My first instinct was to reach for a simple BFS and call it done.
Clarify the problem by defining the search space, matching criteria, and constraints (e.g., multiple matches, duplicates). Then outline a backtracking algorithm that incrementally builds candidates and abandons partial solutions that cannot lead to valid matches. Finally, discuss complexity, optimizations, and test cases.
Pro tip: Emphasize pruning strategies to avoid unnecessary exploration, and discuss how to handle duplicate matches or overlapping solutions to show depth. Also, relate the approach to real-world scenarios like searching ride routes or driver assignments at Lyft.
Ask questions to understand the input format, what constitutes a match, whether duplicates are allowed, and any constraints on time/space. This ensures you solve the right problem.
Describe the state representation, choices at each step, and the backtracking template (choose, explore, unchoose). Explain how to detect and collect valid matches.
Discuss how to prune branches early using constraints or heuristics, and mention techniques like sorting, memoization, or symmetry breaking to improve efficiency.
Provide time and space complexity in terms of input size, and discuss edge cases such as empty input, no matches, or many matches.
Walk through a small example to demonstrate correctness, and mention how you would test the solution, including unit tests for edge cases.
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