Classic BFS problem at its core but the forbidden states plus wraparound tripped me up at first.
Model the lock states as nodes in a graph where edges connect states differing by one digit rotation, then use BFS to find the shortest path from '0000' to the target while avoiding forbidden states. After explaining the algorithm, outline unit tests that cover edge cases like target being the start, forbidden start, unreachable targets, duplicate forbidden entries, and large forbidden sets.
Pro tip: Mention that you can optimize BFS by using a bidirectional search or A* with a heuristic like the sum of minimum rotations per digit, but only if the interviewer shows interest in optimization. Also, emphasize the importance of validating input and handling edge cases early in the code.
Confirm that each move changes one digit by ±1 with wraparound (0↔9), forbidden states cannot be visited, and the target may be forbidden. Ask about input size and performance expectations.
Use BFS because each move has uniform cost and we need the shortest path. Represent states as strings or integers, use a queue for BFS, and a set for forbidden states for O(1) lookups.
Start from '0000', if it's forbidden return -1. For each state, generate neighbors by rotating each digit up and down, skip if forbidden or visited, and stop when target is reached. Return distance or -1 if queue exhausts.
Write tests for: target is '0000' (should return 0), forbidden includes '0000' (return -1), unreachable target (e.g., all neighbors forbidden), duplicate forbidden entries (should not affect result), and large forbidden sets (e.g., 1000 states) to test performance and correctness.
Discuss time and space complexity: O(10^4) states, each with 8 neighbors, so O(1) effectively. Mention potential optimizations like bidirectional BFS or A* if needed, and trade-offs between pre-processing forbidden set vs. checking on the fly.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.