EulerLib, P10, P77, P128, P130, P132: Refactored copies of Haskell isPrime function into library module.

P10: Tweaked Haskell solution to fix error-causing ambiguities.

Author: nayuki

haskell/EulerLib.hs

@@ -7,7 +7,7 @@
  -}
 
 module EulerLib
-	(digitSum, sqrt)
+	(digitSum, sqrt, isPrime)
 	where
 
 import Prelude hiding (sqrt)
@@ -28,3 +28,7 @@ sqrt n = sqrtAlpha 1 where
 		| otherwise = sqrtAlpha (Data.Bits.shiftL i 1)
 	sqrtBeta 0 acc = acc
 	sqrtBeta i acc = sqrtBeta (div i 2) (if (i + acc)^2 <= n then i + acc else acc)
+
+
+isPrime :: (Integral a, Data.Bits.Bits a) => a -> Bool
+isPrime n = n > 1 && null [() | k <- [2 .. (sqrt n)], mod n k == 0]

haskell/p010.hs

@@ -9,8 +9,6 @@
 import EulerLib
 
 
+limit = 2000000 :: Int
 main = putStrLn (show ans)
-ans = sum (filter isPrime [2 .. 2000000-1])
-
-isPrime :: Int -> Bool
-isPrime n = n > 1 && null [() | k <- [2 .. (EulerLib.sqrt n)], mod n k == 0]
+ans = sum (filter EulerLib.isPrime [2 .. (limit - 1)])

haskell/p077.hs

@@ -6,6 +6,8 @@
  - https://github.com/nayuki/Project-Euler-solutions
  -}
 
+import EulerLib
+
 
 target = 5000
 main = putStrLn (show ans)
@@ -25,8 +27,5 @@ ans = head $ dropWhile (\n -> partitions n n <= target) [0..]
 partitions :: Int -> Int -> Int
 partitions _ 0 = 1
 partitions 0 _ = 0
-partitions i n = (if ((isPrime i) && i <= n) then (partitionsMemo !! i !! (n - i)) else 0) + (partitionsMemo !! (i - 1) !! n)
+partitions i n = (if ((EulerLib.isPrime i) && i <= n) then (partitionsMemo !! i !! (n - i)) else 0) + (partitionsMemo !! (i - 1) !! n)
 partitionsMemo = [[partitions i n | n <- [0..]] | i <- [0..]]
-
-isPrime :: Int -> Bool
-isPrime n = n > 1 && null [() | k <- [2 .. n-1], mod n k == 0]

haskell/p128.hs

@@ -175,15 +175,12 @@ ans = find 2 (target - 2)  -- Already found 2 because n = 1 and 2 satisfy PD(n)
 
 find :: Integer -> Integer -> Integer
 find ring remain = let
-		a = all isPrime [ring * 6 - 1, ring * 6 + 1, ring * 12 + 5]
-		b = all isPrime [ring * 6 - 1, ring * 6 + 5, ring * 12 - 7]
+		a = all EulerLib.isPrime [ring * 6 - 1, ring * 6 + 1, ring * 12 + 5]
+		b = all EulerLib.isPrime [ring * 6 - 1, ring * 6 + 5, ring * 12 - 7]
 		remain' = remain - (if a then 1 else 0)
 		remain'' = remain' - (if b then 1 else 0)
 	in if remain' == 0
 		then (ring * (ring - 1) * 3 + 2)
 		else if remain'' == 0
 			then (ring * (ring + 1) * 3 + 1)
 			else find (ring + 1) remain''
-
-isPrime :: Integer -> Bool
-isPrime n = n > 1 && null [() | k <- [2 .. (EulerLib.sqrt n)], mod n k == 0]

haskell/p130.hs

@@ -10,7 +10,7 @@ import EulerLib
 
 
 main = putStrLn (show ans)
-cond i = (mod i 5 /= 0) && (not (isPrime i)) && mod (i - 1) (findLeastDivisibleRepunit i) == 0
+cond i = (mod i 5 /= 0) && (not (EulerLib.isPrime i)) && mod (i - 1) (findLeastDivisibleRepunit i) == 0
 ans = sum (take 25 (filter cond [7,9..]))
 
 findLeastDivisibleRepunit :: Integer -> Integer
@@ -20,6 +20,3 @@ findLeastDivisibleRepunit n = if (mod n 2) == 0 || (mod n 5) == 0
 		func 0 _ k = k
 		func s p k = func (mod (s + p * 10) n) (mod (p * 10) n) (k + 1)
 	in func 1 1 1
-
-isPrime :: Integer -> Bool
-isPrime n = n > 1 && null [() | k <- [2 .. (EulerLib.sqrt n)], mod n k == 0]

haskell/p132.hs

@@ -10,7 +10,7 @@ import EulerLib
 
 
 main = putStrLn (show ans)
-cond i = isPrime i && (repunitMod (10^9) i) == 0
+cond i = EulerLib.isPrime i && (repunitMod (10^9) i) == 0
 ans = sum (take 40 (filter cond [2..]))
 
 repunitMod :: Integer -> Integer -> Integer
@@ -20,6 +20,3 @@ powMod :: Integer -> Integer -> Integer -> Integer
 powMod _ 0 _ = 1
 powMod x 1 m = mod x m
 powMod x y m = mod ((powMod x (div y 2) m)^2 * (if ((mod y 2) == 0) then 1 else x)) m
-
-isPrime :: Integer -> Bool
-isPrime n = n > 1 && null [() | k <- [2 .. (EulerLib.sqrt n)], mod n k == 0]