Lecture 130 247 Queue

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Data Structure and

Algorithm (CS 102)NITRKL

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Queue

A queue is a linear list of elements inwhich deletion can take place only at one end

called Front, and

Insertion takes place at one end calledRear

Queues are also known as First-In-

First-Out (FIFO) list

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Queue

Queue are represented in two-ways

Linear Array One-way Linked List

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Array representation of Queue

A queue is maintained by a linear array QUEUE Two pointer variable

FRONT : Containing the location of the frontelement of the queue

REAR : Containing the location of the rearelement of the queue

FRONT == NULL indicates that thequeue is empty

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Queue

AA BB CC DD

1 2 3 4 5 6 7 N

FRONT: 2

REAR: 4BB CC DD

1 2 3 4 5 6 7 N

Whenever an element is deleted from thequeue, the value of FRONT is increased by 1FRONT = FRONT + 1

FRONT: 1REAR: 4

Delete an element

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Queue

BB CC DD

1 2 3 4 5 6 7 N

FRONT: 2

REAR: 4

Insert an element

BB CC DD EE

1 2 3 4 5 6 7 N

FRONT: 2REAR: 5

Whenever an element is inserted into thequeue, the value of REAR is increased by 1REAR = REAR + 1

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Queue

REAR = N and Insert an element intoqueue

XX

ZZ1 2 3 4 5 6 7 N

FRONT: 7

REAR: N

Move the entire queue to the beginning of the

arrayChange the FRONT and REAR accordinglyInsert the element

This procedure is too expensive

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Queue

Queue is assumed to be circular QUEUE[1] comes after QUEUE[N]

Instead of increasing REAR to N +1, we

reset REAR = 1 and then assignQUEUE[REAR] = ITEM

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Queue

FRONT = N and an element of QUEUEis Deleted

XX

ZZ1 2 3 4 5 6 7 N

FRONT: N

REAR:

We reset FRONT = 1, instead of increasingFRONT to N + 1

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Queue

QUEUE contain one elementFRONT = REAR NULL

XX

1 2 3 4 5 6 7 N

FRONT: 7

REAR: 7

FRONT = NULL and REAR = NULL

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Algorithm to Insert in Q

[1] If FRONT = 1 andREAR = N or ifFRONT =

REAR + 1 then Print: Overflow and Exit[2] If FRONT = NULL then

Set FRONT = 1 and REAR = 1

Else If REAR = N thenSet REAR = 1Else

Set REAR = REAR + 1

[3] Set QUEUE[REAR] = ITEM[4] Exit

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Queue

AA BB CC DD EE FF XX

ZZ1 2 3 4 5 6 7 N

FRONT: 7

REAR: 6

FRONT = REAR + 1 [FULL QUEUE]

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Algorithm to Delete from Q

[1] If FRONT = NULL then Print: Underflow andExit

[2] Set ITEM = QUEUE[FRONT]

[3] If FRONT = REAR thenSet FRONT = NULL and REAR = NULL

Else If FRONT = N thenSet FRONT = 1

ElseSet FRONT = FRONT + 1

[4] Exit

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Linked List Representation of Queue

A linked queue is a queue implementedas linked list with two pointer variable

FRONT and REAR pointing to the nodeswhich is in the FRONT and REAR of thequeue

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Linked List Representation ofQueue

CC XAABB

FRONT

15

REAR

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Insertion in a Queue

AA XCCBB

FRONT

16

REAR

DDNEW

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Insertion in a Queue

AA XCCBB

FRONT

17

REAR

DD

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Delete from a Queue

CC XAABB

FRONT

18

REAR

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Delete from a Queue

XAABB

FRONT

19

REAR

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Linked Queue

No need to check for overflow conditionduring insertion

No need to view it as circular forefficient management of space

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Insertion

[1] NEW -> INFO = ITEMNEW -> LINK = NULL

[2] If (FRONT = NULL) then

FRONT = REAR = NULLelse

Set REAR -> LINK = NEW

REAR = NEW

[3] Exit

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Deletion

[1] If (FRONT = NULL) thenPrint: Underflow, and Exit

[2] FRONT = FRONT -> LINK

[3] Exit

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Deque

A deque is a linear list in whichelements can be added or removed ateither end but not in the middle

Deque is implemented by a circulararray DEQUE with pointers LEFT and

RIGHT which points to the two end ofthe deque

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Deque LEFT = NULL indicate deque is empty

AA BB CC DD

1 2 3 4 5 6 7 8

LEFT: 4

RIGHT: 7

YY ZZ WW XX1 2 3 4 5 6 7 8

LEFT: 2

RIGHT: 7

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Variation of deque

There are two variation of deque

[1] Input-restricted queue: Deque whichallows insertions at only one end of the list

but allows deletion at both ends of the list

[2] Output-restricted queue: Deque which

allows deletion at only one end of the listbut allows insertion at both ends of thelist

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Deque

A C D

1 2 3 4 5 6

LEFT: 2RIGHT: 4

F is added to the right

A C D F1 2 3 4 5 6

LEFT: 2

RIGHT: 5

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Deque

A C D F

1 2 3 4 5 6

LEFT: 2RIGHT: 5

Two Letters on right is deleted

A C1 2 3 4 5 6

LEFT: 2

RIGHT: 3

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Deque

A C

1 2 3 4 5 6

LEFT: 2RIGHT: 3

K, L and M are added to the Left

K A C M L1 2 3 4 5 6

LEFT: 5

RIGHT: 3

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Priority Queue A priority queue is a collection of elements

such that each elements has been assigneda priority and such that the order in whichelements are deleted and processed comes

from the following rules:[1] Elements of higher priority is processed

before any elements of lower priority

[2] Two elements with the same priority areprocessed according to the order in whichthey were added to the queue

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Priority Queue

There are different ways a priorityqueue can be represented such as

[1] One-way List

[2] Multiple queue

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One-Way List Representation ofa Priority Queue

[1] Each node in the list will contain threeitems of information: an informationfield INFO, a priority number PRN,

and a link number LINK

[2] A node X precedes a node Y in the list

(a) when X has higher priority than Y or(b) when both have same priority but Xwas added to the list before Y

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Queue

32

1A 2B 2F 3D

Head

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Insertion and Deletion

Deletion : Delete the first node in thelist.

Insertion: Find the location of Insertion

Add an ITEM with priority number N[a] Traverse the list until finding a node X

whose priority exceeds N. Insert ITEM

in front of node X[b] If no such node is found, insert ITEM

as the last element of the list

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Array representation of PriorityQueue

Separate queue for each level ofpriority

Each queue will appear in its owncircular array and must have its ownpair of pointers, FRONT and REAR

If each queue is given the same amountspace then a 2D queue can be used

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Deletion Algorithm [outline]

[1] Find the smallest K such thatFRONT[K] NULL

[2] Delete and process the front elementin row K of QUEUE

[3] Exit

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Insertion Algorithm [outline]

[1] Insert ITEM as the rear element inrow M of QUEUE

[2] Exit