1041 Robot Bounded In Circle

On an infinite plane, a robot initially stands at (0, 0) and faces north. Note that:

• The north direction is the positive direction of the y-axis.
• The south direction is the negative direction of the y-axis.
• The east direction is the positive direction of the x-axis.
• The west direction is the negative direction of the x-axis.

The robot can receive one of three instructions:

• "G": go straight 1 unit.
• "L": turn 90 degrees to the left (i.e., anti-clockwise direction).
• "R": turn 90 degrees to the right (i.e., clockwise direction).

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 is initially at (0, 0) facing the north direction.
"G": move one step. Position: (0, 1). Direction: North.
"G": move one step. Position: (0, 2). Direction: North.
"L": turn 90 degrees anti-clockwise. Position: (0, 2). Direction: West.
"L": turn 90 degrees anti-clockwise. Position: (0, 2). Direction: South.
"G": move one step. Position: (0, 1). Direction: South.
"G": move one step. Position: (0, 0). Direction: South.
Repeating the instructions, the robot goes into the cycle:
(0, 0) --> (0, 1) --> (0, 2) --> (0, 1) --> (0, 0).
Based on that, we return true.

Example 2:

Input: instructions = "GG"
Output: false
Explanation: The robot is initially at (0, 0) facing the north direction.
"G": move one step. Position: (0, 1). Direction: North.
"G": move one step. Position: (0, 2). Direction: North.
Repeating the instructions, keeps advancing in the north direction
and does not go into cycles.
Based on that, we return false.

Example 3:

Input: instructions = "GL"
Output: true
Explanation: The robot is initially at (0, 0) facing the north direction.
"G": move one step. Position: (0, 1). Direction: North.
"L": turn 90 degrees anti-clockwise. Position: (0, 1). Direction: West.
"G": move one step. Position: (-1, 1). Direction: West.
"L": turn 90 degrees anti-clockwise. Position: (-1, 1). Direction: South.
"G": move one step. Position: (-1, 0). Direction: South.
"L": turn 90 degrees anti-clockwise. Position: (-1, 0). Direction: East.
"G": move one step. Position: (0, 0). Direction: East.
"L": turn 90 degrees anti-clockwise. Position: (0, 0). Direction: North.
Repeating the instructions, the robot goes into the cycle:
(0, 0) --> (0, 1) --> (-1, 1) --> (-1, 0) --> (0, 0).
Based on that, we return true.

Constraints:

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

 1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12
13
14
15

class Solution:
    def isRobotBounded(self, instructions: str) -> bool:
        x, y = 0, 0
        MOVES = [(0, 1), (1, 0), (0, -1), (-1, 0)]
        direction = 0
        for i in instructions:
            if i == 'G':
                move = MOVES[direction]
                x += move[0]
                y += move[1]
            elif i == 'R':
                direction = (direction + 1) % 4
            else:
                direction = (direction - 1) % 4
        return direction != 0 or (x == 0 and y == 0)