{"id":1780,"date":"2015-11-30T06:00:48","date_gmt":"2015-11-30T04:00:48","guid":{"rendered":"http:\/\/www.glc.us.es\/~jalonso\/exercitium\/?p=1780"},"modified":"2015-12-07T08:41:21","modified_gmt":"2015-12-07T06:41:21","slug":"separacion-y-mezcla-de-listas","status":"publish","type":"post","link":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/separacion-y-mezcla-de-listas\/","title":{"rendered":"Separaci\u00f3n y mezcla de listas"},"content":{"rendered":"<p>Definir las funciones<\/p>\n<pre lang=\"text\">\n   separacion :: [a] -> ([a],[a])\n   mezcla     :: ([a],[a]) -> [a]\n<\/pre>\n<p>tales que (separacion xs) es el par formado eligiendo alternativamente  elementos de xs mientras que mezcla intercala los elementos de las dos listas. Por ejemplo,<\/p>\n<pre lang=\"text\">\n   separacion [1..5]                   ==  ([1,3,5],[2,4])\n   mezcla ([1,3,5],[2,4])              ==  [1,2,3,4,5]\n   separacion \"Telescopio\"             ==  (\"Tlsoi\",\"eecpo\")\n   mezcla (\"Tlsoi\",\"eecpo\")            ==  \"Telescopio\"\n   take 5 (fst (separacion [2,4..]))   ==  [2,6,10,14,18]\n   take 6 (mezcla ([2,4..],[7,14..]))  ==  [2,7,4,14,6,21]\n<\/pre>\n<p>Comprobar con QuickCheck que<\/p>\n<pre lang=\"text\">\n   mezcla (separacion xs) == xs\n<\/pre>\n<h4>Soluciones<\/h4>\n<pre lang=\"haskell\">\nimport Test.QuickCheck\n\n-- 1\u00aa definici\u00f3n (por recursi\u00f3n):\nseparacion1 :: [a] -> ([a],[a])\nseparacion1 []       = ([],  [])\nseparacion1 [x]      = ([x], [])\nseparacion1 (x:y:zs) = (x:us,y:vs)\n    where (us,vs) = separacion1 zs\n\n-- 2\u00aa definici\u00f3n (por comprensi\u00f3n):\nseparacion2 :: [a] -> ([a],[a])\nseparacion2 xs = ([x | (x,n) <- aux, even n], \n                  [x | (x,n) <- aux, odd n])\n    where aux = zip xs [0..]                                           \n\n-- 3\u00aa definici\u00f3n \nseparacion3 :: [a] -> ([a],[a])\nseparacion3 []       = ([],[])\nseparacion3 (x:xs)   = (x:zs, ys)\n    where (ys, zs) = separacion3 xs \n\n-- Comprobaci\u00f3n de eficiencia\n--    ghci> last (snd (separacion1 [1..10000000]))\n--    10000000\n--    (10.73 secs, 2,945,794,552 bytes)\n--\n--    ghci> last (snd (separacion2 [1..10000000]))\n--    10000000\n--    (16.33 secs, 4,351,366,976 bytes)\n--    \n--    \u03bb> last (snd (separacion3 [1..10000000]))\n--    10000000\n--    (15.67 secs, 4,423,573,048 bytes)\n\nmezcla :: ([a],[a]) -> [a]\nmezcla ([],ys)     = ys \nmezcla (xs,[])     = xs \nmezcla (x:xs,y:ys) = x : y : mezcla (xs,ys)\n\n-- La propiedad es\nprop_mezcla_separacion :: [Int] -> Bool\nprop_mezcla_separacion xs =\n    mezcla (separacion xs) == xs\n\n-- La comprobaci\u00f3n es\n--    ghci> quickCheck prop_mezcla_separacion\n--    +++ OK, passed 100 tests.\n<\/pre>\n","protected":false},"excerpt":{"rendered":"<p>Definir las funciones separacion :: [a] -> ([a],[a]) mezcla :: ([a],[a]) -> [a] tales que (separacion xs) es el par formado eligiendo alternativamente elementos de xs mientras que mezcla intercala los elementos de las dos listas. Por ejemplo, separacion [1..5] == ([1,3,5],[2,4]) mezcla ([1,3,5],[2,4]) == [1,2,3,4,5] separacion \u00abTelescopio\u00bb == (\u00abTlsoi\u00bb,\u00bbeecpo\u00bb) mezcla (\u00abTlsoi\u00bb,\u00bbeecpo\u00bb) == \u00abTelescopio\u00bb take&#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":[4],"tags":[91,92,6,146,9],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/1780"}],"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=1780"}],"version-history":[{"count":4,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/1780\/revisions"}],"predecessor-version":[{"id":1824,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/1780\/revisions\/1824"}],"wp:attachment":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/media?parent=1780"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/categories?post=1780"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/tags?post=1780"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}