, aB, …, aZ, ba, bb, …, bz, bA, bB, …, bZ, … za, zb, …, zz, zA, zB, …, zZ, aaa, aab, …, aaz, aaA, aaB, …, aaZ, baa,…<\/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":[2],"tags":[],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/2510"}],"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=2510"}],"version-history":[{"count":1,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/2510\/revisions"}],"predecessor-version":[{"id":2511,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/2510\/revisions\/2511"}],"wp:attachment":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/media?parent=2510"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/categories?post=2510"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/tags?post=2510"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}