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May 11, 2014 10:48
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Haskell Nim calculation
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module Data.Nim | |
(Nim) | |
where | |
import Data.Bits | |
class Nim a where | |
(+^*) :: a -> a -> a | |
(*^*) :: a -> a -> a | |
instance Nim Integer where | |
a +^* b = a `xor` b | |
a *^* b = nimMul a b | |
nimMul :: (Bits a, Enum a, Eq a, Num a) => a -> a -> a | |
nimMul _ 0 = 0 | |
nimMul 0 _ = 0 | |
nimMul x 1 = x -- for efficiency | |
nimMul 1 y = y -- for efficiency | |
nimMul x y = mex [ (nimMul x b) `xor` (nimMul a y) `xor` (nimMul a b) | a<-[0..(x-1)], b<-[0..(y-1)]] !! 0 | |
-- helper functions | |
-- diff sets | |
-- ex) | |
-- [3, 10, 7] -> [0, 1, 2, 4, 5, 6, 8, 9, 11, 12, 13, ...] | |
exclusiveList :: (Enum a, Eq a, Num a) => [a] -> [a] | |
exclusiveList z = foldr (λx y -> if elem x z then y else x:y) [] [0..] | |
-- mex z is the smallest ordinal which is not an element of z. | |
-- ex) | |
-- [0, 1] -> [2] | |
-- [1, 2] -> [0] | |
mex :: (Enum a, Eq a, Num a) => [a] -> [a] | |
mex z = take 1 $ exclusiveList z | |
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