Took me a minute to see it as a graph problem.
Model the lock states as nodes in a graph where each state is a 4-digit string, and edges connect states that differ by one digit (with wrap-around). Use BFS from '0000' to find the shortest path to the target, skipping forbidden states. If the target is reached, return the distance; else return -1.
Pro tip: Clarify edge cases upfront: if the target is forbidden or the start is forbidden, return -1 immediately. Also, mention that BFS is optimal for unweighted graphs, and consider bidirectional BFS for large state spaces to reduce time.
Confirm that each move changes one digit by ±1 with wrap-around (0↔9), and that forbidden codes cannot be visited. Clarify that the target may be unreachable.
Represent each 4-digit code as a node. Edges connect codes that differ by one digit in one position (with wrap-around). This forms a graph with up to 10,000 nodes.
Since each move has equal cost, BFS from '0000' guarantees the minimum number of turns. Use a queue and a visited set to avoid cycles and forbidden states.
For each popped state, generate up to 8 neighbors by incrementing/decrementing each digit (mod 10). Skip neighbors that are forbidden or already visited. If target is found, return depth.
If BFS exhausts without reaching target, return -1. Also check if start or target is forbidden at the beginning and return -1 if so.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.