Multi-source BFS from all stores simultaneously, which gets you shortest distances to every reachable cell in one pass.
Use multi-source BFS starting from all store cells simultaneously, treating the grid as an unweighted graph where each cell is a node connected to its 4-directional neighbors. Initialize distances to 0 for stores, infinity for others, and propagate level by level, skipping obstacles. After BFS, replace infinity with -1 for unreachable homes.
Pro tip: Emphasize that multi-source BFS is optimal because it computes all shortest paths in a single pass, avoiding repeated BFS from each home which would be inefficient. Also, mention that this approach naturally handles multiple stores and obstacles.
Confirm grid dimensions, cell types (store, home, road, obstacle), movement allowed (4-directional), and that distance is number of steps. Ask about edge cases like no stores or no homes.
Select multi-source BFS using a queue. Use a 2D array for distances, initialized to -1 (unvisited) or infinity, and set store cells to 0. Use a queue to process cells level by level.
Enqueue all store cells with distance 0. While queue not empty, dequeue a cell, and for each valid neighbor (within bounds, not obstacle, not visited), set distance = current distance + 1 and enqueue. This ensures shortest paths from any store.
After BFS, iterate over all home cells. If distance is still -1 (unvisited), set to -1 (unreachable). Otherwise, keep the computed distance. Return the grid or list of distances for homes as required.
State time complexity O(m*n) since each cell is visited at most once. Space complexity O(m*n) for the queue and distance array. Walk through a small example to verify correctness.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.
Start by clarifying the problem constraints: grid size, frequency of obstacle additions, and query types (e.g., point-to-point or all-pairs). Then propose an incremental algorithm that updates distances only for affected regions, such as dynamic BFS or using a priority queue to propagate changes, and discuss trade-offs between time and space complexity.
Pro tip: Mention that if obstacles are only added (never removed), distances can only increase, so you can avoid recomputing unaffected areas. Also, consider preprocessing for common queries if the pattern is predictable.
Ask about grid size, number of queries, frequency of obstacle additions, and whether obstacles can be removed. This determines the appropriate algorithm.
When an obstacle is added, only paths that previously went through that cell are affected. Use the previous distance map to identify cells whose shortest path might change.
Propose an algorithm like dynamic BFS: start from the new obstacle, update distances of neighbors, and propagate changes using a priority queue (similar to Dijkstra) until distances stabilize.
Compare the incremental approach (O(affected area)) with full BFS (O(V+E)). Discuss when full recomputation might be simpler or more efficient.
Mention techniques like bidirectional BFS, A*, or preprocessing for frequent queries. If obstacles are added in batches, process them together.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.