Project Euler Problem 30

最新推荐文章于 2021-07-19 00:18:41 发布

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最新推荐文章于 2021-07-19 00:18:41 发布

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本文探讨了一类特殊的整数，这类整数等于其每位数字的五次方之和。通过对数字范围的分析，确定了搜索边界，并通过编程实现了对这类特殊整数的查找，最终计算出了所有符合条件的整数之和。

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Problem 30

Surprisingly there are only three numbers that can be written as the sum of fourth powers of their digits:

1634 = 1 ⁴ + 6 ⁴ + 3 ⁴ + 4 ⁴
8208 = 8 ⁴ + 2 ⁴ + 0 ⁴ + 8 ⁴
9474 = 9 ⁴ + 4 ⁴ + 7 ⁴ + 4 ⁴

As 1 = 1⁴ is not a sum it is not included.

The sum of these numbers is 1634 + 8208 + 9474 = 19316.

Find the sum of all the numbers that can be written as the sum of fifth powers of their digits.

# 寻找一些数，他们各位数的5次方相加等于自身，求这些数的和。

i = 2
sum1 = 0
while i < 360000:
    string = str(i)
    l = [(int(x))**5 for x in string]
    if i == sum(l):
        print(i)
        sum1 += i
    i += 1
print(sum1)

思路：如果这个数为7位数，它一定小于7*9！=413343，所以这样的数不会是7位数或更大

如果这个数为6位数，它一定小于6*9！=354294，所以搜索上界就是它

结果：443839