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Two Sigma·Software Engineer·Technical Phone Screen·Intermediate

IntermediatePrefer not to say
May 2026

Summary

Two Sigma SWE interview with a graph/pathfinding problem that looks deceptively simple until you realize it's a max-product path problem dressed up as a currency exchange puzzle. One question, but it had enough layers to keep me busy for the whole session.

Questions Asked (1)

Q1

Given a set of currencies and directed exchange rates between pairs, find the maximum amount of a target currency you can obtain from 1 unit of a starting currency by chaining any sequence of exchanges (no repeated currencies in a path). Return -1 if the target is unreachable.

Algorithms & Data StructuresTechnical Trade-offs
Author's notes

My first instinct was Dijkstra, which was wrong because you want to maximize a product, not minimize a sum.

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AI HintsAI Generated

Suggested Approach

Model the problem as a directed graph where nodes are currencies and edges are exchange rates. Use DFS with backtracking to explore all simple paths from the start to the target, keeping track of the maximum product of rates. If the target is unreachable, return -1.

Pro tip: Clarify whether negative cycles or arbitrage opportunities exist; if so, the problem becomes unbounded and you should discuss how to detect and handle them. Also, mention that using logarithms can transform multiplication into addition, but be cautious with precision.

1. Understand the problem

Restate the problem: find the maximum product of exchange rates along any simple path from start to target. Note that no repeated currencies are allowed, so paths are simple.

2. Choose the right algorithm

Since we need to explore all simple paths, use DFS with backtracking. For each path, compute the product of rates and update the maximum. Alternatively, use Bellman-Ford with logarithms if negative cycles are allowed, but simple paths require DFS.

3. Handle edge cases

Consider cases where start equals target (return 1), target is unreachable (return -1), or there are cycles that could lead to infinite profit (if repeated currencies were allowed, but they are not).

4. Optimize if needed

Discuss time complexity: O(V!) in the worst case for DFS, which is acceptable for small graphs. If the graph is large, consider pruning or using dynamic programming with bitmask for small V.

5. Test and validate

Walk through a small example to verify the approach. Mention potential pitfalls like floating-point precision and how to handle them (e.g., using rational numbers or epsilon comparisons).

Key Points to Mention

  • Graph representation: adjacency list or matrix for currencies and rates.
  • DFS with backtracking to explore all simple paths.
  • Tracking maximum product and updating it.
  • Handling unreachable target by returning -1.
  • Time complexity analysis and potential optimizations.
  • Floating-point precision issues and possible solutions.

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