{"id":5361,"date":"2020-01-13T05:30:14","date_gmt":"2020-01-13T03:30:14","guid":{"rendered":"http:\/\/www.glc.us.es\/~jalonso\/exercitium\/?p=5361"},"modified":"2020-01-20T08:14:33","modified_gmt":"2020-01-20T06:14:33","slug":"numeros-de-munchausen","status":"publish","type":"post","link":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/numeros-de-munchausen\/","title":{"rendered":"N\u00fameros de Munchausen"},"content":{"rendered":"<p>Un <a href=\"http:\/\/bit.ly\/2SYbCqm\">n\u00famero de Munchausen<\/a> es un n\u00famero entero positivo tal que es igual a la suma de sus d\u00edgitos elevados a s\u00ed mismo. Por ejemplo, 3435 es un n\u00famero de Munchausen ya que<\/p>\n<pre lang=\"text\">\n   3\u00b3 + 4\u2074 + 3\u00b3 + 5\u2075 = 27 + 256 + 27 + 3125 = 3435\n<\/pre>\n<p>Definir la funci\u00f3n<\/p>\n<pre lang=\"text\">\n   esMunchausen :: Integer -> Bool\n<\/pre>\n<p>tal que (esMunchausen n) se verifica si n es un n\u00famero de Munchausen. Por ejemplo,<\/p>\n<pre lang=\"text\">\n   esMunchausen 3435  ==  True\n   esMunchausen 2020  ==  False\n<\/pre>\n<p>Comprobar con QuickCheck que que los \u00fanicos n\u00fameros de Munchausen son 1 y 3435.<\/p>\n<p><strong>Nota 1:<\/strong> No usar la propiedad en la definici\u00f3n.<\/p>\n<p><strong>Nota 2:<\/strong> El ejercicio est\u00e1 basado en el art\u00edculo <a href=\"http:\/\/bit.ly\/2Quijiu\">\u00bfPor qu\u00e9 3435 es uno de mis n\u00fameros favoritos?<\/a> de Miguel \u00c1ngel Morales en <a href=\"http:\/\/bit.ly\/35nM0WF\">El Aleph<\/a>.<\/p>\n<h4>Soluciones<\/h4>\n<pre lang=\"haskell\">\nimport Test.QuickCheck\n\nesMunchausen :: Integer -> Bool\nesMunchausen n =\n  n == sum [x^x | x <- digitos n]\n\n-- (digitos n) es la lista de los d\u00edgitos de n. Por ejemplo,\n--    digitos 3435  ==  [3,4,3,5]\ndigitos :: Integer -> [Integer]\ndigitos n = [read [c] | c <- show n]\n\n-- La propiedad es\nprop_Munchausen :: Integer -> Property\nprop_Munchausen n =\n  n > 0\n  ==>\n  esMunchausen n == elem n [1, 3435]\n\n-- La comprobaci\u00f3n es\n--    \u03bb> quickCheck prop_Munchausen\n--    +++ OK, passed 100 tests.\n<\/pre>\n<h4>Pensamiento<\/h4>\n<blockquote><p>\nEscribir\u00e9 en tu abanico:<br \/>\nte quiero para olvidarte,<br \/>\npara quererte te olvido.<\/p>\n<p>Antonio Machado\n<\/p><\/blockquote>\n","protected":false},"excerpt":{"rendered":"<p>Un n\u00famero de Munchausen es un n\u00famero entero positivo tal que es igual a la suma de sus d\u00edgitos elevados a s\u00ed mismo. Por ejemplo, 3435 es un n\u00famero de Munchausen ya que 3\u00b3 + 4\u2074 + 3\u00b3 + 5\u2075 = 27 + 256 + 27 + 3125 = 3435 Definir la funci\u00f3n esMunchausen ::&#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":[8,26,95,33,40,146],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/5361"}],"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=5361"}],"version-history":[{"count":4,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/5361\/revisions"}],"predecessor-version":[{"id":5408,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/5361\/revisions\/5408"}],"wp:attachment":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/media?parent=5361"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/categories?post=5361"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/tags?post=5361"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}