Erd\H{o}s-Ginzburg-Ziv theorem is a popular theorem in additive number theory, which states any sequence of $2n-1$ integers contains a subsequence of $n$ elements, with their sum is a multiple of $n$. In this article, we provide an algorithm finding a solution of Erd\H{o}s-Ginzburg-Ziv in $O(n \log n)$ time. This is the first known quasi-linear time algorithm finding a solution of Erd\H{o}s-Ginzburg-Ziv theorem.
翻译:Erd\H{o}s-Ginzburg-Ziv理论是添加数理论中流行的理论理论,该理论指出,任何序列的$2n-1$整数都包含以美元为单位的子序列,其总和是美元倍数。在本篇文章中,我们提供了一种算法,用$O(n\log n)的时间寻找厄尔德\H{o}s-Ginzburg-Ziv的解决方案。这是第一个已知的准线性时间算法,找到厄尔德/H{o}s-Ginzburg-Zivtheorem的解决方案。