h apter

C
4 Queue

“We could say we want the Web to reflect

a vision of the world where everything is done
democratically. To do that, we get computers
to talk with each other in such a way as to
promote that ideal.”
— Tim Berners-Lee

In this Chapter
»» Introduction to Queue
»» Operations on Queue
»» Implementation of Queue 4.1 Introduction to Queue
using Python
In the previous chapter we learned about a data
»» Introduction to Deque structure called Stack, which works on Last-In-
»» Implementation of Deque First-Out (LIFO) principle. In this chapter, we will
using Python learn about another data structure called Queue
which works on First-In-First-Out (FIFO) principle.
Queue is an ordered linear list of elements, having
different ends for adding
and removing elements
Cashier Next in it.
Examples of queue in
our everyday life include
students standing in
a queue for morning
assembly, customers
forming a queue at the
cash counter in a bank
(Figure 4.1), vehicles
queued at fuel pumps
Figure 4.1: Queue of people at a bank (Figure 4.2), etc.

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 Notes

Figure 4.2: Queue of cars in a petrol pump

4.1.1 First In First Out (FIFO)

Queue follows the principle of First In First Out (FIFO),
since the element entering first in the queue will be the
first one to come out of it. Thus, the element that has
been longest in the queue will be removed first. It is also
known as a First Come First Served (FCFS) approach.
Queue is an arrangement in which new objects/items
always get added at one end, usually called the REAR,
and objects/items always get removed from the other
end, usually called the FRONT of the queue. REAR is
also known as TAIL and FRONT as HEAD of a queue.

4.1.2 Applications of Queue

(A) The concept of queue has many applications in

real-life:
• If a train ticket is in the waiting list (such as W/L1),
it means the ticket is in a queue of tickets waiting to
get confirmed, as per the increasing order of waiting
numbers. If a confirmed ticket is cancelled, the W/
L1 numbered ticket is removed from the FRONT of
the waiting queue and confirmed.
• Sometimes on calling a customer service centre, the
Interactive Voice Response System (IVRS) tells us to
wait till a support person is available. Here the call is
put into a queue of customers waiting to be serviced.
• Imagine there is a single-lane one-way road, then the
vehicle that entered first will exit first, following the
concept of queue. Likewise, vehicles in a highway toll
tax booth are served following the principle of FIFO.

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 (B) Following are some examples of application of
queue in computer science:
• Suppose there is a web-server hosting a web-site to
declare result(s). This server can handle a maximum
of 50 concurrent requests to view result(s). So, to
serve thousands of user requests, a Queue would be
the most appropriate data structure to use.
• Some Operating Systems (OS) are required to handle
multiple tasks called - jobs, seeking to use the
processor. But we know that a processor can handle
only one task at a time. Therefore, in a multitasking In the web-server
example (for result
operating system, jobs are lined up (queued) and then
declaration), suppose
given access to the processor according to some order. the server receives
The simplest way is to give access to the processor on a request from an
a FIFO basis, that is according to the order in which Administrator to
the jobs arrive with a request for the processor. access the result of a
school on an urgent
• When we send print commands from multiple files basis, along with
from the same computer or from different computers other requests from
students to check
using a shared printer. The OS puts these print individual results.
requests in a queue and sends them to the printer Can you suggest some
one by one on a FIFO basis. strategy to ensure
service to all as per
their urgency?
4.2 Operations on Queue
Following the FIFO approach, data structure queue
supports the following operations:
• ENQUEUE: is used to insert a new element to the
queue at the rear end. We can insert elements in
the queue till there is space in the queue for adding
more elements. Inserting elements beyond capacity
of the queue will result in an exception - known as
Overflow.
• DEQUEUE: is used to remove one element at a time
from the front of the queue. We can delete elements
from a queue until it is empty, trying to delete an
element from an empty queue will result in exception
- known as Underflow.
To perform enqueue and dequeue efficiently on a
queue, following operations are also required:
• IS EMPTY : used to check whether the queue has any
element or not, so as to avoid Underflow exception
while performing dequeue operation.

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 • PEEK : used to view elements at the front of the queue,
without removing it from the queue.
While using a
list to implement • IS FULL : used to check whether any more elements
queue, we can can be added to the queue or not, to avoid Overflow
designate either exceptions while performing enqueue operation.
end of the list
as Front or Rear Figure 4.3 shows the various stages of a simple
of the queue. queue containing alphabets. In the figure, Front of the
But we have to
queue is on the left and Rear on the right.
fix either of the
ends index[0]
Operation performed Status of queue after operation
or index[n-1] as
Front and fix the enqueue(z) F Z R
opposite end as
Rear. enqueue(x) F Z X R

enqueue(c) F Z X C R

dequeue() F X C R

enqueue(v) F X C V R

dequeue() F C V R

dequeue() F V R

Figure 4.3: Various Stages of Stack Operations

4.3 Implementation of Queue using Python

There are many ways in which queues can be implemented
in a computer program, one way is using the list data
type of Python. For creating a queue structure in the
program, following functions need to be defined:
• Let’s create a queue named myQueue. We can create
it by assigning an empty list.
myQueue = list()
• A function (enqueue) to insert a new element at
the end of queue. The function has two parameters
- name of the queue and element which is to be
inserted in the queue.
def enqueue(myQueue, element):
myQueue.append(element)
Note: append() function always adds an element at the end of the
list, hence Rear of queue.
• We don’t need to implement Is Full, as Python
being a dynamic language, does not ask for the

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 creation of list having fixed size. Hence, we will never
encounter a situation when the queue is full.
• A function (isEmpty) to check, if the queue has an
element or not? This can be done by checking the
length of the queue. The function has a parameter
-- name of the queue and returns True if the queue
is empty False otherwise.
def isEmpty(myQueue):
if len(myQueue)==0:
return True Can you implement a
queue data structure
else:
using tuple or
return False dictionary?
• A function (dequeue) to delete an element from the
front of the queue. It has one parameter - name
of the queue and returns the deleted element. The
function first checks if the queue is empty or not, for
successful deletion.
def dequeue(myQueue):
if not (isEmpty(myQueue)):
return myQueue.pop(0)
else :
print(“Queue is empty”)
Note: The pop() function with index[0] will delete the element from
the beginning of the list, hence Front of queue.
• A function (size) to get the number of elements in
the queue. We can use the len() function of Python’s
list to find the number of elements in the queue. The
function has one parameter - name of the queue and
returns the number of elements in the queue.
def size(myQueue):
return len(myQueue)
• A function (peek) to simply read, but not to delete,
the element at the front end of the queue. For this,
we can read the element at index[0] of the queue. While choosing
The function has one parameter - name of the queue the name of above
functions general
and returns the value of element at Front if queue is naming convention
not empty, None otherwise. w.r.t. the queue is
def peek(myQueue): followed. As these
if isEmpty(myQueue): are user defined
functions any
print('Queue is empty') other name can
return None also be used.
else:
return myQueue[0]

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 Activity 4.1 Let us consider the example of a queue that people
How can you avoid form while waiting at a bank cash counter. Usually,
printing of None, following are the events that occur in queue:
when trying to • Two friends come together and go to the cash
print an empty
queue? counter, i.e. they form a queue - enqueue operation
is performed two times.
• As soon as the person at the front is serviced, he will
be removed from the queue - thus dequeue operation
is performed. Cashier calls Next to serve the next
Activity 4.2
person who is now at the front of the queue.
What if the content of
the complete queue • Cashier wants to know the length of the queue - size
is to be listed? of the queue is checked.
Write a function
for it. • Meanwhile, a few more people walk in the bank, and
three of them join the queue at the cash counter, i.e.
enqueue happens 3 times.
• Another person gets served and leaves the counter,
i.e. dequeue is performed. Cashier calls Next to serve
another person.
• The Next three people get served one after another,
i.e. dequeue is performed thrice.
• Cashier calls Next and realises that there are no more
people to be served - underflow situation happens
Now, let us write the code for the above scenario of
the bank.

Program 4-1
myQueue = list()
# each person to be assigned a code as P1, P2, P3,...
element = input("enter person’s code to enter in queue :”)
enqueue(myQueue,element)
element = input("enter person’s code for insertion in queue :")
enqueue(myQueue,element)
print("person removed from queue is:", dequeue(myQueue))
print(“Number of people in the queue is :”,size(myQueue))
element = input("enter person’s code to enter in queue :")
enqueue(myQueue,element)
element = input("enter person’s code to enter in queue :")
enqueue(myQueue,element)
element = input("enter person’s code to enter in queue :")
enqueue(myQueue,element)

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 print("Now we are going to remove remaining people from the
queue")
while not isEmpty(myQueue):
print("person removed from queue is ",
dequeue(myQueue))
Output
enter person’s code to enter in queue :P1
enter person’s code to enter in queue :P2
person removed from the queue is :p1
number of people in the queue is :1
enter person’s code to enter in queue :P3
enter person’s code to enter in queue :P4
enter person’s code to enter in queue :P5
Now we are going to remove remaining people from the queue
person removed from the queue is :p2
person removed from the queue is :p3
person removed from the queue is :p4
person removed from the queue is :p5
Queue is empty

4.4 Introduction to Deque

Deque (pronounced as “deck”) is an arrangement in
which addition and removal of element(s) can happen
from any end, i.e. head/front or tail/rear. This data
structure does not apply any restriction on the side from
which addition/removal of elements should happen,
so it can be used to implement stack or queue in the
program. It is also known as Double ended queue,
because it permits insertion, deletion operations from
any end.

(insertion) Push Push (insertion)

(deletion) Pop Pop (deletion)

Front Rear

Figure 4.4: Basic deque structure displaying head and tail to implement stack or queue.

4.4.1 Applications of Deque

• At a train ticket purchasing counter, a normal queue
of people is formed for purchasing a ticket. A person
at the front purchased the ticket and left the counter.
After a while they return back to the counter to ask

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 something. As they have already purchased a ticket,
they may have the privilege to join the queue from
the front.
• Vehicles in a highway toll tax booth are served
following the principle of queue. There are multiple
queues if there are parallel booths at the toll gate. In
case all vehicles of a booth are served then vehicles
from the other booth(s) are asked to form a queue in
front of the vacant booth. So, vehicles at the end of
those queues will leave (removed from the end from
where queue was joined) current booth and join
Activity 4.3 queue at the vacant booth.
In a deque, if insertion Following are some examples where data structure
and deletion of
deque maybe applied in computer science:
elements is done from
the same end, it will • To maintain browser history (URL), usually a stack
behave as is used, because once a tab is closed and if you press
1) Queue ctrl+shift+T, the most recently closed URL is opened
2) Stack
first. As the number of URLs which can be stored in
3) List
4) None of the history is fixed, so when this list of URLs becomes
above large, URLs from the end of the list (i.e. which were
least visited) gets deleted.
• Same happens for providing the Do and Undo option
in any text editor.
• To check whether a given string is palindrome or not?
Activity 4.4 Process string left to right (character wise) and insert
In a deque, if insertion
it in deque from tail/rear like a normal queue. Once
and deletion of the entire string is processed (i.e. inserted in deque)
elements is done from we will take out (delete) a character from both the
the opposite end, it will ends and match them till there is no character left
behave as or only one character left in deque. In either case,
1) Queue string is palindrome.
2) Stack
3) List
4) None of the
4.4.2 Operations on Deque
above • INSERTFRONT: This operation is used to insert a
new element at the front of the deque.
• INSERTREAR: This operation is the same as a
normal queue, i.e. insert a new element at the rear
of the deque.
• DELETIONFRONT: This operation is the same as
normal queue, i.e. to remove an element from the
front of the deque.
• DELETIONREAR: This operation is used to remove
one element at a time from the rear of the deque.

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 To perform above operations efficiently on a deque, Notes
we will need all supporting operations used in normal
queue viz Is Empty, Peek, Size.
Let’s understand how these operations work for
checking whether a string is palindrome or not, using a
deque through the following algorithm.
Algorithm 4.1

Step1: Start traversing string (madam) from left side, a

character at a time.
Step 2: Insert the character in deque as normal queue using
INSERTREAR.
Step 3: Repeat Step 1 and Step 2 for all characters of
string (madam)

m a d a insertrear
(m)

Front Rear
Figure 4.5: Status of Deque after 4th iteration

Step 4: Remove one character from the front and one

character from the rear end of deque using
DELETIONFRONT and DELETIONREAR we can
do it.

removefront a d a insertrear
(m) (m)

Front Rear
Figure 4.6: Status of Deque after removing one character from both
the ends.

Step 5: Match these two removed characters.

Step 6: If they are same then
repeat Step 4 and 5 till deque is empty or left
with only one character,
eventually string is Palindrome
else stop as string is not palindrome

4.5 Implementation of Deque Using Python

Like queue, deque is also an ordered linear list, hence
we use list data type to create deque in our program.
The program should have the following functions/
statement(s) defined in it:

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 Notes • A statement to create deque, with name myDeque.
myDeque = list()

• A function insertFront(), to insert an element at the

front of deque having two parameters - name of
deque and element to be inserted. As the element is
to be inserted in the beginning, we will use insert()
with index 0 for it.
def insertFront(myDeque, element):
myDeque.insert(0,element)

• A function insertRear(), to insert an element at the

rear of deque. It’s implementation will be the same as
enqueue() of normal queue requiring two parameters
same as insertFront().
• A function isEmpty(), to check the presence of
element(s) in deque will be the same as the function,
with the same name, defined for normal queue.
• A function deletionRear(), to delete an element from
the rear of the deque. It only requires the name of
deque and returns the deleted element. We will use
pop() without parameter(s) to delete the last element
of the deque.
def deletionRear(myDeque):
if not (isEmpty()):
return myDeque.pop()
# removing data from end of list
else :
print(“Deque empty”)

• A function deletionFront(), to delete an element from

the front of deque. It’s implementation will be the
same as dequeue() of normal queue.
• A function getFront(), to read value from the front of
deque, without removing it from the queue when the
queue is not empty. It accepts the name of deque as
parameter and returns a copy of value.
def getFront(mydeque):
if not (isEmpty()):
return mydeque[0]
else :
print(“ Queue empty”)
• A function getRear(), to read value from the rear of
the deque, without removing it from the deque. The

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 function accepts deque as argument and returns a Notes
copy of value, when the queue is not empty.
def getRear(mydeque):
if not (isempty()):
return mydeque[len(mydeque)-1]
else :
print(“ Deque empty”)
Let us write a main(), function to invoke various
Deque functions :

Program 4-2 Implementation of Deque in Python

def insertFront(myDeque,element):
myDeque.insert(0,element)

def getFront(myDeque):
if not (isEmpty(myDeque)):
return myDeque[0]
else:
print("Queue underflow")

def getRear(myDeque):
if not (isEmpty(myDeque)):
return myDeque[len(myDeque)-1]
else:
print ("Queue underflow")

def insertRear(myDeque,element):
myDeque.append(element)

def isEmpty(myDeque):
if len(myDeque) == 0:
return True
else:
return False

def deletionRear(myDeque):
if not isEmpty(myDeque):
return myDeque.pop()
else:
print("Queue overflow")

def deletionFront(myDeque):
if isEmpty(myDeque):

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 print("Queue underflow")
else:
return myDeque.pop(0)

def main():
dQu = list()
choice = int(input('enter 1 to use as normal queue 2 otherwise
: '))
if choice == 1:
element = input("data for insertion at rear ")
insertRear(dQu,element)
element = getFront(dQu)
print("data at the beginning of queue is ", element)
element = input("data for insertion at front ")
insertRear(dQu,element)
print('data removed from front of queue is ', deletionFront(dQu))
print('data removed from front of queue is ', deletionFront(dQu))

Output
enter 1 to use as normal queue 2 otherwise : 1
data for insertion at rear 23
data at the beginning of queue is 23
data for insertion at rear 45
data removed from front of queue is 23
data removed from front of queue is 45
Queue underflow
data removed from front of queue is None

enter 1 to use as normal queue 2 otherwise : 2

data for insertion at front 34
data at the end of queue is 34
data for insertion at front 56
data removed from rear of queue is 34
data removed from rear of queue is 56
Queue underflow
data removed from rear of queue is None

Summary
• Queue is an ordered linear data structure,
following FIFO strategy.
• Front and Rear are used to indicate beginning
and end of queue.
• In Python, the use of predefined methods takes
care of Front and Rear.

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 • Insertion in a queue happens at the rear end. Notes
Deletion happens at the front.
• Insertion operation is known as enqueue and
deletion operation is known as dequeue.
• To support enqueue and dequeue operations,
isEmpty, isfull and peek operations are used
• Deque is a version of queue, which allows insertion
and deletion at both ends.
• A deque can support both stack and queue
operations.
• Other operations supported by deque are
insertfront, insertrear, deletefront, deleterear,
getfront, getrear, isempty and isfull.

Exercise
1. Fill in the blank
a) ____________________ is a linear list of elements
in which insertion and deletion takes place from
different ends.
b) Operations on a queue are performed in
__________________ order.
c) Insertion operation in a queue is called ______________
and deletion operation in a queue is called
____________________.
d) Deletion of elements is performed from _______________
end of the queue.
e) Elements ‘A’,’S’,’D’ and ‘F’ are present in the queue, and
they are deleted one at a time, ________________________
is the sequence of element received.
f) _______________ is a data structure where elements
can be added or removed at either end, but not in the
middle.
g) A deque contains ‘z’,’x’,’c’,’v’ and ‘b’ . Elements
received after deletion are ‘z’,’b’,’v’,’x’ and ‘c’. ________
__________________________ is the sequence of deletion
operation performed on deque.

2. Compare and contrast queue with stack.

3. How does FIFO describe queue?

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 Notes 4. Write a menu driven python program using queue, to
implement movement of shuttlecock in it’s box.

5. How is queue data type different from deque data type?

6. Show the status of queue after each operation

enqueue(34)
enqueue(54)
dequeue()
enqueue(12)
dequeue()
enqueue(61)
peek()
dequeue()
dequeue()
dequeue()
dequeue()
enqueue(1)

7. Show the status of deque after each operation

peek()
insertFront(12)
insertRear(67)
deletionFront()
insertRear(43)
deletionRear()
deletionFront()
deletionRear()

8. Write a python program to check whether the given

string is palindrome or not, using deque. (Hint : refer to
algorithm 4.1)

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