Model the tasks and dependencies as a directed graph and use topological sorting (Kahn's algorithm or DFS) to find a valid ordering. If a cycle is detected, return an error indicating no valid ordering exists.
Pro tip: Discuss the trade-offs between Kahn's algorithm and DFS-based topological sort, and mention that Kahn's algorithm naturally detects cycles by checking if all nodes are processed.
Confirm that tasks are nodes and dependencies are directed edges. Ask if the graph is guaranteed to be a DAG or if cycles are possible.
Select either Kahn's algorithm (BFS-based) or DFS-based topological sort. Explain your choice based on cycle detection and implementation simplicity.
For Kahn's: compute in-degrees, use a queue, and process nodes. For DFS: perform depth-first search and track visited and recursion stack.
If using Kahn's, check if the number of processed nodes equals N. If using DFS, check for back edges during traversal.
If no cycle, return the topological order. If cycle, return an indication that no valid ordering exists.
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