{"id":6669,"date":"2022-02-25T06:00:47","date_gmt":"2022-02-25T04:00:47","guid":{"rendered":"http:\/\/www.glc.us.es\/~jalonso\/exercitium\/?p=6669"},"modified":"2022-03-04T07:59:57","modified_gmt":"2022-03-04T05:59:57","slug":"ordenacion-por-el-maximo","status":"publish","type":"post","link":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/ordenacion-por-el-maximo\/","title":{"rendered":"Ordenaci\u00f3n por el m\u00e1ximo"},"content":{"rendered":"<p>Definir la funci\u00f3n<\/p>\n<pre lang=\"text\">\n   ordenadosPorMaximo :: Ord a => [[a]] -> [[a]]\n<\/pre>\n<p>tal que (ordenadosPorMaximo xss) es la lista de los elementos de xss ordenada por sus m\u00e1ximos (se supone que los elementos de xss son listas no vac\u00eda) y cuando tiene el mismo m\u00e1ximo se conserva el orden original. Por ejemplo,<\/p>\n<pre lang=\"text\">\n   \u03bb> ordenadosPorMaximo [[0,8],[9],[8,1],[6,3],[8,2],[6,1],[6,2]]\n   [[6,3],[6,1],[6,2],[0,8],[8,1],[8,2],[9]]\n   \u03bb> ordenadosPorMaximo [\"este\",\"es\",\"el\",\"primero\"]\n   [\"el\",\"primero\",\"es\",\"este\"]\n<\/pre>\n<h4>Soluciones<\/h4>\n<pre lang=\"haskell\">\nimport Data.List (sort, sortBy)\nimport GHC.Exts (sortWith)\nimport Test.QuickCheck (quickCheck)\n\n-- 1\u00aa soluci\u00f3n\nordenadosPorMaximo1 :: Ord a => [[a]] -> [[a]]\nordenadosPorMaximo1 xss =\n  map snd (sort [((maximum xs,k),xs) | (k,xs) <- zip [0..] xss])\n\n-- 2\u00aa soluci\u00f3n\nordenadosPorMaximo2 :: Ord a => [[a]] -> [[a]]\nordenadosPorMaximo2 xss =\n  [xs | (_,xs) <- sort [((maximum xs,k),xs) | (k,xs) <- zip [0..] xss]]\n\n-- 3\u00aa soluci\u00f3n\nordenadosPorMaximo3 :: Ord a => [[a]] -> [[a]]\nordenadosPorMaximo3 =\n  sortBy (\\xs ys -> compare (maximum xs) (maximum ys))\n\n-- 4\u00aa soluci\u00f3n\nordenadosPorMaximo4 :: Ord a => [[a]] -> [[a]]\nordenadosPorMaximo4 = sortWith maximum\n\n-- Equivalencia de las definiciones\n-- ================================\n\n-- La propiedad es\nprop_ordenadosPorMaximo :: [[Int]] -> Bool\nprop_ordenadosPorMaximo xss =\n  all (== ordenadosPorMaximo1 yss)\n      [ordenadosPorMaximo2 yss,\n       ordenadosPorMaximo3 yss,\n       ordenadosPorMaximo4 yss]\n  where yss = filter (not . null) xss\n\nverifica_ordenadosPorMaximo :: IO ()\nverifica_ordenadosPorMaximo =\n  quickCheck prop_ordenadosPorMaximo\n\n-- La comprobaci\u00f3n es\n--    \u03bb> verifica_ordenadosPorMaximo\n--    +++ OK, passed 100 tests.\n\n-- Comparaci\u00f3n de eficiencia\n-- =========================\n\n-- La comparaci\u00f3n es\n--    \u03bb> length (ordenadosPorMaximo1 [[1..k] | k <- [1..10^4]])\n--    10000\n--    (6.00 secs, 8,763,714,848 bytes)\n--    \u03bb> length (ordenadosPorMaximo2 [[1..k] | k <- [1..10^4]])\n--    10000\n--    (6.15 secs, 8,764,177,472 bytes)\n--    \u03bb> length (ordenadosPorMaximo3 [[1..k] | k <- [1..10^4]])\n--    10000\n--    (8.16 secs, 13,914,503,672 bytes)\n--    \u03bb> length (ordenadosPorMaximo4 [[1..k] | k <- [1..10^4]])\n--    10000\n--    (7.77 secs, 13,914,183,776 bytes)\n<\/pre>\n<p>El c\u00f3digo se encuentra en <a href=\"https:\/\/github.com\/jaalonso\/Exercitium\/blob\/main\/src\/Ordenados_por_maximo.hs\">GitHub<\/a>.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Definir la funci\u00f3n ordenadosPorMaximo :: Ord a => [[a]] -> [[a]] tal que (ordenadosPorMaximo xss) es la lista de los elementos de xss ordenada por sus m\u00e1ximos (se supone que los elementos de xss son listas no vac\u00eda) y cuando tiene el mismo m\u00e1ximo se conserva el orden original. Por ejemplo, \u03bb> ordenadosPorMaximo [[0,8],[9],[8,1],[6,3],[8,2],[6,1],[6,2]] [[6,3],[6,1],[6,2],[0,8],[8,1],[8,2],[9]]&#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":[8,498,499,11],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/6669"}],"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=6669"}],"version-history":[{"count":2,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/6669\/revisions"}],"predecessor-version":[{"id":6732,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/6669\/revisions\/6732"}],"wp:attachment":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/media?parent=6669"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/categories?post=6669"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/tags?post=6669"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}