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Took me a moment to strip away the build system flavor and see it was just topological sort.
Model the tasks and dependencies as a directed graph and use topological sorting (Kahn's algorithm or DFS) to produce a valid execution order. Detect cycles by checking if all nodes are processed (Kahn's) or if a back edge is found (DFS).
Pro tip: Clarify the direction of dependencies upfront: [a, b] means a depends on b, so b must come before a. This avoids reversing edges and producing an incorrect order.
Confirm the dependency direction and represent tasks as nodes and dependencies as directed edges. For [a, b], add edge b -> a (b must precede a).
Select topological sort: Kahn's algorithm (BFS with in-degrees) or DFS with temporary/permanent marks. Both handle cycle detection.
For Kahn's: compute in-degrees, enqueue nodes with in-degree 0, process and decrement neighbors. For DFS: recursively visit dependencies, detect back edges.
If Kahn's processes fewer than n nodes, a cycle exists. For DFS, if a back edge is found, return empty list.
Return the topological order as a list of tasks. If cycle detected, return an empty list.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.