## 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 degrees 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: instructions = "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: instructions = "GG"
Output: false
Explanation: The robot moves north indefinitely.```

Example 3:

```Input: instructions = "GL"
Output: true
Explanation: The robot moves from (0, 0) -> (0, 1) -> (-1, 1) -> (-1, 0) -> (0, 0) -> ...```

Constraints:

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

## Rust Solution

``````struct Solution;

impl Solution {
fn is_robot_bounded(instructions: String) -> bool {
let mut x = 0;
let mut y = 0;
let mut i = 0;
let d = [[1, 0], [0, 1], [-1, 0], [0, -1]];
for c in instructions.chars() {
match c {
'G' => {
x += d[i];
y += d[i];
}
'L' => {
i = (i + 1) % 3;
}
'R' => {
i = (i + 3) % 3;
}
_ => (),
}
}
x == 0 && y == 0 || i != 0
}
}

#[test]
fn test() {
assert_eq!(Solution::is_robot_bounded("GGLLGG".to_string()), true);
assert_eq!(Solution::is_robot_bounded("GG".to_string()), false);
assert_eq!(Solution::is_robot_bounded("GL".to_string()), true);
}
``````

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