EularProject 26: 单位分数的循环问题

Reciprocal cycles

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.

Answer: 983 Completed on Wed, 17 Jun 2015, 10:01

python code:

<span style="font-family:Times New Roman;font-size:18px;">def func(k):
    dict={}
    result=''
    left=1
    while True:
        item=left*10//k
        left=left*10-item*k
        s=str(item)+"_"+str(left)
        tempValue=dict.get(s)
        if tempValue==None:
            dict[s]=len(result)
            result+=str(item)
        else:
            break
    return len(result)-tempValue

result=7
num=6
for i in range(2,1000):
    temp=func(i)
    if temp>num:
        result,num=i,temp
print(result)</span>

time: <1s