1041. Robot Bounded In Circle

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. 1 <= instructions.length <= 100
2. instructions[i] is in {'G', 'L', 'R'}

# @lc code=start
using LeetCode

function is_robot_bounded(instructions::String)::Bool
    pos = CartesianIndex(0, 0)
    dirs = CartesianIndex.([(0, 1), (1, 0), (0, -1), (-1, 0)])
    st = 1
    for ch in instructions
        if ch == 'G'
            pos += dirs[st]
        else
            st = mod1(st + (ch == 'R' ? 1 : -1), 4)
        end
    end
    return pos.I == (0, 0) || st != 1
end
# @lc code=end

is_robot_bounded (generic function with 1 method)

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