-- A unit fraction contains 1 in the numerator. The decimal representation of the unit fractions with denominators 2 to 10 are given:
--
-- 1/2	= 	0.5
-- 1/3	= 	0.(3)
-- 1/4	= 	0.25
-- 1/5	= 	0.2
-- 1/6	= 	0.1(6)
-- 1/7	= 	0.(142857)
-- 1/8	= 	0.125
-- 1/9	= 	0.(1)
-- 1/10	= 	0.1
--
-- Where 0.1(6) means 0.166666..., and has a 1-digit recurring cycle. It can be seen that 1/7 has a 6-digit recurring cycle.
--
-- Find the value of d < 1000 for which 1/d contains the longest recurring cycle in its decimal fraction part.

removeFactor :: (Integral a) => a -> a -> a
removeFactor f n
    | n `mod` f /= 0 = n
    | otherwise = removeFactor f (n `div` f)

findCycleLengthRecursive :: (Integral a) => a -> a -> a -> a
findCycleLengthRecursive n j k
    | n == 1 = 0
    | k `mod` n == 0 = j
    | otherwise = findCycleLengthRecursive n (j+1) (k * 10 + 9)

findCycleLength :: (Integral a) =>  a -> a
findCycleLength n = findCycleLengthRecursive ((removeFactor 2 . removeFactor 5) n) 1 9

maxRepeatingCycle :: (Integral a) => a -> a -> a 
maxRepeatingCycle a b = snd . maximum $ zip xs [1..]
    where xs = map findCycleLength [a..b]

main = do
    let result = maxRepeatingCycle 1 999
    putStrLn $ "Project Euler, Problem 26\n"
        ++ "Answer: " ++ show result