Definir la funci\u00f3n<\/p>\n
\n indicesVerdaderos :: [Int] -> [Bool]\n<\/pre>\ntal que (indicesVerdaderos xs)<\/code> es la lista infinita de booleanos tal que s\u00f3lo son verdaderos los elementos cuyos \u00edndices pertenecen a la lista estrictamente creciente xs<\/code>. Por ejemplo,<\/p>\n\n \u03bb> take 6 (indicesVerdaderos [1,4])\n [False,True,False,False,True,False]\n \u03bb> take 6 (indicesVerdaderos [0,2..])\n [True,False,True,False,True,False]\n \u03bb> take 3 (indicesVerdaderos [])\n [False,False,False]\n \u03bb> take 6 (indicesVerdaderos [1..])\n [False,True,True,True,True,True]\n \u03bb> last (take (8*10^7) (indicesVerdaderos [0,5..]))\n False\n<\/pre>\nSoluciones<\/h4>\n
[schedule expon=’2022-04-19′ expat=\u00bb06:00″]<\/p>\n
\n- Las soluciones se pueden escribir en los comentarios.\n
- El c\u00f3digo se debe escribir entre una l\u00ednea con <pre lang="haskell"> y otra con <\/pre>\n<\/ul>\n
[\/schedule]<\/p>\n
[schedule on=’2022-04-19′ at=\u00bb06:00″]<\/p>\n
\r\nimport Data.List.Ordered (member)\r\nimport Test.QuickCheck\r\n\r\n-- 1\u00aa soluci\u00f3n\r\n-- ===========\r\n\r\nindicesVerdaderos1 :: [Int] -> [Bool]\r\nindicesVerdaderos1 [] = repeat False\r\nindicesVerdaderos1 (x:ys) =\r\n replicate x False ++ [True] ++ indicesVerdaderos1 [y-x-1 | y <- ys]\r\n\r\n-- 2\u00aa soluci\u00f3n\r\n-- ===========\r\n\r\nindicesVerdaderos2 :: [Int] -> [Bool]\r\nindicesVerdaderos2 = aux 0\r\n where aux _ [] = repeat False\r\n aux n (x:xs) | x == n = True : aux (n+1) xs\r\n | otherwise = False : aux (n+1) (x:xs)\r\n\r\n-- 3\u00aa soluci\u00f3n\r\n-- ===========\r\n\r\nindicesVerdaderos3 :: [Int] -> [Bool]\r\nindicesVerdaderos3 = aux [0..]\r\n where aux _ [] = repeat False\r\n aux (i:is) (x:xs) | i == x = True : aux is xs\r\n | otherwise = False : aux is (x:xs)\r\n\r\n-- 4\u00aa soluci\u00f3n\r\n-- ===========\r\n\r\nindicesVerdaderos4 :: [Int] -> [Bool]\r\nindicesVerdaderos4 xs = [pertenece x xs | x <- [0..]]\r\n\r\n-- (pertenece x ys) se verifica si x pertenece a la lista estrictamente\r\n-- creciente (posiblemente infinita) ys. Por ejemplo,\r\n-- pertenece 9 [1,3..] == True\r\n-- pertenece 6 [1,3..] == False\r\npertenece :: Int -> [Int] -> Bool\r\npertenece x ys = x `elem` takeWhile (<=x) ys\r\n\r\n-- 5\u00aa soluci\u00f3n\r\n-- ===========\r\n\r\nindicesVerdaderos5 :: [Int] -> [Bool]\r\nindicesVerdaderos5 xs = map (`pertenece2` xs) [0..]\r\n\r\npertenece2 :: Int -> [Int] -> Bool\r\npertenece2 x = aux\r\n where aux [] = False\r\n aux (y:ys) = case compare x y of\r\n LT -> False\r\n EQ -> True\r\n GT -> aux ys\r\n\r\n-- 6\u00aa soluci\u00f3n\r\n-- ===========\r\n\r\nindicesVerdaderos6 :: [Int] -> [Bool]\r\nindicesVerdaderos6 xs = map (`member` xs) [0..]\r\n\r\n-- Comprobaci\u00f3n de equivalencia\r\n-- ============================\r\n\r\n-- ListaCreciente es un tipo de dato para generar lista de enteros\r\n-- crecientes arbitrarias.\r\nnewtype ListaCreciente = LC [Int]\r\n deriving Show\r\n\r\n-- listaCrecienteArbitraria es un generador de lista de enteros\r\n-- crecientes arbitrarias. Por ejemplo,\r\n-- \u03bb> sample listaCrecienteArbitraria\r\n-- LC []\r\n-- LC [2,5]\r\n-- LC [4,8]\r\n-- LC [6,13]\r\n-- LC [7,15,20,28,33]\r\n-- LC [11,15,20,29,35,40]\r\n-- LC [5,17,25,36,42,50,52,64]\r\n-- LC [9,16,31,33,46,59,74,83,85,89,104,113,118]\r\n-- LC [9,22,29,35,37,49,53,62,68,77,83,100]\r\n-- LC []\r\n-- LC [3,22,25,34,36,51,72,75,89]\r\nlistaCrecienteArbitraria :: Gen ListaCreciente\r\nlistaCrecienteArbitraria = do\r\n xs <- arbitrary\r\n return (LC (listaCreciente xs))\r\n\r\n-- (listaCreciente xs) es la lista creciente correspondiente a xs. Por ejemplo,\r\n-- listaCreciente [-1,3,-4,3,0] == [2,6,11,15,16]\r\nlistaCreciente :: [Int] -> [Int]\r\nlistaCreciente xs =\r\n scanl1 (+) (map (succ . abs) xs)\r\n\r\n-- ListaCreciente est\u00e1 contenida en Arbitrary\r\ninstance Arbitrary ListaCreciente where\r\n arbitrary = listaCrecienteArbitraria\r\n\r\n-- La propiedad es\r\nprop_indicesVerdaderos :: ListaCreciente -> Bool\r\nprop_indicesVerdaderos (LC xs) =\r\n all (== take n (indicesVerdaderos1 xs))\r\n [take n (f xs) | f <-[indicesVerdaderos2,\r\n indicesVerdaderos3,\r\n indicesVerdaderos4,\r\n indicesVerdaderos5,\r\n indicesVerdaderos6]]\r\n where n = length xs\r\n\r\n-- La comprobaci\u00f3n es\r\n-- \u03bb> quickCheck prop_indicesVerdaderos\r\n-- +++ OK, passed 100 tests.\r\n\r\n-- Comparaci\u00f3n de eficiencia\r\n-- =========================\r\n\r\n-- La comparaci\u00f3n es\r\n-- \u03bb> last (take (2*10^4) (indicesVerdaderos1 [0,5..]))\r\n-- False\r\n-- (2.69 secs, 2,611,031,544 bytes)\r\n-- \u03bb> last (take (2*10^4) (indicesVerdaderos2 [0,5..]))\r\n-- False\r\n-- (0.03 secs, 10,228,880 bytes)\r\n--\r\n-- \u03bb> last (take (4*10^6) (indicesVerdaderos2 [0,5..]))\r\n-- False\r\n-- (2.37 secs, 1,946,100,856 bytes)\r\n-- \u03bb> last (take (4*10^6) (indicesVerdaderos3 [0,5..]))\r\n-- False\r\n-- (1.54 secs, 1,434,100,984 bytes)\r\n--\r\n-- \u03bb> last (take (6*10^6) (indicesVerdaderos3 [0,5..]))\r\n-- False\r\n-- (2.30 secs, 2,150,900,984 bytes)\r\n-- \u03bb> last (take (6*10^6) (indicesVerdaderos4 [0,5..]))\r\n-- False\r\n-- (1.55 secs, 1,651,701,184 bytes)\r\n-- \u03bb> last (take (6*10^6) (indicesVerdaderos5 [0,5..]))\r\n-- False\r\n-- (0.58 secs, 1,584,514,304 bytes)\r\n--\r\n-- \u03bb> last (take (3*10^7) (indicesVerdaderos5 [0,5..]))\r\n-- False\r\n-- (2.74 secs, 7,920,514,360 bytes)\r\n-- \u03bb> last (take (3*10^7) (indicesVerdaderos6 [0,5..]))\r\n-- False\r\n-- (0.82 secs, 6,960,514,136 bytes)\r\n\r\n-- \u03bb> last (take (2*10^4) (indicesVerdaderos1 [0,5..]))\r\n-- False\r\n-- (2.69 secs, 2,611,031,544 bytes)\r\n-- \u03bb> last (take (2*10^4) (indicesVerdaderos6 [0,5..]))\r\n-- False\r\n-- (0.01 secs, 5,154,040 bytes)\r\n<\/pre>\nEl c\u00f3digo se encuentra en [GitHub](https:\/\/github.com\/jaalonso\/Exercitium\/blob\/main\/src\/Indices_verdaderos.hs).<\/p>\n
La elaboraci\u00f3n de las soluciones se describe en el siguiente v\u00eddeo<\/p>\n
Nuevas soluciones<\/h4>\n\n- En los comentarios se pueden escribir nuevas soluciones.\n
- El c\u00f3digo se debe escribir entre una l\u00ednea con <pre lang="haskell"> y otra con <\/pre>\n<\/ul>\n
[\/schedule]<\/p>\n","protected":false},"excerpt":{"rendered":"
Definir la funci\u00f3n indicesVerdaderos :: [Int] -> [Bool] tal que (indicesVerdaderos xs) es la lista infinita de booleanos tal que s\u00f3lo son verdaderos los elementos cuyos \u00edndices pertenecen a la lista estrictamente creciente xs. Por ejemplo, \u03bb> take 6 (indicesVerdaderos [1,4]) [False,True,False,False,True,False] \u03bb> take 6 (indicesVerdaderos [0,2..]) [True,False,True,False,True,False] \u03bb> take 3 (indicesVerdaderos []) [False,False,False] \u03bb>…<\/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":[130,41,483,161,8,540,26,415,10,473,6,49,19,371,252,52,47,34,146],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/6897"}],"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=6897"}],"version-history":[{"count":1,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/6897\/revisions"}],"predecessor-version":[{"id":6898,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/6897\/revisions\/6898"}],"wp:attachment":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/media?parent=6897"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/categories?post=6897"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/tags?post=6897"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}