有几种方法来处理柱旋转。 关于柱旋转深，有三个线性算法。（点击的这里检查）

There are several ways to deal with string rotation. "Programming Pearls" talks about string rotation in deep, with three linear algorithms.(click here to check it)

第一个是所谓的杂耍算法，这是我花了很多时间去研究它，但我仍然无法理解的作用大公因式扮演它。任何人都可以详细解释一下？

The first one is called "Juggling algorithm", which I spent a lot time to study it, but I still can't understand the role that Great Common Divisor plays in it. Can anybody explain it in detail ?

推荐答案

您通过移动，步长为 D 旋转的元素。这个过程返回一定数量的举动后，这样你需要申请 M 长周期 L = N / M 的总和。

You rotate the elements by moving them in steps of d. This process loops back after a certain number of moves, so that you need to apply m cycles of length l=n/m in total.

→是解决方程的第一个值 LD = 0（MOD N），使 M 是precisely GCD（N，D）。

l is the first value that solves the equation l.d = 0 (mod n), so that m is precisely gcd(n, d).

Example 1: for n=12, d=3, 3 cycles of length 4:
 0  3  6  9
 1  4  7 10
 2  5  8 11

Example 2: for n=12, d=10, 2 cycles of length 6:
 0 10 8 6 4 2
 1 11 9 7 5 3