I knew BFS for shortest path on a grid, but the multi-source angle threw me a bit at first.
Start by clarifying the problem constraints (grid size, number of DashMarts, obstacles) and then propose a multi-source BFS from all DashMart locations simultaneously. Explain that this computes the shortest distance to the nearest DashMart for every cell in O(m*n) time, which is optimal, and contrast it with running BFS from each source which would be O(k*m*n) where k is the number of DashMarts.
Pro tip: Mention that multi-source BFS is equivalent to adding a virtual super-source connected to all DashMarts with zero-weight edges, which unifies the search and avoids redundant work. Also, note that if the grid is huge but DashMarts are few, a bidirectional BFS or A* might be considered, but multi-source BFS is simpler and often fast enough.
Ask about grid dimensions, number of DashMarts, obstacle representation, and whether distance is Manhattan or 4-directional. Confirm that we need distances from every cell to the nearest DashMart.
Initialize a queue with all DashMart cells, set their distance to 0, and perform BFS level by level. For each cell, update its distance when first visited, ensuring the shortest path to any DashMart.
Explain that multi-source BFS visits each cell at most once, giving O(m*n) time and O(m*n) space for the queue and distance grid. Compare with running BFS from each DashMart: O(k*m*n) time, which is inefficient when k is large.
Mention that multi-source BFS is optimal for unweighted grids. If the grid is weighted, Dijkstra with multiple sources would be needed. Also, note that if only a few cells need distances, a different approach might be better.
Address obstacles (skip them), unreachable cells (distance remains infinity), and multiple DashMarts in the same cell. Ensure the BFS explores only valid neighbors.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.