Knew it was topological sort pretty fast, the dependency framing makes it obvious.
Model the resources as a directed graph where edges represent dependencies, then perform a topological sort using Kahn's algorithm (BFS) or DFS. If the sort processes all nodes, return the order; otherwise, a cycle exists and the problem is unsatisfiable.
Pro tip: Mention that Kahn's algorithm naturally detects cycles by checking if the number of processed nodes equals the total number of resources, and discuss how to handle large-scale systems with distributed resources.
Ask if dependencies are directed (A must be initialized before B) and if there can be multiple valid orders. Confirm that a cycle means no valid order exists.
Represent each resource as a node and each dependency as a directed edge. Compute in-degrees for all nodes.
Use Kahn's algorithm (BFS with queue) or DFS with recursion stack. Explain the trade-offs: Kahn's is iterative and easier to detect cycles; DFS can be more concise but requires recursion stack tracking.
Process nodes with zero in-degree, reducing in-degrees of neighbors. If all nodes are processed, return the order; if not, a cycle exists.
State time complexity O(V+E) and space O(V+E). Discuss edge cases: empty input, single node, multiple disconnected components, and self-dependencies.
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