Sorting Magazines and Boxes

Abstract

It is a rainy Sunday. Agata has decided to sort the magazines on her shelf. Because the magazines are quite thin, she refuses to insert one between two others, preferring to move them only to the ends of the shelf. She has conceived a strategy for this but is unsure of its efficiency. Meanwhile, in the adjacent room, her three-year-old son, Szymon, has just finished his Montessori tower puzzle and is figuring out how to put it away. He has adopted a very intuitive approach to nesting the boxes, though he is not certain it will ultimately succeed.
Agata and Szymon are employing very primitive strategies. While many sorting algorithms are remarkably simple to explain and implement-specifically, the class of in-place sorting algorithms with 𝒪(n²) worst-case and average-case running time and constant space requirements (e.g., Bubble Sort, Gnome Sort)-the strategies discussed here offer a unique perspective on "intuitive" sorting. Our contribution aims to enrich the field of simple sorting algorithms. Interestingly, determining the exact worst-case complexity of some of the proposed algorithms remains an open problem.