Binary Indexed Tree (Fenwick Tree)

The Binary Indexed Tree (Fenwick Tree) technique is applied when tackling problems characterized by specific invariants in the problem state or constraints:

• Core Strategy: Use a BIT/Fenwick tree to answer prefix sum queries or range queries with point updates in O(log n) time, typically when the operation is associative and invertible.
• When to use: Look for opportunities where repeated re-computation can be replaced by maintaining monotonic properties, state windows, or relational pointers.
• Interview Signal: Demonstrating this pattern shows mastery of Trees foundations, reducing worst-case algorithmic complexity.