26.py

#-*- coding:utf-8 -*-

"""
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.
"""

import time

def cycle(n):
    i = 1
    if n % 2 == 0:
        return cycle(n/2)
    if n % 5 == 0:
        return cycle(n/5)
    while True:
        if (pow(10, i)-1)%n == 0:
            return i
        i = i + 1


def main():
    m = 0
    n = 0
    for x in xrange(1, 1000):
        t = cycle(x)
        if t > m:
            m = t
            n = x
    print n


if __name__ == "__main__":
    start = time.time()
    main()
    end = time.time()
    print "time: " + str(end-start)