Context

Algorithm analysis is a core interview skill because it shows whether you can reason about scalability before optimizing code. Interviewers want to see that you can estimate runtime, memory usage, and pinpoint the operation that dominates performance.

Core Question

Explain how you would calculate time complexity and space complexity for an algorithm, and how you would identify its bottleneck.

Address these sub-questions:

1. How do you analyze common structures such as loops, nested loops, recursion, and helper data structures?
2. How do you distinguish total work from the dominant term in Big-O notation?
3. How do you determine which part of the algorithm is the true bottleneck, and when that bottleneck is time versus space?

Scope Guidance

Give a practical interview-style explanation rather than a formal proof. You should define the concepts, walk through how to analyze code step by step, and use small code examples to show how bottlenecks are identified.