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Task/Chinese-remainder-theorem/Haskell/chinese-remainder-theorem.hs

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+module CRT ( chineseRemainder ) where
+
+egcd :: Integral a => a -> a -> (a, a)
+egcd _ 0 = (1, 0)
+egcd a b = (t, s - q * t)
+  where
+    (s, t) = egcd b r
+    (q, r) = a `quotRem` b
+
+modInv :: Integral a => a -> a -> Maybe a
+modInv a b = case egcd a b of
+  (x, y) | a * x + b * y == 1 -> Just x
+         | otherwise          -> Nothing
+
+chineseRemainder :: Integral a => [a] -> [a] -> Maybe a
+chineseRemainder residues modulii = do
+  inverses <- sequence $ zipWith modInv crtModulii modulii
+  return . (`mod` modPI) . sum $
+    zipWith (*) crtModulii (zipWith (*) residues inverses)
+  where
+    modPI = product modulii
+    crtModulii = map (modPI `div`) modulii