{"id":6737,"date":"2022-03-10T06:00:23","date_gmt":"2022-03-10T04:00:23","guid":{"rendered":"http:\/\/www.glc.us.es\/~jalonso\/exercitium\/?p=6737"},"modified":"2022-03-17T09:12:32","modified_gmt":"2022-03-17T07:12:32","slug":"lista-cuadrada","status":"publish","type":"post","link":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/lista-cuadrada\/","title":{"rendered":"Lista cuadrada"},"content":{"rendered":"<p>Definir la funci\u00f3n<\/p>\n<pre lang=\"text\">\n   listaCuadrada :: Int -> a -> [a] -> [[a]]\n<\/pre>\n<p>tal que (listaCuadrada n x xs) es una lista de n listas de longitud n formadas con los elementos de xs completada con x, si no xs no tiene suficientes elementos. Por ejemplo,<\/p>\n<pre lang=\"text\">\n   listaCuadrada 3 7 [0,3,5,2,4]  ==  [[0,3,5],[2,4,7],[7,7,7]]\n   listaCuadrada 3 7 [0..]        ==  [[0,1,2],[3,4,5],[6,7,8]]\n   listaCuadrada 2 'p' \"eva\"      ==  [\"ev\",\"ap\"]\n   listaCuadrada 2 'p' ['a'..]    ==  [\"ab\",\"cd\"]\n<\/pre>\n<h4>Soluciones<\/h4>\n<pre lang=\"haskell\">\nimport Data.List.Split (chunksOf)\nimport Test.QuickCheck\n\n-- 1\u00aa soluci\u00f3n\n-- ===========\n\nlistaCuadrada1 :: Int -> a -> [a] -> [[a]]\nlistaCuadrada1 n x xs =\n  take n (grupos n (xs ++ repeat x))\n\n-- (grupos n xs) es la lista obtenida agrupando los elementos de xs en\n-- grupos de n elementos, salvo el \u00faltimo que puede tener menos. Por\n-- ejemplo,\n--    grupos 2 [4,2,5,7,6]     ==  [[4,2],[5,7],[6]]\n--    take 3 (grupos 3 [1..])  ==  [[1,2,3],[4,5,6],[7,8,9]]\ngrupos :: Int -> [a] -> [[a]]\ngrupos _ [] = []\ngrupos n xs = take n xs : grupos n (drop n xs)\n\n-- 2\u00aa soluci\u00f3n\n-- ===========\n\nlistaCuadrada2 :: Int -> a -> [a] -> [[a]]\nlistaCuadrada2 n x xs =\n  take n (grupos2 n (xs ++ repeat x))\n\ngrupos2 :: Int -> [a] -> [[a]]\ngrupos2 _ [] = []\ngrupos2 n xs = ys : grupos n zs\n  where (ys,zs) = splitAt n xs\n\n-- 3\u00aa soluci\u00f3n\n-- ===========\n\nlistaCuadrada3 :: Int -> a -> [a] -> [[a]]\nlistaCuadrada3 n x xs =\n  take n (chunksOf n (xs ++ repeat x))\n\n-- Comprobaci\u00f3n de la equivalencia\n-- ===============================\n\n-- La propiedad es\nprop_listaCuadrada :: Int -> Int -> [Int] -> Bool\nprop_listaCuadrada n x xs =\n  all (== listaCuadrada1 n x xs)\n      [listaCuadrada2 n x xs,\n       listaCuadrada3 n x xs]\n\n-- La comprobaci\u00f3n es\n--    \u03bb> quickCheck prop_listaCuadrada\n--    +++ OK, passed 100 tests.\n\n-- Comparaci\u00f3n de eficiencia\n-- =========================\n\n-- La comparaci\u00f3n es\n--    \u03bb> length (listaCuadrada1 (10^4) 5 [1..])\n--    10000\n--    (2.02 secs, 12,801,918,616 bytes)\n--    \u03bb> length (listaCuadrada2 (10^4) 5 [1..])\n--    10000\n--    (1.89 secs, 12,803,198,576 bytes)\n--    \u03bb> length (listaCuadrada3 (10^4) 5 [1..])\n--    10000\n--    (1.85 secs, 12,801,518,728 bytes)\n<\/pre>\n<p>El c\u00f3digo se encuentra en <a href=\"https:\/\/github.com\/jaalonso\/Exercitium\/blob\/main\/src\/Lista_cuadrada.hs\">GitHub<\/a>.<\/p>\n<p>La elaboraci\u00f3n de la soluci\u00f3n se muestra en el siguiente v\u00eddeo:<\/p>\n<p><iframe loading=\"lazy\" width=\"560\" height=\"315\" src=\"https:\/\/www.youtube.com\/embed\/nJHiCebyZVE\" title=\"YouTube video player\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture\" allowfullscreen><\/iframe><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Definir la funci\u00f3n listaCuadrada :: Int -> a -> [a] -> [[a]] tal que (listaCuadrada n x xs) es una lista de n listas de longitud n formadas con los elementos de xs completada con x, si no xs no tiene suficientes elementos. Por ejemplo, listaCuadrada 3 7 [0,3,5,2,4] == [[0,3,5],[2,4,7],[7,7,7]] listaCuadrada 3 7 [0..]&#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":[2],"tags":[8,508,415,11,6],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/6737"}],"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=6737"}],"version-history":[{"count":5,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/6737\/revisions"}],"predecessor-version":[{"id":6794,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/6737\/revisions\/6794"}],"wp:attachment":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/media?parent=6737"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/categories?post=6737"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/tags?post=6737"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}