Use multi-source BFS starting from all source cells simultaneously, treating the grid as an unweighted graph. Initialize a queue with all sources, set their distance to 0, and perform BFS to propagate distances to all reachable cells. For unreachable cells, leave distance as infinity or -1.
Pro tip: Clarify upfront that you assume 4-directional movement and that sources have distance 0; this shows attention to problem constraints and avoids ambiguity. Also, mention that if the grid is large, you can optimize space by using a 2D array for distances and a queue for BFS, but avoid recursion due to stack overflow.
Ask about movement directions (4 or 8), whether diagonal moves are allowed, and what to return for unreachable cells. Confirm that sources are given and distances are Manhattan if only 4-directional.
Explain that BFS from all sources simultaneously computes shortest distances in O(rows*cols) time. Contrast with running BFS from each empty cell, which would be O((rows*cols)^2).
Create a distance matrix initialized to infinity (or -1) and a queue. Enqueue all source cells and set their distance to 0.
While queue is not empty, dequeue a cell, explore its valid neighbors (within bounds, not walls, and not yet visited), update their distance as current distance + 1, and enqueue them.
After BFS, the distance matrix holds the shortest distance from each cell to the nearest source. State time complexity O(rows*cols) and space complexity O(rows*cols) for the queue and distance matrix.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Clarify the problem constraints first, such as the number of moving sources, update frequency, and query types. Then propose a data structure that supports efficient updates and queries, discussing trade-offs between different approaches. Finally, outline how you would handle edge cases and scale the solution.
Pro tip: Mention that in real-world systems, you often need to balance update and query costs, and consider using a combination of data structures or lazy updates to optimize for the dominant operation.
Ask about the number of sources, how often they move, the types of queries (e.g., nearest source, range queries), and performance requirements.
Select a data structure that supports dynamic updates and efficient queries, such as a k-d tree with rebuilding, a quadtree, or a spatial index like R-tree.
Describe how to update the data structure when a source moves, considering strategies like lazy deletion, periodic rebuilding, or incremental updates.
Explain how queries are performed efficiently, possibly using techniques like bounding boxes, pruning, or caching.
Compare alternatives, highlighting time/space complexity, update vs. query performance, and suitability for different scenarios.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.