Problem 26

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.

この手の無限小数は前にもやったことがあったが、どうやったかは忘れた。

import Data.List
import Data.Function
divSeq m n =unfoldr (\x -> if x==0 then Nothing else Just(divMod x n,(*10).mod x $ n)) m
fracSeq n = fracSeq' [] .divSeq n
    where fracSeq' xs [] = (map fst xs,[])
          fracSeq' xs (y:ys)| elem y xs = let (a,b) = span (/=y) xs in (map fst a,map fst b)
                            | otherwise = fracSeq' (xs++[y]) ys
p026 =maximumBy(compare `on` snd). zip [1..] $map(length.snd.fracSeq 1) [1..999]

調子に乗ってunfoldrを使ってみた。