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CS212: DATA STRUCTURES
Computer Science
Department
Lecture 7: Queues
Lecture Contents
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
What is Queue?
Basic Queue Operation.
The Queue Abstract Data Type.
A Simple Array-Based Queue Implementation.
Using an Array in a Circular Way.

Using the Modulo Operator to Implement a Circular Array.

Priority Queues.
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Queues
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What is
Queue?
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A queue is a linear list in which data can
only be inserted at one end ,called rear ,
and deleted from the other end , called the
front
A queue is simply a waiting line that grows
or shrinks by adding or taking elements
form it.
Unlike stack, it’s a structure in which both
ends are used.
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Queues
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What is
Queue?
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
Aqueue is a first in first out (FIFO)
structure
 no search,
 no adding in arbitrary positions,
 no sorting,
 no access to anything beyond the front
and rear elements.
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Example Applications
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There are several possible applications for queues.
Stores, theaters, reservation centers, and other similar
services typically process customer requests according to
the FIFO principle.
A queue would therefore be a logical choice for a data
structure to handle transaction processing for such
applications.
For example, it would be a natural choice for handling
calls to the reservation center of an airline or to the box
office of a theater.
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The Queue Abstract Data Type
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What is
Queue?
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the queue abstract data type defines a
collection that keeps objects in a sequence
where element access and deletion are
restricted to the first element in the
sequence, which is called the front of the
queue, element insertion is restricted to the
end of the sequence, which is called the
rear of the queue.
This restriction enforces the rule that items
are inserted and deleted in a queue
according to the first-in first-out (FIFO)
principle.
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The Queue Abstract Data Type
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The queue abstract data type (ADT) supports the
following two fundamental methods:
enqueue(e): Insert element e at the rear of the queue.
dequeue( ): Remove and return from the queue the
object at the front; an error occurs if the queue is empty.
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Queue Operations
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Queue
Operation
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
There are four basic queue operations
 Enqueue
 Dequeue
 Queue Front
 Queue Rear
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Queues
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Queue
Operation
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Computer Science Department
Basic Queue Operations
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
Enqueue:
 inserts
an element at the rear of the queue.
grape
Data
apple
front
kiwi
Enqueue
rear
queue
apple
kiwi
rear
front
operation
grape
queue
Basic Queue Operations
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
Dequeue:
 deletes
element at the front of the queue.
apple
Data
apple
kiwi
grape
Dequeue
rear
front
queue
kiwi
front
operation
grape
rear
queue
Basic Queue Operations
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
Queue Front:
 Examines
the element at the front of the queue.
apple
Data
apple
kiwi
grape
rear
front
queue
Queue
Front
operation
apple
front
kiwi
grape
rear
Basic Queue Operations
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
Queue Rear:
 Examines
the element at the rear of the queue.
grape
Data
apple
kiwi
grape
rear
front
queue
Queue
Rear
operation
apple
front
kiwi
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rear
Additional Operations
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
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Additionally, the queue ADT includes the following
supporting methods:
size( ) : Return the number of objects in the queue.
isEmpty( ) : Return a Boolean value that indicates
whether the queue is empty.
front( ) : Return, but do not remove, the front object in
the queue; an error occurs if the queue is empty.
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A Simple Array-Based Queue Implementation
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
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We present a simple realization of a queue by means
of an array, Q, of fixed capacity, storing its elements.
The main rule with the queue ADT is that we insert
and delete objects according to the FIFO principle,
we must decide how we are going to keep track of
the front and rear of the queue.
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A Simple Array-Based Queue Implementation
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One possibility is to adapt the approach we used for
the stack implementation, letting Q[0] be the front of
the queue and then letting the queue grow from there.
This is not an efficient solution, it requires that we
move all the elements forward one array cell each
time we perform a dequeue operation.
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A Simple Array-Based Queue Implementation
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This will take O(n) time to perform the dequeue
method,where n is the current number of objects in the
queue.
If we want to achieve constant time for each queue
method, we need a different approach.
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Using an Array in a Circular Way
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To avoid moving objects once they are placed in Q,
we define two variables f and r, which have the
following meanings:
f is an index to the cell of Q storing the first element
of the queue (which is the next candidate to be
removed by a dequeue operation), unless the queue
is empty (in which case f = r).
r is an index to the next available array cell in Q.
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Computer Science Department
Using an Array in a Circular Way
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
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Initially, we assign f = r = 0, which indicates that the
queue is empty.
Now, when we remove an element from the front of
the queue, we increment f to index the next cell.
Likewise, when we add an element, we store it in cell
Q[r] and increment r to index the next available cell
in Q.
This scheme allows us to implement methods front,
enqueue, and dequeue in constant time.
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Using an Array in a Circular Way
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
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Consider, for example, what happens if we repeatedly
enqueue and dequeue a single element N different times.
We would have f = r = N.
If we were then to try to insert the element just one more
time, we would get an array-out-of-bounds error (since the
N valid locations in Q are from Q[0] to Q[N − 1]), even
though there is plenty of room in the queue in this case.
To avoid this problem and be able to utilize all of the array
Q, we let the f and r indices "wrap around" the end of Q.
That is, we now view Q as a "circular array" that goes from
Q[0] to Q[N − 1] and then immediately back to Q[0] again.
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Using an Array in a Circular Way
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Using the Modulo Operator to Implement a Circular Array
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

Implementing this circular view of Q is actually pretty easy.
Each time we increment f or r, we compute this increment as
"(f + 1) mod N" or "(r + 1) mod N," respectively.
Implementation of a queue using a circular array. The
implementation uses the modulo operator to "wrap" indices
around the end of the array and it also includes two
instance variables, f and r, which index the front of the
queue and first empty cell after the rear of the queue
respectively.
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Computer Science Department
Queue Linked List Design
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
For a linked list implementation of a queue, we use
two types of structures: a head and a node.
apple
kiwi
grape
fig
rear
front
Conceptual queue
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front
apple
kiwi
count
rear
grape
Physical queue
fig
Implementing a Queue with a Generic Linked List
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We can efficiently implement the queue ADT using a generic
singly linked list.
we choose the front of the queue to be at the head of the list,
and the rear of the queue to be at the tail of the list.
In this way, we remove from the head and insert at the tail.
we simply give a Java implementation for the fundamental
queue methods .
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Implementing a Queue with a Generic Linked List
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
enqueue method:
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Implementing a Queue with a Generic Linked List
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
dnqueue method:
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Queue Linked List Design
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
For a linked list implementation of a queue, we use
two types of structures: a head and a node.
apple
kiwi
grape
fig
rear
front
Conceptual queue
4
front
apple
kiwi
count
rear
grape
Physical queue
fig
Priority Queues
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
a priority queue is an abstract data type which is like a
regular queue or stack data structure, but where
additionally each element has a "priority" associated
with it.

In a priority queue, an element with high priority is
served before an element with low priority. If two
elements have the same priority, they are served
according to their order in the queue.
Priority Queues
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
Priority queue returns elements in priority order,
order determined by key. It stores collection of
entries. Each entry is a (key, value) pair.

Stacks and Queues: Removal order determined by
order of inserting

Priority Queue: Order determined by key ( Key may
be part of element data or separate)
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Computer Science Department
Priority Queues
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
Applications:
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Hospital Emergency Rooms
Stock market
Priority Queue
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Suppose that you have a few assignments from different
courses.
Which assignment will you want to work on first?
You set your priority based on due days. Due days are called
keys.
Course
Priority
Due day
Database Systems
2
October 3
UNIX
4
October 10
Data Structure & Algorithm
1
September 29
Structured Systems Analysis
3
October 7
What’s so different?
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Stacks and Queues:
• Removal order determined by order of inserting (stack LIFO, Queue FIFO)
Sequences:
• User chooses exact placement when inserting and explicitly chooses removal
order
Priority Queue
• Removal order determined by key
• Key may be part of element data or separate
Examples:

Processes scheduled by CPU

Hospital Emergency Rooms

College admissions process for students
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End Of Chapter
References:
•
Text book, chapter5: stack & Queues
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Computer Science Department