ProjectEuler 问题 99 的算法

Question

来自 http://projecteuler.net/index.php?section=problems&id=99

Comparing two numbers written in index form like 2¹¹ and 3⁷ is not difficult, as any calculator would confirm that 2¹¹ = 2048 3⁷ = 2187.

However, confirming that 632382⁵¹⁸⁰⁶¹ > 519432⁵²⁵⁸⁰⁶ would be much more difficult, as both numbers contain over three million digits.

Using base_exp.txt (right click and 'Save Link/Target As...'), a 22K text file containing one thousand lines with a base/exponent pair on each line, determine which line number has the greatest numerical value.

我该如何处理？

Answer 1

不是完整的解决方案，而是一些想法。您可以使用以下公式:

log(a^x) = x*loga

log10 可以很容易地估计为位数。通过计算右移可以很容易地估计 log2。

根据以上内容，您可以显着缩小列表范围。对于剩余的数字，您必须进行完整的计算。欧拉项目中是否允许使用数学函数？如果是，最好使用对数。