Even though I know the algorithm, I still find that I need to think a nontrivial amount to see why it will not miss anything. I mean, sure, you are strictly imp

Even though I know the algorithm, I still find that I need to think a nontrivial amount to see why it will not miss anything. I mean, sure, you are strictly improving the "sortedness" by a discrete amount in each pass and crucually, you don't destroy any progress you made before (not totally trivial), and there's only a finite amount of "sortedness" to attain, so it will converge to the sorted state. But how exactly and, as you say, after how many iterations, is not so clear. In more complex algorithms, you may get stuck in a local optimum with such a greedy approach though. But contrast that with insertion sort. I have a sorted pile that grows after each insertion. I find it trivially clear that it works and when I will be done. It's also something that people will intuitively do in the physical world to sort paper documents I think: just grow a pile of sorted documents by adding the next one in the right place.