robot-bounded-in-circle.md

<p>On an infinite plane, a&nbsp;robot initially stands at <code>(0, 0)</code> and faces north.&nbsp;&nbsp;The robot can receive one of three instructions:</p>

<ul>
	<li><code>&quot;G&quot;</code>: go straight 1 unit;</li>
	<li><code>&quot;L&quot;</code>: turn 90 degrees to the left;</li>
	<li><code>&quot;R&quot;</code>: turn 90 degress to the right.</li>
</ul>

<p>The robot performs the <code>instructions</code> given in order, and repeats them forever.</p>

<p>Return <code>true</code> if and only if there exists a circle in the plane such that the robot never leaves the circle.</p>

<p>&nbsp;</p>

<p><strong>Example 1:</strong></p>

<pre>
<strong>Input: </strong>&quot;GGLLGG&quot;
<strong>Output: </strong>true
<strong>Explanation: </strong>
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.
</pre>

<p><strong>Example 2:</strong></p>

<pre>
<strong>Input: </strong>&quot;GG&quot;
<strong>Output: </strong>false
<strong>Explanation: </strong>
The robot moves north indefinitely.
</pre>

<p><strong>Example 3:</strong></p>

<pre>
<strong>Input: </strong>&quot;GL&quot;
<strong>Output: </strong>true
<strong>Explanation: </strong>
The robot moves from (0, 0) -&gt; (0, 1) -&gt; (-1, 1) -&gt; (-1, 0) -&gt; (0, 0) -&gt; ...
</pre>

<p>&nbsp;</p>

<p><strong>Note:</strong></p>

<ol>
	<li><code>1 &lt;= instructions.length &lt;= 100</code></li>
	<li><code>instructions[i]</code> is in <code>{&#39;G&#39;, &#39;L&#39;, &#39;R&#39;}</code></li>
</ol>