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Two Sigma·Software Engineer·Technical Phone Screen·Intermediate

Intermediate
May 2026

Summary

Two Sigma software engineer interview with a grid-based traversal problem. The problem had enough edge cases to keep things interesting, and the DFS angle felt pretty standard for this type of company.

Questions Asked (1)

Q1

Given a grid representing a sewer or drain layout, determine whether water can flow from a source cell to a destination cell through connected pipes. Use DFS to traverse the grid, handle visited cells to prevent cycles, and explain how adjacency or connectivity is defined between cells.

Algorithms & Data StructuresSystem DesignTechnical Trade-offs
Author's notes

The connectivity definition part is what tripped me up a bit.

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AI HintsAI Generated

Suggested Approach

Clarify the grid representation and pipe connectivity rules, then explain a DFS-based traversal that marks visited cells to avoid cycles, and finally discuss complexity and potential optimizations. Emphasize correctness and edge cases.

Pro tip: Explicitly define the adjacency rules (e.g., pipe openings must align) and mention that DFS can be implemented iteratively to avoid stack overflow for large grids. Also, consider bidirectional flow if pipes allow it.

1. Clarify the problem

Ask about grid size, pipe types, and how connectivity is defined (e.g., based on pipe openings). Confirm if flow is directional or bidirectional.

2. Define adjacency

Explain that two adjacent cells are connected if their pipe openings align (e.g., a cell with a right opening connects to a cell with a left opening).

3. DFS traversal

Describe using DFS from the source, recursively or iteratively, visiting only connected neighbors. Mark cells as visited to prevent cycles.

4. Termination and result

If the destination is reached, return true; if DFS exhausts all reachable cells without finding it, return false.

5. Complexity and optimizations

Analyze time and space complexity (O(N) for N cells). Mention possible optimizations like early exit or using BFS for shortest path if needed.

Key Points to Mention

  • Definition of pipe connectivity based on openings (e.g., up, down, left, right).
  • Use of a visited set or 2D boolean array to avoid infinite loops.
  • DFS can be implemented recursively or iteratively (explicit stack).
  • Time and space complexity: O(rows * cols) time and space in worst case.
  • Handling of edge cases: source or destination out of bounds, no path, cycles.
  • Potential for bidirectional flow if pipes are undirected.

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