Definir la funci\u00f3n<\/p>\n
\n mayorBorrando :: Int -> Integer -> Integer\n<\/pre>\ntal que (mayorBorrando k n) es el mayor n\u00famero obtenido borrando k d\u00edgitos de n (se supone que n tiene m\u00e1s de k d\u00edgitos). Por ejemplo,<\/p>\n
\n mayorBorrando 1 6782334 == 782334\n mayorBorrando 3 6782334 == 8334\n mayorBorrando 3 10020 == 20\n mayorBorrando 1000000 (4256 + 10^1000004) == 14256\n<\/pre>\nSoluciones<\/h4>\n\nimport Data.List (subsequences)\n\n-- 1\u00aa definici\u00f3n\n-- =============\n\nmayorBorrando :: Int -> Integer -> Integer\nmayorBorrando k n = read (mayorBorrandoLista1 k (show n))\n\n-- (mayorBorrandoLista1 k xs) es la mayor lista obtenida borrando k elementos de\n-- xs (se supone que xs tiene m\u00e1s de k elementos). Por ejemplo,\n-- mayorBorrandoLista1 1 \"6782334\" == \"782334\"\n-- mayorBorrandoLista1 3 \"6782334\" == \"8334\"\nmayorBorrandoLista1 :: Ord a => Int -> [a] -> [a]\nmayorBorrandoLista1 k xs = maximum (borra1 k xs)\n\n-- (borra1 k xs) es la lista de las listas obtenidas borrando k elementos\n-- de xs. Por ejemplo,\n-- borra1 1 \"abcd\" == [\"abc\",\"abd\",\"acd\",\"bcd\"]\n-- borra1 2 \"abcd\" == [\"ab\",\"ac\",\"bc\",\"ad\",\"bd\",\"cd\"]\n-- borra1 3 \"abcd\" == [\"a\",\"b\",\"c\",\"d\"]\nborra1 n xs = [ys | ys <- subsequences xs, length ys == k]\n where k = length xs - n\n\n-- 2\u00aa definici\u00f3n\n-- =============\n\nmayorBorrando2 :: Int -> Integer -> Integer\nmayorBorrando2 k n = read (mayorBorrandoLista2 k (show n))\n\n-- (mayorBorrandoLista2 k xs) es la mayor lista obtenida borrando k elementos de\n-- xs (se supone que xs tiene m\u00e1s de k elementos). Por ejemplo,\n-- mayorBorrandoLista2 1 \"6782334\" == \"782334\"\n-- mayorBorrandoLista2 3 \"6782334\" == \"8334\"\nmayorBorrandoLista2 :: Ord a => Int -> [a] -> [a]\nmayorBorrandoLista2 k xs = maximum (borra2 k xs)\n\n-- (borra2 k xs) es la lista de las listas obtenidas borrando k elementos\n-- de xs. Por ejemplo,\n-- borra2 1 \"abcd\" == [\"abc\",\"abd\",\"acd\",\"bcd\"]\n-- borra2 2 \"abcd\" == [\"ab\",\"ac\",\"ad\",\"bc\",\"bd\",\"cd\"]\n-- borra2 3 \"abcd\" == [\"a\",\"b\",\"c\",\"d\"]\nborra2 :: Eq a => Int -> [a] -> [[a]]\nborra2 0 xs = [xs]\nborra2 n [] = []\nborra2 n (x:xs) = [x:ys | ys <- borra2 n xs] ++ borra2 (n-1) xs\n\n-- 3\u00aa definici\u00f3n\n-- =============\n\nmayorBorrando3 :: Int -> Integer -> Integer\nmayorBorrando3 k n = read (mayorBorrandoLista3 k (show n))\n\n-- (mayorBorrandoLista3 k xs) es la mayor lista obtenida borrando k elementos de\n-- xs (se supone que xs tiene m\u00e1s de k elementos). Por ejemplo,\n-- mayorBorrandoLista3 1 \"6782334\" == \"782334\"\n-- mayorBorrandoLista3 3 \"6782334\" == \"8334\"\nmayorBorrandoLista3 :: Ord a => Int -> [a] -> [a]\nmayorBorrandoLista3 k xs = maximum (itera k borraUnoListas [xs])\n\n-- (borraUnoListas xss) es la lista obtenida borrando un elemento (de\n-- todas las formas posibles de la lista de listas no vac\u00edas xss. Por\n-- ejemplo,\n-- borraUnoListas [\"abc\",\"def\"] == [\"bc\",\"ac\",\"ab\",\"ef\",\"df\",\"de\"]\nborraUnoListas :: [[a]] -> [[a]]\nborraUnoListas = concatMap borraUno\n\n-- (borraUno xs) es la lista de listas obtenidas borrando un elemento de la\n-- lista no vac\u00eda xs de todas las formas posibles. Por ejemplo,\n-- borraUno \"abcde\" == [\"bcde\",\"acde\",\"abde\",\"abce\",\"abcd\"]\nborraUno :: [a] -> [[a]]\nborraUno [x] = [[]]\nborraUno (x:xs) = xs : map (x:) (borraUno xs)\n\n-- (itera k f x) es el resultado de aplicar k veces la funci\u00f3n f al\n-- elemento x. Por ejmplo,\n-- itera 3 (*2) 1 == 8\n-- itera 4 (+2) 10 == 18\nitera :: Eq a => Int -> (a -> a) -> a -> a\nitera 0 _ x = x\nitera n f x = itera (n-1) f (f x)\n\n-- 4\u00aa definici\u00f3n\n-- =============\n\nmayorBorrando4 :: Int -> Integer -> Integer\nmayorBorrando4 k n = read (mayorBorrandoLista4 k (show n))\n\n-- (mayorBorrandoLista4 k xs) es la mayor lista obtenida borrando k elementos de\n-- xs (se supone que xs tiene m\u00e1s de k elementos). Por ejemplo,\n-- mayorBorrandoLista4 1 \"6782334\" == \"782334\"\n-- mayorBorrandoLista4 3 \"6782334\" == \"8334\"\nmayorBorrandoLista4 :: Ord a => Int -> [a] -> [a]\nmayorBorrandoLista4 k = itera k mayorBorraUno\n\n-- (mayorBorraUno xs) es la mayor lista obtenida eliminando un elemento de\n-- xs. Por ejemplo,\n-- mayorBorraUno \"6782334\" == \"782334\"\n-- mayorBorraUno \"782334\" == \"82334\"\n-- mayorBorraUno \"82334\" == \"8334\"\nmayorBorraUno :: Ord a => [a] -> [a]\nmayorBorraUno = maximum . borraUno\n\n-- 5\u00aa definici\u00f3n\n-- =============\n\nmayorBorrando5 :: Int -> Integer -> Integer\nmayorBorrando5 k n = read (mayorBorrandoLista5 k (show n))\n\n-- (mayorBorrandoLista5 k xs) es la mayor lista obtenida borrando k elementos de\n-- xs (se supone que xs tiene m\u00e1s de k elementos). Por ejemplo,\n-- mayorBorrandoLista5 1 \"6782334\" == \"782334\"\n-- mayorBorrandoLista5 3 \"6782334\" == \"8334\"\nmayorBorrandoLista5 :: Ord a => Int -> [a] -> [a]\nmayorBorrandoLista5 k = itera k mayorBorraUno2\n\n-- (mayorBorraUno2 xs) es la mayor lista obtenida eliminando un elemento de\n-- xs. Por ejemplo,\n-- mayorBorraUno2 \"6782334\" == \"782334\"\n-- mayorBorraUno2 \"782334\" == \"82334\"\n-- mayorBorraUno2 \"82334\" == \"8334\"\nmayorBorraUno2 :: Ord a => [a] -> [a]\nmayorBorraUno2 [x] = []\nmayorBorraUno2 (x:y:xs) | x < y = y:xs\n | otherwise = x : mayorBorraUno2 (y:xs)\n\n-- 6\u00aa definici\u00f3n\n-- =============\n\nmayorBorrando6 :: Int -> Integer -> Integer\nmayorBorrando6 k n = read (mayorBorrandoLista6 k (show n))\n\n-- (mayorBorrandoLista6 k xs) es la mayor lista obtenida borrando k elementos de\n-- xs (se supone que xs tiene m\u00e1s de k elementos). Por ejemplo,\n-- mayorBorrandoLista6 1 \"6782334\" == \"782334\"\n-- mayorBorrandoLista6 3 \"6782334\" == \"8334\"\nmayorBorrandoLista6 :: Ord a => Int -> [a] -> [a]\nmayorBorrandoLista6 k xs = aux k [] xs\n\naux 0 ys xs = reverse ys ++ xs\naux k ys [] = reverse (drop k ys)\naux k [] (x:xs) = aux k [x] xs\naux k (y:ys) (x:xs) | y >= x = aux k (x:y:ys) xs\n | otherwise = aux (k-1) ys (x:xs)\n\n-- Comparaci\u00f3n de eficiencia\n-- =========================\n\n-- La comparaci\u00f3n es\n-- \u03bb> mayorBorrando 6 (product [1..18])\n-- 7705728000\n-- (0.06 secs, 15,165,496 bytes)\n-- \u03bb> mayorBorrando2 6 (product [1..18])\n-- 7705728000\n-- (0.04 secs, 19,662,816 bytes)\n-- \u03bb> mayorBorrando3 6 (product [1..18])\n-- 7705728000\n-- (6.93 secs, 5,143,807,064 bytes)\n-- \u03bb> mayorBorrando4 6 (product [1..18])\n-- 7705728000\n-- (0.01 secs, 183,728 bytes)\n-- \u03bb> mayorBorrando5 6 (product [1..18])\n-- 7705728000\n-- (0.01 secs, 118,984 bytes)\n-- \u03bb> mayorBorrando6 6 (product [1..18])\n-- 7705728000\n--\n-- \u03bb> mayorBorrando 17 (product [1..25])\n-- 998400000\n-- (19.09 secs, 14,516,359,464 bytes)\n-- \u03bb> mayorBorrando2 17 (product [1..25])\n-- 998400000\n-- (47.39 secs, 30,066,413,608 bytes)\n-- \u03bb> mayorBorrando4 17 (product [1..25])\n-- 998400000\n-- (0.01 secs, 458,320 bytes)\n-- \u03bb> mayorBorrando5 17 (product [1..25])\n-- 998400000\n-- (0.01 secs, 134,424 bytes)\n-- \u03bb> mayorBorrando6 17 (product [1..25])\n-- 984000000\n-- (0.01 secs, 124,600 bytes)\n--\n-- \u03bb> mayorBorrando4 600 (product [1..300])\n-- 999999999999999\n-- (3.29 secs, 4,421,841,944 bytes)\n-- \u03bb> mayorBorrando5 600 (product [1..300])\n-- 999999999999999\n-- (0.03 secs, 6,690,440 bytes)\n-- \u03bb> mayorBorrando6 600 (product [1..300])\n-- 960000000000000\n-- (0.01 secs, 593,864 bytes)\n--\n-- \u03bb> mayorBorrando5 10000 (4256 + 10^10004)\n-- 14256\n-- (16.04 secs, 18,221,784,872 bytes)\n-- \u03bb> mayorBorrando6 10000 (4256 + 10^10004)\n-- 14256\n-- (0.02 secs, 6,669,592 bytes)\n--\n-- \u03bb> mayorBorrando6 1000000 (4256 + 10^1000004)\n-- 14256\n-- (1.04 secs, 655,561,656 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 mayorBorrando :: Int -> Integer -> Integer tal que (mayorBorrando k n) es el mayor n\u00famero obtenido borrando k d\u00edgitos de n (se supone que n tiene m\u00e1s de k d\u00edgitos). Por ejemplo, mayorBorrando 1 6782334 == 782334 mayorBorrando 3 6782334 == 8334 mayorBorrando 3 10020 == 20 mayorBorrando 1000000 (4256 +…<\/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":[7],"tags":[],"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/6039"}],"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=6039"}],"version-history":[{"count":4,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/6039\/revisions"}],"predecessor-version":[{"id":6087,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/posts\/6039\/revisions\/6087"}],"wp:attachment":[{"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/media?parent=6039"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/categories?post=6039"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.glc.us.es\/~jalonso\/exercitium\/wp-json\/wp\/v2\/tags?post=6039"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}