1041 Robot Bounded In Circle.py

#!/usr/bin/python3
"""
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 <= 100
instructions[i] is in {'G', 'L', 'R'}
"""

dirs = [(-1, 0), (0, 1), (1, 0), (0, -1)]


class Solution:
    def isRobotBounded(self, instructions: str) -> bool:
        """
        LL: op
        LLL: R

        L, R 90 degree
        (GL) 90 needs 4 cycles to return back
        180 needs 2 cycles
        270 needs 4 cycles

        After 4 cycles, check whether the robot is at (0, 0)
        """
        x, y = 0, 0
        i = 0
        for _ in range(4):
            for cmd in instructions:
                if cmd == "G":
                    dx, dy = dirs[i]
                    x += dx
                    y += dy
                elif cmd == "L":
                    i = (i - 1) % 4
                else:
                    i = (i + 1) % 4
                    
        return x == 0 and y == 0