Start by clarifying the problem: confirm whether the graph is guaranteed acyclic, whether paths can share nodes, and what output format is expected. Then propose a DFS-based backtracking solution that explores all paths from the source, using a visited set to avoid cycles (though DAG ensures no cycles, it's good practice). Discuss time complexity as O(2^n) in the worst case due to exponential number of paths.
Pro tip: Mention that for very large graphs, enumerating all paths is inherently exponential, so you should ask if the interviewer expects an optimized approach for a specific subset (e.g., shortest paths) or if the problem is purely about enumeration. This shows awareness of practical constraints.
Ask about input format, whether the graph is guaranteed acyclic, if paths can repeat nodes, and if the source is always valid. Confirm output should be a list of paths.
Use DFS with backtracking to explore all paths. Since it's a DAG, no cycle detection is needed, but you can still use a visited set to avoid revisiting nodes in the current path.
Write a recursive function that takes the current node and the path so far. If the current node has no outgoing edges, add the path to the result. Otherwise, iterate over neighbors and recurse.
State that time complexity is O(2^n) in the worst case (exponential number of paths) and space is O(n) for recursion depth plus output storage. Discuss potential optimizations like pruning if only paths to a specific target are needed.
Walk through a small example (e.g., 4 nodes) to verify correctness, including edge cases like source with no outgoing edges or single-node graph.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.