Haskell 009

haskell/e009.hs

@@ -0,0 +1,27 @@
+{- 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
+
+triplet sum = do
+    let cs = reverse (takeWhile (<= sum - 3) [3,5..])
+    let tri = head (concat (map (\x -> diffs sum x) cs))
+    let (a, b, c) = tri
+    a * b * c
+diffs sum c = do
+    let diff = sum - c
+    let range = [1..(floor ((fromIntegral diff) / 2)) + 1]
+    let triangles = filter is_triangle (map (\x -> (x, diff - x, c)) range)
+    triangles
+is_triangle (a, b, c) =
+    a^2 + b^2 == c^2
+
+main = do
+    printf "Pythagorean triplet product having a + b + c = 1000: %d\n" (triplet 1000 :: Integer)