1. Data Structures and Algorithms
Objectives
In this session, you will learn to:
Identify the features of queues
Implement the different types of queues
Apply queues to solve programming problems
Store and search data by using hashing
Ver. 1.0 Session 11

2. Data Structures and Algorithms
Defining Queues
Consider a situation where you have to create an
application with the following set of requirements:
Application should serve the requests of multiple users.
At a time, only one request can be processed.
The request, which came first should be given priority.
However, the rate at which the requests are received is
much faster than the rate at which they are processed.
Therefore, you need to store the request somewhere until they
are processed.
How can you solve this problem?
You can solve this problem by storing the requests in such a
manner so that they are retrieved in the order of their arrival.
A data structure called queue stores and retrieves data in the
order of its arrival.
A queue is also called a FIFO list.
Ver. 1.0 Session 11

3. Data Structures and Algorithms
Defining Queues (Contd.)
Elements are of elements in which an element is from the
Queue is a listinserted at the rear end and deleted inserted
front end.
at one end and deleted from the other end of the queue.
FRONT REAR
B A E C D
Ver. 1.0 Session 11

4. Data Structures and Algorithms
Just a minute
A queue is also known as a __________ list.
Answer:
FIFO
Ver. 1.0 Session 11

5. Data Structures and Algorithms
Identifying Various Operations on Queues
Various operations implemented on a queue are:
Insert
Delete
FRONT REAR
B A E C D
Ver. 1.0 Session 11

6. Data Structures and Algorithms
Identifying Various Operations on Queues (Contd.)
• Insert: It refers to the addition of an item in the queue.
Suppose you want to add an item F in the following queue.
Since the items are inserted at the rear end, therefore, F is
inserted after D.
Now F becomes the rear end.
FRONT REAR REAR
F
B A E C D F
Ver. 1.0 Session 11

7. Data Structures and Algorithms
Identifying Various Operations on Queues (Contd.)
• Delete: It refers to the deletion of an item from the queue.
Since the items are deleted from the front end, therefore, item
B is removed from the queue.
Now A becomes the front end of the queue.
FRONT FRONT REAR
B A E C D F
Ver. 1.0 Session 11

8. Data Structures and Algorithms
Just a minute
Queues are the data structures in which data can be added
at one end called ______ and deleted from the other end
called _________.
Answer:
rear, front
Ver. 1.0 Session 11

9. Data Structures and Algorithms
Implementing a Queue Using an Array
Problem Statement:
Consider a scenario of a bank. When the customer visits the
counter, a request entry is made and the customer is given a
request number. After receiving request numbers, a customer
has to wait for some time. The customer requests needs to be
queued into the system and processed on the basis of their
arrival. You need to implement an appropriate data storage
mechanism to store these requests in the system.
Ver. 1.0 Session 11

10. Data Structures and Algorithms
Implementing a Queue Using an Array (Contd.)
How can a request this problem? positions, you need
To keep tracksolve number, you need to perform the to
insert you of the rear and front
following steps:
declare two solve this problem by implementing a queue.
You can integer variables, REAR and FRONT.
Let us implementvalue of REAR by FRONT are stores these
Increment the a queue using 1.
If the queue is empty, REAR andan array that set to –1.
request numbers in theindex position REAR in the array.
Insert the element at order of their arrival.
FRONT = –1
REAR = –1
0 1 2 3 4
Ver. 1.0 Session 11

11. Data Structures and Algorithms
Implementing a Queue Using an Array (Contd.)
Write an algorithm to insert values in a queue implemented
through array.
Algorithm to insert values in a queue:
1. If the queue is empty:
a. Set FRONT = 0.
3. Increment REAR by 1.
5. Store the element at index position REAR in the array.
Ver. 1.0 Session 11

12. Data Structures and Algorithms
Implementing a Queue Using an Array (Contd.)
Let us now insert request numbers 1. If the queue is empty:
Requestin the following queue.
number generated 3 a. Set FRONT = 0.
3. Increment REAR by 1.
5. Store the element at index position
REAR in the array.
FRONT = –1
10
REAR = –1
0 1 2 3 4
Ver. 1.0 Session 11

13. Data Structures and Algorithms
Implementing a Queue Using an Array (Contd.)
1. If the queue is empty:
Request number generated 3 a. Set FRONT = 0.
3. Increment REAR by 1.
5. Store the element at index position
REAR in the array.
FRONT = –1
10
REAR = –1
0 1 2 3 4
Ver. 1.0 Session 11

14. Data Structures and Algorithms
Implementing a Queue Using an Array (Contd.)
1. If the queue is empty:
Request number generated 3 a. Set FRONT = 0.
3. Increment REAR by 1.
5. Store the element at index position
REAR in the array.
FRONT = 0
FRONT = –1
10
REAR = –1
0 1 2 3 4
Ver. 1.0 Session 11

15. Data Structures and Algorithms
Implementing a Queue Using an Array (Contd.)
1. If the queue is empty:
Request number generated 3 a. Set FRONT = 0.
• Increment REAR by 1.
• Store the element at index position
REAR in the array.
FRONT = 0 REAR = 0
10
REAR = –1
0 1 2 3 4
Ver. 1.0 Session 11

16. Data Structures and Algorithms
Implementing a Queue Using an Array (Contd.)
1. If the queue is empty:
Request number generated 3 a. Set FRONT = 0.
• Increment REAR by 1.
• Store the element at index position
REAR in the array.
FRONT = 0 REAR = 0
310
0 1 2 3 4
Insertion complete
Ver. 1.0 Session 11

17. Data Structures and Algorithms
Implementing a Queue Using an Array (Contd.)
1. If the queue is empty:
Request number generated 5 a. Set FRONT = 0.
3. Increment REAR by 1.
5. Store the element at index position
REAR in the array.
FRONT = 0 REAR = 0
310
0 1 2 3 4
Ver. 1.0 Session 11

18. Data Structures and Algorithms
Implementing a Queue Using an Array (Contd.)
• If the queue is empty:
Request number generated 5 a. Set FRONT = 0.
3. Increment REAR by 1.
5. Store the element at index position
REAR in the array.
FRONT = 0 REAR = 0
310
0 1 2 3 4
Ver. 1.0 Session 11

19. Data Structures and Algorithms
Implementing a Queue Using an Array (Contd.)
1. If the queue is empty:
Request number generated 5 a. Set FRONT = 0.
• Increment REAR by 1.
• Store the element at index position
REAR in the array.
FRONT = 0 REARREAR = 1
=0
310
0 1 2 3 4
Ver. 1.0 Session 11

20. Data Structures and Algorithms
Implementing a Queue Using an Array (Contd.)
1. If the queue is empty:
Request number generated 5 a. Set FRONT = 0.
• Increment REAR by 1.
• Store the element at index position
REAR in the array.
FRONT = 0 REAR = 1
310 5
0 1 2 3 4
Insertion complete
Ver. 1.0 Session 11

21. Data Structures and Algorithms
Implementing a Queue Using an Array (Contd.)
1. If the queue is empty:
Request number generated 7 a. Set FRONT = 0.
3. Increment REAR by 1.
5. Store the element at index position
REAR in the array.
FRONT = 0 REAR = 1
310 5
0 1 2 3 4
Ver. 1.0 Session 11

22. Data Structures and Algorithms
Implementing a Queue Using an Array (Contd.)
1. If the queue is empty:
Request number generated 7 a. Set FRONT = 0.
3. Increment REAR by 1.
5. Store the element at index position
REAR in the array.
FRONT = 0 REAR = 1
310 5
0 1 2 3 4
Ver. 1.0 Session 11

23. Data Structures and Algorithms
Implementing a Queue Using an Array (Contd.)
1. If the queue is empty:
Request number generated 7 a. Set FRONT = 0.
• Increment REAR by 1.
• Store the element at index position
REAR in the array.
FRONT = 0 REAR = REAR = 2
1
310 5
0 1 2 3 4
Ver. 1.0 Session 11

24. Data Structures and Algorithms
Implementing a Queue Using an Array (Contd.)
1. If the queue is empty:
Request number generated 7 a. Set FRONT = 0.
• Increment REAR by 1.
• Store the element at index position
REAR in the array.
FRONT = 0 REAR = 2
310 5 7
0 1 2 3 4
Insertion complete
Ver. 1.0 Session 11

25. Data Structures and Algorithms
Implementing a Queue Using an Array (Contd.)
1. If the queue is empty:
Request number generated 10 a. Set FRONT = 0.
3. Increment REAR by 1.
5. Store the element at index position
REAR in the array.
FRONT = 0 REAR = 2
310 5 7
0 1 2 3 4
Ver. 1.0 Session 11

26. Data Structures and Algorithms
Implementing a Queue Using an Array (Contd.)
1. If the queue is empty:
Request number generated 10 a. Set FRONT = 0.
3. Increment REAR by 1.
5. Store the element at index position
REAR in the array.
FRONT = 0 REAR = 2
310 5 7
0 1 2 3 4
Ver. 1.0 Session 11

27. Data Structures and Algorithms
Implementing a Queue Using an Array (Contd.)
1. If the queue is empty:
Request number generated 10 a. Set FRONT = 0.
• Increment REAR by 1.
• Store the element at index position
REAR in the array.
FRONT = 0 REAR = REAR = 3
2
310 5 7
0 1 2 3 4
Ver. 1.0 Session 11

28. Data Structures and Algorithms
Implementing a Queue Using an Array (Contd.)
1. If the queue is empty:
Request number generated 10 a. Set FRONT = 0.
• Increment REAR by 1.
• Store the element at index position
REAR in the array.
FRONT = 0 REAR = 3
310 5 7 10
0 1 2 3 4
Insertion complete
Ver. 1.0 Session 11

29. Data Structures and Algorithms
Implementing a Queue Using an Array (Contd.)
1. If the queue is empty:
Request number generated 15 a. Set FRONT = 0.
3. Increment REAR by 1.
5. Store the element at index position
REAR in the array.
FRONT = 0 REAR = 3
310 5 7 10
0 1 2 3 4
Ver. 1.0 Session 11

30. Data Structures and Algorithms
Implementing a Queue Using an Array (Contd.)
1. If the queue is empty:
Request number generated 15 a. Set FRONT = 0.
3. Increment REAR by 1.
5. Store the element at index position
REAR in the array.
FRONT = 0 REAR = 3
310 5 7 10
0 1 2 3 4
Ver. 1.0 Session 11

31. Data Structures and Algorithms
Implementing a Queue Using an Array (Contd.)
1. If the queue is empty:
Request number generated 15 a. Set FRONT = 0.
• Increment REAR by 1.
• Store the element at index position
REAR in the array.
FRONT = 0 REAR =REAR = 4
3
310 5 7 10
0 1 2 3 4
Ver. 1.0 Session 11

32. Data Structures and Algorithms
Implementing a Queue Using an Array (Contd.)
1. If the queue is empty:
Request number generated 15 a. Set FRONT = 0.
• Increment REAR by 1.
• Store the element at index position
REAR in the array.
FRONT = 0 REAR = 4
310 5 7 10 15
0 1 2 3 4
Insertion complete
Ver. 1.0 Session 11

33. Data Structures and Algorithms
Implementing a Queue Using an Array (Contd.)
The requests stored in the queue are served on a
first-come-first-served basis.
As the requests are being served, the corresponding
request numbers needs to be deleted from the queue.
Ver. 1.0 Session 11

34. Data Structures and Algorithms
Implementing a Queue Using an Array (Contd.)
Write an algorithm to delete an element from a queue
implemented through array.
Algorithm to delete an element from a queue:
1. Retrieve the element at index FRONT.
3. Increment FRONT by 1.
Ver. 1.0 Session 11

35. Data Structures and Algorithms
Implementing a Queue Using an Array (Contd.)
One request processed
Let us see how requests are 1. Retrieve the element at index
FRONT.
deleted from the queue once they
3. Increment FRONT by 1.
get processed.
FRONT = 0 REAR = 4
3 5 7 10 15
0 1 2 3 4
Ver. 1.0 Session 11

36. Data Structures and Algorithms
Implementing a Queue Using an Array (Contd.)
One request processed • Retrieve the element at index
FRONT.
• Increment FRONT by 1.
FRONT = 0 REAR = 4
310 5 7 10 15
0 1 2 3 4
Ver. 1.0 Session 11

37. Data Structures and Algorithms
Implementing a Queue Using an Array (Contd.)
• Retrieve the element at index
FRONT.
• Increment FRONT by 1.
FRONT = 0
FRONT = 1 REAR = 4
10 5 7 10 15
0 1 2 3 4
Delete operation complete
Ver. 1.0 Session 11

38. Data Structures and Algorithms
Implementing a Queue Using an Array (Contd.)
One request processed 1. Retrieve the element at index
FRONT.
3. Increment FRONT by 1.
FRONT = 1 REAR = 4
10 5 7 10 15
0 1 2 3 4
Ver. 1.0 Session 11

39. Data Structures and Algorithms
Implementing a Queue Using an Array (Contd.)
One request processed • Retrieve the element at index
FRONT.
• Increment FRONT by 1.
FRONT = 1 REAR = 4
10 5 7 10 15
0 1 2 3 4
Ver. 1.0 Session 11

40. Data Structures and Algorithms
Implementing a Queue Using an Array (Contd.)
• Retrieve the element at index
FRONT.
• Increment FRONT by 1.
FRONT = FRONT = 2
1 REAR = 4
10 7 10 15
0 1 2 3 4
Delete operation complete
Ver. 1.0 Session 11

41. Data Structures and Algorithms
Implementing a Queue Using an Array (Contd.)
To you delete an insert or delete operation, you need to
As implement elements from the queue, the queue moves
incrementarray.
down the the values of REAR or FRONT by one,
respectively.
The disadvantage of this approach is that the storage space
However, these values are never never used again.
in the beginning is discarded and decremented.
Consider the following queue.
FRONT = 3 REAR = 4
10 10 15
0 1 2 3 4
REAR is at the last index position.
Therefore, you cannot insert elements in this queue, even
though there is space for them.
This means that all the initial vacant positions go waste.
Ver. 1.0 Session 11

42. Data Structures and Algorithms
Implementing a Queue Using an Array (Contd.)
How can you solve this zero index position, every delete
To maintain FRONT at problem?
operation would requireproblem shift keep FRONT always at the
One way to solve this you to is to all the succeeding
elements in the array one position left.
zero index position.
Let Refer to the following queue.
us implement a delete operation on the following queue.
FRONT = 0 REAR = 3
3
10 5 7 10
0 1 2 3 4
Ver. 1.0 Session 11

43. Data Structures and Algorithms
Implementing a Queue Using an Array (Contd.)
To maintain FRONT at zero index position, every delete
operation would require you to shift all the succeeding
elements in the array one position left.
Let us implement a delete operation on the following queue.
FRONT = 0 REAR = 3
5
10 5 7 10
0 1 2 3 4
Ver. 1.0 Session 11

44. Data Structures and Algorithms
Implementing a Queue Using an Array (Contd.)
To maintain FRONT at zero index position, every delete
operation would require you to shift all the succeeding
elements in the array one position left.
Let us implement a delete operation on the following queue.
FRONT = 0 REAR = 3
5
10 7 7 10
0 1 2 3 4
Ver. 1.0 Session 11

45. Data Structures and Algorithms
Implementing a Queue Using an Array (Contd.)
To maintain FRONT at zero index position, every delete
operation would require you to shift all the succeeding
elements in the array one position left.
Let us implement a delete operation on the following queue.
FRONT = 0 REAR = 3
5
10 7 10 10
0 1 2 3 4
Ver. 1.0 Session 11

46. Data Structures and Algorithms
Implementing a Queue Using an Array (Contd.)
To maintain FRONT at zero index position, every delete
operation would require you to shift all the succeeding
elements in the array one position left.
Let us implement a delete operation on the following queue.
FRONT = 0 REAR = 2REAR = 3
5
10 7 10
0 1 2 3 4
Ver. 1.0 Session 11

47. Data Structures and Algorithms
Implementing a Queue Using an Array (Contd.)
Disadvantage of this approach:
Advantage of this approach:
Every delete operation all the empty positions in an array.
It enables you to utilize requires you to shift all the succeeding
elements in the queue one position there
Therefore, unlike the previous case,left. is no wastage of
space. is lengthy, this can be very time consuming.
If the list
FRONT = 0 REAR = 2
5
10 7 10
0 1 2 3 4
Ver. 1.0 Session 11

48. Data Structures and Algorithms
Implementing a Queue Using an Array (Contd.)
An effective way to solve this problem is to implement the
queue in the form of a circular array.
In this approach, if REAR is at the last index position and if
there is space in the beginning of an array, then you can set
the value of REAR to zero and start inserting elements from
the beginning.
REAR = 0 FRONT = 3 REAR = 4
Insert 5
510 10 15
0 1 2 3 4
Ver. 1.0 Session 11

49. Data Structures and Algorithms
Implementing a Queue Using an Array (Contd.)
The cells in the array are treated as if they are arranged in a
ring.
[0]
[4] [1]
REAR = 3 10 7 FRONT = 2
[3] [2]
Ver. 1.0 Session 11

50. Data Structures and Algorithms
Implementing a Queue Using an Array (Contd.)
Let usan algorithm to insert
Write now implement a few 1. If the queue is empty (If FRONT= –1):
Requestinsert operations on the following
values in a queue implemented
number generated 15 a. Set FRONT = 0
b. Set REAR = 0
circular queue:
as a circular array. c. Go to step 4
FRONT = 1 REAR = 3
• If REAR is at the last index position:
a. Set REAR = 0
10 20 23 10 b. Go to step 4
• Increment REAR by 1
0 1 2 3 4
• Queue[REAR] = element
Ver. 1.0 Session 11

51. Data Structures and Algorithms
Implementing a Queue Using an Array (Contd.)
1. If the queue is empty (If FRONT= –1):
Request number generated 15 a. Set FRONT = 0
b. Set REAR = 0
c. Go to step 4
FRONT = 1 REAR = 3
• If REAR is at the last index position:
a. Set REAR = 0
10 20 23 10 b. Go to step 4
• Increment REAR by 1
0 1 2 3 4
• Queue[REAR] = element
Ver. 1.0 Session 11

52. Data Structures and Algorithms
Implementing a Queue Using an Array (Contd.)
1. If the queue is empty (If FRONT= –1):
Request number generated 15 a. Set FRONT = 0
b. Set REAR = 0
c. Go to step 4
FRONT = 1 REAR = 3
3. If REAR is at the last index position:
a. Set REAR = 0
10 20 23 10 b. Go to step 4
• Increment REAR by 1
0 1 2 3 4
• Queue[REAR] = element
Ver. 1.0 Session 11

53. Data Structures and Algorithms
Implementing a Queue Using an Array (Contd.)
1. If the queue is empty (If FRONT= –1):
Request number generated 15 a. Set FRONT = 0
b. Set REAR = 0
c. Go to step 4
FRONT = 1 REAR = 3 = 4
REAR
3. If REAR is at the last index position:
a. Set REAR = 0
10 20 23 10 b. Go to step 4
• Increment REAR by 1
0 1 2 3 4
• Queue[REAR] = element
Ver. 1.0 Session 11

54. Data Structures and Algorithms
Implementing a Queue Using an Array (Contd.)
1. If the queue is empty (If FRONT= –1):
Request number generated 15 a. Set FRONT = 0
b. Set REAR = 0
c. Go to step 4
FRONT = 1 REAR = 4
3. If REAR is at the last index position:
a. Set REAR = 0
10 20 23 10 15 b. Go to step 4
• Increment REAR by 1
0 1 2 3 4
• Queue[REAR] = element
Insertion complete
Ver. 1.0 Session 11

55. Data Structures and Algorithms
Implementing a Queue Using an Array (Contd.)
1. If the queue is empty (If FRONT= –1):
Request number generated 17 a. Set FRONT = 0
b. Set REAR = 0
c. Go to step 4
FRONT = 1 REAR = 4
3. If REAR is at the last index position:
a. Set REAR = 0
10 20 23 10 15 b. Go to step 4
• Increment REAR by 1
0 1 2 3 4
• Queue[REAR] = element
Ver. 1.0 Session 11

56. Data Structures and Algorithms
Implementing a Queue Using an Array (Contd.)
1. If the queue is empty (If FRONT= –1):
Request number generated 17 a. Set FRONT = 0
b. Set REAR = 0
c. Go to step 4
FRONT = 1 REAR = 4
3. If REAR is at the last index position:
a. Set REAR = 0
10 20 23 10 15 b. Go to step 4
• Increment REAR by 1
0 1 2 3 4
• Queue[REAR] = element
Ver. 1.0 Session 11

57. Data Structures and Algorithms
Implementing a Queue Using an Array (Contd.)
1. If the queue is empty (If FRONT= –1):
Request number generated 17 a. Set FRONT = 0
b. Set REAR = 0
c. Go to step 4
FRONT = 1 REAR = 4
3. If REAR is at the last index position:
a. Set REAR = 0
10 20 23 10 15 b. Go to step 4
• Increment REAR by 1
0 1 2 3 4
• Queue[REAR] = element
Ver. 1.0 Session 11

58. Data Structures and Algorithms
Implementing a Queue Using an Array (Contd.)
1. If the queue is empty (If FRONT= –1):
Request number generated 17 a. Set FRONT = 0
b. Set REAR = 0
c. Go to step 4
REAR = 0 FRONT = 1 REAR = 4
3. If REAR is at the last index position:
• Set REAR = 0
10 20 23 10 15 • Go to step 4
• Increment REAR by 1
0 1 2 3 4
• Queue[REAR] = element
Ver. 1.0 Session 11

59. Data Structures and Algorithms
Implementing a Queue Using an Array (Contd.)
1. If the queue is empty (If FRONT= –1):
Request number generated 17 a. Set FRONT = 0
b. Set REAR = 0
c. Go to step 4
REAR = 0 FRONT = 1
3. If REAR is at the last index position:
• Set REAR = 0
10 20 23 10 15 • Go to step 4
• Increment REAR by 1
0 1 2 3 4
• Queue[REAR] = element
Ver. 1.0 Session 11

60. Data Structures and Algorithms
Implementing a Queue Using an Array (Contd.)
1. If the queue is empty (If FRONT= –1):
Request number generated 17 a. Set FRONT = 0
b. Set REAR = 0
c. Go to step 4
REAR = 0 FRONT = 1
3. If REAR is at the last index position:
a. Set REAR = 0
17
10 20 23 10 15 b. Go to step 4
• Increment REAR by 1
0 1 2 3 4
• Queue[REAR] = element
Insertion complete
Ver. 1.0 Session 11

61. Data Structures and Algorithms
Implementing a Queue Using an Array (Contd.)
1. If the queue is empty (If FRONT= –1):
Request number generated 25 a. Set FRONT = 0
b. Set REAR = 0
c. Go to step 4
REAR = 0 FRONT = 1
3. If REAR is at the last index position:
a. Set REAR = 0
17
10 20 23 10 15 b. Go to step 4
• Increment REAR by 1
0 1 2 3 4
• Queue[REAR] = element
Ver. 1.0 Session 11

62. Data Structures and Algorithms
Implementing a Queue Using an Array (Contd.)
1. If the queue is empty (If FRONT= –1):
Request number generated 25 a. Set FRONT = 0
b. Set REAR = 0
c. Go to step 4
REAR = 0 FRONT = 1
3. If REAR is at the last index position:
a. Set REAR = 0
17
10 20 23 10 15 b. Go to step 4
• Increment REAR by 1
0 1 2 3 4
• Queue[REAR] = element
Ver. 1.0 Session 11

63. Data Structures and Algorithms
Implementing a Queue Using an Array (Contd.)
1. If the queue is empty (If FRONT= –1):
Request number generated 25 a. Set FRONT = 0
b. Set REAR = 0
c. Go to step 4
REAR = 0 FRONT = 1
3. If REAR is at the last index position:
a. Set REAR = 0
17
10 20 23 10 15 b. Go to step 4
• Increment REAR by 1
0 1 2 3 4
• Queue[REAR] = element
Ver. 1.0 Session 11

64. Data Structures and Algorithms
Implementing a Queue Using an Array (Contd.)
1. If the queue is empty (If FRONT= –1):
Request number generated 25 a. Set FRONT = 0
b. Set REAR = 0
c. Go to step 4
REAR = 0 FRONT = 1
3. If REAR is at the last index position:
a. Set REAR = 0
17
10 20 23 10 15 b. Go to step 4
• Increment REAR by 1
0 1 2 3 4
• Queue[REAR] = element
Before cannot be incremented operation, you should always check for the
Inserting an element in ainsert because the queue is full.
REAR implementing an full queue leads to queue overflow.
queue full condition.
Ver. 1.0 Session 11

65. Data Structures and Algorithms
Implementing a Queue Using an Array (Contd.)
The conditions for queue full are as follows:
If FRONT = 0 and REAR If FRONT = REAR + 1
is at the last index position
OR
FRONT = 0 REAR = 4 REAR = 2 FRONT = 3
310 5 7 10 15 17
10 20 23 10 15
0 1 2 3 4 0 1 2 3 4
Ver. 1.0 Session 11

66. Data Structures and Algorithms
Implementing a Queue Using an Array (Contd.)
Modified algorithm for inserting an 1. If the queue is full:
element in a circular queue. a. Display “Queue overflow”
b. Exit
3. If queue is empty (If FRONT = –1):
a. Set FRONT = 0
b. Set REAR = 0
c. Go to Step 5
• If REAR is at the last index position:
a. Set REAR = 0
b. Go to step 5
• Increment REAR by 1
• Queue[REAR] = element
Ver. 1.0 Session 11

67. Data Structures and Algorithms
Implementing a Queue Using an Array (Contd.)
Writelet us implementimplement delete operation in a queue
Now an algorithm to a delete operation on a queue
implemented asthe form ofarray.
in a circular a circular array.
To delete an element, you need to increment the value of
FRONT by one. This is same as that of a linear queue.
However, if the element to be deleted is present at the last
index position, then the value FRONT is reset to zero.
If there is only one element present in the queue, then the
value of FRONT and REAR is set to –1.
Ver. 1.0 Session 11

68. Data Structures and Algorithms
Implementing a Queue Using an Array (Contd.)
Algorithm to delete an element 1. If there is only one element in the
queue:
from a circular queue.
a. Set FRONT = –1
b. Set REAR = –1
c. Exit
REAR = 0 FRONT = 4 4. If FRONT is at the last index
position:
a. Set FRONT = 0
b. Exit
17
10 20 15
• Increment FRONT by 1
0 1 2 3 4
Ver. 1.0 Session 11

69. Data Structures and Algorithms
Implementing a Queue Using an Array (Contd.)
One request processed 1. If there is only one element in the
queue:
a. Set FRONT = –1
b. Set REAR = –1
c. Exit
REAR = 0 FRONT = 4 4. If FRONT is at the last index
position:
a. Set FRONT = 0
b. Exit
17
10 20 15
• Increment FRONT by 1
0 1 2 3 4
Ver. 1.0 Session 11

70. Data Structures and Algorithms
Implementing a Queue Using an Array (Contd.)
One request processed • If there is only one element in the
queue:
a. Set FRONT = –1
b. Set REAR = –1
c. Exit
REAR = 0 FRONT = 4 4. If FRONT is at the last index
position:
a. Set FRONT = 0
b. Exit
17
10 20 15
• Increment FRONT by 1
0 1 2 3 4
Ver. 1.0 Session 11

71. Data Structures and Algorithms
Implementing a Queue Using an Array (Contd.)
One request processed 1. If there is only one element in the
queue:
a. Set FRONT = –1
b. Set REAR = –1
c. Exit
REAR = 0 FRONT = 4 • If FRONT is at the last index
position:
a. Set FRONT = 0
b. Exit
17
10 20 15
• Increment FRONT by 1
0 1 2 3 4
Ver. 1.0 Session 11

72. Data Structures and Algorithms
Implementing a Queue Using an Array (Contd.)
One request processed 1. If there is only one element in the
queue:
a. Set FRONT = –1
b. Set REAR = –1
c. Exit
FRONT = 0 REAR = 0 FRONT = 4 4. If FRONT is at the last index
position:
• Set FRONT = 0
• Exit
17
10 20 15
• Increment FRONT by 1
0 1 2 3 4
Ver. 1.0 Session 11

73. Data Structures and Algorithms
Implementing a Queue Using an Array (Contd.)
One request processed 1. If there is only one element in the
queue:
a. Set FRONT = –1
b. Set REAR = –1
c. Exit
FRONT = 0 REAR = 0 4. If FRONT is at the last index
position:
• Set FRONT = 0
• Exit
17
10 20
• Increment FRONT by 1
0 1 2 3 4
Deletion complete
Ver. 1.0 Session 11

74. Data Structures and Algorithms
Implementing a Queue Using an Array (Contd.)
One request processed 1. If there is only one element in the
queue:
a. Set FRONT = –1
b. Set REAR = –1
c. Exit
FRONT = 0 REAR = 0 4. If FRONT is at the last index
position:
a. Set FRONT = 0
b. Exit
17
10 20
• Increment FRONT by 1
0 1 2 3 4
Ver. 1.0 Session 11

75. Data Structures and Algorithms
Implementing a Queue Using an Array (Contd.)
One request processed • If there is only one element in the
queue:
a. Set FRONT = –1
b. Set REAR = –1
c. Exit
FRONT = 0 REAR = 0 4. If FRONT is at the last index
position:
a. Set FRONT = 0
b. Exit
17
10 20
• Increment FRONT by 1
0 1 2 3 4
Ver. 1.0 Session 11

76. Data Structures and Algorithms
Implementing a Queue Using an Array (Contd.)
One request processed 1. If there is only one element in the
queue:
a. Set FRONT = –1
b. Set REAR = –1
c. Exit
FRONT = 0 REAR = 0 • If FRONT is at the last index
position:
a. Set FRONT = 0
b. Exit
17
10 20
• Increment FRONT by 1
0 1 2 3 4
Ver. 1.0 Session 11

77. Data Structures and Algorithms
Implementing a Queue Using an Array (Contd.)
One request processed 1. If there is only one element in the
queue:
a. Set FRONT = –1
b. Set REAR = –1
c. Exit
FRONT = 0
FRONT = 0 REAR = 0 4. If FRONT is at the last index
position:
a. Set FRONT = 0
b. Exit
17
10 20
• Increment FRONT by 1
0 1 2 3 4
Deletion complete
Ver. 1.0 Session 11

78. Data Structures and Algorithms
Implementing a Queue Using an Array (Contd.)
One request processed 1. If there is only one element in the
queue:
a. Set FRONT = –1
b. Set REAR = –1
c. Exit
FRONT = 0
REAR = 0 4. If FRONT is at the last index
position:
a. Set FRONT = 0
b. Exit
10 20
• Increment FRONT by 1
0 1 2 3 4
Ver. 1.0 Session 11

79. Data Structures and Algorithms
Implementing a Queue Using an Array (Contd.)
One request processed 1. If there is only one element in the
queue:
a. Set FRONT = –1
b. Set REAR = –1
c. Exit
FRONT = 0
REAR = 0 4. If FRONT is at the last index
position:
a. Set FRONT = 0
b. Exit
10 20
• Increment FRONT by 1
0 1 2 3 4
Ver. 1.0 Session 11

80. Data Structures and Algorithms
Implementing a Queue Using an Array (Contd.)
One request processed 1. If there is only one element in the
queue:
• Set FRONT = –1
• Set REAR = –1
• Exit
FRONT = 0
REAR = 0 4. If FRONT is at the last index
position:
a. Set FRONT = 0
b. Exit
FRONT = –1 10 20
• Increment FRONT by 1
0 1 2 3 4
Ver. 1.0 Session 11

81. Data Structures and Algorithms
Implementing a Queue Using an Array (Contd.)
One request processed 1. If there is only one element in the
queue:
• Set FRONT = –1
• Set REAR = –1
• Exit
REAR = 0 4. If FRONT is at the last index
position:
a. Set FRONT = 0
b. Exit
FRONT = –1 10
• Increment FRONT by 1
REAR = –1 0 1 2 3 4
Ver. 1.0 Session 11

82. Data Structures and Algorithms
Implementing a Queue Using an Array (Contd.)
One request processed 1. If there is only one element in the
queue:
• Set FRONT = –1
• Set REAR = –1
• Exit
• If FRONT is at the last index
position:
a. Set FRONT = 0
b. Exit
FRONT = –1 10
• Increment FRONT by 1
REAR = –1 0 1 2 3 4
Deletion complete
Ver. 1.0 Session 11

83. Data Structures and Algorithms
Implementing a Queue Using an Array (Contd.)
The queue stage, empty. try to
At this is now if you 1. If there is only one element in the
queue:
implement a delete operation, it
a. Set FRONT = –1
will result in queue underflow. b. Set REAR = –1
c. Exit
4. If FRONT is at the last index
position:
a. Set FRONT = 0
b. Exit
FRONT = –1 10
• Increment FRONT by 1
REAR = –1 0 1 2 3 4
Therefore, before implementing a
delete operation, you first need to
check whether the queue is
empty or not.
Ver. 1.0 Session 11

84. Data Structures and Algorithms
Implementing a Queue Using an Array (Contd.)
The condition for queue empty an
Modified algorithm for deleting is: • If the queue is empty: // If
// FRONT = –1
element from a circular queue:
FRONT = –1 a. Display “Queue underflow”
b. Exit
• If there is only one element in the
queue: // If FRONT = REAR
a. Set FRONT = –1
b. Set REAR = –1
c. Exit
7. If FRONT is at the last index
position:
a. Set FRONT = 0
b. Exit
• Increment FRONT by 1
Ver. 1.0 Session 11

85. Data Structures and Algorithms
Just a minute
What is the advantage of implementing a queue in the form
of a circular array, instead of a linear array structure?
Answer:
If you implement a queue in the form of a linear array, you can
add elements only in the successive index positions. However,
when you reach the end of the queue, you cannot start
inserting elements from the beginning, even if there is space
for them at the beginning. You can overcome this
disadvantage by implementing a queue in the form of a
circular array. In this case, you can keep inserting elements till
all the index positions are filled. Hence, it solves the problem
of unutilized space.
Ver. 1.0 Session 11

86. Data Structures and Algorithms
Activity: Implementing a Queue Using Circular Array
Problem Statement:
Write a program to implement insert and delete operations on
a queue implemented in the form of a circular array.
Ver. 1.0 Session 11

87. Data Structures and Algorithms
Implementing a Queue Using a Linked List
What is the disadvantage of implementing a queue as an
array?
To implement a queue using an array, you must know the
maximum number of elements in the queue in advance.
To solve this problem, you should implement the queue in
the form of a linked list.
Ver. 1.0 Session 11

88. Data Structures and Algorithms
Implementing a Queue Using a Linked List (Contd.)
To keep track of the rear and front positions, you need to
declare two variables/pointers, REAR and FRONT, that will
always point to the rear and front end of the queue
respectively.
If the queue is empty, REAR and FRONT point to NULL.
FRONT REAR
310 5 7 15
Ver. 1.0 Session 11

89. Data Structures and Algorithms
Inserting an Element in a Linked Queue
Write an algorithm to implement insert operation in a linked
queue.
Ver. 1.0 Session 11

90. Data Structures and Algorithms
Inserting an Element in a Linked Queue (Contd.)
Algorithminitially, the queue
Suppose to insert an 1. Allocate memory for the new node.
Requestelement generated queue.
number
is empty.in a linked 3 3. Assign value to the data field of the new
node.
5. Make the next field of the new node point to
NULL.
REAR = NULL
7. If the queue is empty, execute the following
FRONT = NULL
steps:
a. Make FRONT point to the new node
b. Make REAR point to the new node
c. Exit
9. Make the next field of REAR point to the new
node.
11. Make REAR point to the new node.
Ver. 1.0 Session 11

91. Data Structures and Algorithms
Inserting an Element in a Linked Queue (Contd.)
• Allocate memory for the new node.
Request number generated 3 • Assign value to the data field of the new
node.
• Make the next field of the new node point to
NULL.
REAR = NULL
• If the queue is empty, execute the following
FRONT = NULL
steps:
a. Make FRONT point to the new node
b. Make REAR point to the new node
c. Exit
9. Make the next field of REAR point to the new
node.
11. Make REAR point to the new node.
Ver. 1.0 Session 11

92. Data Structures and Algorithms
Inserting an Element in a Linked Queue (Contd.)
• Allocate memory for the new node.
Request number generated 3 • Assign value to the data field of the new
node.
• Make the next field of the new node point to
NULL.
REAR = NULL
• If the queue is empty, execute the following
FRONT = NULL
steps:
a. Make FRONT point to the new node
b. Make REAR point to the new node
c. Exit
9. Make the next field of REAR point to the new
10
3 node.
11. Make REAR point to the new node.
Ver. 1.0 Session 11

93. Data Structures and Algorithms
Inserting an Element in a Linked Queue (Contd.)
• Allocate memory for the new node.
Request number generated 3 • Assign value to the data field of the new
node.
• Make the next field of the new node point to
NULL.
REAR = NULL
• If the queue is empty, execute the following
FRONT = NULL
steps:
a. Make FRONT point to the new node
b. Make REAR point to the new node
c. Exit
9. Make the next field of REAR point to the new
10
3 node.
11. Make REAR point to the new node.
Ver. 1.0 Session 11

94. Data Structures and Algorithms
Inserting an Element in a Linked Queue (Contd.)
• Allocate memory for the new node.
Request number generated 3 • Assign value to the data field of the new
node.
• Make the next field of the new node point to
NULL.
REAR = NULL
• If the queue is empty, execute the following
FRONT = NULL
steps:
a. Make FRONT point to the new node
b. Make REAR point to the new node
c. Exit
9. Make the next field of REAR point to the new
10
3 node.
11. Make REAR point to the new node.
Ver. 1.0 Session 11

95. Data Structures and Algorithms
Inserting an Element in a Linked Queue (Contd.)
1. Allocate memory for the new node.
Request number generated 3 3. Assign value to the data field of the new
node.
5. Make the next field of the new node point to
NULL.
REAR = NULL
7. If the queue is empty, execute the following
FRONT = NULL
steps:
FRONT
• Make FRONT point to the new node
• Make REAR point to the new node
• Exit
9. Make the next field of REAR point to the new
10
3 node.
11. Make REAR point to the new node.
Ver. 1.0 Session 11

96. Data Structures and Algorithms
Inserting an Element in a Linked Queue (Contd.)
1. Allocate memory for the new node.
Request number generated 3 3. Assign value to the data field of the new
node.
5. Make the next field of the new node point to
NULL.
REAR = NULL
7. If the queue is empty, execute the following
steps:
FRONT REAR
• Make FRONT point to the new node
• Make REAR point to the new node
• Exit
9. Make the next field of REAR point to the new
10
3 node.
11. Make REAR point to the new node.
Ver. 1.0 Session 11

97. Data Structures and Algorithms
Inserting an Element in a Linked Queue (Contd.)
1. Allocate memory for the new node.
Request number generated 3 3. Assign value to the data field of the new
node.
5. Make the next field of the new node point to
NULL.
7. If the queue is empty, execute the following
steps:
FRONT REAR
• Make FRONT point to the new node
• Make REAR point to the new node
• Exit
9. Make the next field of REAR point to the new
10
3 node.
11. Make REAR point to the new node.
Insert operation complete
Ver. 1.0 Session 11

98. Data Structures and Algorithms
Inserting an Element in a Linked Queue (Contd.)
1. Allocate memory for the new node.
Request number generated 5 3. Assign value to the data field of the new
node.
5. Make the next field of the new node point to
NULL.
7. If the queue is empty, execute the following
steps:
FRONT REAR
a. Make FRONT point to the new node
b. Make REAR point to the new node
c. Exit
9. Make the next field of REAR point to the new
10
3 node.
11. Make REAR point to the new node.
Ver. 1.0 Session 11

99. Data Structures and Algorithms
Inserting an Element in a Linked Queue (Contd.)
• Allocate memory for the new node.
Request number generated 5 • Assign value to the data field of the new
node.
• Make the next field of the new node point to
NULL.
• If the queue is empty, execute the following
steps:
FRONT REAR
a. Make FRONT point to the new node
b. Make REAR point to the new node
c. Exit
9. Make the next field of REAR point to the new
10
3 node.
11. Make REAR point to the new node.
Ver. 1.0 Session 11

100. Data Structures and Algorithms
Inserting an Element in a Linked Queue (Contd.)
• Allocate memory for the new node.
Request number generated 5 • Assign value to the data field of the new
node.
• Make the next field of the new node point to
NULL.
• If the queue is empty, execute the following
steps:
FRONT REAR
a. Make FRONT point to the new node
b. Make REAR point to the new node
c. Exit
9. Make the next field of REAR point to the new
10
3 10
5 node.
11. Make REAR point to the new node.
Ver. 1.0 Session 11

101. Data Structures and Algorithms
Inserting an Element in a Linked Queue (Contd.)
• Allocate memory for the new node.
Request number generated 5 • Assign value to the data field of the new
node.
• Make the next field of the new node point to
NULL.
• If the queue is empty, execute the following
steps:
FRONT REAR
a. Make FRONT point to the new node
b. Make REAR point to the new node
c. Exit
9. Make the next field of REAR point to the new
10
3 10
5 node.
11. Make REAR point to the new node.
Ver. 1.0 Session 11

102. Data Structures and Algorithms
Inserting an Element in a Linked Queue (Contd.)
• Allocate memory for the new node.
Request number generated 5 • Assign value to the data field of the new
node.
• Make the next field of the new node point to
NULL.
• If the queue is empty, execute the following
steps:
FRONT REAR
a. Make FRONT point to the new node
b. Make REAR point to the new node
c. Exit
9. Make the next field of REAR point to the new
10
3 10
5 node.
11. Make REAR point to the new node.
Ver. 1.0 Session 11

103. Data Structures and Algorithms
Inserting an Element in a Linked Queue (Contd.)
1. Allocate memory for the new node.
Request number generated 5 3. Assign value to the data field of the new
node.
5. Make the next field of the new node point to
NULL.
7. If the queue is empty, execute the following
steps:
FRONT REAR
a. Make FRONT point to the new node
b. Make REAR point to the new node
c. Exit
• Make the next field of REAR point to the new
10
3 10
5 node.
• Make REAR point to the new node.
Ver. 1.0 Session 11

104. Data Structures and Algorithms
Inserting an Element in a Linked Queue (Contd.)
1. Allocate memory for the new node.
Request number generated 5 3. Assign value to the data field of the new
node.
5. Make the next field of the new node point to
NULL.
7. If the queue is empty, execute the following
steps:
FRONT REAR REAR
a. Make FRONT point to the new node
b. Make REAR point to the new node
c. Exit
• Make the next field of REAR point to the new
10
3 10
5 node.
• Make REAR point to the new node.
Insert operation complete
Ver. 1.0 Session 11

105. Data Structures and Algorithms
Deleting an Element from a Linked Queue
Write an algorithm to implement the delete operation on a
linked queue.
Ver. 1.0 Session 11

106. Data Structures and Algorithms
Deleting an Element from a Linked Queue (Contd.)
One request processed delete
Algorithm to implement • If the queue is empty: // FRONT = NULL
operation on a linked queue. a. Display “Queue empty”
b. Exit
3. Mark the node marked FRONT as current
5. Make FRONT point to the next node in its
sequence
FRONT REAR
7. Release the memory for the node marked
as current
310 5 7 10
Ver. 1.0 Session 11

107. Data Structures and Algorithms
Deleting an Element from a Linked Queue (Contd.)
One request processed • If the queue is empty: // FRONT = NULL
a. Display “Queue empty”
b. Exit
3. Mark the node marked FRONT as current
5. Make FRONT point to the next node in its
sequence
FRONT REAR
7. Release the memory for the node marked
as current
310 5 7 10
Ver. 1.0 Session 11

108. Data Structures and Algorithms
Deleting an Element from a Linked Queue (Contd.)
One request processed • If the queue is empty: // FRONT = NULL
a. Display “Queue empty”
b. Exit
• Mark the node marked FRONT as current
• Make FRONT point to the next node in its
sequence
FRONT REAR
• Release the memory for the node marked
as current
310 5 7 10
current
Ver. 1.0 Session 11

109. Data Structures and Algorithms
Deleting an Element from a Linked Queue (Contd.)
One request processed • If the queue is empty: // FRONT = NULL
a. Display “Queue empty”
b. Exit
• Mark the node marked FRONT as current
• Make FRONT point to the next node in its
sequence
FRONT FRONT REAR
• Release the memory for the node marked
as current
310 5 7 10
current
Ver. 1.0 Session 11

110. Data Structures and Algorithms
Deleting an Element from a Linked Queue (Contd.)
One request processed • If the queue is empty: // FRONT = NULL
a. Display “Queue empty”
b. Exit
• Mark the node marked FRONT as current
• Make FRONT point to the next node in its
sequence
FRONT REAR
• Release the memory for the node marked
as current
3 5 7 10
current
Delete operation complete
Memory released
Ver. 1.0 Session 11

111. Data Structures and Algorithms
Just a minute
How does the implementation of a linked list differ from that
of a linked queue?
Answer:
In a linked list, you can insert and delete elements anywhere
in the list. However, in a linked queue, insertion and deletion
takes place only from the ends. More specifically, insertion
takes place at the rear end and deletion takes place at the
front end of the queue.
Ver. 1.0 Session 11

112. Data Structures and Algorithms
Applications of Queues
Queues offer a lot of practical applications, such as:
Printer Spooling
CPU Scheduling
Mail Service
Keyboard Buffering
Elevator
Ver. 1.0 Session 11