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Roblox·Software Engineer·Technical Phone Screen·Intermediate

Intermediate
Jul 2026

Summary

Roblox technical phone screen for a software engineering role, one algorithmic question about robot movement simulation. Pretty focused session, no fluff, just code and complexity analysis.

Questions Asked (1)

Q1

A robot starts at the origin facing north on an infinite 2D grid. It follows a command string of move-forward, turn-left, and turn-right instructions. Given that this string is repeated up to a billion times, implement a solution that (a) returns the robot's position and direction after one pass of the string, and (b) determines whether the robot's path stays bounded if the string repeats forever. What are your time and space complexities, and how do you avoid simulating all repetitions?

Algorithms & Data StructuresTechnical Trade-offs
Author's notes

The key insight I kept circling around was that you only need to simulate one cycle.

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AI HintsAI Generated

Suggested Approach

First, simulate one pass of the command string to compute the net displacement and final direction. Then, analyze the repeated behavior: if the robot returns to the origin or faces north after one pass, the path is bounded; otherwise, it's unbounded. This avoids simulating all repetitions and gives O(n) time and O(1) space.

Pro tip: Mention that the boundedness condition can be determined by checking if the robot's final direction is north or if it returns to the origin after one pass—this shows you understand the mathematical insight behind the problem.

1. Simulate one pass

Iterate through the command string once, updating the robot's position (x, y) and direction (dx, dy) based on each instruction.

2. Compute net displacement and final direction

After one pass, record the net displacement vector (x, y) and the final direction vector (dx, dy).

3. Determine boundedness

If the final direction is north (0,1), the path is bounded. If the net displacement is (0,0), the path is bounded. Otherwise, the path is unbounded.

4. Analyze complexity

Time complexity is O(n) for one pass, and space complexity is O(1). No need to simulate all repetitions.

Key Points to Mention

  • Simulating one pass is sufficient to determine the robot's state after any number of repetitions due to linearity.
  • The robot's path is bounded if and only if it returns to the origin after one pass or its final direction is north.
  • If the final direction is not north and the net displacement is non-zero, the robot will drift infinitely in some direction.
  • Time complexity: O(n) where n is the length of the command string; space complexity: O(1).
  • Avoid simulating up to a billion repetitions by using the mathematical properties of the movement.
  • Consider edge cases: empty string, commands that result in no net movement, etc.

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