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== 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。

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Older// Problem 27