这个整数编码如何工作？ [英] How does this integer encoding work?

问题描述

在此代码高尔夫问题中，有一个 python answer 将所有整数的长度从1到99编码为英文大写：

In this code golf question, there is a python answer that encodes the lengths of all integers from 1 to 99 in english to a big number:

7886778663788677866389978897746775667552677566755267756675527886778663788677866355644553301220112001

要获得 n 的长度，您只需要计算 3 +（the_big_number /（10 ** n））％10 。这是如何工作的？

To get the length of n, you just have to calculate 3 + (the_big_number / (10**n)) % 10. How does this work?

推荐答案

（the_big_number /（10 ^ n））％10 拉出大数字的 n 最低有效位，所以长度只是以零（1 + 3 = 4） ），最左边的九十九（7 + 3 = 10）的长度继续下去。

(the_big_number / (10^n)) % 10 pulls out the nth least significant digit of the big number, so the lengths are just stored starting with the length of "zero" (1+3=4) at the far right, and following over to the length of "ninety-nine" (7+3=10) at the far left.

最短的英文数字是三个字母（一，二，六，10），所以每个长度存储与三个偏移。 100之前最长的是9 + 3 = 12个字母（例如七十八），所以每个数字都可以存储为一位数字。

The shortest English numbers are three letters ("one", "two", "six", "ten"), so each length is stored with an offset of three. The longest prior to 100 are 9 + 3 = 12 letters (e.g. "seventy-eight"), so each number can be stored as a single digit.

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