robot-bounded-in-circle

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1041. Robot Bounded In Circle (Medium)

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. 1 <= instructions.length <= 100
2. instructions[i] is in {'G', 'L', 'R'}

Related Topics

[Math]

Hints

Hint 1

Calculate the final vector of how the robot travels after executing all instructions once - it consists of a change in position plus a change in direction.

Hint 2

The robot stays in the circle iff (looking at the final vector) it changes direction (ie. doesn't stay pointing north), or it moves 0.