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Robinhood·Software Engineer·Technical Phone Screen·Intermediate

Intermediate
Jun 2026

Summary

Robinhood software engineer interview with a classic DSU problem. Pretty standard algorithmic round, nothing too surprising if you've done competitive programming before.

Questions Asked (1)

Q1

Implement a Union-Find (Disjoint Set Union) data structure supporting union and find operations, then use it to answer a series of connectivity queries.

Algorithms & Data Structures
Author's notes

Knew this one cold so I jumped straight into the implementation.

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AI HintsAI Generated

Suggested Approach

Start by clearly defining the Union-Find data structure with parent and rank arrays, then implement find with path compression and union by rank. After building the structure, process each connectivity query by checking if the roots of the two elements are the same.

Pro tip: Mention that with both path compression and union by rank, the amortized time per operation is nearly O(1) (inverse Ackermann), which is crucial for handling large datasets efficiently. Also, discuss potential real-world applications like detecting cycles in financial transaction graphs, which is relevant to Robinhood's domain.

1. Clarify requirements and constraints

Ask about the number of elements, number of operations, and whether the graph is dynamic. Confirm if the queries are online or offline.

2. Design the data structure

Explain the parent array and rank/size array. Describe how find follows parent pointers to the root and how union attaches the smaller tree under the larger one.

3. Implement optimizations

Detail path compression in find (pointing nodes directly to the root) and union by rank/size to keep trees shallow. Discuss the combined effect on time complexity.

4. Process queries

For each connectivity query (u, v), call find(u) and find(v) and compare the roots. If equal, they are connected; otherwise, not.

5. Analyze complexity and edge cases

State the amortized time per operation and overall space. Mention edge cases like self-loops, duplicate unions, and large inputs.

Key Points to Mention

  • Path compression: flattening the tree during find to reduce future traversal time.
  • Union by rank/size: attaching the smaller tree under the larger to keep depth logarithmic.
  • Amortized time complexity: O(α(n)) per operation, where α is the inverse Ackermann function, effectively constant.
  • Space complexity: O(n) for parent and rank arrays.
  • Handling dynamic connectivity: Union-Find supports incremental unions but not deletions.
  • Real-world application: detecting connected components in networks, such as user transactions or social graphs.

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