Explain Binary Indexed Tree vs Segment Tree.
A Binary Indexed Tree (BIT) and a Segment Tree are efficient data structures for performing range queries and updates, but they differ in complexity, flexibility, and memory usage.
When to Use
Use a BIT when you need fast prefix sums or frequency counts.
Choose a Segment Tree for advanced range queries like minimum, maximum, or GCD. BITs are ideal for problems involving cumulative sums or Fenwick Tree-style updates.
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Example
For a leaderboard app, use a BIT to update a player’s score and get total points quickly. To find the maximum score in a range, use a Segment Tree.
Why Is It Important
These structures optimize query performance from O(n) to O(log n) and are frequently used in competitive programming and FAANG interviews.
Interview Tips
Know that both have O(log n) per operation.
Highlight that BITs are simpler for prefix sums, while Segment Trees handle diverse operations efficiently.
Trade-offs
- BIT: Easier, less memory (~N).
- Segment Tree: More versatile, more memory (~4N).
Pitfalls
Using BITs for complex queries is limiting, while Segment Trees can be overkill for simple sum problems. Always consider problem constraints and update frequency before choosing.
Also recommended: Grokking the System Design Interview and Grokking Database Fundamentals for Tech Interviews.
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