{- Find the only Pythagorean triplet, {a, b, c}, for which a + b + c = 1000.

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.
-}

import Text.Printf
import Util.Triangle

-- |Return the product of the sides of the first triangle having the sum of the sides 'sum'
triplet :: Int -> Int
triplet sum = do
    let cs = reverse (takeWhile (<= sum - 3) [3,5..])
    let tri = head (concat (map (\x -> right_triangles sum x) cs))
    let (Triangle a b c) = tri
    a * b * c


main = do
    printf "Pythagorean triplet product having a + b + c = 1000: %d\n" (triplet 1000 :: Int)