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

To keep the explanation brief, you can efficiently augment a BST to select a key of a specified rank in O(h) by having each node store the number of nodes in its left subtree. If you can guarantee that the tree is balanced, you can reduce this to O(log(n)). Consider using an AVL which is height-balanced (or red-black tree which is roughly balanced), then you can select any key in O(log(n)). When you insert or delete a node into the AVL you can increment or decrement a variable that keeps track of the total number of nodes in the tree to determine the rank of the median which you can then select in O(log(n)).