design-front-middle-back-queue

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Algorithms

Design a queue that supports <code>push</code> and <code>pop</code> operations in the front, middle, and back.

Implement the <code>FrontMiddleBack</code> class:

<ul>
	<li><code>FrontMiddleBack()</code> Initializes the queue.</li>
	<li><code>void pushFront(int val)</code> Adds <code>val</code> to the front of the queue.</li>
	<li><code>void pushMiddle(int val)</code> Adds <code>val</code> to the middle of the queue.</li>
	<li><code>void pushBack(int val)</code> Adds <code>val</code> to the back of the queue.</li>
	<li><code>int popFront()</code> Removes the front element of the queue and returns it. If the queue is empty, return <code>-1</code>.</li>
	<li><code>int popMiddle()</code> Removes the middle element of the queue and returns it. If the queue is empty, return <code>-1</code>.</li>
	<li><code>int popBack()</code> Removes the back element of the queue and returns it. If the queue is empty, return <code>-1</code>.</li>
</ul>

Notice that when there are two middle position choices, the operation is performed on the frontmost middle position choice. For example:

<ul>
	<li>Pushing <code>6</code> into the middle of <code>[1, 2, 3, 4, 5]</code> results in <code>[1, 2, 6, 3, 4, 5]</code>.</li>
	<li>Popping the middle from <code>[1, 2, 3, 4, 5, 6]</code> returns <code>3</code> and results in <code>[1, 2, 4, 5, 6]</code>.</li>
</ul>

&nbsp;
Example 1:

<pre>
Input:
[&quot;FrontMiddleBackQueue&quot;, &quot;pushFront&quot;, &quot;pushBack&quot;, &quot;pushMiddle&quot;, &quot;pushMiddle&quot;, &quot;popFront&quot;, &quot;popMiddle&quot;, &quot;popMiddle&quot;, &quot;popBack&quot;, &quot;popFront&quot;]
[[], [1], [2], [3], [4], [], [], [], [], []]
Output:
[null, null, null, null, null, 1, 3, 4, 2, -1]

Explanation:
FrontMiddleBackQueue q = new FrontMiddleBackQueue();
q.pushFront(1); // [1]
q.pushBack(2); // [1, 2]
q.pushMiddle(3); // [1, 3, 2]
q.pushMiddle(4); // [1, 4, 3, 2]
q.popFront(); // return 1 -&gt; [4, 3, 2]
q.popMiddle(); // return 3 -&gt; [4, 2]
q.popMiddle(); // return 4 -&gt; [2]
q.popBack(); // return 2 -&gt; []
q.popFront(); // return -1 -&gt; [] (The queue is empty)
</pre>

&nbsp;
Constraints:

<ul>
	<li><code>1 &lt;= val &lt;= 109</code></li>
	<li>At most&nbsp;<code>1000</code>&nbsp;calls will be made to&nbsp;<code>pushFront</code>,&nbsp;<code>pushMiddle</code>,&nbsp;<code>pushBack</code>, <code>popFront</code>, <code>popMiddle</code>, and <code>popBack</code>.</li>
</ul>