Question

I need a data structure that holds unique values (like a set), but also sorts them (like a priority queue) and allows random access for binary searching (like an array). Which type of data structure would fit these needs? I could live without the sorting (I can always sort it myself at the end)

Answer 1

That sounds like a balanced binary tree, with a restriction of uniqueness in its insert operation, and implementing the OS-SELECT operation (see: Introduction to Algorithms, chapter 14 in the 3rd edition) for retrieving an element given its rank (“index”) in O(lg n).

The proposed data structure and augmented operations will allow you to:

• Hold unique values, performing the insertion operation in O(lg n)
• Keep the elements sorted, with a O(lg n) search operation
• Access an element given its rank in O(lg n)