{"id":4680,"date":"2019-02-05T06:00:51","date_gmt":"2019-02-05T04:00:51","guid":{"rendered":"http:\/\/www.glc.us.es\/~jalonso\/exercitium\/?p=4680"},"modified":"2021-04-25T16:23:45","modified_gmt":"2021-04-25T14:23:45","slug":"medias-de-digitos-de-pi-2019","status":"publish","type":"post","link":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/medias-de-digitos-de-pi-2019\/","title":{"rendered":"Medias de d\u00edgitos de pi"},"content":{"rendered":"<p>El fichero <a href=\"Digitos_de_pi.txt\">Digitos_de_pi.txt<\/a> contiene el n\u00famero pi con un mill\u00f3n de decimales; es decir,<\/p>\n<pre lang=\"text\"> \n   3.1415926535897932384626433832 ... 83996346460422090106105779458151\n<\/pre>\n<p>Definir las funciones<\/p>\n<pre lang=\"text\"> \n   mediasDigitosDePi        :: IO [Double]\n   graficaMediasDigitosDePi :: Int -> IO ()\n<\/pre>\n<p>tales que<\/p>\n<ul>\n<li>mediasDigitosDePi es la sucesi\u00f3n cuyo n-\u00e9simo elemento es la media de los n primeros d\u00edgitos de pi. Por ejemplo,<\/li>\n<\/ul>\n<pre lang=\"text\">   \n     \u03bb> xs <- mediasDigitosDePi\n     \u03bb> take 5 xs\n     [1.0,2.5,2.0,2.75,4.0]\n     \u03bb> take 10 xs\n     [1.0,2.5,2.0,2.75,4.0,3.6666666666666665,4.0,4.125,4.0,4.1]\n     \u03bb> take 10 <$> mediasDigitosDePi\n     [1.0,2.5,2.0,2.75,4.0,3.6666666666666665,4.0,4.125,4.0,4.1]\n<\/pre>\n<ul>\n<li>(graficaMediasDigitosDePi n) dibuja la gr\u00e1fica de los n primeros t\u00e9rminos de mediasDigitosDePi. Por ejemplo,\n<ul>\n<li>(graficaMediasDigitosDePi 20) dibuja<br \/>\n<a href=\"https:\/\/i0.wp.com\/www.glc.us.es\/~jalonso\/exercitium\/wp-content\/uploads\/2019\/02\/Medias_de_digitos_de_pi_20.png\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/i0.wp.com\/www.glc.us.es\/~jalonso\/exercitium\/wp-content\/uploads\/2019\/02\/Medias_de_digitos_de_pi_20.png?resize=640%2C480\" alt=\"\" width=\"640\" height=\"480\" class=\"aligncenter size-full wp-image-4681\" srcset=\"https:\/\/i0.wp.com\/www.glc.us.es\/~jalonso\/exercitium\/wp-content\/uploads\/2019\/02\/Medias_de_digitos_de_pi_20.png?w=640&amp;ssl=1 640w, https:\/\/i0.wp.com\/www.glc.us.es\/~jalonso\/exercitium\/wp-content\/uploads\/2019\/02\/Medias_de_digitos_de_pi_20.png?resize=300%2C225&amp;ssl=1 300w\" sizes=\"(max-width: 640px) 100vw, 640px\" data-recalc-dims=\"1\" \/><\/a><\/li>\n<li>(graficaMediasDigitosDePi 200) dibuja<br \/>\n<a href=\"https:\/\/i0.wp.com\/www.glc.us.es\/~jalonso\/exercitium\/wp-content\/uploads\/2019\/02\/Medias_de_digitos_de_pi_200.png\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/i0.wp.com\/www.glc.us.es\/~jalonso\/exercitium\/wp-content\/uploads\/2019\/02\/Medias_de_digitos_de_pi_200.png?resize=640%2C480\" alt=\"\" width=\"640\" height=\"480\" class=\"aligncenter size-full wp-image-4682\" srcset=\"https:\/\/i0.wp.com\/www.glc.us.es\/~jalonso\/exercitium\/wp-content\/uploads\/2019\/02\/Medias_de_digitos_de_pi_200.png?w=640&amp;ssl=1 640w, https:\/\/i0.wp.com\/www.glc.us.es\/~jalonso\/exercitium\/wp-content\/uploads\/2019\/02\/Medias_de_digitos_de_pi_200.png?resize=300%2C225&amp;ssl=1 300w\" sizes=\"(max-width: 640px) 100vw, 640px\" data-recalc-dims=\"1\" \/><\/a><\/li>\n<li>(graficaMediasDigitosDePi 2000) dibuja<br \/>\n<a href=\"https:\/\/i0.wp.com\/www.glc.us.es\/~jalonso\/exercitium\/wp-content\/uploads\/2019\/02\/Medias_de_digitos_de_pi_2000.png\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/i0.wp.com\/www.glc.us.es\/~jalonso\/exercitium\/wp-content\/uploads\/2019\/02\/Medias_de_digitos_de_pi_2000.png?resize=640%2C480\" alt=\"\" width=\"640\" height=\"480\" class=\"aligncenter size-full wp-image-4683\" srcset=\"https:\/\/i0.wp.com\/www.glc.us.es\/~jalonso\/exercitium\/wp-content\/uploads\/2019\/02\/Medias_de_digitos_de_pi_2000.png?w=640&amp;ssl=1 640w, https:\/\/i0.wp.com\/www.glc.us.es\/~jalonso\/exercitium\/wp-content\/uploads\/2019\/02\/Medias_de_digitos_de_pi_2000.png?resize=300%2C225&amp;ssl=1 300w\" sizes=\"(max-width: 640px) 100vw, 640px\" data-recalc-dims=\"1\" \/><\/a><\/li>\n<\/ul>\n<\/li>\n<\/ul>\n<h4>Soluciones<\/h4>\n<pre lang=\"haskell\">\nimport Data.Char (digitToInt)\nimport Data.List (genericLength, inits, tails)\nimport Graphics.Gnuplot.Simple ( Attribute (Key, PNG)\n                               , plotList )\n\n-- Definici\u00f3n de mediasDigitosDePi\n-- ===============================\n\nmediasDigitosDePi :: IO [Double]\nmediasDigitosDePi = do\n  (_:_:ds) <- readFile \"Digitos_de_pi.txt\"\n  return (medias (digitos ds))\n\n-- (digitos cs) es la lista de los digitos de cs. Por ejempplo,\n--    digitos \"1415926535\"  ==  [1,4,1,5,9,2,6,5,3,5]\ndigitos :: String -> [Int]\ndigitos = map digitToInt\n\n-- (medias xs) es la lista de las medias de los segmentos iniciales de\n-- xs. Por ejemplo,\n--    \u03bb> medias [1,4,1,5,9,2,6,5,3,5]\n--    [1.0,2.5,2.0,2.75,4.0,3.6666666666666665,4.0,4.125,4.0,4.1]\nmedias :: [Int] -> [Double]\nmedias xs = map media (tail (inits xs))\n\n-- (media xs) es la media aritm\u00e9tica de xs. Por ejemplo,\n--    media [1,4,1,5,9]  ==  4.0\nmedia :: [Int] -> Double\nmedia xs = fromIntegral (sum xs) \/ genericLength xs\n\n-- Definici\u00f3n de graficaMediasDigitosDePi\n-- ======================================\n\ngraficaMediasDigitosDePi :: Int -> IO ()\ngraficaMediasDigitosDePi n = do\n  xs <- mediasDigitosDePi\n  plotList [ Key Nothing\n           , PNG (\"Medias_de_digitos_de_pi_\" ++ show n ++ \".png\")\n           ]\n           (take n xs)\n<\/pre>\n<h4>Pensamiento<\/h4>\n<blockquote><p>\nEs el mejor de los buenos<br \/>\nquien sabe que en esta vida<br \/>\ntodo es cuesti\u00f3n de medida:<br \/>\nun poco m\u00e1s, algo menos.<\/p>\n<p>Antonio Machado\n<\/p><\/blockquote>\n","protected":false},"excerpt":{"rendered":"<p>El fichero Digitos_de_pi.txt contiene el n\u00famero pi con un mill\u00f3n de decimales; es decir, 3.1415926535897932384626433832 &#8230; 83996346460422090106105779458151 Definir las funciones mediasDigitosDePi :: IO [Double] graficaMediasDigitosDePi :: Int -> IO () tales que mediasDigitosDePi es la sucesi\u00f3n cuyo n-\u00e9simo elemento es la media de los n primeros d\u00edgitos de pi. Por ejemplo, \u03bb> xs take 5&#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":[5],"tags":[248,369,183,258,376,74,10,11,309,370,371,33,40,45,47],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/4680"}],"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=4680"}],"version-history":[{"count":2,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/4680\/revisions"}],"predecessor-version":[{"id":4719,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/4680\/revisions\/4719"}],"wp:attachment":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/media?parent=4680"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/categories?post=4680"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/tags?post=4680"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}