I use an algorithmic question that I'd been working on for years and that I'm finally writing up the answer to. It's basically: given a sequence of heap operat

I use an algorithmic question that I'd been working on for years and that I'm finally writing up the answer to. It's basically: given a sequence of heap operations (insert element, delete minimum element), can you predict the left-over elements (that are in the heap at the end) in linear time in the comparison model? (The answer is surprisingly: Yes.)