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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:**

<pre><code>Input: instructions = "GGLLGG"
<strong>Output:
</strong> true
<strong>Explanation:
</strong> 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.
</code></pre>

**Example 2:**

<pre><code>Input: instructions = "GG"
<strong>Output:
</strong> false
<strong>Explanation:
</strong> 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.
</code></pre>

**Example 3:**

<pre><code>Input: instructions = "GL"
<strong>Output:
</strong> true
<strong>Explanation:
</strong> 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.
</code></pre>

&#x20;

**Constraints:**

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