Erd\H{o}s-Ginzburg-Ziv theorem is a famous theorem in additive number theory, which states any sequence of $2n-1$ integers contains a subsequence of $n$ elements, with their sum being a multiple of $n$. In this article, we provide an algorithm finding a solution of Erd\H{o}s-Ginzburg-Ziv theorem in $\mathcal{O}(n \log n)$ time. This is the first known deterministic $\mathcal{O}(n \log n)$ 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著名的理论。 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, 以 $\ mathcal{O} (n\log n) 时间来寻找 Erd\ H{ o}s- Ginzburg- Ziv 理论的解决方案。 这是第一个已知的确定性 $\ mathcal{O} (n\log n) 时间算法, 找到 Erd\ H{o}s- Ginzburg- Ziv theorem 的解决方案 。