A New 0(klog n) Algorithm for Josephus Problem
Data Structures and Algorithms
2024-11-27 v1
Abstract
We present a new O(k log n) algorithm of the Josephus problem. The time complexity of our algorithm is O(k log n), and this time complexity is on a par with the existing O(k log n) algorithm. We do not have any recursion overhead or stack overflow because we do not use any recursion. Therefore, the space complexity of our algorithm is O(1), and ours is better than the existing O(k log n) algorithm in this respect. When k is small and n is large, our algorithm is better than the existing O(k log n) algorithm. This new algorithm is based on a relation between the Josephus problem and a maximum Nim of combinatorial game theory.
Cite
@article{arxiv.2411.16696,
title = {A New 0(klog n) Algorithm for Josephus Problem},
author = {Hikaru Manabe and Ryohei Miyadera and Yuji Sasaki and Shoei Takahashi and Yuki Tokuni},
journal= {arXiv preprint arXiv:2411.16696},
year = {2024}
}
Comments
This research was presented at JCDCG 2024