reciprocal.hs

reciprocal :: Int -> (String, Int)
reciprocal n | n > 1 = ('0' : '.' : digits, recur)
             | otherwise = error
                 "attempting to compute reciprocal of number <= 1"
  where
    (digits, recur) = divide n 1 []

divide :: Int -> Int -> [Int] -> (String, Int)
divide n c cs | c `elem` cs = ([], position c cs)
              | r == 0      = (show q, 0)
              | r /= 0      = (show q ++ digits, recur)
  where
     (q, r) = (c*10) `quotRem` n
     (digits, recur) = divide n r (c:cs)

position :: Int -> [Int] -> Int
position n (x:xs) | n == x    = 1
                  | otherwise = 1 + position n xs

showRecip :: Int -> String
showRecip n =
  "1/" ++ show n ++ " = " ++
  if r == 0 then d else take p d ++ "(" ++ drop p d ++ ")"
  where
    p = length d - r
    (d, r) = reciprocal n

main = do
  n <- readLn
  putStrLn (showRecip n)
  main