Fulfillment-Center Inventory Transfer

Given bidirectional routes between fulfillment centers, a destination, a maximum hop count, and per-center inventory, return every non-destination center with positive inventory whose shortest path to the destination uses at most the allowed number of routes. Requirements connections is a list of pairs [u, v], each representing a bidirectional delivery route between fulfillment centers. destination is the center that needs inventory, and maxStep is the maximum number of routes a transfer may traverse. inventory maps each center ID to its current item count. Return every center ID that is not destination, has inventory greater than zero, and has a shortest-path distance to destination no greater than maxStep. The result may be returned in any order. Examples connections = [[1, 2], [1, 3], [2, 4], [3, 4], [4, 5]] destination = 4 maxStep = 1 inventory = {1: 2, 2: 0, 3: 5, 4: 3, 5: 6} output = [3, 5] Notes Run the search once from destination rather than from every candidate center: a level-bounded BFS answers all centers in one pass, stopping expansion when the depth reaches maxStep. Overall O(V + E) time with a visited set. Build the adjacency structure from the pair list first (hash map of ID → neighbor list) and insert both directions — the routes are bidirectional. Filter as you collect: skip destination itself and any center whose inventory is zero or missing. In the worked example center 2 is reachable within one hop but holds zero inventory, which is exactly the trap the eligibility rules encode. Edge cases to state before coding: maxStep = 0 (empty result), centers that appear in inventory but not in connections (unreachable), and duplicate route pairs. Preparation Implement a level-bounded BFS from a single source that returns every node within k hops, and check it against the worked example (expect [3, 5]). Drill restating a domain prompt in graph vocabulary before coding — centers as nodes, routes as undirected edges, maxStep as BFS depth — so the eligibility rules become filters over a plain traversal.