Walking Robot Simulation

Walking Robot Simulation

What is this problem about?

The Walking Robot Simulation coding problem tasks you with navigating a robot on an infinite 2D grid. The robot starts at (0, 0) facing North. It receives a sequence of commands: move forward k units, turn left 90 degrees, or turn right 90 degrees. Additionally, there are obstacles on the grid. If the robot's path is blocked by an obstacle, it stays in its current position and moves to the next command. The goal is to find the maximum Euclidean distance squared from the origin that the robot ever reaches during its journey.

Why is this asked in interviews?

Companies like Apple, Google, and Amazon use this problem to test a candidate's ability to implement complex Simulation logic. It requires careful state management (tracking coordinates and direction) and efficient lookup of obstacles. It's an excellent test of "clean code" principles—how you structure your direction vectors and how you handle boundary conditions or obstacle detection without writing messy, repetitive code.

Algorithmic pattern used

This problem follows the Simulation and Hash Table interview pattern. To handle obstacles efficiently, instead of searching a list of obstacles every time the robot moves a step, you store the obstacle coordinates in a Hash Set. This allows for O(1) checks. For movement, using a direction array (e.g., dx = [0, 1, 0, -1] and dy = [1, 0, -1, 0]) simplifies turning: a right turn is just incrementing the direction index, and a left turn is decrementing it (with modulo math).

Example explanation

Suppose the robot is at (0,0) facing North (direction index 0). Commands: [4, -1, 3], Obstacles: [[0, 2]].

1. Command 4: Move North 4 steps.
   • Step 1: (0,1) - Clear.
   • Step 2: (0,2) - Obstacle! Stop at (0,1).
2. Command -1: Turn right. Now facing East.
3. Command 3: Move East 3 steps.
   • Step 1: (1,1) - Clear.
   • Step 2: (2,1) - Clear.
   • Step 3: (3,1) - Clear. Max distance squared reached was at (3,1), which is 3^2 + 1^2 = 10.

Common mistakes candidates make

One major pitfall is checking for obstacles incorrectly—for example, only checking the final destination of a move command rather than every step along the way. Another mistake is inefficiently storing obstacles in a list and using linear search, which leads to time limit exceeded (TLE) errors. Finally, improper handling of negative coordinates in hash functions or custom set implementations can cause bugs.

Interview preparation tip

Master the "Direction Vector" technique. Instead of using multiple if-else blocks for "North", "South", etc., use an array to represent the changes in x and y. This makes your code more extensible and much easier to debug during a high-pressure interview.