{-

- Solution to Project Euler problem 26

- Copyright (c) Project Nayuki. All rights reserved.

-

- https://www.nayuki.io/page/project-euler-solutions

- https://github.com/nayuki/Project-Euler-solutions

-}

import Data.List (elemIndex, foldl1')

main = putStrLn (show ans)

ans = argMax cycleLength [1..1000]

-- Length of the repeating decimal cycle of 1/n.

-- e.g. 1/4 = 0.25(0), which is length 1.

-- e.g. 1/7 = 0.(142857), which is length 6.

cycleLength :: Int -> Int

cycleLength n =

let

remainders = iterate (\x -> mod (x * 10) n) 1

findCycle [] (x:xs) = findCycle (x:[]) xs

findCycle acc (x:xs) = case elemIndex x acc of

Nothing -> findCycle (x:acc) xs

Just i -> i + 1

in

findCycle [] remainders

-- The earliest element x in the list such that (f x) >= (f y) for each element y in the list.

argMax :: Ord b => (a -> b) -> [a] -> a

argMax f = foldl1' (\x y -> if (f y) > (f x) then y else x)