1. Cs212: Data Structures
Computer Science Department
Lecture 7: Queues

2. Lecture Contents 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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3. Queues
What is Queue?
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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4. Queues Aqueue is a first in first out (FIFO) structure no search,
What is Queue?
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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Computer Science Department

5. Example Applications
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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6. The Queue Abstract Data Type
What is Queue?
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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7. The Queue Abstract Data Type
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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8. Queue Operations There are four basic queue operations Enqueue Dequeue
Queue Front
Queue Rear
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9. Queues
Queue Operation
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10. Basic Queue Operations
Enqueue:
inserts an element at the rear of the queue.
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11. Basic Queue Operations
Dequeue:
deletes element at the front of the queue.
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12. Basic Queue Operations
Queue Front:
Examines the element at the front of the queue.
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13. Basic Queue Operations
Queue Rear:
Examines the element at the rear of the queue.
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14. Additional Operations
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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15. A Simple Array-Based Queue Implementation
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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16. A Simple Array-Based Queue Implementation
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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17. A Simple Array-Based Queue Implementation
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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18. Using an Array in a Circular Way
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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19. Using an Array in a Circular Way
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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20. Using an Array in a Circular Way
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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21. Using an Array in a Circular Way
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22. Using the Modulo Operator to Implement a Circular Array
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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24. Queue Linked List Design
For a linked list implementation of a queue, we use two types of structures: a head and a node.
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25. Implementing a Queue with a Generic Linked List
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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26. Implementing a Queue with a Generic Linked List
enqueue method:
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27. Implementing a Queue with a Generic Linked List
dnqueue method:
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28. Queue Linked List Design
For a linked list implementation of a queue, we use two types of structures: a head and a node.
apple
kiwi
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front
rear
Conceptual queue 4
front
count
rear
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Physical queue

29. Priority Queues
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.

30. Priority Queues
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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31. Priority Queues
Applications:
Hospital Emergency Rooms
Stock market

32. Priority Queue
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

33. What’s so different? 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

34. End Of Chapter References: Text book, chapter5: stack & Queues
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