Optiver·Data Scientist·Technical Phone Screen·Intermediate

Intermediate

Apr 2026

Summary

Interviewed for a Data Scientist role at Optiver and got hit with a pretty deep code equivalence problem. Not your typical ML or stats question, this was closer to something you'd see in a systems or algorithms round.

Questions Asked (1)

Given two short programs that each process an integer array of up to 100,000 elements, determine whether they are functionally equivalent for all valid inputs under specified preconditions (such as 32-bit signed arithmetic with overflow defined or prohibited). If not equivalent, produce a concrete counterexample. Also compare their time and space complexities, identify hidden behavioral differences like mutation, ordering stability, overflow, or integer division semantics, and design property-based tests and edge cases to validate your conclusion.

Algorithms & Data StructuresTechnical Trade-offs

Author's notes

This one genuinely surprised me coming from a data science interview.

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AI HintsAI Generated

Suggested Approach

Start by clarifying the exact preconditions and semantics (e.g., overflow behavior, mutation allowed, ordering stability) before analyzing the programs. Then systematically compare their logic, complexity, and edge-case behavior, using property-based tests and concrete counterexamples to validate equivalence or difference.

Pro tip: Demonstrate rigor by explicitly stating assumptions and testing them—interviewers at Optiver value candidates who proactively identify hidden behavioral differences like overflow and mutation, rather than just comparing algorithmic complexity.

1. Clarify preconditions and semantics

Ask about input constraints, overflow handling, mutation permissions, and ordering requirements to establish the exact equivalence criteria.

2. Analyze algorithmic logic and complexity

Compare the programs' time and space complexities, and identify any differences in algorithmic approach that could affect behavior.

3. Identify hidden behavioral differences

Examine mutation of inputs, ordering stability, overflow/underflow, integer division semantics, and other edge-case behaviors.

4. Design property-based tests and edge cases

Propose tests for empty arrays, single elements, duplicates, sorted/reverse-sorted, large values, and boundary conditions to validate equivalence.

5. Conclude and provide counterexample if needed

State whether the programs are equivalent; if not, give a concrete counterexample and explain the root cause.

Key Points to Mention

Overflow semantics: 32-bit signed arithmetic with overflow defined vs. prohibited (e.g., undefined behavior in C++).
Mutation of input array: whether the programs modify the array in-place or use extra space.
Ordering stability: if the programs sort or reorder elements, does the relative order of equal elements matter?
Integer division semantics: truncation toward zero vs. floor division, especially for negative numbers.
Time and space complexity: O(n) vs. O(n log n) etc., and constant factors that may matter for large n.
Property-based testing: using frameworks like Hypothesis or QuickCheck to generate random arrays and compare outputs.

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