From Brute Force to Hash Maps: Solving Two Sum with Linear Efficiency

For developers aiming to master algorithm interviews and improve code performance, understanding the trade-off between time and space complexity is essential. This solution demonstrates how replacing nested iteration with a hash map lookup transforms Two Sum from O(n²) to O(n), illustrating a fundamental principle: strategic data structure selection can dramatically improve scalability. This hash map pattern is widely applicable across many coding problems, making it a critical technique to master.