Queues in data structure

8/9/2019 Queues in data structure

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Queues


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Queue Overview Queue ADT Basic operations of queue

insert, delete etc.

Implementations of queues using array linked list

ircular queue

!riority queue


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Queue "tores a set of elements in a particular

order "tack principle# $I%"T I& $I%"T O'T ( $I$O It means# t)e *rst element inserted is t)e

*rst one to +e removed -ample

T)e *rst one in line is t)e *rst one to +eserved


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)at is a queue/ Queues are linear data structures in w)ic) we add elements

to one end and remove t)em from t)e ot)er end.

T)e *rst item to +e en0queued is t)e *rst to +e de0queued.Queue is t)erefore called a $irst In $irst Out 1$I$O2 structure.

Queue operations# nqueue 3Insert Dequeue 3 Delete mpty


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BA

BA

D

BA

D

Brearfront

rearfron

t

rear

front

rear

front

rear

front

First In First Out

A


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Queue ADTabstract typedef44eltyper5 Q'' 1eltype26

abstractempty1q2

Q''1eltype2 q6

postconditionempty(( len1q2((76

abstracteltype remove1q2

Q'' 1eltype2 q6

precondition: empty1q2 (( $A8"

postconditionremove (( *rst1q926

q(( su+1q9,:, len1q92 0:6


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Queue ADTAbstractinsert1q, elt26

Q'' 1eltype2 q6

eltype elt6

postcondition q (( q; < 4elt5 6


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Implementation of Queues Any list implementation could +e used to

implement a queues

Arrays and ircular Arrays1static# t)e si=e ofqueue is given initially2

8inked lists 1dynamic# never +ecome full2

e will e-plore implementations +ased on

array and linked list 8et;s see )ow to useanarray to

implement a queue *rst


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Array Implementation A queue in ects An array to )old elements of t)e stacks Integer to indicate position of stack top?de*ne "I@ :77

struct queue

int items"I@C6 int front, rear6

6

Earia+le of type queue can +e declared in main12 as

queue q6

q.rear (0:6 q.front (7


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int remove(queue *q)

{ if (empty())

{

cout


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Queue F Array "tore queue as elements in array !ro+lem

Queue contents move

As result, can not add to +ack of queue,even t)oug) queue is not full


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/o,ution 45en e6er remo6e is ca,,ed mo6e a,, t5e e,ements in t5estart of "ueue2

x 1 "2items%7'for (int i17; i


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/o,ution 8T)ese pro+lems can +e avoided +yusing a circular array F an array in

w)ic) t)e location of t)e front and+ack inde- are allowed to c)angeand t)e contents to wrap around

w)en t)e last position in t)e +uGeris *lled.


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ircular Queue

H

7

:

J

K

LM

N

rearfront

Imagine t)at t)e two ends are >oined toget)er to form acircle

T)e Queue maintains two indices, frontand rear, t)at initially are

+ot) "I@ 0:

Queue implemented +y a circulararray


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7

:

J

K

L

M

N

H

+ack

front

Insertion in queue

-

rear


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front 7

:

J

K

L

M

N

H

+ack-

-

- -

-rear

Assume t)at P denotes t)e indices in t)e +uGer t)at )oldan o+>ect.

+uGer

front

Queue implemented using circular array


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front 7

:

J

K

L

M

N

H

+ack

-

- -

- rear

Assume t)at P denotes t)e indices in t)e +uGer t)at )oldan o+>ect.

+uGer

Deletion of element from queue


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ircular Array

Implementation?de*ne "I@ :77struct queue

int items"I@C6 int front, rear6

q6

q.rear ( q.front ( "I@ 0:6


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int empty("ueue 9"){

if ("#$rear 11 "#$front)return(*+) e,se

return (-A./+);!a,,in is as empty(=")int remo6e("ueue 9"){ if (empty(")) {

cout


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7

:

J

K

L

M

N

H

P

P P

P

P

PPP

P

P

front

rear

QueueOperations

)en array is full again front is equal to rearso we can not diGerentiate w)et)er array is

full or empty


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7

:

J

K

L

M

N

H

P

P P

P

P

PPP

P

front

rear

QueueOperations

"o we sacri*ce one element.


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6oid insert("ueue 9"@ int x){

if ("#$rear 11 />?+#) "#$rear 1 7; e,se

"#$rear&&;if (p"#$rear 11 p"#$front)

{ cout


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!riority Queues

!riority queue is a data structure in w)ic)

intrinsic ordering of elements t)e resultof +asic operations.

Two kinds of priority queues#

Ascending priority queue3Rin priorityQueueDescending priority queue3RAP priority

Queue


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Rin !riority Queue

ollection of elements into w)ic)elements are inserted ar+itrarily andsmallest element is removed.

ac) element )as a priority or key. "upports following operations#

ismpty insert an element into t)e priority queue get element wit) minpriority remove element wit) minpriority


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Ra- !riority Queue

ollection of elements into w)ic)elements are inserted ar+itrarily andsmallest element is removed.

ac) element )as a priority or key. "upports following operations#

ismpty insert an element into t)e priority queue get element wit)ma-priority remove element wit) ma-priority


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Applications

"orting use element key as priority put elements to +e sorted into a

priority queue e-tract elements in priority order

if a min priority queue is used, elements

are e-tracted in ascending order ofpriority

if a ma- priority queue is used, elements

are e-tracted in descending order of


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"orting -ample

"ort *ve elements w)ose keys are M, ,, K, : using a ma- priority queue. !ut t)e *ve elements into a ma- priority

queue. Do *veremovema-12 operations placing

removed elements into t)e sorted arrayfrom rig)t to left.


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After !utting Into Ra- !riorityQueue

"orted Array

M

K

:Ra-

!riority

Queue


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After $irst %emove Ra-Operation

"orted Array

M

K

:

Ra-!riority

Queue


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After "econd %emove Ra-Operation

"orted Array

K

:

M

Ra-!riority

Queue


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After T)ird %emove Ra-Operation

"orted Array

:

MK

Ra-!riority

Queue


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After $ourt) %emove Ra-Operation

"orted Array

:

MK

Ra-!riority

Queue


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After $ift) %emove Ra-Operation

"orted Array

MK:

Ra-!riority

Queue


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/uppose n e,ements of a priority "ueue are maintained inpositions 7 to n# of an array maxp" t5en p"insert(p"@x) isstri5tforward2

6oid insert("ueue 9p"@ int x)

{if ("#$rear $1 maxp"#)

{cout


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2A specia, empty() indicator can be p,acedinto a de,eted position2 >nsertion is doneas i6en before2

82Be,etion operation ,abe,s a position asempty but insertion is done at t5e Crstempty position2

D2+ac5 de,etion compact t5e array bys5iftin a,, e,ements past t5e de,etede,ement by one position anddecrementin p"2rear by 2

E2Feep t5e array sorted2

Be,etion Operation

/o,utions

Queues in data structure

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