Question

Suppose I have a balanced BST (binary search tree). Each tree node contains a special field count, which counts all descendants of that node + the node itself. They call this data structure order statistics binary tree.

This data structure supports two operations of O(logN):

• rank(x) — number of elements that are less than x
• findByRank(k) — find the node with rank == k

Now I would like to add a new operation median() to find the median. Can I assume this operation is O(1) if the tree is balanced?

Answer 1

If the tree is complete (i.e. all levels completely filled), yes you can.