← Robinhood Interview Insights
The example they gave made it look easy until D showed up with two parents and I realized you can't just do a simple BFS count.
Model the problem as computing the number of distinct paths from the entry node to each node in a DAG. Use topological sorting to process nodes in order, propagating counts along edges, and handle large numbers with modulo arithmetic if needed.
Pro tip: Clarify whether the graph is guaranteed to be a DAG and whether the entry node is unique; if not, discuss handling cycles or multiple sources. Also, mention that the count can grow exponentially, so consider using modulo or big integers.
Ask about graph size, whether the entry node is unique, if the graph is guaranteed acyclic, and if counts should be modulo something. This ensures you address the right problem.
Decide between topological sort with DP or DFS with memoization. Both work, but topological sort is often more straightforward for path counting in a DAG.
Set the entry node's count to 1 and others to 0. Process nodes in topological order, adding the current node's count to each of its outgoing neighbors.
Discuss what happens if the graph has cycles (not a DAG), if the entry node is not unique, or if counts overflow. Mention time and space complexity: O(V+E) time and O(V) space.
Walk through a small example to verify correctness, such as a diamond-shaped DAG, and check that counts match the number of paths.
AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.