La reiteraci\u00f3n de la suma de los elementos consecutivos de la lista [1,5,3] es 14 como se explica en el siguiente diagrama<\/p>\n
\n 1 + 5 = 6\n \\\n ==> 14\n \/\n 5 + 3 = 8\n<\/pre>\ny la de la lista [1,5,3,4] es 29 como se explica en el siguiente diagrama<\/p>\n
\n 1 + 5 = 6\n \\\n ==> 14\n \/ \\\n 5 + 3 = 8 ==> 29\n \\ \/\n ==> 15\n \/\n 3 + 4 = 7\n<\/pre>\nDefinir la funci\u00f3n<\/p>\n
\n sumaReiterada :: Num a => [a] -> a\n<\/pre>\ntal que (sumaReiterada xs) es la suma reiterada de los elementos consecutivos de la lista no vac\u00eda xs. Por ejemplo,<\/p>\n
\n sumaReiterada [1,5,3] == 14\n sumaReiterada [1,5,3,4] == 29\n<\/pre>\nSoluciones<\/h4>\n\nimport Test.QuickCheck\n\nimport Test.QuickCheck\n\n-- 1\u00aa soluci\u00f3n\n-- ===========\n\nsumaReiterada1 :: Num a => [a] -> a\nsumaReiterada1 [x] = x\nsumaReiterada1 xs = sumaReiterada1 [x+y | (x,y) <- consecutivos xs]\n\n-- (consecutivos xs) es la lista de pares de elementos consecutivos de\n-- xs. Por ejemplo,\n-- consecutivos [1,5,3,4] == [(1,5),(5,3),(3,4)]\nconsecutivos :: [a] -> [(a,a)]\nconsecutivos xs = zip xs (tail xs)\n\n-- 2\u00aa soluci\u00f3n\n-- ===========\n\nsumaReiterada2 :: Num a => [a] -> a\nsumaReiterada2 [x] = x\nsumaReiterada2 xs = sumaReiterada2 (sumaConsecutivos xs)\n\n-- (sumaConsecutivos xs) es la suma de los de pares de elementos\n-- consecutivos de xs. Por ejemplo,\n-- sumaConsecutivos [1,5,3,4] == [6,8,7]\nsumaConsecutivos :: Num a => [a] -> [a]\nsumaConsecutivos xs = zipWith (+) xs (tail xs)\n\n-- 3\u00aa soluci\u00f3n\n-- ===========\n\nsumaReiterada3 :: Num a => [a] -> a\nsumaReiterada3 [x] = x\nsumaReiterada3 xs = sumaReiterada3 (zipWith (+) xs (tail xs))\n\n-- 4\u00aa soluci\u00f3n\n-- ===========\n\nsumaReiterada4 :: Num a => [a] -> a\nsumaReiterada4 [x] = x\nsumaReiterada4 (x:xs) = sumaReiterada4 (zipWith (+) (x:xs) xs)\n\n-- 5\u00aa soluci\u00f3n\n-- ===========\n\nsumaReiterada5 :: Num a => [a] -> a\nsumaReiterada5 [x] = x\nsumaReiterada5 xs@(_:ys) = sumaReiterada5 (zipWith (+) xs ys)\n\n-- 6\u00aa soluci\u00f3n\n-- ===========\n\nsumaReiterada6 :: Num a => [a] -> a\nsumaReiterada6 xs =\n head (head (dropWhile noEsUnitaria (iterate sumaConsecutivos xs)))\n\n-- (noEsUnitaria xs) se verifica si la lista xs no tiene s\u00f3lo un\n-- elemento. Por ejemplo,\n-- noEsUnitaria [] == True\n-- noEsUnitaria [7,5] == True\n-- noEsUnitaria [7] == False\nnoEsUnitaria :: [a] -> Bool\nnoEsUnitaria [_] = False\nnoEsUnitaria _ = True\n\n-- 7\u00aa soluci\u00f3n\n-- ===========\n\nsumaReiterada7 :: Num a => [a] -> a\nsumaReiterada7 =\n head . head . dropWhile (not . null . tail) . iterate sumaConsecutivos\n\n-- 8\u00aa soluci\u00f3n\n-- ===========\n\nsumaReiterada8 :: Num a => [a] -> a\nsumaReiterada8 =\n head . head . dropWhile (not . null . tail) . iterate (zipWith (+) =<< tail)\n\n-- 9\u00aa soluci\u00f3n\n-- ===========\n\nsumaReiterada9 :: Num a => [a] -> a\nsumaReiterada9 = head . until ((==1) . length) (zipWith (+) <*> tail)\n\n-- 10\u00aa soluci\u00f3n\n-- ===========\n\nsumaReiterada10 :: Num a => [a] -> a\nsumaReiterada10 xs =\n sum (zipWith (*) xs (map fromIntegral (pascal !! (length xs - 1))))\n\n-- pascal es la lista de las filas del tri\u00e1ngulo de Pascal. Por ejemplo,\n-- \u03bb> take 7 pascal\n-- [[1],[1,1],[1,2,1],[1,3,3,1],[1,4,6,4,1],[1,5,10,10,5,1],[1,6,15,20,15,6,1]]\npascal :: [[Integer]]\npascal = [1] : map f pascal\n where f xs = zipWith (+) (0:xs) (xs++[0])\n\n-- Equivalencia de las definiciones\n-- ================================\n\n-- La propiedad es\nprop_sumaReiterada :: [Integer] -> Property\nprop_sumaReiterada xs =\n not (null xs) ==>\n all (== (sumaReiterada1 xs))\n [f xs | f <- [sumaReiterada2,\n sumaReiterada3,\n sumaReiterada4,\n sumaReiterada5,\n sumaReiterada6,\n sumaReiterada7,\n sumaReiterada8,\n sumaReiterada9,\n sumaReiterada10 ]]\n\n-- La comprobaci\u00f3n es\n-- \u03bb> quickCheck prop_sumaReiterada\n-- +++ OK, passed 100 tests.\n\n-- Comparaci\u00f3n de eficiencia\n-- =========================\n\n-- La comparaci\u00f3n es\n-- \u03bb> length (show (sumaReiterada1 [1..4000]))\n-- 1208\n-- (4.84 secs, 4,444,754,000 bytes)\n-- \u03bb> length (show (sumaReiterada2 [1..4000]))\n-- 1208\n-- (3.07 secs, 3,332,858,616 bytes)\n-- \u03bb> length (show (sumaReiterada3 [1..4000]))\n-- 1208\n-- (3.04 secs, 3,270,112,112 bytes)\n-- \u03bb> length (show (sumaReiterada4 [1..4000]))\n-- 1208\n-- (3.05 secs, 3,332,857,768 bytes)\n-- \u03bb> length (show (sumaReiterada5 [1..4000]))\n-- 1208\n-- (3.08 secs, 3,332,570,672 bytes)\n-- \u03bb> length (show (sumaReiterada6 [1..4000]))\n-- 1208\n-- (3.03 secs, 3,270,469,704 bytes)\n-- \u03bb> length (show (sumaReiterada7 [1..4000]))\n-- 1208\n-- (3.03 secs, 3,270,598,416 bytes)\n-- \u03bb> length (show (sumaReiterada8 [1..4000]))\n-- 1208\n-- (3.14 secs, 3,202,183,352 bytes)\n-- \u03bb> length (show (sumaReiterada9 [1..4000]))\n-- 1208\n-- (3.71 secs, 2,869,137,232 bytes)\n-- \u03bb> length (show (sumaReiterada10 [1..4000]))\n-- 1208\n-- (6.48 secs, 4,621,303,752 bytes)\n<\/pre>\n