A Counted B-tree stores the number of elements in each subtree to efficiently retrieve order statistics like medians as the data set changes. A (a,b) Tree and Van Emde Boas Tree are data structures where the Van Emde Boas Tree supports search, insert, delete and other operations in O(lglgN) time, faster than related structures, and returns minimum and maximum in O(1) time where N is the size of the universe.

1. COUNTED B TREE, (a , b) Tree, Van Emde Boas Priority Queue

2. COUNTED B TREE
• Counted B-tree is simply this: alongside every link to a subtree, we
store a count of the number of elements stored in that whole subtree.

3. • Counted B-tree allows you to easily extract order statistics from a
changing data set: percentiles and medians. I can't think of any
circumstances in which you might want to insert and remove items
from a data set while keeping a running track of the median value, but
if you need to do it, counted B-trees will let you.

4. (a, b) Tree

6. Van Emde Boas Tree
• Van Emde Boas Tree supports search, successor, predecessor,
insert and delete operations in O(lglgN) time which is faster
than any of related data structures like priority queue, binary
search tree, etc.
• Van Emde Boas Tree works with O(1) time-complexity for
minimum and maximum query.
• Here N is the size of the universe over which tree is defined and
lg is log base 2.