Definir la funci\u00f3n<\/p>\n
\n particiones :: Eq a => [a] -> a -> [([a],[a])]\n<\/pre>\ntal que (particiones xs y) es la lista de las particiones de xs en dos partes tales que el primer elemento de la segunda parte es y. Por ejemplo,<\/p>\n
\n particiones [2,9,1,3,9,4] 9 == [([2],[9,1,3,9,4]),([2,9,1,3],[9,4])]\n particiones [2,9,1,3,9,4] 3 == [([2,9,1],[3,9,4])]\n particiones [2,9,1,3,9,4] 7 == []\n particiones \"Particiones\" 'i' == [(\"Part\",\"iciones\"),(\"Partic\",\"iones\")]\n<\/pre>\nSoluciones<\/h4>\n\nimport Data.List (tails, inits)\n\n-- 1\u00aa soluci\u00f3n\n-- ===========\n\nparticiones :: Eq a => [a] -> a -> [([a],[a])]\nparticiones [] _ = []\nparticiones xs y\n | null vs = []\n | otherwise = (us,vs) : [(us ++ y:us', vs')\n | (us',vs') <- particiones (tail vs) y ]\n where (us,vs) = span (\/=y) xs\n\n-- 2\u00aa soluci\u00f3n\n-- ===========\n\nparticiones2 :: Eq a => [a] -> a -> [([a],[a])]\nparticiones2 xs y =\n [(ys,z:zs) | (ys,z:zs) <- listaPares xs, z == y]\n\n-- (listaPares xs) es la lista de los pares que resultan al dividir la\n-- lista xs en dos partes. Por ejemplo,\n-- \u03bb> listaPares [2,9,1,3,9,4]\n-- [([],[2,9,1,3,9,4]),([2],[9,1,3,9,4]),([2,9],[1,3,9,4]),([2,9,1],[3,9,4]),\n-- ([2,9,1,3],[9,4]),([2,9,1,3,9],[4])]\nlistaPares :: [a] -> [([a],[a])]\nlistaPares xs = init (zip (inits xs) (tails xs))\n\n-- 3\u00aa soluci\u00f3n\n-- ===========\n\nparticiones3 :: Eq a => [a] -> a -> [([a],[a])]\nparticiones3 xs y =\n [(prefijoSufijo xs zs,zs) | zs <- sufijos xs y]\n\n-- (sufijos xs y) es la lista de los sufijos de xs que empiezan por\n-- y. Por ejemplo,\n-- \u03bb> sufijos \"particiones\" 'i'\n-- [\"iciones\",\"iones\"]\nsufijos :: Eq a => [a] -> a -> [[a]]\nsufijos xs y = filter ((== y) . head) (init (tails xs))\n\n-- (prefijoSufijo xs zs) es el prefijo de xs que junto con el sufijo zs\n-- forma la lista xs. Por ejemplo,\n-- \u03bb> prefijoSufijo \"particiones\" \"iciones\"\n-- \"part\"\nprefijoSufijo :: [a] -> [a] -> [a]\nprefijoSufijo xs zs = (inits xs) !! (length xs - length zs)\n\n-- Comprobaci\u00f3n de la equivalencia\n-- ===============================\n\n-- La propiedad es\nprop_equivalencia :: [Int] -> Int -> Bool\nprop_equivalencia xs y =\n particiones xs y' == particiones2 xs y' &&\n particiones2 xs y' == particiones3 xs y'\n where y' = y `mod` length xs\n\n-- La comprobaci\u00f3n es\n-- \u03bb> quickCheck prop_equivalencia\n-- +++ OK, passed 100 tests.\n\n-- Comparaci\u00f3n de eficiencia\n-- =========================\n\n-- La comparaci\u00f3n es\n-- \u03bb> length (particiones (take (10^5) (cycle [1..9])) 5)\n-- 11111\n-- (9.10 secs, 13,375,324,416 bytes)\n-- \u03bb> length (particiones2 (take (10^5) (cycle [1..9])) 5)\n-- 11111\n-- (0.08 secs, 44,107,672 bytes)\n-- \u03bb> length (particiones3 (take (10^5) (cycle [1..9])) 5)\n-- 11111\n-- (0.07 secs, 21,524,936 bytes)\n--\n-- \u03bb> length (particiones2 (take (10^7) (cycle [1..9])) 5)\n-- 1111111\n-- (3.93 secs, 4,400,105,800 bytes)\n-- \u03bb> length (particiones3 (take (10^7) (cycle [1..9])) 5)\n-- 1111111\n-- (1.88 secs, 2,142,328,800 bytes)\n<\/pre>\nNuevas 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","protected":false},"excerpt":{"rendered":"
Definir la funci\u00f3n particiones :: Eq a => [a] -> a -> [([a],[a])] tal que (particiones xs y) es la lista de las particiones de xs en dos partes tales que el primer elemento de la segunda parte es y. Por ejemplo, particiones [2,9,1,3,9,4] 9 == [([2],[9,1,3,9,4]),([2,9,1,3],[9,4])] particiones [2,9,1,3,9,4] 3 == [([2,9,1],[3,9,4])] particiones [2,9,1,3,9,4] 7…<\/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":[],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/6100"}],"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=6100"}],"version-history":[{"count":5,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/6100\/revisions"}],"predecessor-version":[{"id":6139,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/6100\/revisions\/6139"}],"wp:attachment":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/media?parent=6100"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/categories?post=6100"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/tags?post=6100"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}