Problem 56

Problem 56

https://projecteuler.net/problem=56

Powerful digit sum

A googol (10¹⁰⁰) is a massive number: one followed by one-hundred zeros; 100¹⁰⁰ is almost unimaginably large: one followed by two-hundred zeros. Despite their size, the sum of the digits in each number is only 1.

一个古戈尔(10¹⁰⁰) 数虽然巨大无比，但是它的位数之和仅仅为1。

Considering natural numbers of the form, a^b, where a, b < 100, what is the maximum digital sum?

考虑以下情况：

　　 a^b, a, b < 100,

　　最大的位数之和为多少？

from power import power

maximum = 0
for a in range(1, 100):
    for b in range(1, 100):
        num = power(a, b)
        digits = list(str(num))
        digits_sum = 0
        for i in digits:
            digits_sum += int(i)
        if digits_sum > maximum:
            maximum = digits_sum
print(maximum)

# power.py
def power(x, y):
    if y == 1:
        return x
    tot = 1
    for i in range(y):
        tot *= x
    return tot

if __name__ == '__main__':
    for x in range(1, 5):
        for y in range(1, 5):
            print('power({0}, {1}) = {2}'.format(x, y, power(x, y)))