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

Although wrang-wrang already answered, I wish to describe a modification of your binary search tree method that is sub-linear.

• We use a binary search tree that is balanced (AVL/Red-Black/etc), but not super-balanced like you described. So adding an item is O(log n)
• One modification to the tree: for every node we also store the number of nodes in its subtree. This doesn't change the complexity. (For a leaf this count would be 1, for a node with two leaf children this would be 3, etc)

We can now access the Kth smallest element in O(log n) using these counts:

def get_kth_item(subtree, k):
  left_size = 0 if subtree.left is None else subtree.left.size
  if k < left_size:
    return get_kth_item(subtree.left, k)
  elif k == left_size:
    return subtree.value
  else: # k > left_size
    return get_kth_item(subtree.right, k-1-left_size)

A median is a special case of Kth smallest element (given that you know the size of the set).

So all in all this is another O(log n) solution.