BFS was the obvious move and I knew that immediately, but I fumbled around with how to reconstruct the actual path coordinates instead of just returning a boolean or a length.
Model the grid as a graph and use BFS from one boundary point to find the shortest path to the other, since BFS guarantees the shortest path in unweighted graphs. During BFS, maintain a parent pointer for each visited cell to reconstruct the path once the target is reached. If the queue empties without reaching the target, return 'No Path'.
Pro tip: Clarify assumptions upfront: whether boundary points are guaranteed to be walkable, if diagonal moves are allowed, and if the path should include both endpoints. Also, mention that BFS is optimal here but if the grid is huge, bidirectional BFS can reduce search space.
Confirm the input format, movement rules (4-directional or 8-directional), and output format. Ask if the start and end are guaranteed to be walkable and distinct.
Explain that BFS is ideal for unweighted grids because it explores level by level, guaranteeing the shortest path. Mention that DFS would not guarantee shortest path.
Use a queue to explore neighbors, a visited set to avoid cycles, and a parent map to record the previous cell for each visited cell. Stop when the target is reached.
Backtrack from the target using the parent map to build the path from start to end. If the target was never reached, output 'No Path'.
State time and space complexity: O(n*m) for both. Discuss edge cases like start equals end, no path, or blocked start/end.
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