1041. 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.

My idea：循环一次后面北且有位移返回FALSE

class Solution:
    def isRobotBounded(self, instructions: str) -> bool:
        # 仅当循环一次后方向仍向北且有位移才不会困于环中，不然循环四次之后都会达到同一个状态(同方向，同坐标）
        x, y = 0, 0
        dx, dy = 0, 1
        for ins in instructions:
            if ins == 'L':
                dx, dy = -dy, dx
            elif ins == 'R':
                dx, dy = dy, -dx
            else:
                x, y = x+dx, y+dy
        return (dx, dy) != (0, 1) or (x, y) == (0, 0)

学习一下方向的这种写法，其实是向量，这样容易理解