My first instinct was BFS and that was right, but I fumbled the exit condition initially.
Model the grid as a graph and perform BFS from the starting cell to find the shortest path to any border cell. Treat the start as distance 0, and when exploring neighbors, check if a neighbor is on the border and empty; if so, return the current distance + 1. If BFS exhausts without finding an exit, return -1.
Pro tip: Clarify edge cases upfront: what if the start is already on the border? (It doesn't count, so you must move away and come back to a different border cell.) Also, confirm whether diagonal moves are allowed—typically only 4-directional moves are considered.
Ask about grid dimensions, movement directions (4 or 8), and whether the start cell can be on the border. Confirm that the start cell itself is not an exit even if on the border.
Explain that BFS is optimal because each step has equal cost. Use a queue to explore level by level, ensuring the first border cell reached is the nearest.
Initialize a queue with the start cell and a visited set. For each cell, check its neighbors; if a neighbor is empty, unvisited, and on the border, return distance+1. Otherwise, enqueue it with distance+1.
If the queue empties without finding a border cell, return -1. Ensure the start cell is marked visited to avoid cycles.
State that time complexity is O(m*n) since each cell is visited at most once, and space complexity is O(m*n) for the queue and visited set in the worst case.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.