One (more) line on the most Ancient Algorithm in History

TL;DR

This paper presents a concise, one-line analysis of the Euclidean Algorithm's runtime, providing a near-optimal upper bound with a simple and elegant approach.

Contribution

It introduces a novel, simplified analysis method for the Euclidean Algorithm's runtime, making the understanding more accessible and concise.

Findings

The analysis yields a near-optimal upper bound.

The method simplifies understanding of the Euclidean Algorithm.

The approach is notably shorter and more elegant than previous analyses.

Abstract

We give a new simple and short ("one-line") analysis for the runtime of the well-known Euclidean Algorithm. While very short simple, the obtained upper bound in near-optimal.