September 2017 Update

Task/Pythagorean-triples/Haskell/pythagorean-triples-1.hs

@@ -1,5 +1,22 @@
-pytr n = filter (\(_, a, b, c) -> a+b+c <= n) [(prim a b c, a, b, c) | a <- [1..n], b <- [1..n], c <- [1..n], a < b && b < c, a^2 + b^2 == c^2]
-    where prim a b _ = gcd a b == 1
+pytr :: Int -> [(Bool, Int, Int, Int)]
+pytr n =
+  filter
+    (\(_, a, b, c) -> a + b + c <= n)
+    [ (prim a b c, a, b, c)
+    | a <- xs
+    , b <- drop a xs
+    , c <- drop b xs
+    , a ^ 2 + b ^ 2 == c ^ 2 ]
+  where
+    xs = [1 .. n]
+    prim a b _ = gcd a b == 1
 
-main = putStrLn $ "Up to 100 there are " ++ (show $ length xs) ++ " triples, of which " ++ (show $ length $ filter (\(x,_,_,_) -> x == True) xs) ++ " are primitive."
-    where xs = pytr 100
+main :: IO ()
+main =
+  putStrLn $
+  "Up to 100 there are " ++
+  show (length xs) ++
+  " triples, of which " ++
+  show (length $ filter (\(x, _, _, _) -> x) xs) ++ " are primitive."
+  where
+    xs = pytr 100

Task/Pythagorean-triples/Haskell/pythagorean-triples-2.hs

@@ -1,15 +1,22 @@
-triangles :: Int -> [[Int]]
-triangles max_peri | max_peri < 12 = []
-           | otherwise = concat tiers where
-    tiers = takeWhile (not.null) $ iterate tier [[3,4,5]]
-    tier = concatMap (filter ((<=max_peri).sum).tmul)
-    tmul t = map (map (sum . zipWith (*) t))
-        [[[ 1,-2,2],[ 2,-1,2],[ 2,-2,3]],
-         [[ 1, 2,2],[ 2, 1,2],[ 2, 2,3]],
-         [[-1, 2,2],[-2, 1,2],[-2, 2,3]]]
+pythagoreanTriplesBelow :: Int -> [[Int]]
+pythagoreanTriplesBelow n =
+  let m = quot n 2
+  in concatMap
+       (\x ->
+           concatMap
+             (\y ->
+                 concatMap
+                   (\z ->
+                       if x + y + z <= n && x ^ 2 + y ^ 2 == z ^ 2
+                         then [[x, y, z]]
+                         else [])
+                   [y + 1 .. m])
+             [x + 1 .. m])
+       [1 .. m]
 
-triangle_count max_p = (length t, sum $ map ((max_p `div`).sum) t)
-    where t = triangles max_p
-
-main = mapM_ putStrLn $
-    map (\n -> show n ++ " " ++ show (triangle_count n)) $ map (10^) [1..]
+-- TEST -------------------------------------------------------------------------
+main :: IO ()
+main =
+  mapM_
+    (print . length)
+    ([id, filter (\[x, y, _] -> gcd x y == 1)] <*> [pythagoreanTriplesBelow 100])

Task/Pythagorean-triples/Haskell/pythagorean-triples-3.hs

@@ -0,0 +1,24 @@
+triangles :: Int -> [[Int]]
+triangles max_peri
+  | max_peri < 12 = []
+  | otherwise = concat tiers
+  where
+    tiers = takeWhile (not . null) $ iterate tier [[3, 4, 5]]
+    tier = concatMap (filter ((<= max_peri) . sum) . tmul)
+    tmul t =
+      map
+        (map (sum . zipWith (*) t))
+        [ [[1, -2, 2], [2, -1, 2], [2, -2, 3]]
+        , [[1, 2, 2], [2, 1, 2], [2, 2, 3]]
+        , [[-1, 2, 2], [-2, 1, 2], [-2, 2, 3]]
+        ]
+
+triangleCount max_p = (length t, sum $ map ((max_p `div`) . sum) t)
+  where
+    t = triangles max_p
+
+main :: IO ()
+main =
+  mapM_
+    ((putStrLn . (\n -> show n ++ " " ++ show (triangleCount n))) . (10 ^))
+    [1 .. 7]