Robinhood·Software Engineer·Technical Phone Screen·Intermediate

Intermediate

Apr 2026

Summary

Robinhood SWE interview that came down to a graph problem with a twist I didn't fully see coming. The dependency propagation angle made it less obvious than a standard topological sort.

Questions Asked (1)

You're given a list of programs and a list of prerequisite pairs where (a, b) means a depends on b. For each program, compute how many programs directly or transitively depend on it. Ignore any pairs that reference programs outside the initial list. Return a map of program name to that count.

Algorithms & Data Structures

Author's notes

I went straight to topological sort and built a reverse adjacency list, which was the right instinct.

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AI HintsAI Generated

Suggested Approach

Model the dependencies as a directed graph where an edge from b to a means b is a prerequisite for a, so that dependents flow in the opposite direction. Compute the transitive closure of this graph to count all programs that directly or indirectly depend on each program. Use DFS with memoization or BFS from each node to accumulate counts, ensuring to handle cycles and ignore invalid pairs.

Pro tip: Clarify the direction of dependency early: if (a, b) means a depends on b, then b has a as a dependent, so the graph edge should be b -> a for counting dependents. Also, mention that cycles are possible and should be handled gracefully, as they can cause infinite loops in naive DFS.

1. Clarify and Validate Input

Confirm the meaning of (a, b) and filter out any pairs where either program is not in the given list. Build a set of valid programs for quick lookup.

2. Build Dependency Graph

Construct an adjacency list where for each valid pair (a, b), add a directed edge from b to a, representing that b is a prerequisite for a, so a depends on b. This graph will be used to find all dependents of a program.

3. Compute Transitive Dependents

For each program, perform a graph traversal (DFS or BFS) to find all programs that can be reached from it, which are exactly the programs that depend on it directly or transitively. Use memoization to cache results and avoid redundant computations.

4. Handle Cycles and Count

If cycles exist, ensure the traversal does not revisit nodes within the same path (e.g., using a visited set per traversal or a global visited set with careful reset). Count the number of unique reachable nodes for each program.

5. Return Result Map

Create a map from each program name to its count of transitive dependents. Ensure all programs from the original list are included, even if they have zero dependents.

Key Points to Mention

Graph representation: adjacency list for efficient traversal.
Direction of edges: from prerequisite to dependent to count dependents.
Transitive closure: using DFS/BFS to find all reachable nodes.
Cycle handling: avoid infinite loops by tracking visited nodes.
Memoization: cache results to improve time complexity, especially for DAGs.
Time and space complexity: O(V+E) per traversal, or O(V*(V+E)) without memoization; with memoization, O(V+E) overall for DAGs.

AI-generated suggestions, not part of the candidate's original notes. May be inaccurate — verify before relying on them.