Each time a discussion about sorting starts, I'm reminded of a "lively debate" I had with my boss/friend about the most optimal sorting approach. He claimed it's O(n) pointing to counting sort as an example. This didn't sit well with me. A sorting algorithm, I insisted, should be defined something like "a function taking an unsorted array of elements and returning a sorted one". But it seems there is no agreed upon definition and you can have something like counting sort where you get an array in O(n) but still need O(m) to get the index of a specific element. I argued that then the best sorting algorithm is the do-nothing algorithm. It returns the initial array in O(1), but needd O(m log m) to get you the index of an element (it uses merge sort to do it).

Usually when one talk about sorting, without specifying closer, one means comparison sort [1], which indeed has an average-case lower bound of O(n*log(n)). In more special cases all kinds of other runtimes are possible.

1: https://en.wikipedia.org/wiki/Comparison_sort

counting sort is O(nW), where W is largest value

if you don't care about W or it is essentially constant - then it can be dropped

but it is an input parameter that will change execution time

I can’t think of a single time I’ve needed a sorted list of only numbers. It’s always numbers and something else, like names or dates. Maybe for median calculations, but I don’t even use those that much either. Especially in telemetry, where mean is easy and median is not.

"ordering" means arranging things in order by some metric.

"sorting" means assigning things into bins (which are usually ordered).

You reminded me of "Sleep Sort" [0]

[0] https://news.ycombinator.com/item?id=2657277