The weighted scoring part from the base problem was already established, so this was really about layering BFS on top of it and capping depth at 2.
Clarify the graph representation (adjacency list) and whether the graph is directed or undirected. Then perform a bounded BFS from the target merchant up to depth 2, collecting all visited nodes. Return the set of reachable merchants, excluding the target itself if required.
Pro tip: Mention that for depth 2, a simple two-level expansion (neighbors of neighbors) is sufficient and more efficient than a full BFS, but BFS generalizes to any depth. Also discuss handling large graphs with distributed processing if needed.
Ask whether the graph is directed or undirected, if the target merchant should be included in the result, and if there are any constraints on graph size or memory.
Select BFS with a depth limit of 2, as it naturally explores level by level and avoids deep recursion. Alternatively, for exactly 2 hops, you can iterate over direct neighbors and their neighbors.
Use a queue to track nodes and their depth, and a set to avoid revisiting nodes. Stop expanding when depth exceeds 2.
Consider isolated nodes, cycles, and self-loops. Return the set of reachable merchants, ensuring no duplicates.
Discuss time and space complexity (O(V+E) for BFS, but for depth 2 it's O(deg(target) + sum of degrees of neighbors)). Mention how to scale for large graphs using distributed BFS or graph databases.
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