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Optiver·Software Engineer·Technical Phone Screen·Intermediate

Intermediate
Jul 2026

Summary

Optiver Software Engineer interview with a single algorithmic problem that looked manageable on the surface but had a lot of edge cases stacked on top of each other. The problem combined parsing, graph validation, and tree serialization all in one, which made it more of a gauntlet than a typical coding question.

Questions Asked (1)

Q1

Given a string of parent-child pairs describing a binary tree (e.g. "(A,B) (B,C) (A,D)"), validate the input format and graph structure, then either print the tree's S-expression or the highest-priority error code among: invalid format, duplicate pair, node with more than 2 children, multiple roots, or cycle/multiple parents.

Algorithms & Data StructuresTechnical Trade-offs
Author's notes

This one took me a while to fully unpack.

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AI HintsAI Generated

Suggested Approach

First, clarify the exact input format and error priority order with the interviewer, then outline a two-phase algorithm: parse and validate the string format, then build the graph while checking structural constraints. Finally, if no errors, reconstruct the tree and print its S-expression, ensuring you handle edge cases like empty input or single node.

Pro tip: Explicitly state the error priority order and confirm it with the interviewer before coding; this shows you understand the importance of requirements clarification and prevents wasted effort on the wrong error.

1. Clarify requirements and edge cases

Ask about the exact format (spaces, parentheses, commas), error priority order, and what to do with empty input or single node. Confirm the definition of a valid S-expression.

2. Parse and validate format

Use a regex or manual parser to check each pair matches the expected pattern. If any pair fails, return 'invalid format' immediately.

3. Build graph and check structural errors

Iterate through pairs, tracking children per parent, parents per child, and detecting duplicate pairs. Check for >2 children, multiple parents (cycle), and multiple roots in the correct priority order.

4. Reconstruct and print S-expression

If no errors, find the root (node with no parent) and recursively build the S-expression. Handle the case of a single node (no pairs) by printing just the node.

Key Points to Mention

  • Error priority order: invalid format > duplicate pair > >2 children > multiple roots > cycle/multiple parents
  • Use of hash maps to track children and parents for efficient validation
  • Handling of edge cases: empty input, single node, disconnected components
  • Time and space complexity: O(n) for n pairs, with O(n) space for maps
  • Recursive vs iterative S-expression construction and potential stack overflow for deep trees
  • Importance of clarifying ambiguous format details (e.g., spaces, case sensitivity) before implementation

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