Optimizing Prefix Search: HashSet-Based Algorithm for Finding Common Prefixes

This problem demonstrates how hash sets enable efficient O(1) lookup times for prefix matching, a technique essential for real-world applications like autocomplete systems and IP address validation. The solution highlights the critical trade-off between preprocessing overhead and query performance, illustrating why hash-based approaches dominate scenarios requiring rapid pattern matching. Mastering this algorithm pattern is fundamental for building scalable systems that handle large datasets with demanding lookup requirements.