Project Euler - Problem 9

DIRECTORY.md

@@ -49,6 +49,8 @@
       * [Problem6](https://github.com/TheAlgorithms/Haskell/blob/master/src/ProjectEuler/Problem6/Problem6.hs)
     * Problem7
       * [Problem7](https://github.com/TheAlgorithms/Haskell/blob/master/src/ProjectEuler/Problem7/Problem7.hs)
+    * Problem9
+      * [Problem9](https://github.com/TheAlgorithms/Haskell/blob/master/src/ProjectEuler/Problem9/Problem9.hs)
   * Robotics
     * Complementaryfilter
       * [Compfilt](https://github.com/TheAlgorithms/Haskell/blob/master/src/Robotics/ComplementaryFilter/CompFilt.hs)

src/ProjectEuler/Problem9/Problem9.hs

@@ -0,0 +1,20 @@
+module ProjectEuler.Problem9.Problem9 where
+
+-- Generate a list of natural number triples which sum to t
+triples :: (Num a, Enum a) => a -> [(a,a,a)]
+triples t = [(t-i-j, i, j) | i <- [1..t-1], j<- [1..t-i-1]]
+
+-- Determine if a triple is pythagorean
+isPythagorean :: (Num a, Eq a) => (a,a,a) -> Bool
+isPythagorean (a,b,c) = a^2 + b^2 == c^2
+
+-- Finds the pythagorean triple such that a + b + c = x; returns a * b *c
+solution :: Int -> Maybe Int
+solution x = let ts = filter isPythagorean (triples x)
+                 in case ts of
+                     [] -> Nothing
+                     _  -> let (a,b,c) = head ts in Just (a * b * c)
+
+main :: IO ()
+main = do
+    print (solution 1000)