I learned about this from Matt Parker’s Stand-Up Maths channel. It was originally conceived as a counterexample, a sorting algorithm that was obviously broken, but it does actually sort correctly. The algorithm:
for i = 1 to n do
for j = 1 to n do
if A[i] < A[j] then
swap A[i] and A[j]
It has a few quirks (like j accessing elements outside of i’s range, and the A[i] < A[j] comparator being backward) that should break it, but they all work together to make the algorithm correctly (if inefficiently) sort the input.
paper describing the algorithm in more detail.
As the addendum to the paper points out, this is more like insertion sort (with
iandjin a confusing order) than bubble sort. The actual “important” part of the algorithm happens whenj < i. (In fact, I’m quite certain there aren’t even any swaps whenj >= iafter the first outer iteration.) (I think the page about people misremembering bubble sort is also worth looking at.)Honestly, I think this might actually be “better” than bubble sort, in the sense that at least it’s incredibly easy to remember and not that hard to get correct. The only place where you could realistically mess up is confusing the relative order of
iandj– and any amount of nontrivial testing will immediately show the error, since it reverses the sort order. I’d probably reach for this if I, for whatever insane reason, had to code up a sorting algorithm by hand for some task whereO(n^2)sorting was acceptable performance-wise. “Sort a list of 10 items in a very primitive programming language”-type deal.(Now that I say that, I’m kind of tempted to use it in some example program for my own in-development programming language, which currently doesn’t have a builtin sort function…)