-- A Pythagorean triplet is a set of three natural numbers, a < b < c, for which,
--
-- a2 + b2 = c2
--
-- For example, 32 + 42 = 9 + 16 = 25 = 52.
--
-- There exists exactly one Pythagorean triplet for which a + b + c = 1000.
--
-- Find the product abc.

module P009 (p009) where

import Data.List (uncons)
import Data.Maybe (fromJust)

pythagoreanTriplet :: Int -> (Int, Int, Int)
pythagoreanTriplet n = fst . fromJust $ uncons [(x, y, z) | x <- [1 .. n], y <- [x .. n], z <- [y .. n], x + y + z == n, x ^ (2 :: Int) + y ^ (2 :: Int) == z ^ (2 :: Int)]

prodTriplet :: (Int, Int, Int) -> Int
prodTriplet (x, y, z) = x * y * z

p009 :: IO ()
p009 = do
  let result = prodTriplet $ pythagoreanTriplet 1000
  putStrLn $
    "Project Euler, Problem 9\n"
      ++ "Answer: "
      ++ show result