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<!DOCTYPE html>

<head>

<title>Queue Data Structure</title>

window.dataLayer = window.dataLayer || [];

function gtag() { dataLayer.push(arguments); }

gtag('js', new Date());

gtag('config', 'G-HCERBDV76D');

</script>

</head>

<body>

<nav>

Python Tutorial

</a>

</div>

<span>

</span>

<span>

</span>

<span>

</span>

</div>

</div>

<li>

Home

</a>

</li>

<li>

Projects

</a>

</li>

<li>

Free Course

</a>

</li>

<li>

DSA

</a>

</li>

</ul>

</div>

</nav>

</div>

<h3>Page Index</h3>

<ul>

<li><a href="/dsa.html#data-structure-1" title="Data Structures (I)">Data Structures

(I)</a></li>

<li><a href="/dsa.html#data-structure-2" title="Data Structures (II)">Data Structures

(II)</a></li>

<li><a href="/dsa.html#tree-1" title="Tree based DSA (I)">Tree based DSA (I)</a></li>

<li><a href="/dsa.html#tree-2" title="Tree based DSA (II)">Tree based DSA (II)</a></li>

<li><a href="/dsa.html#graph" title="Graph Data Structures and Algorithm">Graph based

DSA</a></li>

<li><a href="/dsa.html#sorting-searching" title="Sorting and Searching">Sorting and

Searching</a></li>

<li><a href="/dsa.html#greedy-algorithm" title="Greedy Algorithms">Greedy Algorithms</a>

</li>

<li><a href="/dsa.html#dynamic-programming" title="Dynamic Programming">Dynamic

Programming</a></li>

<li><a href="/dsa.html#other-algorithms" title="Other Algorithms">Other Algorithms</a>

</li>

</ul>

</div>

<h1>Queue Data Structure</h1>

<p class="editor-contents__short-description">In this tutorial, you will learn what a queue is. Also, you will find implementation of queue in C, C++, Java and Python.</p>

<p id="introduction">A queue is a useful data structure in programming. It is similar to the ticket queue outside a cinema hall, where the first person entering the queue is the first person who gets the ticket.</p>

<p>Queue follows the <strong>First In First Out (FIFO)</strong> rule - the item that goes in first is the item that comes out first.</p>

<figure><img alt="Representation of Queue in first in first out principle" src="//cdn.programiz.com/sites/tutorial2program/files/queue.png" title="Queue" width="946" height="147"><figcaption>FIFO Representation of Queue</figcaption></figure><p>In the above image, since 1 was kept in the queue before 2, it is the first to be removed from the queue as well. It follows the <strong>FIFO</strong> rule.</p>

<p>In programming terms, putting items in the queue is called <strong>enqueue</strong>, and removing items from the queue is called <strong>dequeue</strong>.</p>

<p>We can implement the queue in any programming language like C, C++, Java, Python or C#, but the specification is pretty much the same.</p>

<hr><h2 id="spec">Basic Operations of Queue</h2>

<p>A queue is an object (an abstract data structure - ADT) that allows the following operations:</p>

<ul><li><strong>Enqueue</strong>: Add an element to the end of the queue</li>

<li><strong>Dequeue</strong>: Remove an element from the front of the queue</li>

<li><strong>IsEmpty</strong>: Check if the queue is empty</li>

<li><strong>IsFull</strong>: Check if the queue is full</li>

<li><strong>Peek</strong>: Get the value of the front of the queue without removing it</li>

</ul><hr><h2 id="working">Working of Queue</h2>

<p>Queue operations work as follows:</p>

<ul><li>two pointers <var>FRONT</var> and <var>REAR</var></li>

<li><var>FRONT</var> track the first element of the queue</li>

<li><var>REAR</var> track the last element of the queue</li>

<li>initially, set value of <var>FRONT</var> and <var>REAR</var> to -1</li>

</ul><h3>Enqueue Operation</h3>

<ul><li>check if the queue is full</li>

<li>for the first element, set the value of <var>FRONT</var> to 0</li>

<li>increase the <var>REAR</var> index by 1</li>

<li>add the new element in the position pointed to by <var>REAR</var></li>

</ul><h3>Dequeue Operation</h3>

<ul><li>check if the queue is empty</li>

<li>return the value pointed by <var>FRONT</var></li>

<li>increase the <var>FRONT</var> index by 1</li>

<li>for the last element, reset the values of <var>FRONT</var> and <var>REAR</var> to -1</li>

</ul><figure><img alt="Demonstrating how front and rear indexes are modified during enqueue and dequeue operations" src="//cdn.programiz.com/sites/tutorial2program/files/Queue-program-enqueue-dequeue.png" title="Working of queue operations" width="432" height="1396"><figcaption>Enqueue and Dequeue Operations</figcaption></figure><hr><h2 id="code">Queue Implementations in Python, Java, C, and C++</h2>

<p></p><div class="clearfix"></div><p>We usually use arrays to implement queues in Java and C/++. In the case of Python, we use lists.</p>

<div id="py1" onclick="changepy()" class="tabbed-editor__node tabbed-editor__node--active"><a href="#python-code">Python</a></div>

</div>

<div class="pre-code-wrapper"><div title="Click to copy" class="copy-code-button"></div><pre class="exec" style="max-height: 600px;"><code class="python hljs"><span class="hljs-comment"># Queue implementation in Python</span>

<span class="hljs-class"><span class="hljs-keyword">class</span> <span class="hljs-title">Queue</span>:</span>

self.queue = []

<span class="hljs-comment"># Add an element</span>

<span class="hljs-function"><span class="hljs-keyword">def</span> <span class="hljs-title">enqueue</span><span class="hljs-params">(self, item)</span>:</span>

self.queue.append(item)

<span class="hljs-comment"># Remove an element</span>

<span class="hljs-function"><span class="hljs-keyword">def</span> <span class="hljs-title">dequeue</span><span class="hljs-params">(self)</span>:</span>

<span class="hljs-keyword">if</span> len(self.queue) < <span class="hljs-number">1</span>:

<span class="hljs-keyword">return</span> <span class="hljs-literal">None</span>

<span class="hljs-keyword">return</span> self.queue.pop(<span class="hljs-number">0</span>)

<span class="hljs-comment"># Display the queue</span>

<span class="hljs-function"><span class="hljs-keyword">def</span> <span class="hljs-title">display</span><span class="hljs-params">(self)</span>:</span>

<span class="hljs-keyword">print</span>(self.queue)

<span class="hljs-keyword">return</span> len(self.queue)

q = Queue()

q.enqueue(<span class="hljs-number">1</span>)

q.enqueue(<span class="hljs-number">2</span>)

q.enqueue(<span class="hljs-number">3</span>)

q.enqueue(<span class="hljs-number">4</span>)

q.enqueue(<span class="hljs-number">5</span>)

q.display()

q.dequeue()

<span class="hljs-keyword">print</span>(<span class="hljs-string">"After removing an element"</span>)

q.display()

</code></pre></div>

</div>

<div class="pre-code-wrapper"><div title="Click to copy" class="copy-code-button"></div><pre class="exec" style="max-height: 600px;"><code class="java hljs"><span class="hljs-comment">// Queue implementation in Java</span>

<span class="hljs-keyword">public</span> <span class="hljs-class"><span class="hljs-keyword">class</span> <span class="hljs-title">Queue</span> </span>{

<span class="hljs-keyword">int</span> SIZE = <span class="hljs-number">5</span>;

<span class="hljs-keyword">int</span> items[] = <span class="hljs-keyword">new</span> <span class="hljs-keyword">int</span>[SIZE];

<span class="hljs-keyword">int</span> front, rear;

Queue() {

front = -<span class="hljs-number">1</span>;

rear = -<span class="hljs-number">1</span>;

}

<span class="hljs-function"><span class="hljs-keyword">boolean</span> <span class="hljs-title">isFull</span><span class="hljs-params">()</span> </span>{

<span class="hljs-keyword">if</span> (front == <span class="hljs-number">0</span> && rear == SIZE - <span class="hljs-number">1</span>) {

<span class="hljs-keyword">return</span> <span class="hljs-keyword">true</span>;

}

<span class="hljs-keyword">return</span> <span class="hljs-keyword">false</span>;

}

<span class="hljs-function"><span class="hljs-keyword">boolean</span> <span class="hljs-title">isEmpty</span><span class="hljs-params">()</span> </span>{

<span class="hljs-keyword">if</span> (front == -<span class="hljs-number">1</span>)

<span class="hljs-keyword">return</span> <span class="hljs-keyword">true</span>;

<span class="hljs-keyword">return</span> <span class="hljs-keyword">false</span>;

}

<span class="hljs-function"><span class="hljs-keyword">void</span> <span class="hljs-title">enQueue</span><span class="hljs-params">(<span class="hljs-keyword">int</span> element)</span> </span>{

<span class="hljs-keyword">if</span> (isFull()) {

System.out.println(<span class="hljs-string">"Queue is full"</span>);

} <span class="hljs-keyword">else</span> {

<span class="hljs-keyword">if</span> (front == -<span class="hljs-number">1</span>)

front = <span class="hljs-number">0</span>;

rear++;

items[rear] = element;

System.out.println(<span class="hljs-string">"Inserted "</span> + element);

}

<span class="hljs-function"><span class="hljs-keyword">int</span> <span class="hljs-title">deQueue</span><span class="hljs-params">()</span> </span>{

<span class="hljs-keyword">int</span> element;

<span class="hljs-keyword">if</span> (isEmpty()) {

System.out.println(<span class="hljs-string">"Queue is empty"</span>);

<span class="hljs-keyword">return</span> (-<span class="hljs-number">1</span>);

} <span class="hljs-keyword">else</span> {

element = items[front];

<span class="hljs-keyword">if</span> (front >= rear) {

front = -<span class="hljs-number">1</span>;

rear = -<span class="hljs-number">1</span>;

} <span class="hljs-comment">/* Q has only one element, so we reset the queue after deleting it. */</span>

<span class="hljs-keyword">else</span> {

front++;

}

System.out.println(<span class="hljs-string">"Deleted -> "</span> + element);

<span class="hljs-keyword">return</span> (element);

}

<span class="hljs-function"><span class="hljs-keyword">void</span> <span class="hljs-title">display</span><span class="hljs-params">()</span> </span>{

<span class="hljs-comment">/* Function to display elements of Queue */</span>

<span class="hljs-keyword">int</span> i;

<span class="hljs-keyword">if</span> (isEmpty()) {

System.out.println(<span class="hljs-string">"Empty Queue"</span>);

} <span class="hljs-keyword">else</span> {

System.out.println(<span class="hljs-string">"\nFront index-> "</span> + front);

System.out.println(<span class="hljs-string">"Items -> "</span>);

<span class="hljs-keyword">for</span> (i = front; i <= rear; i++)

System.out.print(items[i] + <span class="hljs-string">" "</span>);

System.out.println(<span class="hljs-string">"\nRear index-> "</span> + rear);

}

<span class="hljs-function"><span class="hljs-keyword">public</span> <span class="hljs-keyword">static</span> <span class="hljs-keyword">void</span> <span class="hljs-title">main</span><span class="hljs-params">(String[] args)</span> </span>{

Queue q = <span class="hljs-keyword">new</span> Queue();

<span class="hljs-comment">// deQueue is not possible on empty queue</span>

q.deQueue();

<span class="hljs-comment">// enQueue 5 elements</span>

q.enQueue(<span class="hljs-number">1</span>);

q.enQueue(<span class="hljs-number">2</span>);

q.enQueue(<span class="hljs-number">3</span>);

q.enQueue(<span class="hljs-number">4</span>);

q.enQueue(<span class="hljs-number">5</span>);

<span class="hljs-comment">// 6th element can't be added to because the queue is full</span>

q.enQueue(<span class="hljs-number">6</span>);

q.display();

<span class="hljs-comment">// deQueue removes element entered first i.e. 1</span>

q.deQueue();

<span class="hljs-comment">// Now we have just 4 elements</span>

q.display();

}

}</code></pre></div>

</div>

<div class="pre-code-wrapper"><div title="Click to copy" class="copy-code-button"></div><pre class="exec" style="max-height: 600px;"><code class="c hljs cpp"><span class="hljs-comment">// Queue implementation in C</span>

<span class="hljs-meta">#<span class="hljs-meta-keyword">include</span> <span class="hljs-meta-string"><stdio.h></span></span>

<span class="hljs-meta">#<span class="hljs-meta-keyword">define</span> SIZE 5</span>

<span class="hljs-function"><span class="hljs-keyword">void</span> <span class="hljs-title">enQueue</span><span class="hljs-params">(<span class="hljs-keyword">int</span>)</span></span>;

<span class="hljs-function"><span class="hljs-keyword">void</span> <span class="hljs-title">deQueue</span><span class="hljs-params">()</span></span>;

<span class="hljs-function"><span class="hljs-keyword">void</span> <span class="hljs-title">display</span><span class="hljs-params">()</span></span>;

<span class="hljs-keyword">int</span> items[SIZE], front = <span class="hljs-number">-1</span>, rear = <span class="hljs-number">-1</span>;

<span class="hljs-function"><span class="hljs-keyword">int</span> <span class="hljs-title">main</span><span class="hljs-params">()</span> </span>{

<span class="hljs-comment">//deQueue is not possible on empty queue</span>

deQueue();

<span class="hljs-comment">//enQueue 5 elements</span>

enQueue(<span class="hljs-number">1</span>);

enQueue(<span class="hljs-number">2</span>);

enQueue(<span class="hljs-number">3</span>);

enQueue(<span class="hljs-number">4</span>);

enQueue(<span class="hljs-number">5</span>);

<span class="hljs-comment">// 6th element can't be added to because the queue is full</span>

enQueue(<span class="hljs-number">6</span>);

display();

<span class="hljs-comment">//deQueue removes element entered first i.e. 1</span>

deQueue();

<span class="hljs-comment">//Now we have just 4 elements</span>

display();

<span class="hljs-keyword">return</span> <span class="hljs-number">0</span>;

}

<span class="hljs-function"><span class="hljs-keyword">void</span> <span class="hljs-title">enQueue</span><span class="hljs-params">(<span class="hljs-keyword">int</span> value)</span> </span>{

<span class="hljs-keyword">if</span> (rear == SIZE - <span class="hljs-number">1</span>)

<span class="hljs-built_in">printf</span>(<span class="hljs-string">"\nQueue is Full!!"</span>);

<span class="hljs-keyword">else</span> {

<span class="hljs-keyword">if</span> (front == <span class="hljs-number">-1</span>)

front = <span class="hljs-number">0</span>;

rear++;

items[rear] = value;

<span class="hljs-built_in">printf</span>(<span class="hljs-string">"\nInserted -> %d"</span>, value);

}

<span class="hljs-function"><span class="hljs-keyword">void</span> <span class="hljs-title">deQueue</span><span class="hljs-params">()</span> </span>{

<span class="hljs-keyword">if</span> (front == <span class="hljs-number">-1</span>)

<span class="hljs-built_in">printf</span>(<span class="hljs-string">"\nQueue is Empty!!"</span>);

<span class="hljs-keyword">else</span> {

<span class="hljs-built_in">printf</span>(<span class="hljs-string">"\nDeleted : %d"</span>, items[front]);

front++;

<span class="hljs-keyword">if</span> (front > rear)

front = rear = <span class="hljs-number">-1</span>;

}

<span class="hljs-comment">// Function to print the queue</span>

<span class="hljs-function"><span class="hljs-keyword">void</span> <span class="hljs-title">display</span><span class="hljs-params">()</span> </span>{

<span class="hljs-keyword">if</span> (rear == <span class="hljs-number">-1</span>)

<span class="hljs-built_in">printf</span>(<span class="hljs-string">"\nQueue is Empty!!!"</span>);

<span class="hljs-keyword">else</span> {

<span class="hljs-keyword">int</span> i;

<span class="hljs-built_in">printf</span>(<span class="hljs-string">"\nQueue elements are:\n"</span>);

<span class="hljs-keyword">for</span> (i = front; i <= rear; i++)

<span class="hljs-built_in">printf</span>(<span class="hljs-string">"%d "</span>, items[i]);

}

<span class="hljs-built_in">printf</span>(<span class="hljs-string">"\n"</span>);

}</code></pre></div>

</div>

<div class="pre-code-wrapper"><div title="Click to copy" class="copy-code-button"></div><pre class="exec" style="max-height: 600px;"><code class="cpp hljs"><span class="hljs-comment">// Queue implementation in C++</span>

<span class="hljs-meta">#<span class="hljs-meta-keyword">include</span> <span class="hljs-meta-string"><iostream></span></span>

<span class="hljs-meta">#<span class="hljs-meta-keyword">define</span> SIZE 5</span>

<span class="hljs-keyword">using</span> <span class="hljs-keyword">namespace</span> <span class="hljs-built_in">std</span>;

<span class="hljs-class"><span class="hljs-keyword">class</span> <span class="hljs-title">Queue</span> {</span>

<span class="hljs-keyword">private</span>:

<span class="hljs-keyword">int</span> items[SIZE], front, rear;

<span class="hljs-keyword">public</span>:

Queue() {

front = <span class="hljs-number">-1</span>;

rear = <span class="hljs-number">-1</span>;

}

<span class="hljs-function"><span class="hljs-keyword">bool</span> <span class="hljs-title">isFull</span><span class="hljs-params">()</span> </span>{

<span class="hljs-keyword">if</span> (front == <span class="hljs-number">0</span> && rear == SIZE - <span class="hljs-number">1</span>) {

<span class="hljs-keyword">return</span> <span class="hljs-literal">true</span>;

}

<span class="hljs-keyword">return</span> <span class="hljs-literal">false</span>;

}

<span class="hljs-function"><span class="hljs-keyword">bool</span> <span class="hljs-title">isEmpty</span><span class="hljs-params">()</span> </span>{

<span class="hljs-keyword">if</span> (front == <span class="hljs-number">-1</span>)

<span class="hljs-keyword">return</span> <span class="hljs-literal">true</span>;

<span class="hljs-keyword">return</span> <span class="hljs-literal">false</span>;

}

<span class="hljs-function"><span class="hljs-keyword">void</span> <span class="hljs-title">enQueue</span><span class="hljs-params">(<span class="hljs-keyword">int</span> element)</span> </span>{

<span class="hljs-keyword">if</span> (isFull()) {

<span class="hljs-built_in">cout</span> << <span class="hljs-string">"Queue is full"</span>;

} <span class="hljs-keyword">else</span> {

<span class="hljs-keyword">if</span> (front == <span class="hljs-number">-1</span>) front = <span class="hljs-number">0</span>;

rear++;

items[rear] = element;

<< <span class="hljs-string">"Inserted "</span> << element << <span class="hljs-built_in">endl</span>;

}

<span class="hljs-function"><span class="hljs-keyword">int</span> <span class="hljs-title">deQueue</span><span class="hljs-params">()</span> </span>{

<span class="hljs-keyword">int</span> element;

<span class="hljs-keyword">if</span> (isEmpty()) {

<span class="hljs-built_in">cout</span> << <span class="hljs-string">"Queue is empty"</span> << <span class="hljs-built_in">endl</span>;

<span class="hljs-keyword">return</span> (<span class="hljs-number">-1</span>);

} <span class="hljs-keyword">else</span> {

element = items[front];

<span class="hljs-keyword">if</span> (front >= rear) {

front = <span class="hljs-number">-1</span>;

rear = <span class="hljs-number">-1</span>;

} <span class="hljs-comment">/* Q has only one element, so we reset the queue after deleting it. */</span>

<span class="hljs-keyword">else</span> {

front++;

}

<< <span class="hljs-string">"Deleted -> "</span> << element << <span class="hljs-built_in">endl</span>;

<span class="hljs-keyword">return</span> (element);

}

<span class="hljs-function"><span class="hljs-keyword">void</span> <span class="hljs-title">display</span><span class="hljs-params">()</span> </span>{

<span class="hljs-comment">/* Function to display elements of Queue */</span>

<span class="hljs-keyword">int</span> i;

<span class="hljs-keyword">if</span> (isEmpty()) {

<< <span class="hljs-string">"Empty Queue"</span> << <span class="hljs-built_in">endl</span>;

} <span class="hljs-keyword">else</span> {

<< <span class="hljs-string">"Front index-> "</span> << front;

<< <span class="hljs-string">"Items -> "</span>;

<span class="hljs-keyword">for</span> (i = front; i <= rear; i++)

<span class="hljs-built_in">cout</span> << items[i] << <span class="hljs-string">" "</span>;

<< <span class="hljs-string">"Rear index-> "</span> << rear << <span class="hljs-built_in">endl</span>;

}

};

<span class="hljs-function"><span class="hljs-keyword">int</span> <span class="hljs-title">main</span><span class="hljs-params">()</span> </span>{

Queue q;

<span class="hljs-comment">//deQueue is not possible on empty queue</span>

q.deQueue();

<span class="hljs-comment">//enQueue 5 elements</span>

q.enQueue(<span class="hljs-number">1</span>);

q.enQueue(<span class="hljs-number">2</span>);

q.enQueue(<span class="hljs-number">3</span>);

q.enQueue(<span class="hljs-number">4</span>);

q.enQueue(<span class="hljs-number">5</span>);

<span class="hljs-comment">// 6th element can't be added to because the queue is full</span>

q.enQueue(<span class="hljs-number">6</span>);

q.display();

<span class="hljs-comment">//deQueue removes element entered first i.e. 1</span>

q.deQueue();

<span class="hljs-comment">//Now we have just 4 elements</span>

q.display();

<span class="hljs-keyword">return</span> <span class="hljs-number">0</span>;

}</code></pre></div>

</div>

<hr><h2 id="limitation">Limitations of Queue</h2>

<p>As you can see in the image below, after a bit of enqueuing and dequeuing, the size of the queue has been reduced.</p>

<figure><img alt="the empty spaces at front cannot be used after dequeing from a full queue" src="//cdn.programiz.com/sites/tutorial2program/files/why-circular-queue_0.png" title="Queue representation" width="337" height="178"><figcaption>Limitation of a queue</figcaption></figure><p>And we can only add indexes 0 and 1 only when the queue is reset (when all the elements have been dequeued).</p>

<p>After <var>REAR</var> reaches the last index, if we can store extra elements in the empty spaces (0 and 1), we can make use of the empty spaces. This is implemented by a modified queue called the <a href="/dsa/circular-queue.html">circular queue</a>.</p>

<hr><h2 id="complexity">Complexity Analysis</h2>

<p>The complexity of enqueue and dequeue operations in a queue using an array is <code>O(1)</code>. If you use <code>pop(N)</code> in python code, then the complexity might be <code>O(n)</code> depending on the position of the item to be popped.</p>

<hr><h2 id="application">Applications of Queue</h2>

<ul><li>CPU scheduling, Disk Scheduling</li>

<li>When data is transferred asynchronously between two processes.The queue is used for synchronization. For example: IO Buffers, pipes, file IO, etc</li>

<li>Handling of interrupts in real-time systems.</li>

<li>Call Center phone systems use Queues to hold people calling them in order.</li>

</ul><hr></div>

</div>

<div class="tutorial-toc"><div class="tutorial-toc__inner"><h3 class="tutorial-toc__title">Table of Contents

<li><a href="#working">How Queue Works</a></li>

<li><a href="#code">Python, Java and C/C++ Examples</a></li>

<li><a href="#limitation">Limitation of this implementation</a></li>

<li><a href="#complexity">Queue Complexity</a></li>

<li><a href="#application">Queue Applications</a></li>

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