Robot Bounded In Circle
On an infinite plane, a robot initially stands at (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; "R" : turn 90 degress to the right. The robot performs the instructions given in order, and repeats them forever. Return true if and only if there exists a circle in the plane such that the robot never leaves the circle. Example 1: Input: "GGLLGG" Output: true Explanation: The robot moves from (0,0) to (0,2), turns 180 degrees, and then returns to (0,0). When repeating these instructions, the robot remains in the circle of radius 2 centered at the origin. Example 2: Input: "GG" Output: false Explanation: The robot moves north indefinitely. Example 3: Input: "GL" Output: true Explanation: The robot moves from (0, 0) -> (0, 1) -> (-1, 1) -> (-1, 0) -> (0, 0) -> ... Note: 1 <= instructions.length <=