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<!DOCTYPE html>

<head>

<title>Dequeue</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>

</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>Deque Data Structure</h1>

In this tutorial, you will learn what a double ended queue (deque) is. Also, you will find working examples of different operations on a deque in C, C++, Java and Python.

Deque or Double Ended Queue is a type of <a href="/dsa/queue.html">queue</a> in which insertion and removal of elements can either be performed from the front or the rear. Thus, it does not follow FIFO rule (First In First Out).

<figure><img alt="representation of deque data structure" src="//cdn.programiz.com/sites/tutorial2program/files/deque.png" title="Double ended queue" width="637" height="102"><figcaption>Representation of Deque</figcaption></figure><hr><h2 id="types">Types of Deque</h2>

<ul><li>Input Restricted Deque

In this deque, input is restricted at a single end but allows deletion at both the ends.</li>

<li>Output Restricted Deque

In this deque, output is restricted at a single end but allows insertion at both the ends.</li>

</ul><hr><h2 id="operations">Operations on a Deque</h2>

Below is <a href="/dsa/circular-queue.html">the circular array</a> implementation of deque. In a circular array, if the array is full, we start from the beginning.

But in a linear array implementation, if the array is full, no more elements can be inserted. In each of the operations below, if the array is full, "overflow message" is thrown.

Before performing the following operations, these steps are followed.

<ol><li>Take an array (deque) of size <var>n</var>.</li>

<li>Set two pointers at the first position and set <code>front = -1</code> and <code>rear = 0</code>.</li>

</ol><figure><img alt="initialize an array and pointers for deque operations" src="//cdn.programiz.com/sites/tutorial2program/files/deque-array.png" title="Initialize array" width="383" height="191"><figcaption>Initialize an array and pointers for deque</figcaption></figure><h3>1. Insert at the Front</h3>

This operation adds an element at the front.

<ol><li>Check the position of front.

<figure><img alt="check the position of front" src="//cdn.programiz.com/sites/tutorial2program/files/deque-insert-front-1.png" title="Deque - insert at the front" width="377" height="167"><figcaption>Check the position of front</figcaption></figure></li>

<li>If <code>front < 1</code>, reinitialize <code>front = n-1</code> (last index).

<figure><img alt="if front is less than 1 shift front to the end" src="//cdn.programiz.com/sites/tutorial2program/files/deque-insert-front-2.png" title="Deque - insert at the front" width="377" height="167"><figcaption>Shift front to the end</figcaption></figure></li>

<li>Else, decrease <var>front</var> by 1.</li>

<li>Add the new key <var>5</var> into <code>array[front]</code>.

<figure><img alt="Insert element at the position of front" src="//cdn.programiz.com/sites/tutorial2program/files/deque-insert-front-3.png" title="Deque - insert at the front" width="377" height="167"><figcaption>Insert the element at Front</figcaption></figure></li>

</ol><h3>2. Insert at the Rear</h3>

This operation adds an element to the rear.

<ol><li>Check if the array is full.

<figure><img alt="check if deque is full" src="//cdn.programiz.com/sites/tutorial2program/files/deque-insert-rear-1.png" title="Deque - insert at the rear" width="377" height="167"><figcaption>Check if deque is full</figcaption></figure></li>

<li>If the deque is full, reinitialize <code>rear = 0</code>.</li>

<li>Else, increase <var>rear</var> by 1.

<figure><img alt="if deque is not full increase rear" src="//cdn.programiz.com/sites/tutorial2program/files/deque-insert-rear-2.png" title="Deque - insert at the rear" width="377" height="167"><figcaption>Increase the rear</figcaption></figure></li>

<li>Add the new key <var>5</var> into <code>array[rear]</code>.

<figure><img alt="insert element at the rear" src="//cdn.programiz.com/sites/tutorial2program/files/deque-insert-rear-3.png" title="Deque - insert at the rear" width="377" height="167"><figcaption>Insert the element at rear</figcaption></figure></li>

</ol><h3>3. Delete from the Front</h3>

<div class="clearfix"></div>The operation deletes an element from the front.

<ol><li>Check if the deque is empty.

<figure><img alt="check if deque is empty" src="//cdn.programiz.com/sites/tutorial2program/files/deque-delete-front-1.png" title="Deque - delete from the front" width="377" height="167"><figcaption>Check if deque is empty</figcaption></figure></li>

<li>If the deque is empty (i.e. <code>front = -1</code>), deletion cannot be performed (underflow condition).</li>

<li>If the deque has only one element (i.e. <code>front = rear</code>), set <code>front = -1</code> and <code>rear = -1</code>.</li>

<li>Else if <var>front</var> is at the end (i.e. <code>front = n - 1</code>), set go to the front <code>front = 0</code>.</li>

<li>Else, <code>front = front + 1</code>.

<figure><img alt="increase the index of front" src="//cdn.programiz.com/sites/tutorial2program/files/deque-delete-front-2.png" title="Deque - delete from the front" width="377" height="167"><figcaption>Increase the front</figcaption></figure></li>

</ol><h3>4. Delete from the Rear</h3>

This operation deletes an element from the rear.

<ol><li>Check if the deque is empty.

<figure><img alt="check if deque is empty" src="//cdn.programiz.com/sites/tutorial2program/files/deque-delete-rear-1.png" title="Deque - delete from the rear" width="377" height="167"><figcaption>Check if deque is empty</figcaption></figure></li>

<li>If the deque is empty (i.e. <code>front = -1</code>), deletion cannot be performed (underflow condition).</li>

<li>If the deque has only one element (i.e. <code>front = rear</code>), set <code>front = -1</code> and <code>rear = -1</code>, else follow the steps below.</li>

<li>If <var>rear</var> is at the front (i.e. <code>rear = 0</code>), set go to the front <code>rear = n - 1</code>.</li>

<li>Else, <code>rear = rear - 1</code>.

<figure><img alt="decrease the position of rear" src="//cdn.programiz.com/sites/tutorial2program/files/deque-delete-rear-2.png" title="Deque - delete from the rear" width="377" height="167"><figcaption>Decrease the rear</figcaption></figure></li>

</ol><h3>5. Check Empty</h3>

This operation checks if the deque is empty. If <code>front = -1</code>, the deque is empty.

<h3>6. Check Full</h3>

This operation checks if the deque is full. If <code>front = 0</code> and <code>rear = n - 1</code> OR <code>front = rear + 1</code>, the deque is full.

<hr><h2 id="code">Deque Implementation in Python, Java, C, and C++</h2>

<div id='py1'class="tabbed-editor__node tabbed-editor__node--active" onclick="changepy()"><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"># Deque implementaion in python

class Deque:

def __init__(self):

self.items = []

def isEmpty(self):

return self.items == []

def addRear(self, item):

self.items.append(item)

def addFront(self, item):

self.items.insert(0, item)

def removeFront(self):

return self.items.pop(0)

def removeRear(self):

return self.items.pop()

def size(self):

return len(self.items)

d = Deque()

print(d.isEmpty())

d.addRear(8)

d.addRear(5)

d.addFront(7)

d.addFront(10)

print(d.size())

print(d.isEmpty())

d.addRear(11)

print(d.removeRear())

print(d.removeFront())

d.addFront(55)

d.addRear(45)

print(d.items)</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">// Deque implementation in Java

class Deque {

static final int MAX = 100;

int arr[];

int front;

int rear;

int size;

public Deque(int size) {

arr = new int[MAX];

front = -1;

rear = 0;

this.size = size;

}

boolean isFull() {

return ((front == 0 && rear == size - 1) || front == rear + 1);

}

boolean isEmpty() {

return (front == -1);

}

void insertfront(int key) {

if (isFull()) {

System.out.println("Overflow");

return;

}

if (front == -1) {

front = 0;

rear = 0;

}

else if (front == 0)

front = size - 1;

else

front = front - 1;

arr[front] = key;

}

void insertrear(int key) {

if (isFull()) {

System.out.println(" Overflow ");

return;

}

if (front == -1) {

front = 0;

rear = 0;

}

else if (rear == size - 1)

rear = 0;

else

rear = rear + 1;

arr[rear] = key;

}

void deletefront() {

if (isEmpty()) {

System.out.println("Queue Underflow\n");

return;

}

// Deque has only one element

if (front == rear) {

front = -1;

rear = -1;

} else if (front == size - 1)

front = 0;

else

front = front + 1;

}

void deleterear() {

if (isEmpty()) {

System.out.println(" Underflow");

return;

}

if (front == rear) {

front = -1;

rear = -1;

} else if (rear == 0)

rear = size - 1;

else

rear = rear - 1;

}

int getFront() {

if (isEmpty()) {

System.out.println(" Underflow");

return -1;

}

return arr[front];

}

int getRear() {

if (isEmpty() || rear < 0) {

System.out.println(" Underflow\n");

return -1;

}

return arr[rear];

}

public static void main(String[] args) {

Deque dq = new Deque(4);

System.out.println("Insert element at rear end : 12 ");

dq.insertrear(12);

System.out.println("insert element at rear end : 14 ");

dq.insertrear(14);

System.out.println("get rear element : " + dq.getRear());

dq.deleterear();

System.out.println("After delete rear element new rear become : " + dq.getRear());

System.out.println("inserting element at front end");

dq.insertfront(13);

System.out.println("get front element: " + dq.getFront());

dq.deletefront();

System.out.println("After delete front element new front become : " + +dq.getFront());

}

}</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">// Deque implementation in C

#include <stdio.h>

#define MAX 10

void addFront(int *, int, int *, int *);

void addRear(int *, int, int *, int *);

int delFront(int *, int *, int *);

int delRear(int *, int *, int *);

void display(int *);

int count(int *);

int main() {

int arr[MAX];

int front, rear, i, n;

front = rear = -1;

for (i = 0; i < MAX; i++)

arr[i] = 0;

addRear(arr, 5, &front, &rear);

addFront(arr, 12, &front, &rear);

addRear(arr, 11, &front, &rear);

addFront(arr, 5, &front, &rear);

addRear(arr, 6, &front, &rear);

addFront(arr, 8, &front, &rear);

printf("\nElements in a deque: ");

display(arr);

i = delFront(arr, &front, &rear);

printf("\nremoved item: %d", i);

printf("\nElements in a deque after deletion: ");

display(arr);

addRear(arr, 16, &front, &rear);

addRear(arr, 7, &front, &rear);

printf("\nElements in a deque after addition: ");

display(arr);

i = delRear(arr, &front, &rear);

printf("\nremoved item: %d", i);

printf("\nElements in a deque after deletion: ");

display(arr);

n = count(arr);

printf("\nTotal number of elements in deque: %d", n);

}

void addFront(int *arr, int item, int *pfront, int *prear) {

int i, k, c;

if (*pfront == 0 && *prear == MAX - 1) {

printf("\nDeque is full.\n");

return;

}

if (*pfront == -1) {

*pfront = *prear = 0;

arr[*pfront] = item;

return;

}

if (*prear != MAX - 1) {

c = count(arr);

k = *prear + 1;

for (i = 1; i <= c; i++) {

arr[k] = arr[k - 1];

k--;

}

arr[k] = item;

*pfront = k;

(*prear)++;

} else {

(*pfront)--;

arr[*pfront] = item;

}

void addRear(int *arr, int item, int *pfront, int *prear) {

int i, k;

if (*pfront == 0 && *prear == MAX - 1) {

printf("\nDeque is full.\n");

return;

}

if (*pfront == -1) {

*prear = *pfront = 0;

arr[*prear] = item;

return;

}

if (*prear == MAX - 1) {

k = *pfront - 1;

for (i = *pfront - 1; i < *prear; i++) {

k = i;

if (k == MAX - 1)

arr[k] = 0;

else

arr[k] = arr[i + 1];

}

(*prear)--;

(*pfront)--;

}

(*prear)++;

arr[*prear] = item;

}

int delFront(int *arr, int *pfront, int *prear) {

int item;

if (*pfront == -1) {

printf("\nDeque is empty.\n");

return 0;

}

item = arr[*pfront];

arr[*pfront] = 0;

if (*pfront == *prear)

*pfront = *prear = -1;

else

(*pfront)++;

return item;

}

int delRear(int *arr, int *pfront, int *prear) {

int item;

if (*pfront == -1) {

printf("\nDeque is empty.\n");

return 0;

}

item = arr[*prear];

arr[*prear] = 0;

(*prear)--;

if (*prear == -1)

*pfront = -1;

return item;

}

void display(int *arr) {

int i;

printf("\n front: ");

for (i = 0; i < MAX; i++)

printf(" %d", arr[i]);

printf(" :rear");

}

int count(int *arr) {

int c = 0, i;

for (i = 0; i < MAX; i++) {

if (arr[i] != 0)

c++;

}

return c;

}</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">// Deque implementation in C++

#include <iostream>

using namespace std;

#define MAX 10

class Deque {

int arr[MAX];

int front;

int rear;

int size;

public:

Deque(int size) {

front = -1;

rear = 0;

this->size = size;

}

void insertfront(int key);

void insertrear(int key);

void deletefront();

void deleterear();

bool isFull();

bool isEmpty();

int getFront();

int getRear();

};

bool Deque::isFull() {

return ((front == 0 && rear == size - 1) ||

front == rear + 1);

}

bool Deque::isEmpty() {

return (front == -1);

}

void Deque::insertfront(int key) {

if (isFull()) {

cout << "Overflow\n"

<< endl;

return;

}

if (front == -1) {

front = 0;

rear = 0;

}

else if (front == 0)

front = size - 1;

else

front = front - 1;

arr[front] = key;

}

void Deque ::insertrear(int key) {

if (isFull()) {

cout << " Overflow\n " << endl;

return;

}

if (front == -1) {

front = 0;

rear = 0;

}

else if (rear == size - 1)

rear = 0;

else

rear = rear + 1;

arr[rear] = key;

}

void Deque ::deletefront() {

if (isEmpty()) {

cout << "Queue Underflow\n"

<< endl;

return;

}

if (front == rear) {

front = -1;

rear = -1;

} else if (front == size - 1)

front = 0;

else

front = front + 1;

}

void Deque::deleterear() {

if (isEmpty()) {

cout << " Underflow\n"

<< endl;

return;

}

if (front == rear) {

front = -1;

rear = -1;

} else if (rear == 0)

rear = size - 1;

else

rear = rear - 1;

}

int Deque::getFront() {

if (isEmpty()) {

cout << " Underflow\n"

<< endl;

return -1;

}

return arr[front];

}

int Deque::getRear() {

if (isEmpty() || rear < 0) {

cout << " Underflow\n"

<< endl;

return -1;

}

return arr[rear];

}

int main() {

Deque dq(4);

cout << "insert element at rear end \n";

dq.insertrear(5);

dq.insertrear(11);

cout << "rear element: "

<< dq.getRear() << endl;

dq.deleterear();

cout << "after deletion of the rear element, the new rear element: " << dq.getRear() << endl;

cout << "insert element at front end \n";

dq.insertfront(8);

cout << "front element: " << dq.getFront() << endl;

dq.deletefront();

cout << "after deletion of front element new front element: " << dq.getFront() << endl;

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

</div>

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

The time complexity of all the above operations is constant i.e. <code>O(1)</code>.

<hr><h2 id="applications">Applications of Deque Data Structure</h2>

<ol><li>In undo operations on software.</li>

<li>To store history in browsers.</li>

<li>For implementing both <a href="/dsa/stack.html">stacks</a> and <a href="/dsa/queue.html">queues</a>.</li>

</ol></div>

</div>

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

<li><a href="#types">Types of Deque</a></li>

<li><a href="#operations">Operations on a Deque</a></li>

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

<li><a href="#complexity">Deque Complexities</a></li>

<li><a href="#applications">Deque Applications</a></li>

</ul></div></div></div> </div>

<div>

<ul>