{"id":4793,"date":"2019-03-06T06:00:45","date_gmt":"2019-03-06T04:00:45","guid":{"rendered":"http:\/\/www.glc.us.es\/~jalonso\/exercitium\/?p=4793"},"modified":"2021-04-25T16:23:09","modified_gmt":"2021-04-25T14:23:09","slug":"numeros-como-suma-de-sus-digitos-2019","status":"publish","type":"post","link":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/numeros-como-suma-de-sus-digitos-2019\/","title":{"rendered":"N\u00fameros como suma de sus d\u00edgitos"},"content":{"rendered":"<p>El n\u00famero 23 se puede escribir de 4 formas como suma de sus d\u00edgitos<\/p>\n<pre lang=\"text\"> \n   2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 + 3\n   2 + 2 + 2 + 2 + 2 + 2 + 2 + 3 + 3 + 3\n   2 + 2 + 2 + 2 + 3 + 3 + 3 + 3 + 3\n   2 + 3 + 3 + 3 + 3 + 3 + 3 + 3\n<\/pre>\n<p>La de menor n\u00famero de sumando es la \u00faltima, que tiene 8 sumandos.<\/p>\n<p>Definir las funciones<\/p>\n<pre lang=\"text\"> \n   minimoSumandosDigitos        :: Integer -> Integer\n   graficaMinimoSumandosDigitos :: Integer -> IO ()\n<\/pre>\n<p>tales que<\/p>\n<ul>\n<li>(minimoSumandosDigitos n) es el menor n\u00famero de d\u00edgitos de n cuya suma es n. Por ejemplo,<\/li>\n<\/ul>\n<pre lang=\"text\">   \n     minimoSumandosDigitos 23    ==  8\n     minimoSumandosDigitos 232   ==  78\n     minimoSumandosDigitos 2323  ==  775\n     map minimoSumandosDigitos [10..20] == [10,11,6,5,5,3,6,5,4,3,10]\n<\/pre>\n<ul>\n<li>(graficaMinimoSumandosDigitos n) dibuja la gr\u00e1fica de (minimoSumandosDigitos k) par los k primeros n\u00fameros naturales. Por ejemplo, (graficaMinimoSumandosDigitos 300) dibuja<\/li>\n<\/ul>\n<p><a href=\"https:\/\/i0.wp.com\/www.glc.us.es\/~jalonso\/exercitium\/wp-content\/uploads\/2019\/03\/Numero_como_suma_de_sus_digitos.png\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/i0.wp.com\/www.glc.us.es\/~jalonso\/exercitium\/wp-content\/uploads\/2019\/03\/Numero_como_suma_de_sus_digitos.png?resize=640%2C480\" alt=\"\" width=\"640\" height=\"480\" class=\"aligncenter size-full wp-image-4795\" srcset=\"https:\/\/i0.wp.com\/www.glc.us.es\/~jalonso\/exercitium\/wp-content\/uploads\/2019\/03\/Numero_como_suma_de_sus_digitos.png?w=640&amp;ssl=1 640w, https:\/\/i0.wp.com\/www.glc.us.es\/~jalonso\/exercitium\/wp-content\/uploads\/2019\/03\/Numero_como_suma_de_sus_digitos.png?resize=300%2C225&amp;ssl=1 300w\" sizes=\"(max-width: 640px) 100vw, 640px\" data-recalc-dims=\"1\" \/><\/a><\/p>\n<h4>Soluciones<\/h4>\n<pre lang=\"haskell\">\nimport Data.List (nub, genericLength, sort)\nimport Graphics.Gnuplot.Simple\n\nminimoSumandosDigitos :: Integer -> Integer\nminimoSumandosDigitos n =\n  minimoSumandos (digitos n) n\n\n-- (digitos n) es el conjunto de los d\u00edgitos no nulos de n. Por ejemplo,\n--    digitos 2032  ==  [2,3]\ndigitos :: Integer -> [Integer]\ndigitos n =\n  nub [read [c] | c <- show n, c \/= '0']\n\n-- (minimoSumandos xs n) es el menor n\u00famero de elementos de la lista de\n-- enteros positivos xs (con posibles repeticiones) cuya suma es n. Por\n-- ejemplo, \n--    minimoSumandos [7,2,4] 11  ==  2\nminimoSumandos :: [Integer] -> Integer -> Integer\nminimoSumandos xs n =\n  minimum (mapo genericLength (sumas xs n))\n\n-- (sumas xs n) es la lista de elementos de la lista de enteros\n-- positivos xs (con posibles repeticiones) cuya suma es n. Por ejemplo,  \n--    sumas [7,2,4] 11  ==  [[7,2,2],[7,4]]\nsumas :: [Integer] -> Integer -> [[Integer]]\nsumas [] 0 = [[]]\nsumas [] _ = []\nsumas (x:xs) n\n  | x <= n    = map (x:) (sumas (x:xs) (n-x)) ++ sumas xs n\n  | otherwise = sumas xs n\n\ngraficaMinimoSumandosDigitos :: Integer -> IO ()\ngraficaMinimoSumandosDigitos n =\n  plotList [ Key Nothing\n           , PNG \"Numero_como_suma_de_sus_digitos.png\"\n           ]\n           [minimoSumandosDigitos k | k <- [0..n-1]]\n<\/pre>\n<h4>Pensamiento<\/h4>\n<blockquote><p>\nCaminante, son tus huellas<br \/>\nel camino, y nada m\u00e1s;<br \/>\ncaminante no hay camino,<br \/>\nse hace camino al andar.<\/p>\n<p>Antonio Machado\n<\/p><\/blockquote>\n","protected":false},"excerpt":{"rendered":"<p>El n\u00famero 23 se puede escribir de 4 formas como suma de sus d\u00edgitos 2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 + 2 + 3 2 + 2 + 2 + 2 + 2 + 2 + 2 + 3 + 3 + 3 2&#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":[7],"tags":[8,258,10,340,24,11,95,6,32,33,14],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/4793"}],"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=4793"}],"version-history":[{"count":5,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/4793\/revisions"}],"predecessor-version":[{"id":4821,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/4793\/revisions\/4821"}],"wp:attachment":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/media?parent=4793"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/categories?post=4793"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/tags?post=4793"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}