Is it possible to query number of distinct integers in a range in O(lg N)?

Question

I have read through some tutorials about two common data structure which can achieve range update and query in O(lg N): Segment tree and Binary Indexed Tree (BIT / Fenwick T

Answer 1

The given problem can also be solved using Mo's (offline) algorithm also called Square Root decomposition algorithm.

Overall time complexity is O(N*SQRT(N)).

Refer mos-algorithm for detailed explanation, it even has complexity analysis and a SPOJ problem that can be solved with this approach.