euler_p26.py

# 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 decimalcycles(num, den):
    isrepeat, ndigits, rems = False, 0, []
    while not isrepeat:
        rem = 10*num - int(10*num / den) * den
        if rem in rems:
            isrepeat = True
            return ndigits
        rems.append(rem)
        num = rem
        ndigits += 1

for den in range(999,1,-1):
    ndigits = decimalcycles(1, den)
    if ndigits == den-1:
        print(den)
        break