Haskell 039

haskell/Util/Triangle.hs

@@ -0,0 +1,18 @@
+module Util.Triangle where
+
+-- |A triangle consisting of three integral sides
+data Triangle = Triangle Int Int Int
+    deriving(Show, Eq)
+
+-- |Find all right triangles having sum of sides 'sum' and side c length of 'c'
+right_triangles :: Int -> Int -> [Triangle]
+right_triangles sum c = do
+    let diff = sum - c
+    let range = [1..(floor ((fromIntegral diff) / 2)) + 1]
+    let triangles = filter is_right_triangle (map (\x -> Triangle x (diff - x) c) range)
+    triangles
+
+-- |Return whether the provided triangle is a right triangle using the pythagorean theorem
+is_right_triangle :: Triangle -> Bool
+is_right_triangle (Triangle a b c) =
+    a^2 + b^2 == c^2

haskell/e009.hs

@@ -9,9 +9,7 @@ Find the product abc.
 -}
 
 import Text.Printf
-
+import Util.Triangle
--- |A triangle consisting of three integral sides
-data Triangle = Triangle Int Int Int
 
 -- |Return the product of the sides of the first triangle having the sum of the sides 'sum'
 triplet :: Int -> Int
@@ -21,18 +19,6 @@ triplet sum = do
     let (Triangle a b c) = tri
     a * b * c
 
--- |Find all right triangles having sum of sides 'sum' and side c length of 'c'
-right_triangles :: Int -> Int -> [Triangle]
-right_triangles sum c = do
-    let diff = sum - c
-    let range = [1..(floor ((fromIntegral diff) / 2)) + 1]
-    let triangles = filter is_right_triangle (map (\x -> Triangle x (diff - x) c) range)
-    triangles
-
--- |Return whether the provided triangle is a right triangle using the pythagorean theorem
-is_right_triangle :: Triangle -> Bool
-is_right_triangle (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 :: Int)

haskell/e039.hs

@@ -0,0 +1,24 @@
+{-
+
+If p is the perimeter of a right angle triangle with integral length sides, {a,b,c}, there are exactly three solutions for p = 120.
+
+{20,48,52}, {24,45,51}, {30,40,50}
+
+For which value of p  1000, is the number of solutions maximised?
+-}
+
+import Data.List
+import Data.Ord
+import Text.Printf
+import Util.Triangle
+
+trimap = do
+    let totals = map (\x -> (x, (length . triangles) x)) [1..999]
+    last (sortBy (comparing snd) totals)
+
+triangles sum = do
+    let cs = reverse (takeWhile (<= sum - 3) [3..])
+    concat (map (\x -> right_triangles sum x) cs)
+
+main = do
+    printf "Maximum triangles found with sum = %d\n" (fst trimap)