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.

＃＃运用了ｐｙｔｈｏｎ的ｄｅｃｉｍａｌ模块取小数点精度，然后转换成ｓｔｒ格式查找是否有重复的，从而计算出重复的长度。

＃控制在１Ｓ内～

import decimal

decimal.getcontext().prec = 100

import time

start = time.time()

d = 7

l = 6

for i in range(1,1000):

    s = str(decimal.Decimal(1)/decimal.Decimal(i))

    for j in range(len(s)):

        temp = s[j+3:].find(s[j:j+3])

        if temp > 0 and 3+temp > l:

            d = i

            l = 3 + temp

          #  print(d,l)

            decimal.getcontext().prec = 100 + l

            break

print(d,l)

print(time.time()-start)

>>>

983 982

0.6900279521942139

>>>