Project Euler Problem 26

最新推荐文章于 2018-10-17 13:22:37 发布

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最新推荐文章于 2018-10-17 13:22:37 发布

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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.

# 找到 d<1000, 1/d 写成小数后拥有最长循环节的d。

def recur_cycle(n):
    reminder = 1
    re_list = [1]
    while True:
        reminder = reminder*10 % n
        if reminder in re_list:
            length = len(re_list) - re_list.index(reminder)
            return length
        else:
            re_list.append(reminder)

longest = 0
num = 0
for i in range(2,1000):
    if longest < recur_cycle(i):
        longest = recur_cycle(i)
        num = i

print(longest,num)
print(recur_cycle(7))

思路：分子为上一次除法的余数乘10，将余数存于列表中，当出现一个重复的余数时，循环节产生

结果：983 has a 982-digit recurring cycle.