1041.RobotBoundedInCircle.py

"""
    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:
    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:
    Input: "GG"
    Output: false
    Explanation: 
    The robot moves north indefinitely.

    Example:
    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'}
"""
#Difficulty: Medium
#110 / 110 test cases passed.
#Runtime: 28 ms
#Memory Usage: 13.8 MB

#Runtime: 28 ms, faster than 82.06% of Python3 online submissions for Robot Bounded In Circle.
#Memory Usage: 13.8 MB, less than 62.31% of Python3 online submissions for Robot Bounded In Circle.

class Solution:
    def isRobotBounded(self, instructions: str) -> bool:
        x, y = 0, 0
        direction = 'N'
        directions = {'N' : ['W', 'E'], 'S' : ['E', 'W'], 'E' : ['N', 'S'],'W' : ['S', 'N']}
        positions = {'N' : [0, 1], 'S' : [0, -1], 'E' : [1, 0], 'W' : [-1, 0]}
        for instruction in instructions:
            if instruction == 'L':
                direction = directions[direction][0]
            elif instruction == 'R':
                direction = directions[direction][1]
            else:
                x += positions[direction][0]
                y += positions[direction][1]
        return direction != 'N' or x == y == 0