{"id":6123,"date":"2021-03-03T06:00:13","date_gmt":"2021-03-03T04:00:13","guid":{"rendered":"http:\/\/www.glc.us.es\/~jalonso\/exercitium\/?p=6123"},"modified":"2021-03-10T12:15:16","modified_gmt":"2021-03-10T10:15:16","slug":"espirales","status":"publish","type":"post","link":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/espirales\/","title":{"rendered":"Espirales"},"content":{"rendered":"<p>Definir la funci\u00f3n<\/p>\n<pre lang=\"text\">\n   espiral :: Int -> [[Int]]\n<\/pre>\n<p>tal que (espiral n) es la espiral de orden n (es decir, con n filas y n columnas). Por ejemplo,<\/p>\n<pre lang=\"text\">\n   \u03bb> mapM_ print (espiral 5)\n   [1,1,1,1,1]\n   [0,0,0,0,1]\n   [1,1,1,0,1]\n   [1,0,0,0,1]\n   [1,1,1,1,1]\n   \u03bb> mapM_ print (espiral 6)\n   [1,1,1,1,1,1]\n   [0,0,0,0,0,1]\n   [1,1,1,1,0,1]\n   [1,0,0,1,0,1]\n   [1,0,0,0,0,1]\n   [1,1,1,1,1,1]\n   \u03bb> mapM_ print (espiral 7)\n   [1,1,1,1,1,1,1]\n   [0,0,0,0,0,0,1]\n   [1,1,1,1,1,0,1]\n   [1,0,0,0,1,0,1]\n   [1,0,1,1,1,0,1]\n   [1,0,0,0,0,0,1]\n   [1,1,1,1,1,1,1]\n   \u03bb> mapM_ print (espiral 8)\n   [1,1,1,1,1,1,1,1]\n   [0,0,0,0,0,0,0,1]\n   [1,1,1,1,1,1,0,1]\n   [1,0,0,0,0,1,0,1]\n   [1,0,1,0,0,1,0,1]\n   [1,0,1,1,1,1,0,1]\n   [1,0,0,0,0,0,0,1]\n   [1,1,1,1,1,1,1,1]\n<\/pre>\n<p>Nota: La serpiente (formada por los 1) nunca se puede tocar a ella misma.<\/p>\n<h4>Soluciones<\/h4>\n<pre lang=\"haskell\">\nimport Data.List (transpose)\n\nespiral :: Int -> [[Int]]\nespiral n = espiralAux n n\n\nespiralAux :: Int -> Int -> [[Int]]\nespiralAux 0 _ = []\nespiralAux 1 1 = [[1]]\nespiralAux n m = primeraFila n : segundaFila n : filasDesdeTercera n m\n\n-- (primeraFila n) es la primera fila de la espiral de orden n. Por\n-- ejemplo,\n--    \u03bb> primeraFila 5\n--    [1,1,1,1,1]\nprimeraFila :: Int -> [Int]\nprimeraFila n = replicate n 1\n\n-- (segundaFila n) es la segunda de la espiral de orden n. Por\n-- ejemplo,\n--    \u03bb> segundaFila 5\n--    [0,0,0,0,1]\nsegundaFila :: Int -> [Int]\nsegundaFila n = replicate (n-1) 0 ++ [1]\n\n-- (filasDesdeTercera n m), cuando n = m, es la lista de las filas de la\n-- espiral de orden n a partir de la tercera. Por ejemplo,\n--    \u03bb> mapM_ print (filasDesdeTercera 5 5)\n--    [1,1,1,0,1]\n--    [1,0,0,0,1]\n--    [1,1,1,1,1]\nfilasDesdeTercera :: Int -> Int -> [[Int]]\nfilasDesdeTercera n m = map reverse (transpose (espiralAux (m-2) n))\n<\/pre>\n<h4>Nuevas soluciones<\/h4>\n<ul>\n<li>En los comentarios se pueden escribir nuevas soluciones.\n<li>El c\u00f3digo se debe escribir entre una l\u00ednea con &#60;pre lang=&quot;haskell&quot;&#62; y otra con &#60;\/pre&#62;\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>Definir la funci\u00f3n espiral :: Int -> [[Int]] tal que (espiral n) es la espiral de orden n (es decir, con n filas y n columnas). Por ejemplo, \u03bb> mapM_ print (espiral 5) [1,1,1,1,1] [0,0,0,0,1] [1,1,1,0,1] [1,0,0,0,1] [1,1,1,1,1] \u03bb> mapM_ print (espiral 6) [1,1,1,1,1,1] [0,0,0,0,0,1] [1,1,1,1,0,1] [1,0,0,1,0,1] [1,0,0,0,0,1] [1,1,1,1,1,1] \u03bb> mapM_ print (espiral 7) [1,1,1,1,1,1,1]&#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":[],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/6123"}],"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=6123"}],"version-history":[{"count":5,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/6123\/revisions"}],"predecessor-version":[{"id":6170,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/6123\/revisions\/6170"}],"wp:attachment":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/media?parent=6123"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/categories?post=6123"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/tags?post=6123"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}