I'm not sure I could be a computer science teacher and only teach one sorting algorithm.
At a bare minimum the students should be taught at least one of each of the major sorting types, namely an exchanging sort, a selection sort, an insertion sort, and a merge sort. In addition to one of each of these types, I would also cover Quicksort which falls under the partitioning sort heading.
As for the specific sorts from each of the types that I would cover:
- Bubble Sort as an example of the exchanging sort category as it is one of the simplest sort types and one that they likely have already seen or stumbled across on their own. This is also the sort they will most likely use the most often if they have to roll their own for something simple so it makes sense for them to understand it.
- Heapsort from the selection sort category. This would likely be the most confusing sort next to Quicksort but once they understand how it sets them up for understanding the Quicksort algorithm.
- Insertion Sort as an example of the insertion sort category would be covered as it is also a simple sort that they can get a lot of use out of. Since they might encounter scenarios where they need to merge two lists together, knowing this one makes sense.
- Merge Sort is somewhat of a specialized sort so you don't see it too often, but it is very good at what it does and is still useful in situations where you need to sort data that you are getting in a piecemeal fashion.
If I had to narrow things down to just one sort that I could teach, but I had the time to make sure that the student understood exactly what was going on then I would teach Quicksort. While it is not easy to grasp, the vast majority of frameworks out there use it for their sorting algorithm so an understanding of how it works is useful in your development with that framework. Also, it is quite likely that if someone is able to understand Quicksort then they should be able to learn the Bubble Sort and Insertion Sort on their own.
