Thank you for making my point. So not only does this do different comparisons, it "radically" changes the number of "common floor" work. And by the way, there

Thank you for making my point. So not only does this do different comparisons, it "radically" changes the number of "common floor" work. And by the way, there's something wrong with your analysis of the number of scans needed for the 20 element bubble sort. I don't understand your argument, but I did some experiments with a randomly distributed array. I never saw it sort in fewer than 12 scans, after a few dozen trials.