Project Euler, Problem #9, Haskell

-- A Pythagorean triplet is a set of three natural numbers, a < b < c,
-- for which, a^2 + b^2 = c^2. For example,
-- 3^2 + 4^2 = 9 + 16 = 25 = 5^2. There exists exactly one Pythagorean
-- triplet for which a + b + c = 1000. Find the product abc.

-- A more efficient solution

ac :: Integral t => t -> [t]
ac c =
  [ a * b * c
  | a <- [1 .. div (1000 - c) 2 - 1]
  , let b = (1000 - c) - a
  , a ^ 2 + b ^ 2 == c ^ 2
  ]

main :: IO ()
main = print $ head $ concatMap ac [997,996 .. 3]

-- 31875000

-- real 0m0,330s
-- user 0m0,317s
-- sys  0m0,012s

-- ################################################################################################

-- A less efficient solution

main :: IO ()
main =
  print $
  head
    [ x * y * z
    | x <- [1 .. 1000]
    , y <- [1 .. 1000]
    , let z = 1000 - (x + y)
    , x + y + z == 1000
    , x ^ 2 + y ^ 2 == z ^ 2
    , x < y && y < z
    ]

-- 31875000

-- real 0m0,782s
-- user 0m0,777s
-- sys  0m0,004s