Fenwick vs Segment Tree
Both Fenwick Tree and Segment Tree support point updates and range sum queries. But they have differences in functionality, memory, and ease of implementation.
Fenwick Tree
- Pros: Simple to implement, uses less memory (n+1), faster constant factor.
- Cons: Only supports prefix sum queries (range sum via subtraction) and point updates. Cannot handle range updates directly (without modifications). Not easily adaptable for min/max or non-invertible operations.
Segment Tree
- Pros: Highly flexible; supports any associative operation (sum, min, max, gcd, etc.). Can handle range updates with lazy propagation.
- Cons: More complex to implement, uses about 4n memory, higher constant factor.
When to use which:
- Use Fenwick Tree when you only need prefix sums (or range sums) with point updates. It's often faster in practice.
- Use Segment Tree when you need range updates, min/max queries, or non-invertible operations.
Two Minute Drill
- Fenwick Tree: simpler, less memory, prefix sum + point updates only.
- Segment Tree: flexible, supports any associative operation and range updates (with lazy).
- Choose based on problem requirements: if only sum and point updates, BIT is great; otherwise segment tree.
- Both run in O(log n) for basic operations.
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