Robot Bounded In Circle

On an infinite plane, a robot initially stands at position (0, 0) and faces north. The robot can receive one of three instructions: "G" -- go straight 1 unit, "L" -- turn 90 degrees to the left, and "R" -- turn 90 degrees to the right. The robot performs the instructions given in order, and repeats them forever. Given the infinite string of instructions, determine whether the robot will be bounded within a circle of radius 1 centered at the origin.

class Solution {
  
  public: bool isRobotBounded(string instructions) {
    int x = 0, y = 0, dir = 0;
    for (char c : instructions) {
      if (c == 'G') {
        if (dir == 0) y++;
        if (dir == 1) x++;
        if (dir == 2) y--;
        if (dir == 3) x--;
      }
      else if (c == 'L') dir = (dir + 3) % 4;
      else dir = (dir + 1) % 4;
    }
    return x == 0 && y == 0 || dir != 0;
  }
}
;