Your Topic Goes Here Queue

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Claude Harmon
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1 Your Subtopics Go Here Your Topic Goes Here Queue Compiled By: Kiran Joshi 1

2 Queue Roadmap. 1. Definition 2. Queue examples 3. Working of Queue 4. Applications 2

3 Definition * A data structure of ordered items such that items can be inserted only at one end and removed at the other end. 3

4 2 Examples 4

5 Ticket 5

6 Parking 6

7 Ball 7

8 Toll 8

9 Counting 9

10 3 Working of Queue 10

11 Queues What is a queue? A data structure of ordered items such that items can be inserted only at one end and removed at the other end. Example A line at the supermarket 11

12 Queues What can we do with a queue? Enqueue - Add an item to the queue Dequeue - Remove an item from the queue

13 The Queue ADT Another form of restricted list Insertion is done at one end, whereas deletion is performed at the other end Basic operations: enqueue: insert an element at the rear of the list dequeue: delete the element at the front of the list First-in First-out (FIFO) list 13

14 Queue ADT Like a stack, a queue is also a list. However, with a queue, insertion is done at one end, while deletion is performed at the other end. Accessing the elements of queues follows a First In, First Out (FIFO) order. Like customers standing in a check-out line in a store, the first customer in is the first customer served. 14

15 Enqueue and Dequeue Primary queue operations: Enqueue and Dequeue Like check-out lines in a store, a queue has a front and a rear. Enqueue Insert an element at the rear of the queue Dequeue Remove an element from the front of the queue Remove (Dequeue) front rear Insert (Enqueue) 15

16 Implementation of Queue Just as stacks can be implemented as arrays or linked lists, so with queues. Dynamic queues have the same advantages over static queues as dynamic stacks have over static stacks 16

17 Queue Implementation of Array There are several different algorithms to implement Enqueue and Dequeue Naïve way When enqueuing, the front index is always fixed rear and the rear index moves forward in the array. rear rear front front front Enqueue(3) Enqueue(6) Enqueue(9) 17

18 Queue Implementation of Array Naïve way When enqueuing, the front index is always fixed and the rear index moves forward in the array. When dequeuing, the element at the front the queue is removed. Move all the elements after it by one position. (Inefficient!!!) rear rear rear = front front front Dequeue() Dequeue() Dequeue() 18

19 Queue Example Operation Output Q enqueue(5) (5) enqueue(3) (5, 3) dequeue() 5 (3) enqueue(7) (3, 7) dequeue() 3 (7) front() 7 (7) dequeue() 7 () dequeue() error () isempty() true () enqueue(9) (9) enqueue(7) (9, 7) size() 2 (9, 7) enqueue(3) (9, 7, 3) enqueue(5) (9, 7, 3, 5) dequeue() 9 (7, 3, 5) 19

20 Implementing a Queue Just like a stack, we can implementing a queue in two ways: Using an array Using a linked list 20

21 Implementing a Queue Using an array to implement a queue is significantly harder than using an array to implement a stack. Why? Unlike a stack, where we add and remove at the same end, in a queue we add to one end and remove from the other. 21

22 Implementing a Queue There are two options for implementing a queue using an array: Option 1: Enqueue at data[0] and shift all of the rest of the items in the array down to make room. Dequeue from data[numitems-1] 22

23 Implementing a Queue Option 2 Enqueue at data[rear+1] Dequeue at data[front] The rear variable always contains the index of the last item in the queue. The front variable always contains the index of the first item in the queue. When we reach the end of the array, wrap around to the front again. 23

24 Implementing a Queue // option 2 sketch of insert insert(object item) { if(manyitems == 0) front = rear = 0; else rear = (rear + 1) mod size; data[rear] = item; manyitems++; } 24

25 Implementing a Queue // option 2 sketch of getfront Object getfront() { answer = data[front]; front = (front + 1) mod size; manyitems--; return answer } 25

26 Implementing a Queue Implementing a queue using a linked list is still easy: Front of the queue is stored as the head node of the linked list, rear of the queue is stored as the tail node. Enqueue by adding to the end of the list Dequeue by removing from the front of the list. 26

27 Queue Implementation of Array Better way When an item is enqueued, make the rear index move forward. When an item is dequeued, the front index moves by one element towards the back of the queue (thus removing the front item, so no copying to neighboring elements is needed). (front) XXXXOOOOO (rear) OXXXXOOOO (after 1 dequeue, and 1 enqueue) OOXXXXXOO (after another dequeue, and 2 enqueues) OOOOXXXXX (after 2 more dequeues, and 2 enqueues) The problem here is that the rear index cannot move beyond the last element in the array. 27

28 Implementation using Circular Array Using a circular array When an element moves past the end of a circular array, it wraps around to the beginning, e.g. OOOOO7963 4OOOO7963 (after Enqueue(4)) After Enqueue(4), the rear index moves from 3 to 4. 28

29 Circular Queue Use Linear Array to implement a queue. Waste of memory: The deleted elements can not be re-used. Solution: to use circular queue. Two implementations: Using n-1 space. Using n space + full tag 29

30 Implementation of Circular queue with (n- 1) space used Create(Q) Q: Array[0 n-1] n-1 front = rear = 0 //initialize Enqueue(item, Q) Queue begin R rear = (rear+1) mod n; //rear moves forward; R = (R+1) mod n if rear = front QueueFull; // Queue is full. rear = rear-1 mod n; // rear back to the previous position; else Q[rear]=item; end; 30

31 Implementation of Circular queue with (n- 1) space used Dequeue(Q) item begin if front=rear X X X X X X QueueEmpty; else front = (front+1) mod n; item = Q[front]; X R F X X X X X end; end; Note: only (n-1 ) space used; 31

32 Implementation of Circular Queue with n space used A parameter Tag is introduced to help to make sure the queue is Empty or Full: Boolean If Tag = True, combined with other conditions => queue is Full If Tag = False, combined with other conditions => queue is Null Tag can determine the states of the queue solely! 32

33 Applications Direct applications Waiting lists, bureaucracy Access to shared resources (e.g., printer) Multiprogramming Indirect applications Auxiliary data structure for algorithms Component of other data structures 33

34 Application: Round Robin Schedulers We can implement a round robin scheduler using a queue, Q, by repeatedly performing the following steps: 1. e = Q.dequeue() 2. Service element e 3. Q.enqueue(e) The Queue 1. Deque the next element 2. Service the next element 3. Enqueue the serviced element Shared Service 34

35 Review A stack is a LIFO data structure A queue is a FIFO data structure Both queues and stacks can be implemented using either linked lists or arrays A priority queue is a queue in which the ordering of the items is determined by the priorities assigned to them. 35

36 Thankq *. *. 36

.:: UNIT 4 ::. STACK AND QUEUE

.:: UNIT 4 ::. STACK AND QUEUE 4.1 A stack is a data structure that supports: Push(x) Insert x to the top element in stack Pop Remove the top item from stack A stack is collection of data item arrange