组合数学 - 置换群的幂运算 --- poj CARDS (洗牌机)

原创

于 2017-03-05 17:11:56 发布 · 1k 阅读

2 ·

CC 4.0 BY-SA版权

该博客介绍了如何利用置换群和快速幂运算解决一道关于洗牌的ACM问题。当洗牌次数为奇数时，可以通过置换的平方运算来求解最初的牌序。博客作者提到潘震皓的文章对此问题有清晰的阐述，并提供了时间复杂度为O(n+logs)的解决方案。

摘要生成于 C知道，由 DeepSeek-R1 满血版支持，前往体验 >

CARDS

Time Limit: 1000MS		Memory Limit: 10000K
Total Submissions: 1448		Accepted: 773

Description

Alice and Bob have a set of N cards labelled with numbers 1 ... N (so that no two cards have the same label) and a shuffle machine. We assume that N is an odd integer.
The shuffle machine accepts the set of cards arranged in an arbitrary order and performs the following operation of double shuffle : for all positions i, 1 <= i <= N, if the card at the position i is j and the card at the position j is k, then after the completion of the operation of dou