# 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)``````