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Diffstat (limited to '2019/22.hs')
-rw-r--r-- | 2019/22.hs | 55 |
1 files changed, 55 insertions, 0 deletions
diff --git a/2019/22.hs b/2019/22.hs new file mode 100644 index 0000000..24609f0 --- /dev/null +++ b/2019/22.hs @@ -0,0 +1,55 @@ +module Main where + +import Input + + +egcd :: Integer -> Integer -> (Integer, Integer, Integer) +egcd m n = go 1 0 m 0 1 n + where + go a1 b1 r1 _ _ 0 = (r1, a1, b1) + go a1 b1 r1 a2 b2 r2 = + let (q, r) = r1 `divMod` r2 + in go a2 b2 r2 (a1 - q * a2) (b1 - q * b2) r + +-- multiplicative inverse of k mod n +multinv :: Integer -> Integer -> Integer +multinv k n = + let (1, x, _) = egcd k n -- x * k + y * n = 1 => x * k = 1 mod n + in x + +-- Affine multiplier addend modulus +data Affine = Affine Integer Integer Integer + deriving (Show) + +instance Semigroup Affine where + Affine a1 b1 m1 <> Affine a2 b2 m2 + | m1 == m2 = Affine ((a1 * a2) `mod` m1) ((a1 * b2 + b1) `mod` m1) m1 + | otherwise = error "<>'ing incompatible Affine's" + +apply :: Affine -> Integer -> Integer +apply (Affine a b m) x = (a * x + b) `mod` m + +inverse :: Affine -> Affine +inverse (Affine a b m) = Affine (multinv a m) 0 m <> Affine 1 (-b) m + +power :: Semigroup m => m -> Int -> m +power x 1 = x +power x n | n < 1 = error "non-positive exponent in 'power'" + | even n = power (x <> x) (n `quot` 2) + | otherwise = power x (n - 1) <> x + +parse :: String -> (Integer, Integer) +parse ('c':'u':'t':' ':s) = (1, negate (read s)) +parse ('d':_:_:_:_:'w':s) = (read (drop 14 s), 0) +parse ('d':_:_:_:_:'i':_) = (-1, -1) +parse _ = undefined + +main :: IO () +main = do + techlist <- map parse <$> getInput 22 + + let technique1 = foldl1 (<>) [Affine a b 10007 | (a, b) <- reverse techlist] + technique2 = foldl1 (<>) [Affine a b 119315717514047 | (a, b) <- reverse techlist] + + print (apply technique1 2019) + print (apply (power (inverse technique2) 101741582076661) 2020) |