Last active
August 29, 2015 14:22
-
-
Save ftiasch/be7067d47030d2669ac5 to your computer and use it in GitHub Desktop.
Project Euler 511 残骸
This file contains bidirectional Unicode text that may be interpreted or compiled differently than what appears below. To review, open the file in an editor that reveals hidden Unicode characters.
Learn more about bidirectional Unicode characters
import Data.Vector (Vector) | |
import qualified Data.Vector as V | |
newtype Zp = Z Int deriving (Show, Eq) | |
modulo :: Int | |
modulo = 10 ^ 9 | |
z :: Int -> Zp | |
z a | a >= 0 = Z a' | |
| otherwise = Z (modulo - a') | |
where a' = a `rem` modulo | |
instance Num Zp where | |
abs = undefined | |
signum = undefined | |
fromInteger = z . fromInteger | |
negate (Z a) = z (-a) | |
(Z a) + (Z b) = z (a + b) | |
(Z a) * (Z b) = z (a - b) | |
newtype Poly a = Poly { unPoly :: Vector a } deriving (Show, Eq) | |
instance Num a => Num (Poly a) where | |
abs = undefined | |
signum = undefined | |
fromInteger = undefined | |
negate = Poly . V.map negate . unPoly | |
a + b = Poly $ V.zipWith (+) (unPoly a') (unPoly b') | |
where (a', b') = align a b | |
a * b = multiply a' b' | |
where (a', b') = align a b | |
align :: (Num a) => Poly a -> Poly a -> (Poly a, Poly a) | |
align a b | |
| offset < 0 = (Poly . (V.++ padding) $ a', b) | |
| otherwise = (a, Poly . (V.++ padding) $ b') | |
where a' = unPoly a | |
b' = unPoly b | |
offset = V.length a' - V.length b' | |
padding = V.replicate (abs offset) 0 | |
degree :: Poly a -> Int | |
degree = V.length . unPoly | |
lift :: (Num a) => Int -> Poly a -> Poly a | |
lift n p = Poly . ((V.replicate n 0) V.++) . unPoly $ p | |
multiply :: (Num a) => Poly a -> Poly a -> Poly a | |
multiply a b | |
| n' == 1 = Poly $ V.zipWith (*) (unPoly a) (unPoly b) | |
| otherwise = p00 + (lift n p01) + (lift (n * 2) p11) | |
where n' = degree a | |
n = n' `quot` 2 | |
divide p = let (a, b) = V.splitAt n . unPoly $ p | |
in (Poly a, Poly b) | |
(a0, a1) = divide a | |
(b0, b1) = divide b | |
p00 = a0 `multiply` b0 | |
p11 = a1 `multiply` b1 | |
p01 = ((a0 + a1) `multiply` (b0 + b1)) - p00 - p11 | |
main :: IO () | |
main = print $ (p [1..4000]) * (p [1..4000]) | |
where p = (Poly . V.fromList) :: [Int] -> Poly Int |
Sign up for free
to join this conversation on GitHub.
Already have an account?
Sign in to comment