I knew the brute-force DFS angle pretty quickly but then completely stalled when the interviewer pushed for optimizations.
Start by clarifying the problem constraints and edge cases, then outline a brute-force DFS solution to establish correctness. Next, identify the additional constraints that enable optimizations (e.g., memoization, pruning, or iterative DFS) and discuss trade-offs between time and space complexity. Finally, walk through a concrete example and analyze the optimized solution's complexity.
Pro tip: At Uber, interviewers value scalability and real-world impact—explicitly connect your optimizations to handling large-scale graphs (e.g., millions of nodes) and mention how you'd test for performance bottlenecks.
Ask questions to understand the graph/tree structure, constraints (e.g., size, edge weights, cycles), and required output. Confirm assumptions about input format and edge cases.
Describe a straightforward recursive or iterative DFS that explores all paths, noting its time and space complexity. This establishes a baseline for correctness.
Leverage the additional constraints to propose optimizations such as memoization, pruning, bidirectional search, or iterative deepening. Explain how each reduces time or space complexity.
Compare the optimized approach with the brute-force in terms of time, space, and code complexity. Discuss scenarios where each is preferable.
Trace the algorithm on a small example to demonstrate correctness and highlight how the optimizations work in practice.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.