Problem 26 - Find the value of d < 1000 for which 1/d contains the longest recurring cycle.

링크

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.

python 

def lengthOfRecurringCycle(n): rems = [-1] * n rems[1] = 0 pos = 1 den = 1 while True: den = den * 10 rem = den % n if rem == 0: return 0 if rems[rem] != -1: return pos - rems[rem] rems[rem] = pos pos += 1 print max([(lengthOfRecurringCycle(x), x) for x in range(2, 1000)])