Order statistic tree

In computer science, an order statistic tree is a variant of the binary search tree (or more generally, a B-tree^[1]) that supports two additional operations beyond insertion, lookup and deletion:

• Select(i) – find the i-th smallest element stored in the tree
• Rank(x) – find the rank of element x in the tree, i.e. its index in the sorted list of elements of the tree

Both operations can be performed in O(log n) worst case time when a self-balancing tree is used as the base data structure.