Simulate robot path and detect boundedness
Company: Roblox
Role: Software Engineer
Category: Coding & Algorithms
Difficulty: Medium
Interview Round: Onsite
A robot starts at (0,
0) facing north on an infinite 2D plane. It executes a command string s consisting of 'G' (move forward one unit), 'L' (turn left 90°), and 'R' (turn right 90°). After finishing s once, the robot repeats the same string k times, where k can be as large as 10^9. Implement an algorithm that
(a) returns the robot’s final position and facing direction after one execution of s, and
(b) determines whether the trajectory remains within a bounded region if s is repeated indefinitely. Provide time and space complexity and avoid simulating all k repetitions.
Quick Answer: This question evaluates the ability to simulate iterative movement and reason about repeated state transformations, testing competencies in algorithm design, cycle detection, and geometric reasoning; it falls under the Coding & Algorithms category.