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

1) As with the previous suggestions, keep two heaps and cache their respective sizes. The left heap keeps values below the median, the right heap keeps values above the median. If you simply negate the values in the right heap the smallest value will be at the root so there is no need to create a special data structure.

2) When you add a new number, you determine the new median from the size of your two heaps, the current median, and the two roots of the L&R heaps, which just takes constant time.

3) Call a private threaded method to perform the actual work to perform the insert and update, but return immediately with the new median value. You only need to block until the heap roots are updated. Then, the thread doing the insert just needs to maintain a lock on the traversing grandparent node as it traverses the tree; this will ensue that you can insert and rebalance without blocking other inserting threads working on other sub-branches.

Getting the median becomes a constant time procedure, of course now you may have to wait on synchronization from further adds.

Rob

Answer 2

A balanced tree (e.g. R/B tree) with augmented size field should find the median in lg(n) time in the worst case. I think it is in Chapter 14 of the classic Algorithm text book.