{"id":3700,"date":"2018-02-05T06:00:57","date_gmt":"2018-02-05T04:00:57","guid":{"rendered":"http:\/\/www.glc.us.es\/~jalonso\/exercitium\/?p=3700"},"modified":"2018-02-12T07:43:09","modified_gmt":"2018-02-12T05:43:09","slug":"celdas-interiores-de-una-reticula","status":"publish","type":"post","link":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/celdas-interiores-de-una-reticula\/","title":{"rendered":"Celdas interiores de una ret\u00edcula"},"content":{"rendered":"<p>Las celdas de una ret\u00edcula cuadrada se numeran consecutivamente. Por ejemplo, la numeraci\u00f3n de la ret\u00edcula cuadrada de lado 4 es<\/p>\n<pre lang=\"text\">\n   1, 2, 3, 4\n   5, 6, 7, 8\n   9,10,11,12\n  13,14,15,16\n<\/pre>\n<p>Los n\u00fameros de sus celdas interiores son 6,7,10,11.<\/p>\n<p>Definir la funci\u00f3n<\/p>\n<pre lang=\"text\">\n   interiores :: Int -> [Int]\n<\/pre>\n<p>tal que (interiores n) es la lista de los n\u00fameros de las celdas interiores de la ret\u00edcula cuadrada de lado n. Por ejemplo,<\/p>\n<pre lang=\"text\">\n   interiores 4  == [6,7,10,11]\n   interiores 5  == [7,8,9,12,13,14,17,18,19]\n   interiores 6  == [8,9,10,11,14,15,16,17,20,21,22,23,26,27,28,29]\n   interiores 2  == []\n   length (interiores 2018)  == 4064256\n<\/pre>\n<p>Comprobar con QuickCheck que el n\u00famero de celdas interiores de la ret\u00edcula cuadrada de lado n, con n > 1, es (n-2)^2.<\/p>\n<h4>Soluciones<\/h4>\n<pre lang=\"haskell\">\nimport Test.QuickCheck\nimport Data.List.Split (divvy)\n\n-- 1\u00aa soluci\u00f3n\ninteriores :: Int -> [Int]\ninteriores n = [i | i <- [n..n*n-n], i `mod` n > 1]\n\n-- 2\u00aa soluci\u00f3n\ninteriores2 :: Int -> [Int]\ninteriores2 n = aux [n+1..n^2-n]\n  where aux xss@(x:xs) = take (n-2) xs ++ aux (drop n xss)\n        aux []         = []\n\n-- 3\u00aa soluci\u00f3n \ninteriores3 :: Int -> [Int]\ninteriores3 n = concat (divvy (n-2) n [n+2..n*(n-1)-1])\n\n-- 4\u00aa soluci\u00f3n\ninteriores4 :: Int -> [Int]\ninteriores4 n = concat [map (+(n*k)) [2..n-1] | k <- [1..n-2]]\n\n-- 5\u00aa soluci\u00f3n\ninteriores5 :: Int -> [Int]\ninteriores5 n = concat (take (n-2) (iterate (map (+n)) [n+2..2*n-1]))\n\n-- La propiedad es\nprop_interiores :: Int -> Property\nprop_interiores n =\n  n > 1 ==> length (interiores n) == (n-2)^2\n\n-- La comprobaci\u00f3n es\n--    \u03bb> quickCheck prop_interiores\n--    +++ OK, passed 100 tests.\n<\/pre>\n","protected":false},"excerpt":{"rendered":"<p>Las celdas de una ret\u00edcula cuadrada se numeran consecutivamente. Por ejemplo, la numeraci\u00f3n de la ret\u00edcula cuadrada de lado 4 es 1, 2, 3, 4 5, 6, 7, 8 9,10,11,12 13,14,15,16 Los n\u00fameros de sus celdas interiores son 6,7,10,11. Definir la funci\u00f3n interiores :: Int -> [Int] tal que (interiores n) es la lista de&#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":[8,12,417,50,28,10,89,11,6,47,146],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/3700"}],"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=3700"}],"version-history":[{"count":6,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/3700\/revisions"}],"predecessor-version":[{"id":3744,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/3700\/revisions\/3744"}],"wp:attachment":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/media?parent=3700"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/categories?post=3700"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/tags?post=3700"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}