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1041. Robot Bounded In Circle

Medium

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'.

Solution

class Solution:
    def isRobotBounded(self, instructions: str) -> bool:
        coords = [0, 0]
        dir = [0, 1]

        for op in instructions:
            if op == "G":
                coords = list(map(sum, zip(coords, dir)))
            elif op == "L":
                dir = [-dir[1], dir[0]]
            elif op == "R":
                dir = [dir[1], -dir[0]]

        if coords == [0, 0] or dir != [0, 1]:
            return True

        return False