Definir la funci\u00f3n<\/p>\n
\n union :: Ord a => [a] -> [a] -> [a]\n<\/pre>\ntal que union xs ys<\/code> es la uni\u00f3n de las listas, sin elementos repetidos, xs<\/code> e ys<\/code>. Por ejemplo,<\/p>\n\n union [3,2,5] [5,7,3,4] == [3,2,5,7,4]\n<\/pre>\nComprobar con QuickCheck que la uni\u00f3n es conmutativa.<\/p>\n
Soluciones<\/b><\/p>\n
A continuaci\u00f3n se muestran las soluciones en Haskell<\/a> y las soluciones en Python<\/a>.<\/p>\n<\/a>
\nSoluciones en Haskell<\/b><\/p>\n\nimport Data.List (nub, sort, union)\nimport qualified Data.Set as S (fromList, toList, union)\nimport Test.QuickCheck\n\n-- 1\u00aa soluci\u00f3n\n-- ===========\n\nunion1 :: Ord a => [a] -> [a] -> [a]\nunion1 xs ys = xs ++ [y | y <- ys, y `notElem` xs]\n\n-- 2\u00aa soluci\u00f3n\n-- ===========\n\nunion2 :: Ord a => [a] -> [a] -> [a]\nunion2 [] ys = ys\nunion2 (x:xs) ys\n | x `elem` ys = xs `union2` ys\n | otherwise = x : xs `union2` ys\n\n-- 3\u00aa soluci\u00f3n\n-- ===========\n\nunion3 :: Ord a => [a] -> [a] -> [a]\nunion3 = union\n\n-- 4\u00aa soluci\u00f3n\n-- ===========\n\nunion4 :: Ord a => [a] -> [a] -> [a]\nunion4 xs ys =\n S.toList (S.fromList xs `S.union` S.fromList ys)\n\n-- Comprobaci\u00f3n de equivalencia\n-- ============================\n\n-- La propiedad es\nprop_union :: [Int] -> [Int] -> Bool\nprop_union xs ys =\n all (== sort (xs' `union1` ys'))\n [sort (xs' `union2` ys'),\n sort (xs' `union3` ys'),\n xs' `union4` ys']\n where xs' = nub xs\n ys' = nub ys\n\n-- La comprobaci\u00f3n es\n-- \u03bb> quickCheck prop_union\n-- +++ OK, passed 100 tests.\n\n-- Comparaci\u00f3n de eficiencia\n-- =========================\n\n-- La comparaci\u00f3n es\n-- \u03bb> length (union1 [0,2..3*10^4] [1,3..3*10^4])\n-- 30001\n-- (2.37 secs, 7,153,536 bytes)\n-- \u03bb> length (union2 [0,2..3*10^4] [1,3..3*10^4])\n-- 30001\n-- (2.38 secs, 6,553,752 bytes)\n-- \u03bb> length (union3 [0,2..3*10^4] [1,3..3*10^4])\n-- 30001\n-- (11.56 secs, 23,253,553,472 bytes)\n-- \u03bb> length (union4 [0,2..3*10^4] [1,3..3*10^4])\n-- 30001\n-- (0.04 secs, 10,992,056 bytes)\n\n-- Comprobaci\u00f3n de la propiedad\n-- ============================\n\n-- La propiedad es\nprop_union_conmutativa :: [Int] -> [Int] -> Bool\nprop_union_conmutativa xs ys =\n iguales (xs `union1` ys) (ys `union1` xs)\n\n-- (iguales xs ys) se verifica si xs e ys son iguales. Por ejemplo,\n-- iguales [3,2,3] [2,3] == True\n-- iguales [3,2,3] [2,3,2] == True\n-- iguales [3,2,3] [2,3,4] == False\n-- iguales [2,3] [4,5] == False\niguales :: Ord a => [a] -> [a] -> Bool\niguales xs ys =\n S.fromList xs == S.fromList ys\n\n-- La comprobaci\u00f3n es\n-- \u03bb> quickCheck prop_union_conmutativa\n-- +++ OK, passed 100 tests.\n<\/pre>\nEl c\u00f3digo se encuentra en GitHub<\/a>.<\/p>\n