歐拉計劃(python) problem 26

標籤：eularproject   數學   

Reciprocal cyclesProblem 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.

python code:

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)-tempValueresult=7num=6for i in range(2,1000):    temp=func(i)    if temp>num:        result,num=i,tempprint(result)

time: <1s

歐拉計劃(python) problem 26