Find median value from a growing set

Question

I came across an interesting algorithm question in an interview. I gave my answer but not sure whether there is any better idea. So I welcome everyone to write something abo

Answer 1

I received the same interview question and came up with the two-heap solution in wrang-wrang's post. As he says, the time per operation is O(log n) worst-case. The expected time is also O(log n) because you have to "pop an element" 1/4 of the time assuming random inputs.

I subsequently thought about it further and figured out how to get constant expected time; indeed, the expected number of comparisons per element becomes 2+o(1). You can see my writeup at http://denenberg.com/omf.pdf .

BTW, the solutions discussed here all require space O(n), since you must save all the elements. A completely different approach, requiring only O(log n) space, gives you an approximation to the median (not the exact median). Sorry I can't post a link (I'm limited to one link per post) but my paper has pointers.