Openai·Machine Learning Engineer·Technical Phone Screen·Senior

SeniorPrefer not to say

Jul 2026

Summary

Interviewed for an ML Engineer role at OpenAI and got hit with a systems-flavored coding problem that I wasn't expecting to go as deep as it did. The dependency resolution angle made it feel more like a compiler or package manager design question than a pure algo problem.

Questions Asked (1)

Given a list of packages where each package has a set of dependencies (potentially with version ranges), write an algorithm to find a valid installation order or determine that no valid order exists. Be prepared to discuss how you'd handle dependency cycles, diamond dependencies, and version constraint conflicts.

Algorithms & Data StructuresSystem DesignTechnical Trade-offs

Author's notes

I started with topological sort which felt right, but then they kept pushing on version ranges and I realized I'd basically been ignoring half the problem.

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AI HintsAI Generated

Suggested Approach

Model the packages and dependencies as a directed graph, then use topological sorting to find a valid installation order. For version constraints, incorporate constraint satisfaction (e.g., backtracking or SAT solving) to resolve conflicts. Discuss cycle detection and how to handle diamond dependencies by merging constraints.

Pro tip: Emphasize that real-world package managers use a combination of topological sorting and constraint solving, and that cycles are often broken by allowing multiple versions or using virtual packages. Mention that in ML environments, reproducibility often requires locking versions, so conflict resolution is critical.

1. Model the problem

Represent packages as nodes and dependencies as directed edges, with version constraints as labels on edges. Clarify that a valid order must satisfy all constraints.

2. Detect cycles

Use DFS or Kahn's algorithm to detect cycles. If a cycle exists, determine if it can be resolved by selecting compatible versions or if it's a true circular dependency.

3. Resolve version constraints

For each package, collect all version constraints from dependents and find a version that satisfies all. If none exists, report a conflict.

4. Topological sort with constraints

Perform a topological sort on the dependency graph, ensuring that when a package is installed, all its dependencies are already installed with compatible versions.

5. Handle conflicts and backtrack

If a conflict arises during sorting, backtrack and try alternative version selections. If no solution exists, report that no valid order exists.

Key Points to Mention

Topological sorting (Kahn's algorithm or DFS) for ordering.
Cycle detection and how to handle cycles (e.g., breaking cycles by allowing multiple versions or reporting error).
Diamond dependencies: merging constraints from multiple paths to find a common version.
Version constraint satisfaction: using backtracking, SAT solvers, or PubGrub algorithm.
Trade-offs: completeness vs. performance, and how real package managers (pip, npm) handle it.
Reproducibility: locking versions and generating a lock file.

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