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Queue as data_structure | PDF
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Data Structure
Introduction
● It is linear data structure
● It is collection of items – List
● Queue means line of items waiting for
  their turn
● Queue has two ends
  ○ Elements are added at one end.
  ○ Elements are removed from the other end.


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Queue
● Removal of data item is restricted at one
  end known as FRONT
● Insertion of data item is restricted at other
  end known as REAR
● The FRONT and REAR are used in
  describing a linear list, when queue is
  implemented
● First element inserted in list, will be the
  first to be removed - FIFO
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Queue as FIFO
● The element inserted first will be removed
  first from the Queue
● Thus, Queue is known as FIFO (First In-
  First Out) or FCFS (First Come First
  Serve)

● Examples of Queue
  ○ People waiting in Queue to purchase tickets at
    railway station or cinema hall, where the first person
    in the queue will be served first
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Representation of Queue
● It has two pointer varaibles
  ○ FRONT : Containing the location of the front
    element of the queue
  ○ REAR : Containing the location of the rear
    element of the queue
● When queue is empty
    FRONT = -1 and REAR = -1



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Operations of Queue
● Insertion
  ○ Adding an element in queue will increased
    value of REAR by 1
     ■ REAR = REAR + 1
● Removal
  ○ Removing an element from queue will
    increased value of FRONT by 1
     ■ FRONT = FRONT + 1



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Queue       FRONT = -1, REAR =
Empty       -1
ADD(Q,10)   FRONT = 0 ,REAR =
            0
ADD(Q,20)   FRONT = 0 ,REAR
            =1
ADD(Q,30)   FRONT = 0 ,REAR
            =2
ADD(Q,40)   FRONT = 0 ,REAR
            =3
ADD(Q,50) FRONT = 0 ,REAR
          =4
Remove(Q) FRONT = 1 ,REAR
          =4
Remove(Q) FRONT = 2 ,REAR
          =4
Remove(Q) FRONT = 3 ,REAR
           =4
ADD(Q,     FRONT = 3 ,REAR
60)        =1         www.eshikshak.co.in
Types of Queue
● Queue as Array
● Circular Queue
● Priority Queue
● Input Restricted Queue
● Output Restricted Queue
● Dqueue



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Queue as Array : Insert
Initially when the QUEUE is empty, set FRONT = NULL and REAR = 0


Step 1: start
Step2: [check for queue is over flow or not]
If (REAR >n) or (REAR==FRONT)
Print “queue is overflow”
else
go to step 3
Step 3: [enter the item]
QUEUE[REAR]=value
REAR=REAR+1
Step 4:[ check condition]
If(FRONT==null)
FRONT=0
Step 5:end
Queue as Array : Delete

Step 1: start
Step 2: [check for queue is under flow or not]
If front>N or front==Null
Print ”queue is underflow”
else
goto step 3
Step 3: [check condition]
If front==rear
Front==null
Rear=0
else
goto step 4
Step 4: [delete element]
Queue[front]=null
Step 5: front=front+1
Step 6: end
Circular Queue
● To solve this problem, queues implement
  wrapping around. Such queues are called
  Circular Queues.
● Both the front and the rear pointers wrap
  around to the beginning of the array.
● It is also called as “Ring buffer”.
● Items can inserted and deleted from a queue in
  O(1) time.



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Circular Queue
● When a new item is inserted at the rear, the
  pointer to rear moves upwards.
● Similarly, when an item is deleted from the
  queue the front arrow moves downwards.
● After a few insert and delete operations the rear
  might reach the end of the queue and no more
  items can be inserted although the items from
  the front of the queue have been deleted and
  there is space in the queue.


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QINSERT(Queue, N, FRONT, REAR, ITEM)
1 [Queue already filled ?]
if FRONT = 0 and REAR = N-1, or if FRONT=REAR + 1 then
write : Overflow and Return
2 [Find new value of REAR]
if FRONT=-1 then [Queue initially empty]
Set FRON T = 0 and REAR = 0
else if REAR = N-1 then
Set REAR = 1
else
Set REAR = REAR + 1
[End of If structure]
3 Set QUEUE[REAR] = ITEM [This inserts new element]
4 Return
QDELETE(Queue, N, FRONT, REAR,
                ITEM)
1 [Queue already empty]
If FRONT = -1, then Write : Underflow and Return
2 Set ITEM = Queue[FRONT]
3 [Find new value of FRONT]
If FRONT = REAR, then [Queue has only one element to start]
Set FRONT = -1 and REAR = -1
Else if FRONT = N-1, then
Set FRONT = 0
Else
Set FRONT = FRONT + 1
[End of If Structure]
4 Return
Priority Queue




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Priority Queue
● It is collection of elements where elements are
  stored according to the their priority levels
● Inserting and removing of elements from queue
  is decided by the priority of the elements
● The two fundamental methods of a priority
  queue P:
   ○ insertItem(k,e): Insert an element e with key k into P.
   ○ removeMin(): Return and remove from P an element
     with the smallest key.




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Priority Queue
● When you want to determine the priority
  for your assignments, you need a value
  for each assignment, that you can
  compare with each other.

● key: An object that is assigned to an
  element as a specific attribute for that
  element, which can be used to identify,
  rank, or weight that element.

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Example: Student records
Any of the attributes, Student Name, Student Number, or Final Score
         Student Name       ID              Final Score (out
can be used as keys.                        of 450)
Note: Keys may not be unique (Final Score).
        Ashwin            09BCA08          310
        Payal             09BCA80          311
        Darshika          09BCA24          380
        Nilkamal          09BCA75          400
        Nikunj            09BCA74          440
        Mori              09BCA102         400




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Rules to maintain a Priority Queue
● The elements with the higher priority will
  be 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




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Priority Queue Insert
PQInsert (M, Item)
Step 1 Find the Row M
Step2 [Reset the Rear Pointer]
If Rear[M] = N-1 then Rear[M] = 0
Else
Rear[M] = Rear[M]+1
Step 3 [Overflow]
If Front[M] = Rear[M] then Write (“This Priority Queue is full”)
Return
Step 4 [Insert Element]
Q[M] [Rear[M]] = then
Step 5 [Is Front Pointer Properly Set]
If Front[M] = -1 then Front[m] = 0
Return
Step 6 Exit



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Priority Queue Delete
PQDelete (K, Item)
Step 1 Initialize K = 0
Step 2 while (Front[K] = -1)
K = K+1
[To find the first non empty queue]
Step 3 [Delete Element]
Item = Q[K] [Front[K]
Step 4 [Queue Empty]
If Front[K] = N-1 then Front[K] = 0
Else
Front[K] = Front[K]+1
Return Item
Step 6 Exit



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Deque
● Deque stands for double-end queue

● A data structure in which elements can be
  added or deleted at either the front or rear

● But no changes can be made in the list

● Deque is generalization of both stack and
  queue

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Removing Element from Deque
● There are two variations of a deque.
  These are
  ○ Input Restricted Deque
     ■ An input restricted deque restricts the insertion of
       elements at one end only, but the deletion of
       elements can perform at both the ends.

  ○ Output Restricted Deque
     ■ An output restricted queue, restricts the deletion
       of elements at one end only, and allows insertion
       to be done at both the ends of deque

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Possibilities
● The two possibilities that must be
  considered while inserting or deleting
  elements into the queue are :
  ○ When an attempt is made to insert an
    element into a deque which is already full, an
    overflow occurs.
  ○ When an attempt is made to delete an
    element from a deque which is empty,
    underflow occurs.



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Representation of Deque


Deletio                                           Insertion
n
Insertion                                         Deletio
                                                  n


              Front                         Rea
                                            r




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Inserting Element in Deque
 InsertQatEnd(dq,7)            7



                       Front        Rear



InsertQatBeg(dq,10)            7



                      Front        Rear




  InsertQatBeg(dq,             7
  10)

                      Front        Rear
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InsertQatBeg(dq,10)    10            7


                      Front        Rear

InsertQatEnd(dq,4)
                       10            7         4


                      Front                   Rear


InsertQatBeg(dq,15)    15            10        7      4


                      Front                          Rear

InsertQatEnd(dq,55)
                       15            10        7      4     55


                      Front   www.eshikshak.co.in           Rear
Removing Element from Deque
delQBeg()                  10          7     4    55


                           Front                  Rear


delQBeg()                              7     4    55


                                     Front        Rear


InsertQatEnd(dq,23)          7          4    55    23


                             Front                Rear




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Deque : Insert
● There are two variations of a deque.
  These are
  ○ Input Restricted Deque
     ■ An input restricted deque restricts the insertion of
       elements at one end only, but the deletion of
       elements can perform at both the ends.

  ○ Output Restricted Deque
     ■ An output restricted queue, restricts the deletion
       of elements at one end only, and allows insertion
       to be done at both the ends of deque

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Input Restricted queue : Insert Element
Step 1: start
Step 2:[check condition for overflow]
If(rear==N-1 && front==0 or front=rear+1)
Print “over flow”
else
goto step 3
Step 3: [check condition]
If(front==null)
front = 0 and rear=-1
else
goto step 4
Step 4: [check condition and value]
If (rear== N -1)
rear=0
Else
rear=rear+1
Step 5: [Add value]
dq[rear]=value
Step 6:end


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Input Restricted queue : Delete Beginning
Step 1: start
Step 2: [check condition for underflow]
If(rear==null & front==null)
Print”underflow”
else
goto step 3
Step 3: [delete]
dq[rear]=null
Step 4: [check condition]
If(rear==front)
front=rear=null
else
rear--;
Step 5: end



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Input Restricted queue : Delete End
Step 1: start
Step2 : [check condition for under flow)
If(rear==null & front==null)
Print “under flow”
else
goto step 3
Step 3: [delete]
dq[front]=null
Step 4: [check condition]
If(rear==front)
rear=-1 and front=null
else
front=front+1
Step 5: end



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Queue as data_structure

  • 1.
    Queue www.eshikshak.co.in Data Structure
  • 2.
    Introduction ● It islinear data structure ● It is collection of items – List ● Queue means line of items waiting for their turn ● Queue has two ends ○ Elements are added at one end. ○ Elements are removed from the other end. www.eshikshak.co.in
  • 3.
    Queue ● Removal ofdata item is restricted at one end known as FRONT ● Insertion of data item is restricted at other end known as REAR ● The FRONT and REAR are used in describing a linear list, when queue is implemented ● First element inserted in list, will be the first to be removed - FIFO www.eshikshak.co.in
  • 4.
    Queue as FIFO ●The element inserted first will be removed first from the Queue ● Thus, Queue is known as FIFO (First In- First Out) or FCFS (First Come First Serve) ● Examples of Queue ○ People waiting in Queue to purchase tickets at railway station or cinema hall, where the first person in the queue will be served first www.eshikshak.co.in
  • 5.
    Representation of Queue ●It has two pointer varaibles ○ FRONT : Containing the location of the front element of the queue ○ REAR : Containing the location of the rear element of the queue ● When queue is empty FRONT = -1 and REAR = -1 www.eshikshak.co.in
  • 6.
    Operations of Queue ●Insertion ○ Adding an element in queue will increased value of REAR by 1 ■ REAR = REAR + 1 ● Removal ○ Removing an element from queue will increased value of FRONT by 1 ■ FRONT = FRONT + 1 www.eshikshak.co.in
  • 7.
    Queue FRONT = -1, REAR = Empty -1 ADD(Q,10) FRONT = 0 ,REAR = 0 ADD(Q,20) FRONT = 0 ,REAR =1 ADD(Q,30) FRONT = 0 ,REAR =2 ADD(Q,40) FRONT = 0 ,REAR =3 ADD(Q,50) FRONT = 0 ,REAR =4 Remove(Q) FRONT = 1 ,REAR =4 Remove(Q) FRONT = 2 ,REAR =4 Remove(Q) FRONT = 3 ,REAR =4 ADD(Q, FRONT = 3 ,REAR 60) =1 www.eshikshak.co.in
  • 8.
    Types of Queue ●Queue as Array ● Circular Queue ● Priority Queue ● Input Restricted Queue ● Output Restricted Queue ● Dqueue www.eshikshak.co.in
  • 9.
    Queue as Array: Insert Initially when the QUEUE is empty, set FRONT = NULL and REAR = 0 Step 1: start Step2: [check for queue is over flow or not] If (REAR >n) or (REAR==FRONT) Print “queue is overflow” else go to step 3 Step 3: [enter the item] QUEUE[REAR]=value REAR=REAR+1 Step 4:[ check condition] If(FRONT==null) FRONT=0 Step 5:end
  • 10.
    Queue as Array: Delete Step 1: start Step 2: [check for queue is under flow or not] If front>N or front==Null Print ”queue is underflow” else goto step 3 Step 3: [check condition] If front==rear Front==null Rear=0 else goto step 4 Step 4: [delete element] Queue[front]=null Step 5: front=front+1 Step 6: end
  • 11.
    Circular Queue ● Tosolve this problem, queues implement wrapping around. Such queues are called Circular Queues. ● Both the front and the rear pointers wrap around to the beginning of the array. ● It is also called as “Ring buffer”. ● Items can inserted and deleted from a queue in O(1) time. www.eshikshak.co.in
  • 12.
    Circular Queue ● Whena new item is inserted at the rear, the pointer to rear moves upwards. ● Similarly, when an item is deleted from the queue the front arrow moves downwards. ● After a few insert and delete operations the rear might reach the end of the queue and no more items can be inserted although the items from the front of the queue have been deleted and there is space in the queue. www.eshikshak.co.in
  • 13.
    QINSERT(Queue, N, FRONT,REAR, ITEM) 1 [Queue already filled ?] if FRONT = 0 and REAR = N-1, or if FRONT=REAR + 1 then write : Overflow and Return 2 [Find new value of REAR] if FRONT=-1 then [Queue initially empty] Set FRON T = 0 and REAR = 0 else if REAR = N-1 then Set REAR = 1 else Set REAR = REAR + 1 [End of If structure] 3 Set QUEUE[REAR] = ITEM [This inserts new element] 4 Return
  • 14.
    QDELETE(Queue, N, FRONT,REAR, ITEM) 1 [Queue already empty] If FRONT = -1, then Write : Underflow and Return 2 Set ITEM = Queue[FRONT] 3 [Find new value of FRONT] If FRONT = REAR, then [Queue has only one element to start] Set FRONT = -1 and REAR = -1 Else if FRONT = N-1, then Set FRONT = 0 Else Set FRONT = FRONT + 1 [End of If Structure] 4 Return
  • 15.
  • 16.
    Priority Queue ● Itis collection of elements where elements are stored according to the their priority levels ● Inserting and removing of elements from queue is decided by the priority of the elements ● The two fundamental methods of a priority queue P: ○ insertItem(k,e): Insert an element e with key k into P. ○ removeMin(): Return and remove from P an element with the smallest key. www.eshikshak.co.in
  • 17.
    Priority Queue ● Whenyou want to determine the priority for your assignments, you need a value for each assignment, that you can compare with each other. ● key: An object that is assigned to an element as a specific attribute for that element, which can be used to identify, rank, or weight that element. www.eshikshak.co.in
  • 18.
    Example: Student records Anyof the attributes, Student Name, Student Number, or Final Score Student Name ID Final Score (out can be used as keys. of 450) Note: Keys may not be unique (Final Score). Ashwin 09BCA08 310 Payal 09BCA80 311 Darshika 09BCA24 380 Nilkamal 09BCA75 400 Nikunj 09BCA74 440 Mori 09BCA102 400 www.eshikshak.co.in
  • 19.
    Rules to maintaina Priority Queue ● The elements with the higher priority will be 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 www.eshikshak.co.in
  • 20.
    Priority Queue Insert PQInsert(M, Item) Step 1 Find the Row M Step2 [Reset the Rear Pointer] If Rear[M] = N-1 then Rear[M] = 0 Else Rear[M] = Rear[M]+1 Step 3 [Overflow] If Front[M] = Rear[M] then Write (“This Priority Queue is full”) Return Step 4 [Insert Element] Q[M] [Rear[M]] = then Step 5 [Is Front Pointer Properly Set] If Front[M] = -1 then Front[m] = 0 Return Step 6 Exit www.eshikshak.co.in
  • 21.
    Priority Queue Delete PQDelete(K, Item) Step 1 Initialize K = 0 Step 2 while (Front[K] = -1) K = K+1 [To find the first non empty queue] Step 3 [Delete Element] Item = Q[K] [Front[K] Step 4 [Queue Empty] If Front[K] = N-1 then Front[K] = 0 Else Front[K] = Front[K]+1 Return Item Step 6 Exit www.eshikshak.co.in
  • 22.
    Deque ● Deque standsfor double-end queue ● A data structure in which elements can be added or deleted at either the front or rear ● But no changes can be made in the list ● Deque is generalization of both stack and queue www.eshikshak.co.in
  • 23.
    Removing Element fromDeque ● There are two variations of a deque. These are ○ Input Restricted Deque ■ An input restricted deque restricts the insertion of elements at one end only, but the deletion of elements can perform at both the ends. ○ Output Restricted Deque ■ An output restricted queue, restricts the deletion of elements at one end only, and allows insertion to be done at both the ends of deque www.eshikshak.co.in
  • 24.
    Possibilities ● The twopossibilities that must be considered while inserting or deleting elements into the queue are : ○ When an attempt is made to insert an element into a deque which is already full, an overflow occurs. ○ When an attempt is made to delete an element from a deque which is empty, underflow occurs. www.eshikshak.co.in
  • 25.
    Representation of Deque Deletio Insertion n Insertion Deletio n Front Rea r www.eshikshak.co.in
  • 26.
    Inserting Element inDeque InsertQatEnd(dq,7) 7 Front Rear InsertQatBeg(dq,10) 7 Front Rear InsertQatBeg(dq, 7 10) Front Rear www.eshikshak.co.in
  • 27.
    InsertQatBeg(dq,10) 10 7 Front Rear InsertQatEnd(dq,4) 10 7 4 Front Rear InsertQatBeg(dq,15) 15 10 7 4 Front Rear InsertQatEnd(dq,55) 15 10 7 4 55 Front www.eshikshak.co.in Rear
  • 28.
    Removing Element fromDeque delQBeg() 10 7 4 55 Front Rear delQBeg() 7 4 55 Front Rear InsertQatEnd(dq,23) 7 4 55 23 Front Rear www.eshikshak.co.in
  • 29.
    Deque : Insert ●There are two variations of a deque. These are ○ Input Restricted Deque ■ An input restricted deque restricts the insertion of elements at one end only, but the deletion of elements can perform at both the ends. ○ Output Restricted Deque ■ An output restricted queue, restricts the deletion of elements at one end only, and allows insertion to be done at both the ends of deque www.eshikshak.co.in
  • 30.
    Input Restricted queue: Insert Element Step 1: start Step 2:[check condition for overflow] If(rear==N-1 && front==0 or front=rear+1) Print “over flow” else goto step 3 Step 3: [check condition] If(front==null) front = 0 and rear=-1 else goto step 4 Step 4: [check condition and value] If (rear== N -1) rear=0 Else rear=rear+1 Step 5: [Add value] dq[rear]=value Step 6:end www.eshikshak.co.in
  • 31.
    Input Restricted queue: Delete Beginning Step 1: start Step 2: [check condition for underflow] If(rear==null & front==null) Print”underflow” else goto step 3 Step 3: [delete] dq[rear]=null Step 4: [check condition] If(rear==front) front=rear=null else rear--; Step 5: end www.eshikshak.co.in
  • 32.
    Input Restricted queue: Delete End Step 1: start Step2 : [check condition for under flow) If(rear==null & front==null) Print “under flow” else goto step 3 Step 3: [delete] dq[front]=null Step 4: [check condition] If(rear==front) rear=-1 and front=null else front=front+1 Step 5: end www.eshikshak.co.in