BFS with a depth limit is something I'd done before but I fumbled the layer-tracking part initially.
Start by clarifying the problem: confirm that the graph is unweighted and that we need all customers within n degrees, not just the shortest path. Then outline a BFS solution that tracks depth, stops expanding beyond n, and uses a visited set to avoid cycles. Finally, discuss time and space complexity and potential optimizations for large graphs.
Pro tip: Mention that BFS naturally finds shortest paths in unweighted graphs, so the first time you visit a node is at its minimum depth. Also, consider early termination when the queue's depth exceeds n, and handle edge cases like n=0 (return only the start node) or n<0 (return empty).
Ask if the graph is directed or undirected, unweighted, and whether the starting customer is included in the result. Confirm that 'within n degrees' means distance ≤ n.
Explain that you'll use a queue to traverse level by level, tracking the depth of each node. Use a visited set to avoid revisiting nodes and infinite loops.
Describe how to track depth: either store (node, depth) pairs in the queue or process level by level. Stop expanding when depth reaches n, but include nodes at depth n in the result.
State time complexity O(V+E) and space O(V). Discuss edge cases: n=0, n<0, disconnected components, and large graphs where memory might be a concern.
Mention bidirectional BFS if n is small relative to graph size, or using iterative deepening if memory is tight. Also, consider if the graph is static and can be preprocessed.
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