CS2006 - Data Structures I

Chapter 7

Queue I

2

Topics

Introduction Queue Application Implementation

Linked List Array ADT List

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Queues A queue differs from a stack in that it follows the

first-in-first-out (FIFO) principle. Inserting an item to the rear is known as

"enqueueing". Removing an item from the front is known as

"dequeueing".

cashier

Front of line Back of line

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Queues Linear, homogeneous structure Has First-In-First-Out (FIFO) behavior;

Items added at one end and removed from the other end

Middle elements are logically inaccessible

Add/

Enqueue

Remove/Dequeue

Back/Rear Front/Head

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Queue Applications

Real-World Applications Buy a movie ticket Check out at a bookstore Cashier lines in any store

 Computer Science Applications OS task scheduling Print lines of a document Convert digit strings to decimal Shared resource usage (CPU, memory access, …)

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ADT Queue

Specification: Elements

Homogeneous Linear

Structure: Elements added to rear & removed from front

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ADT Queue

Specification: Operations

Create an empty queue Destroy a queue Check if a queue is empty / Full Enqueue (Enq, Enque, Add, Insert):

Adding new element at the back (rear) Dequeue (Deq, Deque, Remove, Serve):

Deleting an element from the front Retrieve an element from a queue

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Queue Applications Converting Digit Strings to Decimal

Enter characters from the keyboard and retain them in order

Assumption: No typing mistakes Blank spaces may precede or follow the digits

Formula used: Initial value

DigitSum = 0

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Queue Applications Converting Digit Strings to Decimal

Pseudocode// Convert digits in aQueue into decimal integer n// Get first digit, ignoring any leading blanksdo {

ch=queue.dequeue()} while ( ch is blank)// Assertion: ch contains first digit// Compute n from digits in queuen = 0;done = false;do { n = 10 * n + integer that ch represents

if (! queue.isEmpty( ) ) ch=queue.dequeue()

elsedone = true

} while (! done and ch is a digit)// Assertion: n is result

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Queue Applications

Recognizing Palindromes Uses a queue & a stack Idea:

1. Insert the string in both queue & stack2. Remove characters from both stack's Top & queue's Front,

comparing them3. Repeat until:

a) Either the stack or the queue are empty String is a palindrome

b) The character from the stack and the corresponding character from the queue are not similar String isn't a palindrome

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Queue Applications Recognizing Palindromes

PseudocodeIsPal(in str:string) : boolean// Determines whether String is a palindromeaQueue.createQueue ( ) // Create an empty queue aStack.createStack ( ) // Create an empty stack// Insert each character of String into both aQueue and aStacklength = length of strfor ( i = 1 through length){ nextChar = ith character of str

aQueue.enqueue ( nextChar )aStack.push(NextChar)

} // end for// Compare aQueue with aStackcharactersAreEqual = true;while ( ! aQueue.isEmpty() && charactersAreEqual){ aQueue.getFront ( queueFront )

aStack.getTop ( stackTop )if ( queueFront equals stackTop){ aQueue.dequeue ( )

aStack.pop ( )} else charactersAreEqual = false

} // end whilereturn charactersAreEqual

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ADT Queue Implementation

Possible implementations:

Linked List-based Linear Circular

Array-based Linear Circular

ADT List-based

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Linked List-Based Implementation More straightforward than array-based Possible options:

Linear linked list Two external “pointer” (Front & Back)

Circular linked list One “pointer” will be enough (Back)

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Linked List Queue Implementation

Linked List -Based Implementation: Option 1 Insertion to an empty list

front = newNodeback = newNode

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Linked List Queue Implementation

LL -Based Implementation: Option 1 Insertion to a non-empty list

newNode.setNext ( NULL);Back.setNext (newNode);back = newNode

Deletiontemp = front front = front.getNext()temp.setNext ( NULL )

20 15

front

26 84

back

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Linked List Queue Implementation

LL -Based Implementation: option 1 Deletion

form a one-node (one item) queueIf (front = back&&front!=null){

back = null front=null }

form a non-empty, more than one item queuefront = front.getNext()

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Linked List Queue Implementation

LL based Implementation: option 2 Insertion

Into an empty queuenewNode.setNext (newNode)back = newNode

Into a non-empty queuenewNode.setNext (back.getNext())Back.setNext (newNode);back = newnode

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Linked List Queue Implementation

LL -Based Implementation: option 2 Deletion

form a one-node (one item) queueNode front = back.getNext()If (front = back)

back = NULLFront=null

form a non-empty, more than one item queueNode front = back.getNext()Back.setNext ( front.getNext())Front=null

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Queue Interfacepublic interface QueueInterface {

public boolean isEmpty(); // Determines whether a queue is empty. // Precondition: None. // Postcondition: Returns true if the queue is empty; // otherwise returns false.

public void enqueue(Object newItem) throws QueueException; // Adds an item at the back of a queue. // Precondition: newItem is the item to be inserted. // Postcondition: If the operation was successful, newItem // is at the back of the queue. Some implementations // may throw QueueException if newItem cannot be added to the queue.

public Object dequeue() throws QueueException; // Retrieves and removes the front of a queue. // Precondition: None. // Postcondition: If the queue is not empty, the item that was added to the // queue earliest is returned and the item is removed. If the queue is empty, // the operation is impossible and QueueException is thrown.

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Queue Interface (2)

public void dequeueAll(); // Removes all items of a queue. // Precondition: None. // Postcondition: The queue is empty.

public Object peek() throws QueueException; // Retrieves the item at the front of a queue. // Precondition: None. // Postcondition: If the queue is not empty, the item // that was added to the queue earliest is returned. // If the queue is empty, the operation is impossible // and QueueException is thrown.} // end QueueInterface

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Queue Exception

public class QueueException extends RuntimeException {

public QueueException(String s) {

super(s);

} // end constructor

} // end QueueException

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LListQueue Implementationpublic class LListQueue implements QueueInterface {

private Node lastNode;

public LListQueue() { lastNode = null; } // end default constructor

// queue operations: public boolean isEmpty() { return lastNode == null; } // end isEmpty

public boolean isFull() { return false; } // end isFull

public void dequeueAll() { lastNode = null; } // end dequeueAll

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LListQueue Implementation (2) public void enqueue(Object newItem) { Node newNode = new Node(newItem); if(isFull()) throw new QueueException("QueueException on enqueue:"+ "queue full"); // insert the new node if (isEmpty()) { // insertion into empty queue newNode.setNext(newNode); } else { // insertion into nonempty queue newNode.setNext(lastNode.getNext()); lastNode.setNext(newNode); } // end if lastNode = newNode; // new node is at back } // end enqueue

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LListQueue Implementation (3) public Object dequeue() throws QueueException { if (!isEmpty()) { // queue is not empty; remove front Node firstNode = lastNode.getNext(); if (firstNode == lastNode) { // special case? lastNode = null; // yes, one node in queue } else { lastNode.setNext(firstNode.getNext()); } // end if return firstNode.getItem(); } else { throw new QueueException("QueueException on dequeue:" + "queue empty"); } // end if } // end dequeue

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LListQueue Implementation (4) public Object peek() throws QueueException { if (!isEmpty()) { // queue is not empty; retrieve front Node firstNode = lastNode.getNext(); return firstNode.getItem(); } else { throw new QueueException("QueueException on peek:" + "queue empty"); } // end if } // end peek } // end ListQueue

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LListQueue Testpublic class LListQueueTest {

public static void main(String[ ] args) { LListQueue aQueue = new LListQueue(); System.out.println("Enqueuing:"); for (int i = 0; i < 9; i++) { System.out.print(" "+i); aQueue.enqueue(new Integer(i)); } // end for System.out.println("\nDequeuing:"); for (int i = 0; i < 9; i++) { System.out.print(" "+aQueue.dequeue()); } // end for System.out.println(); } // end main} // QueueTest

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Array-Based Queue Implementation

 Array-Based Implementation Fix-size Have the following definition

final int MAZ_QUEUE = maxinum-size-of-queue;

Object [] items;

Int front;

Int back;

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Array-Based Queue Implementation

1. Linear Array implementation Front & Back are indexes in the array Initial condition: Front =0 & Back = -1

Initial state

After 5 additions

0 4

Front Back

20 45 51 76 84

0 1 2 3 4 MAX_QUEUE -1

0 -1

Front Back 0 1 2 3 4 MAX_QUEUE -1

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Array-Based Queue Implementation

1. Linear Array implementation Back will point to the last added element Initial values:

front = 0 back = -1

Insertion Increment back Insert item in item [ back ]

 Deletion Increment front

 Queue Empty Condition back < front

Queue is Full back == MAX_QUEUE-1

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Array-Based Queue Implementation 1. Linear Array implementation

Problem: Rightward-Drifting: After a sequence of additions & removals, items

will drift towards the end of the array Full if back==MAX_QUEUE-1, even only a few

items

47 49

Front Back

16 60 20

0 1 47 48 49

MAX_QUEUE -1

Rightward drifting

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Array-Based Queue Implementation

1. Linear Array implementation Rightward drifting solutions

Use a circular array: When Front or Back reach the end of the array, wrap them around to the beginning of the array

Problem: Front & Back can't be used to distinguish

between queue-full & queue-empty conditions

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Array-Based Queue Implementation

2. Circular Array Implementation

Back

Front

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51

76

MAX_QUEUE -1

Back

Front

45

51

76

MAX_QUEUE -1

Back

Front

45

51

76

MAX_QUEUE -1

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Deletion and Insertion on the queue

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Array-Based Queue Implementation2. How to determine if queue is full or

empty?

Back

1

76

MAX_QUEUE -1

Front Back

MAX_QUEUE -1

0

Front

0

Queue wiith one itemDelete, queue becomes empty

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Array-Based Queue Implementation2. How to determine if queue is full or

empty?

Back

1

76

MAX_QUEUE -1

0

Front

Queue wiith single empty After insertion, queue becomes full

7

56

32

45

89

5

Back

1

76

MAX_QUEUE -1

0

Front

7

56

32

45

89

5

47

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Array-Based Queue Implementation

2. Circular Arrays Implementation That is why we need a count

If count ==MAX_QUEUEQueue is FULL

Else if count ==0Queue is EMPTY

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Array-Based Queue Implementation

2. Circular Array Implementationfinal int MAZ_QUEUE = maxinum-size-of-queue;

Object [] items;

Int front;

Int back;

int count;

Back

Front

20

45

51

76

MAX_QUEUE -1

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Array-Based Queue Implementation 2. Circular Arrays Implementation

Initial condition: Count = 0, Front = 0, Back = MAX_QUEUE – 1

The Wrap-around effect is obtained by using modulo arithmetic (%-operator)

 Insertion Increment Back, using modulo arithmetic Insert item Increment Count

back = ( back + 1 ) % MAX_QUEUE;items[back} = newItem;++count;

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Array-Based Queue Implementation 2. Circular Array Implementation

Deletion Increment Front using modulo arithmetic Decrement Count

front = ( front + 1 ) % MAX_QUEUE;

- - count;

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Array-Based Queue Implementation

public class ArrayQueue implements QueueInterface { private final int MAX_QUEUE = 50; // maximum size of queue private Object[ ] items; private int front, back, count;

public ArrayQueue() { items = new Object[MAX_QUEUE]; front = 0; back = MAX_QUEUE-1; count = 0; } // end default constructor

// queue operations: public boolean isEmpty() { return count == 0; } // end isEmpty

public boolean isFull() { return count == MAX_QUEUE; } // end isFull

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Array-Based Queue Implementation (2) public void enqueue(Object newItem) {

if (!isFull()) { back = (back+1) % (MAX_QUEUE); items[back] = newItem; ++count; } else throw new QueueException("QueueException on enqueue: "+ "Queue full"); } // end enqueue

public Object dequeue() throws QueueException { if (!isEmpty()) { // queue is not empty; remove front Object queueFront = items[front]; front = (front+1) % (MAX_QUEUE); --count; return queueFront; } else throw new QueueException("QueueException on dequeue: "+ "Queue empty"); } // end dequeue

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Array-Based Queue Implementation (3) public void dequeueAll() {

items = new Object[MAX_QUEUE]; front = 0; back = MAX_QUEUE-1; count = 0; } // end dequeueAll

public Object peek() throws QueueException { if (!isEmpty()) { // queue is not empty; retrieve front return items[front]; } else { throw new QueueException("Queue exception on peek: " + "Queue empty"); } // end if } // end peek } // end ArrayQueue

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Array Based Queue Testpublic class ArrayQueueTest { public static void main(String[] args) { ArrayQueue aQueue = new ArrayQueue(); System.out.println("Enqueuing:"); for (int i = 0; i < 9; i++) { System.out.print(" "+i); aQueue.enqueue(new Integer(i)); } // end for System.out.println("\nDequeuing:"); for (int i = 0; i < 9; i++) { System.out.print(" "+aQueue.dequeue()); } // end for System.out.println();

} // end main} // QueueTest

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Full/Empty Determinationwithout Counters

Disadvantage of Using a counter Overhead of maintaining a counter or flag

Using a flag isFull Flag is set to true when it is full Flag is set to false when the queue is not full Expense as using the counter

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Full/Empty Determinationwithout Counters

Queue size counters will not be used Use extra array location Declare MAX_QUEUE +1 locations, but only use

MAX_QUEUE of them for queue items Full/Empty determinations will be made using

the relative positions of front and back. back will be initialized to –-1 and front to 0 as

before. Both front and back will be incremented with

wraparound.

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Array-Based Queue Implementation

2. Circular Array Implementation

Full Queue Empty Queue

BackFront

7

6

3

8

MAX_QUEUE-1

14

2

0

1

34

5

6

7

2

Front & Back

MAX_QUEUE-1 0

1

34

5

6

7

2

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Final Method for Full/Empty Determination without Counters

To allow different tests for empty and full Sacrifice one array slot so that a full Queue uses all but

one array slot Thus the test for a full Queue becomes:

(back + 1) % (MAX_QUEUE+1) == front While the test for an empty Queue remains:

back== front If the elements of the queue are complex data

structure, the memory wasted may be significant

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ADT List Queue Implementation

Use ADT List to implement the queue Pre- & Post-conditions are the same as

before The implementation is much simpler

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ADT List Queue Implementation

Front is the position 1 of the list Back is the item at the end of the list

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ADT List Queue Implementation

Dequeue ()List.remove(1);

Peek()List.get(1);

Enqueue (newItem)List.add(list.size()+1, newitem);

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ListQueue Implementationpublic class ListQueue implements QueueInterface {

private ListInterface list;

public ListQueue() {

list = new ListReferenceBased ();

} // end default constructor

// queue operations:

public boolean isEmpty() {

return list.isEmpty();

} // end isEmpty

public void dequeueAll() {

list.removeAll();

} // end dequeueAll

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ListQueue Implementation (2) public void enqueue(Object newItem) {

list.add(list.size()+1, newItem);

}

} // end enqueue

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ListQueue Implementation (3) public Object dequeue() throws QueueException {

if (!isEmpty()) {

// queue is not empty; remove front

Object queueFront = list.get(1);

list.remove();

return queueFront;

}

else {

throw new QueueException("QueueException on dequeue:"

+ "queue empty");

} // end if

} // end dequeue

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ListQueue Implementation (4) public Object peek() throws QueueException { if (!isEmpty()) {

return flist.get(1); } else { throw new QueueException("QueueException on peek:" + "queue empty"); } // end if } // end peek } // end ListQueue

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ADT Queue Implementation Comparison

Reference-Based More complicated than ADT List Most flexible No size restrictions

Array-Based   No overhead of pointer manipulation   Prevents adding elements if the array is full

ADT List-Based Simpler to write Not as efficient as using a linked list directly