The Centrifuge Problem

The Centrifuge Problem

Simple+

一台离心机上有n 个相同的槽,每个槽的大小足以放进一个试管。为了防止离心机晃动,必须将k 相同的试管放入这些槽中,使它们的重心正好位于离心机的中心。这个问题的灵感来自另一个视频 "离心机问题",您可以在下面观看。另外,如果您的眼睛读得比耳朵听得快,也可以查看马特-贝克(Matt Baker)的文章“The Balanced Centrifuge Problem”

因此,将k 试管平衡放入n 插槽是可能的,前提是k, n-k 都可以表示为n 的质因数之和,且允许因数重复。例如,当n 等于 6,其质因数为 2 和 3 时,离心机可以容纳 0、2、3、4(= 2 + 2)或 6(= 3 + 3)支试管。 但是,不可能在 6 个插槽中平衡 1 或 5 个试管。即使 5 = 2 + 3 满足规则的第一部分,也没有办法平衡剩余的空槽,尽管空槽没有重量这一违反直觉的事实是需要平衡的!

example

该函数实际上并不需要构建k 试管的平衡配置,而只是确定给定的n, k 是否至少存在一种平衡配置。

输入:两个整数 (int)

输出:逻辑值 (bool).

示例

assert balanced_centrifuge(6,...
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