Transcript
Data Structures & Algorithms
Dated: 06-12-2010
What are Queues?
Representation of Queues
Operations on Queues QInsert QDelete
Today Topics
What are Queues?Queue can be defined as:
A queue is an ordered collection of items from which items may be deleted at one end (called the front of the queue) and into which items may be inserted at the other end (called the rear of the queue).
A queue is a waiting line – seen in daily life A line of people waiting for a bank teller A line of cars at a toll both
queue Features:
A list structure with two access points called the front and rear.
All insertions (enqueue) occur at the rear and deletions (dequeue) occur at the front.
Varying length (dynamic). Homogeneous components Has a First-In, First-Out characteristic (FIFO)
application
Application of QueuePurpose of queue is to provide some form of buffering. Queues are used for:
Process Management: In timesharing system, programs are added to a queue and executed one after the other.
Buffer between the fast computer and a slow printer.
In queues, scheme used is FIFO or LILO
implementation of Queues There are two ways of implementing a queue:
Array (Static) Link List (Dynamic)
A queue can be implemented with an array and two integers.
The first integer front used for deletion item from queue and rear used for insert item in queue
Array Implementation
How to implement queue Decide how many data member are needed to
implement the queue. We need at least four types of variable.
An array to store the element Variables queuefront to keep track of the first element Queuerear to keep track of the last elelment. Maxsize variable
How to use rear and front to access the queue element.????
How they indicate that queue is full or empty.
Bounds of Queue
If FRONT: = NULL “empty” If REARE := NUL “empty” If REARE := N “overflow, full” If FRONT=REARE != NULL then the
queue contain only one element. If FRONT = REARE???????? Very
interesting situation.
Representation of Queues
a[1] a[2] a[3] a[4] a[5] a[6] a[7] a[8] a[9] a[10]
34 12 53 61 9 23 -8 15 24 42
front rear
Queues Working
a[1] a[2] a[3] a[4] a[5] a[6] a[7] a[8] a[9] a[10]
Currently Queue Status
front = 0 rear = 0
Queues Working
a[1] a[2] a[3] a[4] a[5] a[6] a[7] a[8] a[9] a[10]
32
Currently Queue Status
front = 1 rear = 1
QInsert(32)frontrear
Queues Working
a[1] a[2] a[3] a[4] a[5] a[6] a[7] a[8] a[9] a[10]
32 44
Currently Queue Status
front = 1 rear = 2
QInsert(44)front rear
Queues Working
a[1] a[2] a[3] a[4] a[5] a[6] a[7] a[8] a[9] a[10]
32 44 65
Currently Queue Status
front = 1 rear = 3
QInsert(65)
front rear
Queues Working
a[1] a[2] a[3] a[4] a[5] a[6] a[7] a[8] a[9] a[10]
32 44 65 25
Currently Queue Status
front = 1 rear = 4
QInsert(25)
front rear
Queues Working
a[1] a[2] a[3] a[4] a[5] a[6] a[7] a[8] a[9] a[10]
32 44 65 25 53
Currently Queue Status
front = 1 rear = 5
QInsert(53)
front rear
Queues Working
a[1] a[2] a[3] a[4] a[5] a[6] a[7] a[8] a[9] a[10]
44 65 25 53
Currently Queue Status
front = 2 rear = 5
QDelete()
front rear
Queues Working
a[1] a[2] a[3] a[4] a[5] a[6] a[7] a[8] a[9] a[10]
65 25 53
Currently Queue Status
front = 3 rear = 5
QDelete()
front rear
Think about it
What happen when Rear= 10 Front = 9
????????? And you want to insert. Two solution::::::
Check the front, if there is room then slides all the element to fist position, but well when queue is small.
Use circular array.
In case of circular queue how to set rear point Rear= (rear + 1) % maxsize; how??????? If Rear < maxsize -1, then
Rear + 1 <= mzxsize -1 and so (Rear +1) % maxsize= Rear + 1.
If Rear == maxsize -1 (that is rear point to the last position) then Rear + 1 == maxsize and so (Rear + 1) % maxsize==0. in this case Rear is set to 0.
And same can be done for Front adjustment.
Operations on Queue Generally, Queue is implemented with only
two principle operations
InitializeQueue queue to an empty state destroyQuere revome all the elements isEmpthyQueue isFullQueue Front rear Insertion: adds an item to a queue Deletion: delete an item from the queue
Algorithms of Insert Operation QINSERT(QUEUE, N, FRONT, REAR, ITEM)
This algorithm insert an element ITEM into a queue.
Setp1. [Queue already filled]
if FRONT := 1 and REAR:= N,
write “overflow” and return
Step 2. [Find new value of REAR]
if FRONT := NULL [Queue initially empty]
Set FRONT:= 1 and REAR:= 1
Else if REAR:=N than
Set REAR:=1
Else
Set REAR:=REAR+1
[End of if structure]
Step 3. Set QUEUE[REAR]:=ITEM [this insert new item ]
Step 4. exit
Algorithms of Insert OperationQInsert (X)
Algorithm for Insert element into the Queue1. Start2. if rear >= Max then
Print “Queue Overflow!”else
rear = rear + 1Q[rear] = X
if front = 0 thenfront = 1
end ifend if
End
Algorithms of DELETE Operation QDELETE(QUEUE, N, FRONT, REAR, ITEM)
This algorithm delete an element ITEM into a queue.
Setp1. [Queue already empty]
if FRONT := NULL write “UNDERFLOW”
return
Step 2. set ITEM:= QUEUE[FORNT]
Step 3. [Find new value of FRONT]
if FRONT := REAR than [Queue has only one element]
Set FRONT:= NULL and REAR:= NULL
Else if FRONT:=N than
Set FRONT;=1
Else
Set FRONT:=FRONT+1
[End of if structure]
Step 5. exit
Algorithms of Delete OperationQDelete ()
Algorithm for delete element into the Queue1. Start2. if front = 0 then
Print “Queue Underflow!”else
E = Q[front]if front = rear then
front = rear = 0else
front = front + 1end if
end if3. End
Circular Queue When elements are deleted from the front, their spaces
cannot be used to store new elements.
To solve this problem, circular queue is used
Q[1]
Q[2]
Q[3]
Q[4]Q[5]
Q[6]
Q[7]
Q[8]
Algorithms of CQInsert OperationCQInsert (X)
Algorithm for Insert element into the Circular Queue1. Start2. if front = 1 and rear = Max then
Print “Queue Overflow!”else if rear + 1 = front then
Print “Queue Overflow!”else
if front = 0 and rear=0 thenfront = rear = 1
else if rear = Max thenrear = 1
elserear = rear + 1
end ifQ[rear] = X
end if End
Algorithms of CQDelete OperationCQDelete ()
Algorithm for delete element into the Circular Queue1. Start2. if front = 0 then
Print “Queue Underflow!”else
E = Q[rear]if front = rear then
front = rear = 0else if front = Max then
front = 1else
front = front + 1end if
end if End
DeQue
Word deque is a short form of double-ended queue.
Deque defines a data structure in which item can be added or deleted at either the front or rear end.
But no changes can be made elsewhere in the list.
Deque is a generalization of both a stack and a queue.
DeQue
There are two variations of deques. These are:
Input – Restricted DequeIt allows insertions only at one end but allows deletions at both ends.
Output – Restricted DequeIt allows deletions only at one end but allows insertions at both end
Representation of Deque
a[1] a[2] a[3] a[4] a[5] a[6] a[7] a[8] a[9] a[10]
34 12 53 61 9 23 -8 15 24 42
front rear
insert insertdelete delete
Deque
Implementation of Deque
When an item is inserted at the Front of DEQ, then front is decreased by 1.
When an item is inserted at the Rear of DEQ, then rear is increased by 1.
When an item is deleted at the Front of DEQ, then front is increased by 1.
When an item is deleted at the Rear of DEQ, then rear is decreased by 1.
Implementation of Deque
In the following figure, the DEQ has some items stored in it
X Y ZFront Rear
front = 2 rear = 4
Deque
The first element at the front of the deque is empty and two elements at the rear are also empty.
Implementation of Deque
If another item XX is added at the rear, then the DEQ and values of front and rear will be :
X Y Z XXFront Rear
front = 2 rear = 5
Deque
Implementation of Deque
If two items are deleted at the front and one item is deleted at the rear, then the DEQ and values of front and rear will be:
ZFront Rear
front = 4 rear = 4
Deque
Algorithms of DeQInsert OperationDeQInsert (X, Side)
Algorithm for Insert element into the Deque1. Start2. if front = 0 and rear = 0 then
front = rear = 1DQ[front] = XReturn
end if[specify front or rear side to insert value]
3. [insert value at front of the queue] if Side = 1 thenif front > 1 thenfront = front – 1DQ[front] = XelsePrint “No space at front of the Deque!”
Algorithms of DeQInsert Operationend if
elseif rear < Max then
rear = rear + 1DQ[rear] = X
elsePrint “No space at rear of the
Deque!”end if
end if4. End
Algorithms of DeQDelete OperationDeQDelete (Side)
Algorithm for delete element into the Deque1. Start
2. If front = 0 and rear = 0 thenPrint “DeQueue Underflow!”Return
end if
3. if front = rear thenE= DQ[front]front = rear = 0Return
end if
Algorithms of DeQDelete Operation
4. if Side = 1 thenif front = Max then
E = DQ[front]front = 0
elseE = DQ[front]
front = front + 1end if
elseE = DQ[rear]
rear = rear - 1end if
5. End
Priority Queues
Priority queue is a collection of elements where the elements are stored according to their priority levels.
The order in which the elements should get added or removed is decided by the priority of the element.
Following rules are applied to maintain a priority queue:
The element with a higher priority is processed before any element of lower priority.
If there are elements with the same priority, then the element added first in the queue would get processed.
Example for Priority Queues
Priority queues are used for implementing job scheduling by the operating system where jobs with higher priorities are to be processed first.
Another application of priority queues is simulation systems where priority corresponds to event times.
Representation of Priority Queues
Priority queues can be represented in the several ways.
Best way to represent it is to use a separate queue for each level of priority.
Each such queue is represented in circular fashion and has its own front and rear.
Representation of Priority Queues
Usually, an array of arrays, i.e. a two-dimensional array is used to represent.
1 X Y
2 A B C
3 M N O P
4
Next Lecture Pointer Review Linked List Representation of Link List Operations of Linked List Circular Linked List Double Linked List (Two-Way List) Representation of Double Linked List Operations of Double Linked List
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