1041-robot-bounded-in-circle

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Description

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 degrees 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: instructions = "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: instructions = "GG"
Output: false
Explanation: The robot moves north indefinitely.

Example 3:

Input: instructions = "GL"
Output: true
Explanation: The robot moves from (0, 0) -> (0, 1) -> (-1, 1) -> (-1, 0) -> (0, 0) -> ...

 

Constraints:

  • 1 <= instructions.length <= 100
  • instructions[i] is 'G', 'L' or, 'R'.

Solution(Python)

class Solution:
    def isRobotBounded(self, instructions):
        x, y, dx, dy = 0, 0, 0, 1
        for i in instructions:
            if i == "R":
                dx, dy = dy, -dx
            if i == "L":
                dx, dy = -dy, dx
            if i == "G":
                x, y = x + dx, y + dy
        return (x, y) == (0, 0) or (dx, dy) != (0, 1)