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Queues-and-CQueue-Implementation

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shaik faroq

The document provides an introduction to queues, explaining that they are ordered collections where items are added at the rear and removed from the front, following a FIFO (First In First Out) principle. It details operations such as insertion (enqueue), deletion (dequeue), and outlines conditions for queue status (empty or full), as well as representations using arrays and linked lists. The document also discusses applications of queues in algorithms and operating systems.

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Queues UNIT II
Introduction to Queues • A queue is an ordered collection of items where the addition of new items happens at one end, called the “rear,” and the removal of existing items occurs at the other end, commonly called the “front.” • Queue: FIFO (Fist In First Out) : Enqueue and Dequeue, front, rear • Stack: FILO or LIFO , Push and Pop, top
Array representation of Queue There are two variables i.e. front and rear, that are implemented in the case of every queue.
Maxsize=6, rear=front=-1 • Qinsert(item) • 1.If (rear = maxsize-1 ) • print (“queue overflow”) and return • 2.Else • rear = rear + 1 • Queue [rear] = item 0 1 2 3 4 5 rear front Function call Qinsert(item) Rear=maxsize-1? Rear=rear+1 Queue[rear]=item If section Else section
Maxsize=6, rear=0, front=-1 • Qinsert(item) • 1.If (rear = maxsize-1 ) • print (“queue overflow”) and return • 2.Else • rear = rear + 1 • Queue [rear] = item 20 0 1 2 3 4 5 rear front Function call Qinsert(item) Rear=maxsize-1 Rear=rear+1 Queue[rear]=item Qinsert(20) -1=5 ? F Rear=-1+1=0 Queue[0]=20 If section Else section 1
Maxsize=6, rear=1, front=-1 • Qinsert(item) • 1.If (rear = maxsize-1 ) • print (“queue overflow”) and return • 2.Else • rear = rear + 1 • Queue [rear] = item 20 30 0 1 2 3 4 5 rear front Function call Qinsert(item) Rear=maxsize-1 Rear=rear+1 Queue[rear]=item Qinsert(20) -1=5 ? F Rear=-1+1=0 Queue[0]=20 Qinsert(30) 0=5? F Rear= 0+1=1 Queue[1]=30 If section Else section 1 2
Maxsize=6, rear=2, front=-1 • Qinsert(item) • 1.If (rear = maxsize-1 ) • print (“queue overflow”) and return • 2.Else • rear = rear + 1 • Queue [rear] = item 20 30 40 0 1 2 3 4 5 rear front Function call Qinsert(item) Rear=maxsize-1 Rear=rear+1 Queue[rear]=item Qinsert(20) -1=5 ? F Rear=-1+1=0 Queue[0]=20 Qinsert(30) 0=5? F Rear= 0+1=1 Queue[1]=30 Qinsert(40) 1=5? F Rear= 1+1=2 Queue[2]=40 If section Else section 1 2 3
Maxsize=6, rear=3, front=-1 • Qinsert(item) • 1.If (rear = maxsize-1 ) • print (“queue overflow”) and return • 2.Else • rear = rear + 1 • Queue [rear] = item 20 30 40 50 0 1 2 3 4 5 rear front Function call Qinsert(item) Rear=maxsize-1 Rear=rear+1 Queue[rear]=item Qinsert(20) -1=5 ? F Rear=-1+1=0 Queue[0]=20 Qinsert(30) 0=5? F Rear= 0+1=1 Queue[1]=30 Qinsert(40) 1=5? F Rear= 1+1=2 Queue[2]=40 Qinsert(50) 2=5? F Rear= 2+1=3 Queue[3]=50 If section Else section 1 2 3 4
Maxsize=6, rear=4, front=-1 • Qinsert(item) • 1.If (rear = maxsize-1 ) • print (“queue overflow”) and return • 2.Else • rear = rear + 1 • Queue [rear] = item 20 30 40 50 60 0 1 2 3 4 5 rear front Function call Qinsert(item) Rear=maxsize-1 Rear=rear+1 Queue[rear]=item Qinsert(20) -1=5 ? F Rear=-1+1=0 Queue[0]=20 Qinsert(30) 0=5? F Rear= 0+1=1 Queue[1]=30 Qinsert(40) 1=5? F Rear= 1+1=2 Queue[2]=40 Qinsert(50) 2=5? F Rear= 2+1=3 Queue[3]=50 Qinsert(60) 3=5? F Rear= 3+1=4 Queue[4]=60 If section Else section 1 2 3 4 5
Maxsize=6, rear=5, front=-1 • Qinsert(item) • 1.If (rear = maxsize-1 ) • print (“queue overflow”) and return • 2.Else • rear = rear + 1 • Queue [rear] = item 20 30 40 50 60 70 0 1 2 3 4 5 rear front Function call Qinsert(item) Rear=maxsize-1 Rear=rear+1 Queue[rear]=item Qinsert(20) -1=5 ? F Rear=-1+1=0 Queue[0]=20 Qinsert(30) 0=5? F Rear= 0+1=1 Queue[1]=30 Qinsert(40) 1=5? F Rear= 1+1=2 Queue[2]=40 Qinsert(50) 2=5? F Rear= 2+1=3 Queue[3]=50 Qinsert(60) 3=5? F Rear= 3+1=4 Queue[4]=60 Qinsert(70) 4=5? F Rear= 4+1=5 Queue[5]=70 If section Else section 1 2 3 4 5 6
Maxsize=6, rear=5, front=-1 • Qinsert(item) • 1.If (rear = maxsize-1 ) • print (“queue overflow”) and return • 2.Else • rear = rear + 1 • Queue [rear] = item 20 30 40 50 60 70 0 1 2 3 4 5 rear front Function call Qinsert(item) Rear=maxsize-1 Rear=rear+1 Queue[rear]=item Qinsert(20) -1=5 ? F Rear=-1+1=0 Queue[0]=20 Qinsert(30) 0=5? F Rear= 0+1=1 Queue[1]=30 Qinsert(40) 1=5? F Rear= 1+1=2 Queue[2]=40 Qinsert(50) 2=5? F Rear= 2+1=3 Queue[3]=50 Qinsert(60) 3=5? F Rear= 3+1=4 Queue[4]=60 Qinsert(70) 4=5? F Rear= 4+1=5 Queue[5]=70 Qinsert(80) 5=5? T stop If section Else section 1 2 3 4 5 6 7
Maxsize=6, front=-1 rear=5 • Qdelete() • If (front =rear) • print “queue empty” and return • 2. Else • Front = front + 1 • item = queue [front]; • Return item 20 30 40 50 60 70 0 1 2 3 4 5 rear front Function call Qdelete() front=rear Front=front+1 Item=Queeue[front] If section Else section
Maxsize=6, front=0 rear=5 • Qdelete() • If (front =rear) • print “queue empty” and return • 2. Else • Front = front + 1 • item = queue [front]; • Return item 30 40 50 60 70 0 1 2 3 4 5 rear front Function call Qdelete() front=rear Front=front+1 Item=Queeue[front] Qdelete() -1 = 5 ? F front=-1+1=0 item=Queue[0] If section Else section 1 Item=20
Maxsize=6, front=1 rear=5 • Qdelete() • If (front =rear) • print “queue empty” and return • 2. Else • Front = front + 1 • item = queue [front]; • Return item 40 50 60 70 0 1 2 3 4 5 rear front Function call Qdelete() front=rear Front=front+1 Item=Queeue[front] Qdelete() -1 = 5 ? F front=-1+1=0 item=Queue[0] Qdelete() 0 = 5 ? F front=0+1=1 item=Queue[1] If section Else section 1 Item=30 2
Maxsize=6, front=2 rear=5 • Qdelete() • If (front =rear) • print “queue empty” and return • 2. Else • Front = front + 1 • item = queue [front]; • Return item 50 60 70 0 1 2 3 4 5 rear front Function call Qdelete() front=rear Front=front+1 Item=Queeue[front] Qdelete() -1 = 5 ? F front=-1+1=0 item=Queue[0] Qdelete() 0 = 5 ? F front=0+1=1 item=Queue[1] Qdelete() 1 = 5 ? F front=1+1=2 item=Queue[2] If section Else section 1 Item=40 2 3
Maxsize=6, front=3 rear=5 • Qdelete() • If (front =rear) • print “queue empty” and return • 2. Else • Front = front + 1 • item = queue [front]; • Return item 60 70 0 1 2 3 4 5 rear front Function call Qdelete() front=rear Front=front+1 Item=Queeue[front] Qdelete() -1 = 5 ? F front=-1+1=0 item=Queue[0] Qdelete() 0 = 5 ? F front=0+1=1 item=Queue[1] Qdelete() 1 = 5 ? F front=1+1=2 item=Queue[2] Qdelete() 2 = 5 ? F front=2+1=3 item=Queue[3] If section Else section 1 Item=50 2 3 4
Maxsize=6, front=4 rear=5 • Qdelete() • If (front =rear) • print “queue empty” and return • 2. Else • Front = front + 1 • item = queue [front]; • Return item 70 0 1 2 3 4 5 rear front Function call Qdelete() front=rear Front=front+1 Item=Queeue[front] Qdelete() -1 = 5 ? F front=-1+1=0 item=Queue[0] Qdelete() 0 = 5 ? F front=0+1=1 item=Queue[1] Qdelete() 1 = 5 ? F front=1+1=2 item=Queue[2] Qdelete() 2 = 5 ? F front=2+1=3 item=Queue[3] Qdelete() 3 = 5 ? F front=3+1=4 item=Queue[4] If section Else section 1 Item=60 2 3 4 5
Maxsize=6, front=5 rear=5 • Qdelete() • If (front =rear) • print “queue empty” and return • 2. Else • Front = front + 1 • item = queue [front]; • Return item 0 1 2 3 4 5 rear front Function call Qdelete() front=rear Front=front+1 Item=Queeue[front] Qdelete() -1 = 5 ? F front=-1+1=0 item=Queue[0] Qdelete() 0 = 5 ? F front=0+1=1 item=Queue[1] Qdelete() 1 = 5 ? F front=1+1=2 item=Queue[2] Qdelete() 2 = 5 ? F front=2+1=3 item=Queue[3] Qdelete() 3 = 5 ? F front=3+1=4 item=Queue[4] Qdelete() 4= 5 ? F front=4+1=5 item=Queue[5] If section Else section 1 Item=70 2 3 4 5 6
Maxsize=6, front=5 rear=5 • Qdelete() • If (front =rear) • print “queue empty” and return • 2. Else • Front = front + 1 • item = queue [front]; • Return item 0 1 2 3 4 5 rear front Function call Qdelete() front=rear Front=front+1 Item=Queeue[front] Qdelete() -1 = 5 ? F front=-1+1=0 item=Queue[0] Qdelete() 0 = 5 ? F front=0+1=1 item=Queue[1] Qdelete() 1 = 5 ? F front=1+1=2 item=Queue[2] Qdelete() 2 = 5 ? F front=2+1=3 item=Queue[3] Qdelete() 3 = 5 ? F front=3+1=4 item=Queue[4] Qdelete() 4= 5 ? F front=4+1=5 item=Queue[5] Qdelete() 5=5? T queue empty - - If section Else section 1 2 6 7
Conditions to be satisfied in Queue • Queue is empty FRONT=REAR • Queue is full REAR=Maxsize • Queue contains element >= 1 FRONT <REAR NO. OF ELEMENT = REAR-FRONT+1 Disadvantage of Queue: The deleted element’s space in the queuqe cannot be reused-utilized for inserting another element.
Applications of queues Queue is used in BFS. Queue is used by OS to schedule equal priority jobs In recognizing palindrome Simulation
Representation of Queues • Queues can be represented using arrays • Queues can be represented using Linked List
Array representation of Queues 12 9 7 18 45 front rear A[0] A[1] A[2] A[3] A[4]
Linked representation of Queues 290 Front 300 350 360 rear 9 300 7 350 4 360 2 380 5 N 290 front 300 350 360 380 rear Linked queue after inserting a node 300 front 350 360 380 Linked queue after deleting a node
Insert an element in queue using linked list STEP-1: Allocate memory for the new node & name it as TEMP. STEP-2: SET TEMP➔ DATA = NUM SET TEMP→ LINK = NULL STEP-3: IF FRONT = NULL FRONT=REAR=TEMP ELSE REAR→ LINK =TEMP REAR=TEMP [ END OF IF] STEP-4: EXIT FRONT=REAR=NULL
20 NULL 5000 TEMP STEP-1: Allocate memory for the new node & name it as TEMP. STEP-2: SET TEMP➔ DATA = NUM SET TEMP→ LINK = NULL FRONT=REAR=NULL 1. QINSERT_LINK(TEMP) Data link
STEP-3: IF FRONT = NULL FRONT=REAR=TEMP ELSE REAR→ LINK =TEMP REAR=TEMP [ END OF IF] FRONT=REAR=5000 20 NULL 5000 FRONT REAR
30 NULL 6000 TEMP STEP-1: Allocate memory for the new node & name it as TEMP. STEP-2: SET TEMP➔ DATA = NUM SET TEMP→ LINK = NULL FRONT=REAR=TEMP 2. QINSERT_LINK(TEMP)
STEP-3: IF FRONT = NULL FRONT=REAR=TEMP ELSE REAR→ LINK =TEMP REAR=TEMP [ END OF IF] FRONT=5000 REAR=6000 20 NULL 5000 FRONT REAR 30 NULL 6000 TEMP 20 6000 5000 FRONT REAR 30 NULL 6000 TEMP
40 NULL 7000 TEMP STEP-1: Allocate memory for the new node & name it as TEMP. STEP-2: SET TEMP➔ DATA = NUM SET TEMP→ LINK = NULL 3. QINSERT_LINK(TEMP) FRONT=5000 REAR=6000
STEP-3: IF FRONT = NULL FRONT=REAR=TEMP ELSE REAR→ LINK =TEMP REAR=TEMP [ END OF IF] FRONT=5000 REAR=7000 20 6000 5000 FRONT REAR 30 NULL 6000 20 6000 5000 FRONT REAR 30 7000 6000 40 NULL 7000 TEMP
FRONT=5000 REAR=7000 20 6000 5000 FRONT REAR 30 7000 6000 40 NULL 7000
Delete an element in queue using linked list STEP-1: If FRONT = NULL write “underflow” go to step 3. [End of if] STEP-2: SET TEMP = FRONT FRONT=FRONT→ LINK IF FRONT = NULL REAR=NULL STEP-3: EXIT
Delete an element in queue using linked list STEP-1: If FRONT = NULL write “underflow” go to step 3. [End of if] STEP-2: SET TEMP = FRONT FRONT=FRONT→ LINK IF FRONT = NULL REAR=NULL STEP-3: EXIT 20 6000 5000 FRONT REAR 30 7000 6000 40 NULL 7000 1. QDELETE_LINK() TEMP
Delete an element in queue using linked list STEP-1: If FRONT = NULL write “underflow” go to step 4. [End of if] STEP-2: SET TEMP = FRONT FRONT=FRONT→ LINK IF FRONT = NULL REAR=NULL STEP-3: FREE(TEMP) STEP-4: EXIT 20 6000 5000 FRONT REAR 30 7000 6000 40 NULL 7000 1. QDELETE_LINK() TEMP FRONT REAR 30 7000 6000 40 NULL 7000
Delete an element in queue using linked list STEP-1: If FRONT = NULL write “underflow” go to step 4. [End of if] STEP-2: SET TEMP = FRONT FRONT=FRONT→ LINK IF FRONT = NULL REAR=NULL STEP-3: FREE(TEMP) STEP-4: EXIT 2. QDELETE_LINK() TEMP FRONT REAR 30 7000 6000 40 NULL 7000 TEMP FRONT REAR 30 7000 6000 40 NULL 7000 FRONT REAR 40 NULL 7000
Delete an element in queue using linked list STEP-1: If FRONT = NULL write “underflow” go to step 4. [End of if] STEP-2: SET TEMP = FRONT FRONT=FRONT→ LINK IF FRONT = NULL REAR=NULL STEP-3: FREE(TEMP) STEP-4: EXIT 3. QDELETE_LINK() 4. QDELETE_LINK() FRONT=NULL REAR=NULL 40 NULL 7000 TEMP FRONT REAR 40 NULL 7000 TEMP TEMP
Types of Queues • Dequeue • Circular Queue • Priority Queue
Dequeues • Deque stands for double ended queue. • Elements can be inserted or deleted at either end. • Also known as head-tail linked list. 34 12 53 61 9 FRONT Insertion Deleion REAR Insertion Deleion
Types of Dequeues • Input restricted queue 34 12 53 61 9 FRONT Deleion REAR Insertion Deleion
Types of Dequeues • Output restricted queue 34 12 53 61 9 FRONT Deleion REAR Insertion Insertion
Circular Queues • Circular queue are used to remove the drawback of simple queue. • Both the front and the rear pointers wrap around to the beginning of the array. • It is also called as “Ring buffer”.
Algorithm CQ_insert(ITEM) • Step-1: If (REAR+1)%MAX=FRONT • Write Overflow • GoTo Step 4. • [End of if] • Step-2: If FRONT=-1 and REAR =-1 • REAR=FRONT=0 • Else If REAR=MAX-1 AND FRONT!=0 • REAR=0 • Else • REAR=(REAR+1)%MAX • [End of If] • Step-3: CQ[REAR]=ITEM • Step-4: Exit
Algorithm CQ_insert(ITEM) • Step-1: If (REAR+1)%MAX=FRONT • Write Overflow • GoTo Step 4. • [End of if] • Step-2: If FRONT=-1 and REAR =-1 • REAR=FRONT=0 • Else If REAR=MAX-1 AND FRONT!=0 • REAR=0 • Else • REAR=(REAR+1)%MAX • [End of If] • Step-3: CQ[REAR]=ITEM • Step-4: Exit CQ[0] CQ[1] CQ[2] CQ[3] CQ[4] CQ[5] CQ[6] REAR FRONT FRONT=-1 REAR=-1 MAX=7
Algorithm CQ_insert(10) • Step-1: If (REAR+1)%MAX=FRONT • Write Overflow • GoTo Step 4. • [End of if] • Step-2: If FRONT=-1 and REAR =-1 • REAR=FRONT=0 • Else If REAR=MAX-1 AND FRONT!=0 • REAR=0 • Else • REAR=(REAR+1)%MAX • [End of If] • Step-3: CQ[REAR]=ITEM • Step-4: Exit CQ[0] CQ[1] CQ[2] CQ[3] CQ[4] CQ[5] CQ[6] REAR FRONT 10 FRONT=-1 REAR=-1 MAX=7 IF FRONT=-1 & REAR=-1 T REAR=FRONT=0 IF ((REAR+1)%MAX=FRONT) (-1+1)%7=-1 0 = -1 F C1 C2 REAR=(REAR+1)%MAX FRONT=0 REAR=0 MAX=7 REAR=MAX-1 & FRONT!=0 REAR=0 C3 CQ[REAR]=ITEM CQ[0]=10
Algorithm CQ_insert(20) • Step-1: If (REAR+1)%MAX=FRONT • Write Overflow • GoTo Step 4. • [End of if] • Step-2: If FRONT=-1 and REAR =-1 • REAR=FRONT=0 • Else If REAR=MAX-1 AND FRONT!=0 • REAR=0 • Else • REAR=(REAR+1)%MAX • [End of If] • Step-3: CQ[REAR]=ITEM • Step-4: Exit CQ[0] CQ[1] CQ[2] CQ[3] CQ[4] CQ[5] CQ[6] REAR FRONT 10 FRONT=0 REAR=0 MAX=7 IF FRONT=-1 & REAR=-1 F REAR=FRONT=0 IF ((REAR+1)%MAX=FRONT) (0+1)%7= 0 1 = -1 F C1 C2 REAR=(REAR+1)%MAX (0+1)%7= 1 FRONT=0 REAR=1 MAX=7 REAR=MAX-1 & FRONT!=0 0=6 F & 0!0 F REAR=0 C3 CQ[REAR]=ITEM CQ[1]=20 C4 20
Algorithm CQ_insert(30) • Step-1: If (REAR+1)%MAX=FRONT • Write Overflow • GoTo Step 4. • [End of if] • Step-2: If FRONT=-1 and REAR =-1 • REAR=FRONT=0 • Else If REAR=MAX-1 AND FRONT!=0 • REAR=0 • Else • REAR=(REAR+1)%MAX • [End of If] • Step-3: CQ[REAR]=ITEM • Step-4: Exit CQ[0] CQ[1] CQ[2] CQ[3] CQ[4] CQ[5] CQ[6] REAR FRONT 10 FRONT=0 REAR=1 MAX=7 IF FRONT=-1 & REAR=-1 F REAR=FRONT=0 IF ((REAR+1)%MAX=FRONT) (1+1)%7= 0 2 = 0 F C1 C2 REAR=(REAR+1)%MAX (1+1)%7= 2 FRONT=0 REAR=2 MAX=7 REAR=MAX-1 & FRONT!=0 1=6 F REAR=0 C3 CQ[REAR]=ITEM CQ[2]=30 C4 20 30
Algorithm CQ_insert(30) • Step-1: If (REAR+1)%MAX=FRONT • Write Overflow • GoTo Step 4. • [End of if] • Step-2: If FRONT=-1 and REAR =-1 • REAR=FRONT=0 • Else If REAR=MAX-1 AND FRONT!=0 • REAR=0 • Else • REAR=(REAR+1)%MAX • [End of If] • Step-3: CQ[REAR]=ITEM • Step-4: Exit CQ[0] CQ[1] CQ[2] CQ[3] CQ[4] CQ[5] CQ[6] REAR FRONT 10 FRONT=0 REAR=1 MAX=7 IF FRONT=-1 & REAR=-1 F REAR=FRONT=0 IF ((REAR+1)%MAX=FRONT) (1+1)%7= 0 2 = 0 F C1 C2 REAR=(REAR+1)%MAX (1+1)%7= 2 FRONT=0 REAR=2 MAX=7 REAR=MAX-1 & FRONT!=0 1=6 F REAR=0 C3 CQ[REAR]=ITEM CQ[2]=30 C4 20 30
Algorithm CQ_insert(40) • Step-1: If (REAR+1)%MAX=FRONT • Write Overflow • GoTo Step 4. • [End of if] • Step-2: If FRONT=-1 and REAR =-1 • REAR=FRONT=0 • Else If REAR=MAX-1 AND FRONT!=0 • REAR=0 • Else • REAR=(REAR+1)%MAX • [End of If] • Step-3: CQ[REAR]=ITEM • Step-4: Exit CQ[0] CQ[1] CQ[2] CQ[3] CQ[4] CQ[5] CQ[6] REAR FRONT 10 FRONT=0 REAR=2 MAX=7 IF FRONT=-1 & REAR=-1 F REAR=FRONT=0 IF ((REAR+1)%MAX=FRONT) (2+1)%7= 0 3 = 0 F C1 C2 REAR=(REAR+1)%MAX (2+1)%7= 3 FRONT=0 REAR=3 MAX=7 REAR=MAX-1 & FRONT!=0 2=6 F REAR=0 C3 CQ[REAR]=ITEM CQ[3]=40 C4 20 30 40
Algorithm CQ_insert(50) • Step-1: If (REAR+1)%MAX=FRONT • Write Overflow • GoTo Step 4. • [End of if] • Step-2: If FRONT=-1 and REAR =-1 • REAR=FRONT=0 • Else If REAR=MAX-1 AND FRONT!=0 • REAR=0 • Else • REAR=(REAR+1)%MAX • [End of If] • Step-3: CQ[REAR]=ITEM • Step-4: Exit CQ[0] CQ[1] CQ[2] CQ[3] CQ[4] CQ[5] CQ[6] REAR FRONT 10 FRONT=0 REAR=3 MAX=7 IF FRONT=-1 & REAR=-1 F REAR=FRONT=0 IF ((REAR+1)%MAX=FRONT) (3+1)%7= 0 4= 0 F C1 C2 REAR=(REAR+1)%MAX (3+1)%7= 4 FRONT=0 REAR=4 MAX=7 REAR=MAX-1 & FRONT!=0 4=6 F REAR=0 C3 CQ[REAR]=ITEM CQ[4]=50 C4 20 30 40 50
Algorithm CQ_insert(60) • Step-1: If (REAR+1)%MAX=FRONT • Write Overflow • GoTo Step 4. • [End of if] • Step-2: If FRONT=-1 and REAR =-1 • REAR=FRONT=0 • Else If REAR=MAX-1 AND FRONT!=0 • REAR=0 • Else • REAR=(REAR+1)%MAX • [End of If] • Step-3: CQ[REAR]=ITEM • Step-4: Exit CQ[0] CQ[1] CQ[2] CQ[3] CQ[4] CQ[5] CQ[6] REAR FRONT 10 FRONT=0 REAR=4 MAX=7 IF FRONT=-1 & REAR=-1 F REAR=FRONT=0 IF ((REAR+1)%MAX=FRONT) (4+1)%7= 0 5= 0 F C1 C2 REAR=(REAR+1)%MAX (4+1)%7= 5 FRONT=0 REAR=5 MAX=7 REAR=MAX-1 & FRONT!=0 5=6 F REAR=0 C3 CQ[REAR]=ITEM CQ[5]=60 C4 20 30 40 50 60
Algorithm CQ_insert(70) • Step-1: If (REAR+1)%MAX=FRONT • Write Overflow • GoTo Step 4. • [End of if] • Step-2: If FRONT=-1 and REAR =-1 • REAR=FRONT=0 • Else If REAR=MAX-1 AND FRONT!=0 • REAR=0 • Else • REAR=(REAR+1)%MAX • [End of If] • Step-3: CQ[REAR]=ITEM • Step-4: Exit CQ[0] CQ[1] CQ[2] CQ[3] CQ[4] CQ[5] CQ[6] REAR FRONT 10 FRONT=0 REAR=5 MAX=7 IF FRONT=-1 & REAR=-1 F REAR=FRONT=0 IF ((REAR+1)%MAX=FRONT) (5+1)%7= 0 6= 0 F C1 C2 REAR=(REAR+1)%MAX (5+1)%7= 6 FRONT=0 REAR=6 MAX=7 REAR=MAX-1 & FRONT!=0 5=6 F REAR=0 C3 CQ[REAR]=ITEM CQ[6]=70 C4 20 30 40 50 60 70
Algorithm CQ_insert(80) • Step-1: If (REAR+1)%MAX=FRONT • Write Overflow • GoTo Step 4. • [End of if] • Step-2: If FRONT=-1 and REAR =-1 • REAR=FRONT=0 • Else If REAR=MAX-1 AND FRONT!=0 • REAR=0 • Else • REAR=(REAR+1)%MAX • [End of If] • Step-3: CQ[REAR]=ITEM • Step-4: Exit CQ[0] CQ[1] CQ[2] CQ[3] CQ[4] CQ[5] CQ[6] REAR FRONT 10 FRONT=0 REAR=6 MAX=7 IF ((REAR+1)%MAX=FRONT) (6+1)%7= 0 0= 0 T C1 20 30 40 50 60 70
Algorithm CQ_insert(80) • Step-1: If (REAR+1)%MAX=FRONT • Write Overflow • GoTo Step 4. • [End of if] • Step-2: If FRONT=-1 and REAR =-1 • REAR=FRONT=0 • Else If REAR=MAX-1 AND FRONT!=0 • REAR=0 • Else • REAR=(REAR+1)%MAX • [End of If] • Step-3: CQ[REAR]=ITEM • Step-4: Exit CQ[0] CQ[1] CQ[2] CQ[3] CQ[4] CQ[5] CQ[6] REAR FRONT IF FRONT=-1 & REAR=-1 F REAR=FRONT=0 IF ((REAR+1)%MAX=FRONT) (6+1)%7= 1 0= 1 F C1 C2 REAR=(REAR+1)%MAX FRONT=1 REAR=6 MAX=7 REAR=MAX-1 & FRONT!=0 6=6 T & 1!0 T REAR=0 C3 CQ[REAR]=ITEM CQ[0]=80 C4 20 30 40 50 60 70 CQ_delete() 80
Algorithm CQ_delete() • Step-1: If FRONT=-1 • Write Underflow • go to step 4 • [End of if] • Step-2: VAL=CQ[FRONT] • Step-3:If FRONT = REAR • REAR=FRONT=-1 • Else If FRONT=MAX-1 • FRONT=0 • Else • FRONT=FRONT+1 • [End of If] • Step-4: Exit CQ[0] CQ[1] CQ[3] CQ[5] CQ[6] REAR FRONT 10 20 30 40 50 60 CQ[2] 70

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Queues-and-CQueue-Implementation

  • 2. Introduction to Queues • A queue is an ordered collection of items where the addition of new items happens at one end, called the “rear,” and the removal of existing items occurs at the other end, commonly called the “front.” • Queue: FIFO (Fist In First Out) : Enqueue and Dequeue, front, rear • Stack: FILO or LIFO , Push and Pop, top
  • 3. Array representation of Queue There are two variables i.e. front and rear, that are implemented in the case of every queue.
  • 4. Maxsize=6, rear=front=-1 • Qinsert(item) • 1.If (rear = maxsize-1 ) • print (“queue overflow”) and return • 2.Else • rear = rear + 1 • Queue [rear] = item 0 1 2 3 4 5 rear front Function call Qinsert(item) Rear=maxsize-1? Rear=rear+1 Queue[rear]=item If section Else section
  • 5. Maxsize=6, rear=0, front=-1 • Qinsert(item) • 1.If (rear = maxsize-1 ) • print (“queue overflow”) and return • 2.Else • rear = rear + 1 • Queue [rear] = item 20 0 1 2 3 4 5 rear front Function call Qinsert(item) Rear=maxsize-1 Rear=rear+1 Queue[rear]=item Qinsert(20) -1=5 ? F Rear=-1+1=0 Queue[0]=20 If section Else section 1
  • 6. Maxsize=6, rear=1, front=-1 • Qinsert(item) • 1.If (rear = maxsize-1 ) • print (“queue overflow”) and return • 2.Else • rear = rear + 1 • Queue [rear] = item 20 30 0 1 2 3 4 5 rear front Function call Qinsert(item) Rear=maxsize-1 Rear=rear+1 Queue[rear]=item Qinsert(20) -1=5 ? F Rear=-1+1=0 Queue[0]=20 Qinsert(30) 0=5? F Rear= 0+1=1 Queue[1]=30 If section Else section 1 2
  • 7. Maxsize=6, rear=2, front=-1 • Qinsert(item) • 1.If (rear = maxsize-1 ) • print (“queue overflow”) and return • 2.Else • rear = rear + 1 • Queue [rear] = item 20 30 40 0 1 2 3 4 5 rear front Function call Qinsert(item) Rear=maxsize-1 Rear=rear+1 Queue[rear]=item Qinsert(20) -1=5 ? F Rear=-1+1=0 Queue[0]=20 Qinsert(30) 0=5? F Rear= 0+1=1 Queue[1]=30 Qinsert(40) 1=5? F Rear= 1+1=2 Queue[2]=40 If section Else section 1 2 3
  • 8. Maxsize=6, rear=3, front=-1 • Qinsert(item) • 1.If (rear = maxsize-1 ) • print (“queue overflow”) and return • 2.Else • rear = rear + 1 • Queue [rear] = item 20 30 40 50 0 1 2 3 4 5 rear front Function call Qinsert(item) Rear=maxsize-1 Rear=rear+1 Queue[rear]=item Qinsert(20) -1=5 ? F Rear=-1+1=0 Queue[0]=20 Qinsert(30) 0=5? F Rear= 0+1=1 Queue[1]=30 Qinsert(40) 1=5? F Rear= 1+1=2 Queue[2]=40 Qinsert(50) 2=5? F Rear= 2+1=3 Queue[3]=50 If section Else section 1 2 3 4
  • 9. Maxsize=6, rear=4, front=-1 • Qinsert(item) • 1.If (rear = maxsize-1 ) • print (“queue overflow”) and return • 2.Else • rear = rear + 1 • Queue [rear] = item 20 30 40 50 60 0 1 2 3 4 5 rear front Function call Qinsert(item) Rear=maxsize-1 Rear=rear+1 Queue[rear]=item Qinsert(20) -1=5 ? F Rear=-1+1=0 Queue[0]=20 Qinsert(30) 0=5? F Rear= 0+1=1 Queue[1]=30 Qinsert(40) 1=5? F Rear= 1+1=2 Queue[2]=40 Qinsert(50) 2=5? F Rear= 2+1=3 Queue[3]=50 Qinsert(60) 3=5? F Rear= 3+1=4 Queue[4]=60 If section Else section 1 2 3 4 5
  • 10. Maxsize=6, rear=5, front=-1 • Qinsert(item) • 1.If (rear = maxsize-1 ) • print (“queue overflow”) and return • 2.Else • rear = rear + 1 • Queue [rear] = item 20 30 40 50 60 70 0 1 2 3 4 5 rear front Function call Qinsert(item) Rear=maxsize-1 Rear=rear+1 Queue[rear]=item Qinsert(20) -1=5 ? F Rear=-1+1=0 Queue[0]=20 Qinsert(30) 0=5? F Rear= 0+1=1 Queue[1]=30 Qinsert(40) 1=5? F Rear= 1+1=2 Queue[2]=40 Qinsert(50) 2=5? F Rear= 2+1=3 Queue[3]=50 Qinsert(60) 3=5? F Rear= 3+1=4 Queue[4]=60 Qinsert(70) 4=5? F Rear= 4+1=5 Queue[5]=70 If section Else section 1 2 3 4 5 6
  • 11. Maxsize=6, rear=5, front=-1 • Qinsert(item) • 1.If (rear = maxsize-1 ) • print (“queue overflow”) and return • 2.Else • rear = rear + 1 • Queue [rear] = item 20 30 40 50 60 70 0 1 2 3 4 5 rear front Function call Qinsert(item) Rear=maxsize-1 Rear=rear+1 Queue[rear]=item Qinsert(20) -1=5 ? F Rear=-1+1=0 Queue[0]=20 Qinsert(30) 0=5? F Rear= 0+1=1 Queue[1]=30 Qinsert(40) 1=5? F Rear= 1+1=2 Queue[2]=40 Qinsert(50) 2=5? F Rear= 2+1=3 Queue[3]=50 Qinsert(60) 3=5? F Rear= 3+1=4 Queue[4]=60 Qinsert(70) 4=5? F Rear= 4+1=5 Queue[5]=70 Qinsert(80) 5=5? T stop If section Else section 1 2 3 4 5 6 7
  • 12. Maxsize=6, front=-1 rear=5 • Qdelete() • If (front =rear) • print “queue empty” and return • 2. Else • Front = front + 1 • item = queue [front]; • Return item 20 30 40 50 60 70 0 1 2 3 4 5 rear front Function call Qdelete() front=rear Front=front+1 Item=Queeue[front] If section Else section
  • 13. Maxsize=6, front=0 rear=5 • Qdelete() • If (front =rear) • print “queue empty” and return • 2. Else • Front = front + 1 • item = queue [front]; • Return item 30 40 50 60 70 0 1 2 3 4 5 rear front Function call Qdelete() front=rear Front=front+1 Item=Queeue[front] Qdelete() -1 = 5 ? F front=-1+1=0 item=Queue[0] If section Else section 1 Item=20
  • 14. Maxsize=6, front=1 rear=5 • Qdelete() • If (front =rear) • print “queue empty” and return • 2. Else • Front = front + 1 • item = queue [front]; • Return item 40 50 60 70 0 1 2 3 4 5 rear front Function call Qdelete() front=rear Front=front+1 Item=Queeue[front] Qdelete() -1 = 5 ? F front=-1+1=0 item=Queue[0] Qdelete() 0 = 5 ? F front=0+1=1 item=Queue[1] If section Else section 1 Item=30 2
  • 15. Maxsize=6, front=2 rear=5 • Qdelete() • If (front =rear) • print “queue empty” and return • 2. Else • Front = front + 1 • item = queue [front]; • Return item 50 60 70 0 1 2 3 4 5 rear front Function call Qdelete() front=rear Front=front+1 Item=Queeue[front] Qdelete() -1 = 5 ? F front=-1+1=0 item=Queue[0] Qdelete() 0 = 5 ? F front=0+1=1 item=Queue[1] Qdelete() 1 = 5 ? F front=1+1=2 item=Queue[2] If section Else section 1 Item=40 2 3
  • 16. Maxsize=6, front=3 rear=5 • Qdelete() • If (front =rear) • print “queue empty” and return • 2. Else • Front = front + 1 • item = queue [front]; • Return item 60 70 0 1 2 3 4 5 rear front Function call Qdelete() front=rear Front=front+1 Item=Queeue[front] Qdelete() -1 = 5 ? F front=-1+1=0 item=Queue[0] Qdelete() 0 = 5 ? F front=0+1=1 item=Queue[1] Qdelete() 1 = 5 ? F front=1+1=2 item=Queue[2] Qdelete() 2 = 5 ? F front=2+1=3 item=Queue[3] If section Else section 1 Item=50 2 3 4
  • 17. Maxsize=6, front=4 rear=5 • Qdelete() • If (front =rear) • print “queue empty” and return • 2. Else • Front = front + 1 • item = queue [front]; • Return item 70 0 1 2 3 4 5 rear front Function call Qdelete() front=rear Front=front+1 Item=Queeue[front] Qdelete() -1 = 5 ? F front=-1+1=0 item=Queue[0] Qdelete() 0 = 5 ? F front=0+1=1 item=Queue[1] Qdelete() 1 = 5 ? F front=1+1=2 item=Queue[2] Qdelete() 2 = 5 ? F front=2+1=3 item=Queue[3] Qdelete() 3 = 5 ? F front=3+1=4 item=Queue[4] If section Else section 1 Item=60 2 3 4 5
  • 18. Maxsize=6, front=5 rear=5 • Qdelete() • If (front =rear) • print “queue empty” and return • 2. Else • Front = front + 1 • item = queue [front]; • Return item 0 1 2 3 4 5 rear front Function call Qdelete() front=rear Front=front+1 Item=Queeue[front] Qdelete() -1 = 5 ? F front=-1+1=0 item=Queue[0] Qdelete() 0 = 5 ? F front=0+1=1 item=Queue[1] Qdelete() 1 = 5 ? F front=1+1=2 item=Queue[2] Qdelete() 2 = 5 ? F front=2+1=3 item=Queue[3] Qdelete() 3 = 5 ? F front=3+1=4 item=Queue[4] Qdelete() 4= 5 ? F front=4+1=5 item=Queue[5] If section Else section 1 Item=70 2 3 4 5 6
  • 19. Maxsize=6, front=5 rear=5 • Qdelete() • If (front =rear) • print “queue empty” and return • 2. Else • Front = front + 1 • item = queue [front]; • Return item 0 1 2 3 4 5 rear front Function call Qdelete() front=rear Front=front+1 Item=Queeue[front] Qdelete() -1 = 5 ? F front=-1+1=0 item=Queue[0] Qdelete() 0 = 5 ? F front=0+1=1 item=Queue[1] Qdelete() 1 = 5 ? F front=1+1=2 item=Queue[2] Qdelete() 2 = 5 ? F front=2+1=3 item=Queue[3] Qdelete() 3 = 5 ? F front=3+1=4 item=Queue[4] Qdelete() 4= 5 ? F front=4+1=5 item=Queue[5] Qdelete() 5=5? T queue empty - - If section Else section 1 2 6 7
  • 20. Conditions to be satisfied in Queue • Queue is empty FRONT=REAR • Queue is full REAR=Maxsize • Queue contains element >= 1 FRONT <REAR NO. OF ELEMENT = REAR-FRONT+1 Disadvantage of Queue: The deleted element’s space in the queuqe cannot be reused-utilized for inserting another element.
  • 21. Applications of queues Queue is used in BFS. Queue is used by OS to schedule equal priority jobs In recognizing palindrome Simulation
  • 22. Representation of Queues • Queues can be represented using arrays • Queues can be represented using Linked List
  • 23. Array representation of Queues 12 9 7 18 45 front rear A[0] A[1] A[2] A[3] A[4]
  • 24. Linked representation of Queues 290 Front 300 350 360 rear 9 300 7 350 4 360 2 380 5 N 290 front 300 350 360 380 rear Linked queue after inserting a node 300 front 350 360 380 Linked queue after deleting a node
  • 25. Insert an element in queue using linked list STEP-1: Allocate memory for the new node & name it as TEMP. STEP-2: SET TEMP➔ DATA = NUM SET TEMP→ LINK = NULL STEP-3: IF FRONT = NULL FRONT=REAR=TEMP ELSE REAR→ LINK =TEMP REAR=TEMP [ END OF IF] STEP-4: EXIT FRONT=REAR=NULL
  • 26. 20 NULL 5000 TEMP STEP-1: Allocate memory for the new node & name it as TEMP. STEP-2: SET TEMP➔ DATA = NUM SET TEMP→ LINK = NULL FRONT=REAR=NULL 1. QINSERT_LINK(TEMP) Data link
  • 27. STEP-3: IF FRONT = NULL FRONT=REAR=TEMP ELSE REAR→ LINK =TEMP REAR=TEMP [ END OF IF] FRONT=REAR=5000 20 NULL 5000 FRONT REAR
  • 28. 30 NULL 6000 TEMP STEP-1: Allocate memory for the new node & name it as TEMP. STEP-2: SET TEMP➔ DATA = NUM SET TEMP→ LINK = NULL FRONT=REAR=TEMP 2. QINSERT_LINK(TEMP)
  • 29. STEP-3: IF FRONT = NULL FRONT=REAR=TEMP ELSE REAR→ LINK =TEMP REAR=TEMP [ END OF IF] FRONT=5000 REAR=6000 20 NULL 5000 FRONT REAR 30 NULL 6000 TEMP 20 6000 5000 FRONT REAR 30 NULL 6000 TEMP
  • 30. 40 NULL 7000 TEMP STEP-1: Allocate memory for the new node & name it as TEMP. STEP-2: SET TEMP➔ DATA = NUM SET TEMP→ LINK = NULL 3. QINSERT_LINK(TEMP) FRONT=5000 REAR=6000
  • 31. STEP-3: IF FRONT = NULL FRONT=REAR=TEMP ELSE REAR→ LINK =TEMP REAR=TEMP [ END OF IF] FRONT=5000 REAR=7000 20 6000 5000 FRONT REAR 30 NULL 6000 20 6000 5000 FRONT REAR 30 7000 6000 40 NULL 7000 TEMP
  • 33. Delete an element in queue using linked list STEP-1: If FRONT = NULL write “underflow” go to step 3. [End of if] STEP-2: SET TEMP = FRONT FRONT=FRONT→ LINK IF FRONT = NULL REAR=NULL STEP-3: EXIT
  • 34. Delete an element in queue using linked list STEP-1: If FRONT = NULL write “underflow” go to step 3. [End of if] STEP-2: SET TEMP = FRONT FRONT=FRONT→ LINK IF FRONT = NULL REAR=NULL STEP-3: EXIT 20 6000 5000 FRONT REAR 30 7000 6000 40 NULL 7000 1. QDELETE_LINK() TEMP
  • 35. Delete an element in queue using linked list STEP-1: If FRONT = NULL write “underflow” go to step 4. [End of if] STEP-2: SET TEMP = FRONT FRONT=FRONT→ LINK IF FRONT = NULL REAR=NULL STEP-3: FREE(TEMP) STEP-4: EXIT 20 6000 5000 FRONT REAR 30 7000 6000 40 NULL 7000 1. QDELETE_LINK() TEMP FRONT REAR 30 7000 6000 40 NULL 7000
  • 36. Delete an element in queue using linked list STEP-1: If FRONT = NULL write “underflow” go to step 4. [End of if] STEP-2: SET TEMP = FRONT FRONT=FRONT→ LINK IF FRONT = NULL REAR=NULL STEP-3: FREE(TEMP) STEP-4: EXIT 2. QDELETE_LINK() TEMP FRONT REAR 30 7000 6000 40 NULL 7000 TEMP FRONT REAR 30 7000 6000 40 NULL 7000 FRONT REAR 40 NULL 7000
  • 37. Delete an element in queue using linked list STEP-1: If FRONT = NULL write “underflow” go to step 4. [End of if] STEP-2: SET TEMP = FRONT FRONT=FRONT→ LINK IF FRONT = NULL REAR=NULL STEP-3: FREE(TEMP) STEP-4: EXIT 3. QDELETE_LINK() 4. QDELETE_LINK() FRONT=NULL REAR=NULL 40 NULL 7000 TEMP FRONT REAR 40 NULL 7000 TEMP TEMP
  • 38. Types of Queues • Dequeue • Circular Queue • Priority Queue
  • 39. Dequeues • Deque stands for double ended queue. • Elements can be inserted or deleted at either end. • Also known as head-tail linked list. 34 12 53 61 9 FRONT Insertion Deleion REAR Insertion Deleion
  • 40. Types of Dequeues • Input restricted queue 34 12 53 61 9 FRONT Deleion REAR Insertion Deleion
  • 41. Types of Dequeues • Output restricted queue 34 12 53 61 9 FRONT Deleion REAR Insertion Insertion
  • 42. Circular Queues • Circular queue are used to remove the drawback of simple queue. • Both the front and the rear pointers wrap around to the beginning of the array. • It is also called as “Ring buffer”.
  • 43. Algorithm CQ_insert(ITEM) • Step-1: If (REAR+1)%MAX=FRONT • Write Overflow • GoTo Step 4. • [End of if] • Step-2: If FRONT=-1 and REAR =-1 • REAR=FRONT=0 • Else If REAR=MAX-1 AND FRONT!=0 • REAR=0 • Else • REAR=(REAR+1)%MAX • [End of If] • Step-3: CQ[REAR]=ITEM • Step-4: Exit
  • 44. Algorithm CQ_insert(ITEM) • Step-1: If (REAR+1)%MAX=FRONT • Write Overflow • GoTo Step 4. • [End of if] • Step-2: If FRONT=-1 and REAR =-1 • REAR=FRONT=0 • Else If REAR=MAX-1 AND FRONT!=0 • REAR=0 • Else • REAR=(REAR+1)%MAX • [End of If] • Step-3: CQ[REAR]=ITEM • Step-4: Exit CQ[0] CQ[1] CQ[2] CQ[3] CQ[4] CQ[5] CQ[6] REAR FRONT FRONT=-1 REAR=-1 MAX=7
  • 45. Algorithm CQ_insert(10) • Step-1: If (REAR+1)%MAX=FRONT • Write Overflow • GoTo Step 4. • [End of if] • Step-2: If FRONT=-1 and REAR =-1 • REAR=FRONT=0 • Else If REAR=MAX-1 AND FRONT!=0 • REAR=0 • Else • REAR=(REAR+1)%MAX • [End of If] • Step-3: CQ[REAR]=ITEM • Step-4: Exit CQ[0] CQ[1] CQ[2] CQ[3] CQ[4] CQ[5] CQ[6] REAR FRONT 10 FRONT=-1 REAR=-1 MAX=7 IF FRONT=-1 & REAR=-1 T REAR=FRONT=0 IF ((REAR+1)%MAX=FRONT) (-1+1)%7=-1 0 = -1 F C1 C2 REAR=(REAR+1)%MAX FRONT=0 REAR=0 MAX=7 REAR=MAX-1 & FRONT!=0 REAR=0 C3 CQ[REAR]=ITEM CQ[0]=10
  • 46. Algorithm CQ_insert(20) • Step-1: If (REAR+1)%MAX=FRONT • Write Overflow • GoTo Step 4. • [End of if] • Step-2: If FRONT=-1 and REAR =-1 • REAR=FRONT=0 • Else If REAR=MAX-1 AND FRONT!=0 • REAR=0 • Else • REAR=(REAR+1)%MAX • [End of If] • Step-3: CQ[REAR]=ITEM • Step-4: Exit CQ[0] CQ[1] CQ[2] CQ[3] CQ[4] CQ[5] CQ[6] REAR FRONT 10 FRONT=0 REAR=0 MAX=7 IF FRONT=-1 & REAR=-1 F REAR=FRONT=0 IF ((REAR+1)%MAX=FRONT) (0+1)%7= 0 1 = -1 F C1 C2 REAR=(REAR+1)%MAX (0+1)%7= 1 FRONT=0 REAR=1 MAX=7 REAR=MAX-1 & FRONT!=0 0=6 F & 0!0 F REAR=0 C3 CQ[REAR]=ITEM CQ[1]=20 C4 20
  • 47. Algorithm CQ_insert(30) • Step-1: If (REAR+1)%MAX=FRONT • Write Overflow • GoTo Step 4. • [End of if] • Step-2: If FRONT=-1 and REAR =-1 • REAR=FRONT=0 • Else If REAR=MAX-1 AND FRONT!=0 • REAR=0 • Else • REAR=(REAR+1)%MAX • [End of If] • Step-3: CQ[REAR]=ITEM • Step-4: Exit CQ[0] CQ[1] CQ[2] CQ[3] CQ[4] CQ[5] CQ[6] REAR FRONT 10 FRONT=0 REAR=1 MAX=7 IF FRONT=-1 & REAR=-1 F REAR=FRONT=0 IF ((REAR+1)%MAX=FRONT) (1+1)%7= 0 2 = 0 F C1 C2 REAR=(REAR+1)%MAX (1+1)%7= 2 FRONT=0 REAR=2 MAX=7 REAR=MAX-1 & FRONT!=0 1=6 F REAR=0 C3 CQ[REAR]=ITEM CQ[2]=30 C4 20 30
  • 48. Algorithm CQ_insert(30) • Step-1: If (REAR+1)%MAX=FRONT • Write Overflow • GoTo Step 4. • [End of if] • Step-2: If FRONT=-1 and REAR =-1 • REAR=FRONT=0 • Else If REAR=MAX-1 AND FRONT!=0 • REAR=0 • Else • REAR=(REAR+1)%MAX • [End of If] • Step-3: CQ[REAR]=ITEM • Step-4: Exit CQ[0] CQ[1] CQ[2] CQ[3] CQ[4] CQ[5] CQ[6] REAR FRONT 10 FRONT=0 REAR=1 MAX=7 IF FRONT=-1 & REAR=-1 F REAR=FRONT=0 IF ((REAR+1)%MAX=FRONT) (1+1)%7= 0 2 = 0 F C1 C2 REAR=(REAR+1)%MAX (1+1)%7= 2 FRONT=0 REAR=2 MAX=7 REAR=MAX-1 & FRONT!=0 1=6 F REAR=0 C3 CQ[REAR]=ITEM CQ[2]=30 C4 20 30
  • 49. Algorithm CQ_insert(40) • Step-1: If (REAR+1)%MAX=FRONT • Write Overflow • GoTo Step 4. • [End of if] • Step-2: If FRONT=-1 and REAR =-1 • REAR=FRONT=0 • Else If REAR=MAX-1 AND FRONT!=0 • REAR=0 • Else • REAR=(REAR+1)%MAX • [End of If] • Step-3: CQ[REAR]=ITEM • Step-4: Exit CQ[0] CQ[1] CQ[2] CQ[3] CQ[4] CQ[5] CQ[6] REAR FRONT 10 FRONT=0 REAR=2 MAX=7 IF FRONT=-1 & REAR=-1 F REAR=FRONT=0 IF ((REAR+1)%MAX=FRONT) (2+1)%7= 0 3 = 0 F C1 C2 REAR=(REAR+1)%MAX (2+1)%7= 3 FRONT=0 REAR=3 MAX=7 REAR=MAX-1 & FRONT!=0 2=6 F REAR=0 C3 CQ[REAR]=ITEM CQ[3]=40 C4 20 30 40
  • 50. Algorithm CQ_insert(50) • Step-1: If (REAR+1)%MAX=FRONT • Write Overflow • GoTo Step 4. • [End of if] • Step-2: If FRONT=-1 and REAR =-1 • REAR=FRONT=0 • Else If REAR=MAX-1 AND FRONT!=0 • REAR=0 • Else • REAR=(REAR+1)%MAX • [End of If] • Step-3: CQ[REAR]=ITEM • Step-4: Exit CQ[0] CQ[1] CQ[2] CQ[3] CQ[4] CQ[5] CQ[6] REAR FRONT 10 FRONT=0 REAR=3 MAX=7 IF FRONT=-1 & REAR=-1 F REAR=FRONT=0 IF ((REAR+1)%MAX=FRONT) (3+1)%7= 0 4= 0 F C1 C2 REAR=(REAR+1)%MAX (3+1)%7= 4 FRONT=0 REAR=4 MAX=7 REAR=MAX-1 & FRONT!=0 4=6 F REAR=0 C3 CQ[REAR]=ITEM CQ[4]=50 C4 20 30 40 50
  • 51. Algorithm CQ_insert(60) • Step-1: If (REAR+1)%MAX=FRONT • Write Overflow • GoTo Step 4. • [End of if] • Step-2: If FRONT=-1 and REAR =-1 • REAR=FRONT=0 • Else If REAR=MAX-1 AND FRONT!=0 • REAR=0 • Else • REAR=(REAR+1)%MAX • [End of If] • Step-3: CQ[REAR]=ITEM • Step-4: Exit CQ[0] CQ[1] CQ[2] CQ[3] CQ[4] CQ[5] CQ[6] REAR FRONT 10 FRONT=0 REAR=4 MAX=7 IF FRONT=-1 & REAR=-1 F REAR=FRONT=0 IF ((REAR+1)%MAX=FRONT) (4+1)%7= 0 5= 0 F C1 C2 REAR=(REAR+1)%MAX (4+1)%7= 5 FRONT=0 REAR=5 MAX=7 REAR=MAX-1 & FRONT!=0 5=6 F REAR=0 C3 CQ[REAR]=ITEM CQ[5]=60 C4 20 30 40 50 60
  • 52. Algorithm CQ_insert(70) • Step-1: If (REAR+1)%MAX=FRONT • Write Overflow • GoTo Step 4. • [End of if] • Step-2: If FRONT=-1 and REAR =-1 • REAR=FRONT=0 • Else If REAR=MAX-1 AND FRONT!=0 • REAR=0 • Else • REAR=(REAR+1)%MAX • [End of If] • Step-3: CQ[REAR]=ITEM • Step-4: Exit CQ[0] CQ[1] CQ[2] CQ[3] CQ[4] CQ[5] CQ[6] REAR FRONT 10 FRONT=0 REAR=5 MAX=7 IF FRONT=-1 & REAR=-1 F REAR=FRONT=0 IF ((REAR+1)%MAX=FRONT) (5+1)%7= 0 6= 0 F C1 C2 REAR=(REAR+1)%MAX (5+1)%7= 6 FRONT=0 REAR=6 MAX=7 REAR=MAX-1 & FRONT!=0 5=6 F REAR=0 C3 CQ[REAR]=ITEM CQ[6]=70 C4 20 30 40 50 60 70
  • 53. Algorithm CQ_insert(80) • Step-1: If (REAR+1)%MAX=FRONT • Write Overflow • GoTo Step 4. • [End of if] • Step-2: If FRONT=-1 and REAR =-1 • REAR=FRONT=0 • Else If REAR=MAX-1 AND FRONT!=0 • REAR=0 • Else • REAR=(REAR+1)%MAX • [End of If] • Step-3: CQ[REAR]=ITEM • Step-4: Exit CQ[0] CQ[1] CQ[2] CQ[3] CQ[4] CQ[5] CQ[6] REAR FRONT 10 FRONT=0 REAR=6 MAX=7 IF ((REAR+1)%MAX=FRONT) (6+1)%7= 0 0= 0 T C1 20 30 40 50 60 70
  • 54. Algorithm CQ_insert(80) • Step-1: If (REAR+1)%MAX=FRONT • Write Overflow • GoTo Step 4. • [End of if] • Step-2: If FRONT=-1 and REAR =-1 • REAR=FRONT=0 • Else If REAR=MAX-1 AND FRONT!=0 • REAR=0 • Else • REAR=(REAR+1)%MAX • [End of If] • Step-3: CQ[REAR]=ITEM • Step-4: Exit CQ[0] CQ[1] CQ[2] CQ[3] CQ[4] CQ[5] CQ[6] REAR FRONT IF FRONT=-1 & REAR=-1 F REAR=FRONT=0 IF ((REAR+1)%MAX=FRONT) (6+1)%7= 1 0= 1 F C1 C2 REAR=(REAR+1)%MAX FRONT=1 REAR=6 MAX=7 REAR=MAX-1 & FRONT!=0 6=6 T & 1!0 T REAR=0 C3 CQ[REAR]=ITEM CQ[0]=80 C4 20 30 40 50 60 70 CQ_delete() 80
  • 55. Algorithm CQ_delete() • Step-1: If FRONT=-1 • Write Underflow • go to step 4 • [End of if] • Step-2: VAL=CQ[FRONT] • Step-3:If FRONT = REAR • REAR=FRONT=-1 • Else If FRONT=MAX-1 • FRONT=0 • Else • FRONT=FRONT+1 • [End of If] • Step-4: Exit CQ[0] CQ[1] CQ[3] CQ[5] CQ[6] REAR FRONT 10 20 30 40 50 60 CQ[2] 70