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<title>Circular Queue</title>
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<h1>Circular Queue Data Structure</h1>
<p class="editor-contents__short-description">In this tutorial, you will learn what a circular queue is. Also, you will find implementation of circular queue in C, C++, Java and Python.</p>
<div id="node-936" class="node node-algorithm clearfix" about="/dsa/circular-queue" typeof="sioc:Item foaf:Document">
<span property="dc:title" content="Circular Queue Data Structure" class="rdf-meta element-hidden"></span>
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<p id="definition">A circular queue is the extended version of a <a href="/dsa/queue.html">regular queue</a> where the last element is connected to the first element. Thus forming a circle-like structure.</p>
<figure><img alt="Circular increment in circular queue" src="//cdn.programiz.com/sites/tutorial2program/files/circular-increment.png" title="Circular queue" width="274" height="278"><figcaption>Circular queue representation</figcaption></figure><p>The circular queue solves the major limitation of the normal queue. In a normal queue, after a bit of insertion and deletion, there will be non-usable empty space.</p>
<figure><img alt="demonstrate how we cannot add element even after removing some element from the queue" src="//cdn.programiz.com/sites/tutorial2program/files/why-circular-queue.png" title="Demerit of queue" width="337" height="201"><figcaption>Limitation of the regular Queue</figcaption></figure><p>Here, indexes <strong>0</strong> and <strong>1</strong> can only be used after resetting the queue (deletion of all elements). This reduces the actual size of the queue.</p>
<hr><h2 id="working">How Circular Queue Works</h2>
<p>Circular Queue works by the process of circular increment i.e. when we try to increment the pointer and we reach the end of the queue, we start from the beginning of the queue.</p>
<p>Here, the circular increment is performed by modulo division with the queue size. That is,</p>
<pre style="max-height: 600px;"><code class="dsa hljs yaml">
<span class="hljs-string">if</span> <span class="hljs-string">REAR</span> <span class="hljs-string">+</span> <span class="hljs-number">1</span> <span class="hljs-string">==</span> <span class="hljs-number">5</span> <span class="hljs-string">(overflow!),</span> <span class="hljs-string">REAR</span> <span class="hljs-string">=</span> <span class="hljs-string">(REAR</span> <span class="hljs-string">+</span> <span class="hljs-number">1</span><span class="hljs-string">)%5</span> <span class="hljs-string">=</span> <span class="hljs-number">0</span> <span class="hljs-string">(start</span> <span class="hljs-string">of</span> <span class="hljs-string">queue)</span></code></pre>
<hr><h2>Circular Queue Operations</h2>
<p>The circular queue 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 elements of the queue</li>
<li>initially, set value of <var>FRONT</var> and <var>REAR</var> to -1</li>
</ul><h3>1. Enqueue Operation</h3>
<ul><li>check if the queue is full</li>
<li>for the first element, set value of <var>FRONT</var> to 0</li>
<li>circularly increase the <var>REAR</var> index by 1 (i.e. if the rear reaches the end, next it would be at the start of the queue)</li>
<li>add the new element in the position pointed to by <var>REAR</var></li>
</ul><h3>2. Dequeue Operation</h3>
<ul><li>check if the queue is empty</li>
<li>return the value pointed by <var>FRONT</var></li>
<li>circularly 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><p></p><div class="clearfix"></div><p>However, the check for full queue has a new additional case:</p>
<ul><li>Case 1: <var>FRONT</var> = 0 && <code>REAR == SIZE - 1</code></li>
<li>Case 2: <code>FRONT = REAR + 1</code></li>
</ul><p>The second case happens when <var>REAR</var> starts from 0 due to circular increment and when its value is just 1 less than <var>FRONT</var>, the queue is full.</p>
<figure><img alt="enqueue and dequeue operation of the circular queue" src="//cdn.programiz.com/sites/tutorial2program/files/circular-queue-program.png" title="Working of circular queue" width="432" height="1396"><figcaption>Enque and Deque Operations</figcaption></figure><hr><h2 id="code">Circular Queue Implementations in Python, Java, C, and C++</h2>
<p>The most common queue implementation is using arrays, but it can also be implemented using lists.</p>
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<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"># Circular Queue implementation in Python</span>
<span class="hljs-class"><span class="hljs-keyword">class</span> <span class="hljs-title">MyCircularQueue</span><span class="hljs-params">()</span>:</span>
<span class="hljs-function"><span class="hljs-keyword">def</span> <span class="hljs-title">__init__</span><span class="hljs-params">(self, k)</span>:</span>
self.k = k
self.queue = [<span class="hljs-literal">None</span>] * k
self.head = self.tail = <span class="hljs-number">-1</span>
<span class="hljs-comment"># Insert an element into the circular queue</span>
<span class="hljs-function"><span class="hljs-keyword">def</span> <span class="hljs-title">enqueue</span><span class="hljs-params">(self, data)</span>:</span>
<span class="hljs-keyword">if</span> ((self.tail + <span class="hljs-number">1</span>) % self.k == self.head):
<span class="hljs-keyword">print</span>(<span class="hljs-string">"The circular queue is full\n"</span>)
<span class="hljs-keyword">elif</span> (self.head == <span class="hljs-number">-1</span>):
self.head = <span class="hljs-number">0</span>
self.tail = <span class="hljs-number">0</span>
self.queue[self.tail] = data
<span class="hljs-keyword">else</span>:
self.tail = (self.tail + <span class="hljs-number">1</span>) % self.k
self.queue[self.tail] = data
<span class="hljs-comment"># Delete an element from the circular queue</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> (self.head == <span class="hljs-number">-1</span>):
<span class="hljs-keyword">print</span>(<span class="hljs-string">"The circular queue is empty\n"</span>)
<span class="hljs-keyword">elif</span> (self.head == self.tail):
temp = self.queue[self.head]
self.head = <span class="hljs-number">-1</span>
self.tail = <span class="hljs-number">-1</span>
<span class="hljs-keyword">return</span> temp
<span class="hljs-keyword">else</span>:
temp = self.queue[self.head]
self.head = (self.head + <span class="hljs-number">1</span>) % self.k
<span class="hljs-keyword">return</span> temp
<span class="hljs-function"><span class="hljs-keyword">def</span> <span class="hljs-title">printCQueue</span><span class="hljs-params">(self)</span>:</span>
<span class="hljs-keyword">if</span>(self.head == <span class="hljs-number">-1</span>):
<span class="hljs-keyword">print</span>(<span class="hljs-string">"No element in the circular queue"</span>)
<span class="hljs-keyword">elif</span> (self.tail >= self.head):
<span class="hljs-keyword">for</span> i <span class="hljs-keyword">in</span> range(self.head, self.tail + <span class="hljs-number">1</span>):
<span class="hljs-keyword">print</span>(self.queue[i], end=<span class="hljs-string">" "</span>)
<span class="hljs-keyword">print</span>()
<span class="hljs-keyword">else</span>:
<span class="hljs-keyword">for</span> i <span class="hljs-keyword">in</span> range(self.head, self.k):
<span class="hljs-keyword">print</span>(self.queue[i], end=<span class="hljs-string">" "</span>)
<span class="hljs-keyword">for</span> i <span class="hljs-keyword">in</span> range(<span class="hljs-number">0</span>, self.tail + <span class="hljs-number">1</span>):
<span class="hljs-keyword">print</span>(self.queue[i], end=<span class="hljs-string">" "</span>)
<span class="hljs-keyword">print</span>()
<span class="hljs-comment"># Your MyCircularQueue object will be instantiated and called as such:</span>
obj = MyCircularQueue(<span class="hljs-number">5</span>)
obj.enqueue(<span class="hljs-number">1</span>)
obj.enqueue(<span class="hljs-number">2</span>)
obj.enqueue(<span class="hljs-number">3</span>)
obj.enqueue(<span class="hljs-number">4</span>)
obj.enqueue(<span class="hljs-number">5</span>)
<span class="hljs-keyword">print</span>(<span class="hljs-string">"Initial queue"</span>)
obj.printCQueue()
obj.dequeue()
<span class="hljs-keyword">print</span>(<span class="hljs-string">"After removing an element from the queue"</span>)
obj.printCQueue()
</code></pre></div>
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<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">// Circular 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">CQueue</span> </span>{
<span class="hljs-keyword">int</span> SIZE = <span class="hljs-number">5</span>; <span class="hljs-comment">// Size of Circular Queue</span>
<span class="hljs-keyword">int</span> front, rear;
<span class="hljs-keyword">int</span> items[] = <span class="hljs-keyword">new</span> <span class="hljs-keyword">int</span>[SIZE];
CQueue() {
front = -<span class="hljs-number">1</span>;
rear = -<span class="hljs-number">1</span>;
}
<span class="hljs-comment">// Check if the queue is full</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">if</span> (front == rear + <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-comment">// Check if the queue is empty</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">else</span>
<span class="hljs-keyword">return</span> <span class="hljs-keyword">false</span>;
}
<span class="hljs-comment">// Adding an element</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 = (rear + <span class="hljs-number">1</span>) % SIZE;
items[rear] = element;
System.out.println(<span class="hljs-string">"Inserted "</span> + element);
}
}
<span class="hljs-comment">// Removing an element</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()) {
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 = (front + <span class="hljs-number">1</span>) % SIZE;
}
<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 status of Circular 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">"Front -> "</span> + front);
System.out.println(<span class="hljs-string">"Items -> "</span>);
<span class="hljs-keyword">for</span> (i = front; i != rear; i = (i + <span class="hljs-number">1</span>) % SIZE)
System.out.print(items[i] + <span class="hljs-string">" "</span>);
System.out.println(items[i]);
System.out.println(<span class="hljs-string">"Rear -> "</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>{
CQueue q = <span class="hljs-keyword">new</span> CQueue();
<span class="hljs-comment">// Fails because front = -1</span>
q.deQueue();
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">// Fails to enqueue because front == 0 && rear == SIZE - 1</span>
q.enQueue(<span class="hljs-number">6</span>);
q.display();
<span class="hljs-keyword">int</span> elem = q.deQueue();
<span class="hljs-keyword">if</span> (elem != -<span class="hljs-number">1</span>) {
System.out.println(<span class="hljs-string">"Deleted Element is "</span> + elem);
}
q.display();
q.enQueue(<span class="hljs-number">7</span>);
q.display();
<span class="hljs-comment">// Fails to enqueue because front == rear + 1</span>
q.enQueue(<span class="hljs-number">8</span>);
}
}</code></pre></div>
</div>
<div class="code-editor__area" id="c-code">
<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">// Circular 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-keyword">int</span> items[SIZE];
<span class="hljs-keyword">int</span> front = <span class="hljs-number">-1</span>, rear = <span class="hljs-number">-1</span>;
<span class="hljs-comment">// Check if the queue is full</span>
<span class="hljs-function"><span class="hljs-keyword">int</span> <span class="hljs-title">isFull</span><span class="hljs-params">()</span> </span>{
<span class="hljs-keyword">if</span> ((front == rear + <span class="hljs-number">1</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-number">1</span>;
<span class="hljs-keyword">return</span> <span class="hljs-number">0</span>;
}
<span class="hljs-comment">// Check if the queue is empty</span>
<span class="hljs-function"><span class="hljs-keyword">int</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-number">1</span>;
<span class="hljs-keyword">return</span> <span class="hljs-number">0</span>;
}
<span class="hljs-comment">// Adding an element</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">printf</span>(<span class="hljs-string">"\n Queue is full!! \n"</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 = (rear + <span class="hljs-number">1</span>) % SIZE;
items[rear] = element;
<span class="hljs-built_in">printf</span>(<span class="hljs-string">"\n Inserted -> %d"</span>, element);
}
}
<span class="hljs-comment">// Removing an element</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">printf</span>(<span class="hljs-string">"\n Queue is empty !! \n"</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 </span>
<span class="hljs-comment">// queue after dequeing it. ?</span>
<span class="hljs-keyword">else</span> {
front = (front + <span class="hljs-number">1</span>) % SIZE;
}
<span class="hljs-built_in">printf</span>(<span class="hljs-string">"\n Deleted element -> %d \n"</span>, element);
<span class="hljs-keyword">return</span> (element);
}
}
<span class="hljs-comment">// Display 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">int</span> i;
<span class="hljs-keyword">if</span> (isEmpty())
<span class="hljs-built_in">printf</span>(<span class="hljs-string">" \n Empty Queue\n"</span>);
<span class="hljs-keyword">else</span> {
<span class="hljs-built_in">printf</span>(<span class="hljs-string">"\n Front -> %d "</span>, front);
<span class="hljs-built_in">printf</span>(<span class="hljs-string">"\n Items -> "</span>);
<span class="hljs-keyword">for</span> (i = front; i != rear; i = (i + <span class="hljs-number">1</span>) % SIZE) {
<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">"%d "</span>, items[i]);
<span class="hljs-built_in">printf</span>(<span class="hljs-string">"\n Rear -> %d \n"</span>, rear);
}
}
<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">// Fails because front = -1</span>
deQueue();
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">// Fails to enqueue because front == 0 && rear == SIZE - 1</span>
enQueue(<span class="hljs-number">6</span>);
display();
deQueue();
display();
enQueue(<span class="hljs-number">7</span>);
display();
<span class="hljs-comment">// Fails to enqueue because front == rear + 1</span>
enQueue(<span class="hljs-number">8</span>);
<span class="hljs-keyword">return</span> <span class="hljs-number">0</span>;
}</code></pre></div>
</div>
<div class="code-editor__area" id="cpp-code">
<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">// Circular 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 class="hljs-comment">/* Size of Circular Queue */</span></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-comment">// Check if the queue is full</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">if</span> (front == rear + <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-comment">// Check if the queue is empty</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">else</span>
<span class="hljs-keyword">return</span> <span class="hljs-literal">false</span>;
}
<span class="hljs-comment">// Adding an element</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 = (rear + <span class="hljs-number">1</span>) % SIZE;
items[rear] = element;
<span class="hljs-built_in">cout</span> << <span class="hljs-built_in">endl</span>
<< <span class="hljs-string">"Inserted "</span> << element << <span class="hljs-built_in">endl</span>;
}
}
<span class="hljs-comment">// Removing an element</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,</span>
<span class="hljs-comment">// so we reset the queue after deleting it.</span>
<span class="hljs-keyword">else</span> {
front = (front + <span class="hljs-number">1</span>) % SIZE;
}
<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 status of Circular Queue</span>
<span class="hljs-keyword">int</span> i;
<span class="hljs-keyword">if</span> (isEmpty()) {
<span class="hljs-built_in">cout</span> << <span class="hljs-built_in">endl</span>
<< <span class="hljs-string">"Empty Queue"</span> << <span class="hljs-built_in">endl</span>;
} <span class="hljs-keyword">else</span> {
<span class="hljs-built_in">cout</span> << <span class="hljs-string">"Front -> "</span> << front;
<span class="hljs-built_in">cout</span> << <span class="hljs-built_in">endl</span>
<< <span class="hljs-string">"Items -> "</span>;
<span class="hljs-keyword">for</span> (i = front; i != rear; i = (i + <span class="hljs-number">1</span>) % SIZE)
<span class="hljs-built_in">cout</span> << items[i];
<span class="hljs-built_in">cout</span> << items[i];
<span class="hljs-built_in">cout</span> << <span class="hljs-built_in">endl</span>
<< <span class="hljs-string">"Rear -> "</span> << rear;
}
}
};
<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">// Fails because front = -1</span>
q.deQueue();
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">// Fails to enqueue because front == 0 && rear == SIZE - 1</span>
q.enQueue(<span class="hljs-number">6</span>);
q.display();
<span class="hljs-keyword">int</span> elem = q.deQueue();
<span class="hljs-keyword">if</span> (elem != <span class="hljs-number">-1</span>)
<span class="hljs-built_in">cout</span> << <span class="hljs-built_in">endl</span>
<< <span class="hljs-string">"Deleted Element is "</span> << elem;
q.display();
q.enQueue(<span class="hljs-number">7</span>);
q.display();
<span class="hljs-comment">// Fails to enqueue because front == rear + 1</span>
q.enQueue(<span class="hljs-number">8</span>);
<span class="hljs-keyword">return</span> <span class="hljs-number">0</span>;
}</code></pre></div>
</div>
</div>
<hr><h2 id="complexity">Circular Queue Complexity Analysis</h2>
<p>The complexity of the enqueue and dequeue operations of a circular queue is <var>O(1)</var> for (array implementations).</p>
<hr><h2 id="application">Applications of Circular Queue</h2>
<ul><li>CPU scheduling</li>
<li>Memory management</li>
<li>Traffic Management</li>
</ul></div>
</div>
<div class="tutorial-toc"><div class="tutorial-toc__inner"><h3 class="tutorial-toc__title">Table of Contents
<button class="btn btn--clear align-items-center">
<svg class="programiz-icon"><use xlink:href="/sites/all/themes/programiz/assets/feather-sprite.svg#x"></use></svg></button></h3><div class="tutorial-toc__links"><ul><li><a href="#definition">Definition</a></li>
<li><a href="#working">How Circular Queue Works</a></li>
<li><a href="#code">Python, Java and C/C++ Examples</a></li>
<li><a href="#complexity">Circular Queue Complexity</a></li>
<li><a href="#application">Circular Queue Applications</a></li>
</ul></div></div></div> </div>
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Stack</a></button>
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Queue</a></button>
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Types of Queue</a></button>
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Circular Queue</a></button>
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Deque</a></button>
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Linked List Operations</a></button>
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Binary Search Tree</a></button>
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Deletion from Red Black Tree</a></button>
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Graph Data Structure</a></button>
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Spanning Tree</a></button>
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Strongly Connected Components</a></button>
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Adjacency Matrix</a></button>
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Adjacency List</a></button>
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Breadth-first Search</a></button>
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Bellman Ford's Algorithm</a></button>
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Bubble Sort</a></button>
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Selection Sort</a></button>
<button style="padding:5px; margin-bottom:2px"><a href="
/dsa/insertion-sort.html">
Insertion Sort</a></button>
<button style="padding:5px; margin-bottom:2px"><a href="
/dsa/merge-sort.html">
Merge Sort</a></button>
<button style="padding:5px; margin-bottom:2px"><a href="
/dsa/quick-sort.html">
Quick Sort</a></button>
<button style="padding:5px; margin-bottom:2px"><a href="
/dsa/counting-sort.html">
Counting Sort</a></button>
<button style="padding:5px; margin-bottom:2px"><a href="
/dsa/radix-sort.html">
Radix Sort</a></button>
<button style="padding:5px; margin-bottom:2px"><a href="
/dsa/bucket-sort.html">
Bucket Sort</a></button>
<button style="padding:5px; margin-bottom:2px"><a href="
/dsa/heap-sort.html">
Heap Sort</a></button>
<button style="padding:5px; margin-bottom:2px"><a href="
/dsa/shell-sort.html">
Shell Sort</a></button>
<button style="padding:5px; margin-bottom:2px"><a href="
/dsa/linear-search.html">
Linear Search</a></button>
<button style="padding:5px; margin-bottom:2px"><a href="
/dsa/binary-search.html">
Binary Search</a></button>
<br>
<br/>
<button style="padding:5px; margin-bottom:2px"><a href="
/dsa/greedy-algorithm.html">
Greedy Algorithm</a></button>
<button style="padding:5px; margin-bottom:2px"><a href="
/dsa/ford-fulkerson-algorithm.html">
Ford-Fulkerson Algorithm</a></button>
<button style="padding:5px; margin-bottom:2px"><a href="
/dsa/dijkstra-algorithm.html">
Dijkstra's Algorithm</a></button>
<button style="padding:5px; margin-bottom:2px"><a href="
/dsa/kruskal-algorithm.html">
Kruskal's Algorithm</a></button>
<button style="padding:5px; margin-bottom:2px"><a href="
/dsa/prim-algorithm.html">
Prim's Algorithm</a></button>
<button style="padding:5px; margin-bottom:2px"><a href="
/dsa/huffman-coding.html">
Huffman Code</a></button>
<br>
<br/>
<button style="padding:5px; margin-bottom:2px"><a href="
/dsa/dynamic-programming.html">
Dynamic Programming</a></button>
<button style="padding:5px; margin-bottom:2px"><a href="
/dsa/floyd-warshall-algorithm.html">
Floyd Warshall Algorithm</a></button>
<button style="padding:5px; margin-bottom:2px"><a href="
/dsa/longest-common-subsequence.html">
Longest Common Subsequence</a></button>
<br>
<br/>
<button style="padding:5px; margin-bottom:2px"><a href="
/dsa/backtracking-algorithm.html">
Backtracking Algorithm</a></button>
<button style="padding:5px; margin-bottom:2px"><a href="
/dsa/rabin-karp-algorithm.html">
Rabin-Karp Algorithm</a></button>
<br>
<br/>
<h2>Free Courses on YouTube</h2>
<br/>
<img height="35px" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgT9Spnddn1UerjXEbcWQUPhfDHLL9rppkmUp1x4JRPKsdTwmX0kI26Rd0-2qKlwGAAnbgiPz7dZMm5Rv5Fd1QLhkQC6n3ob13ug1bTYtizkDpk2B0LxRiA8QUIjeTmfu6vZHoKJ7pXUgt73sHoXvSpGWjKQ6ZM01IIbJnXmwzXq4RdNYA4swdULgNy/s16000/youtube-logo.png" width="35px"/>
<button style="padding:5px; margin-bottom:2px"><a href="
https://www.youtube.com/watch?v=IbSXF7eT-AU&list=PLR_5PTwg_uAQw40OhdvAwN4NvzWv0xOZ2">
Python Full Course Playlist</a></button>
<br/>
<img height="35px" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgT9Spnddn1UerjXEbcWQUPhfDHLL9rppkmUp1x4JRPKsdTwmX0kI26Rd0-2qKlwGAAnbgiPz7dZMm5Rv5Fd1QLhkQC6n3ob13ug1bTYtizkDpk2B0LxRiA8QUIjeTmfu6vZHoKJ7pXUgt73sHoXvSpGWjKQ6ZM01IIbJnXmwzXq4RdNYA4swdULgNy/s16000/youtube-logo.png" width="35px"/>
<button style="padding:5px; margin-bottom:2px"><a href="https://www.youtube.com/watch?v=UEl6wB90Gs8">
105 STL Algorithms in Less Than an Hour</a></button>
<br/>
<img height="35px" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgT9Spnddn1UerjXEbcWQUPhfDHLL9rppkmUp1x4JRPKsdTwmX0kI26Rd0-2qKlwGAAnbgiPz7dZMm5Rv5Fd1QLhkQC6n3ob13ug1bTYtizkDpk2B0LxRiA8QUIjeTmfu6vZHoKJ7pXUgt73sHoXvSpGWjKQ6ZM01IIbJnXmwzXq4RdNYA4swdULgNy/s16000/youtube-logo.png" width="35px"/>
<button style="padding:5px; margin-bottom:2px"><a href="https://www.youtube.com/watch?v=zZXTgN7L1UU&list=PLR_5PTwg_uAS6C1cSMjU6oVhOcCX8Zu_4">
C++ STL Playlist</a></button>
<br/>
<img height="35px" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgT9Spnddn1UerjXEbcWQUPhfDHLL9rppkmUp1x4JRPKsdTwmX0kI26Rd0-2qKlwGAAnbgiPz7dZMm5Rv5Fd1QLhkQC6n3ob13ug1bTYtizkDpk2B0LxRiA8QUIjeTmfu6vZHoKJ7pXUgt73sHoXvSpGWjKQ6ZM01IIbJnXmwzXq4RdNYA4swdULgNy/s16000/youtube-logo.png" width="35px"/>
<button style="padding:5px; margin-bottom:2px"><a href="https://youtu.be/ty9756v3kc8">
Learn Node.js </a></button>
<br/>
<img height="35px" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgT9Spnddn1UerjXEbcWQUPhfDHLL9rppkmUp1x4JRPKsdTwmX0kI26Rd0-2qKlwGAAnbgiPz7dZMm5Rv5Fd1QLhkQC6n3ob13ug1bTYtizkDpk2B0LxRiA8QUIjeTmfu6vZHoKJ7pXUgt73sHoXvSpGWjKQ6ZM01IIbJnXmwzXq4RdNYA4swdULgNy/s16000/youtube-logo.png" width="35px"/>