026.py

"""
Project Euler Problem 26
========================

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.
"""


def find_cycle(d):
    cycle = []
    dividends = []
    curr_string = ""
    dividend = 10
    while dividend:
        while dividend < d:
            dividend *= 10
            curr_string += "0"
        curr_string += str(int(dividend / d))
        dividend = (dividend % d) * 10
        if dividends and dividend in dividends:
            return len(cycle[dividends.index(dividend) :])
        cycle.append(curr_string)
        dividends.append(dividend)
        curr_string = ""

    return 0


print(max(range(1, 1000), key=find_cycle))