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QueuesQueues

Data structures that wait their turn

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Queue characteristicsQueue characteristics

• FIFO: first in, first out

• insertion of items occurs at one end, removal occurs at the other end

• first item inserted is the first item removed; second inserted is second removed, third is third, etc.

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Queue characteristicsQueue characteristics

• Structure is very similar to stack, with much the same considerations -- still subject to overflow and underflow

• Unlike stack, queue is accessible at both ends

• Entry and removal still occur at one end -- but each operation occurs at a different end

Java’s Queue interfaceJava’s Queue interface

• Unlike the Stack ADT, the Java API doesn’t provide a full implementation of a generic Queue

• The Queue interface specifies methods for working with a queue, most of which are listed on the next slide

• There are several API classes that implement the interface, but each of these adds methods not specified by the interface

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Queue ADT member methodsQueue ADT member methods

• Constructor(s)• Modifiers

– enqueue (insert item at back): add

– dequeue (remove item at front): remove

• Observers– size

– isEmpty

Queue implementationsQueue implementations

• The API classes that implement the Queue interface are designed for more sophisticated uses than the simple interface implies

• We can implement a simple queue using either an array or a linked list as the basic structure

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Array implementationArray implementation

public class ArrayQueue<E> implements Cloneable {

private E[ ] data; private int manyItems; private int front; private int rear;

…

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Array implementationArray implementation

public ArrayQueue( ) { final int INITIAL_CAPACITY = 10; manyItems = 0; data = (E[]) new Object[INITIAL_CAPACITY];}// Since queue is empty, front and rear values

// don’t matter

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Array implementationArray implementation

public ArrayQueue(int initialCapacity) { if (initialCapacity < 0) throw new IllegalArgumentException ("initialCapacity is negative: " + initialCapacity); manyItems = 0; data = (E[]) new Object[initialCapacity]; }

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Array implementationArray implementationpublic ArrayQueue<E> clone( ) {

ArrayQueue<E> answer; try { answer = (ArrayQueue<E>) super.clone( ); } catch (CloneNotSupportedException e) { throw new RuntimeException ("This class does not implement Cloneable"); } answer.data = data.clone( ); return answer;

}

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Enqueue and dequeue – not as Enqueue and dequeue – not as simple as they look!simple as they look!

// first attempt at enqueue

public void add (E item) {

if (manyItems == 0) { front = 0; rear = 0; }rear++;

data[rear]=item;

manyItems++;

}

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dequeue (first attempt)dequeue (first attempt)

public E remove( ) { E answer; if (manyItems == 0) throw new NoSuchElementException("Queue underflow"); answer = data[front];

front++;

manyItems--;

return answer;

}

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• Consider a queue with a capacity of 3:

• As items are added, rear approaches capacity:

• As items are removed, front approaches back:

Problems!!!Problems!!!

• Situation: queue isn’t full (manyItems = 0) but attempt to add an item will go beyond array boundary

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Possible solutionPossible solution

• Maintain fixed front of queue:// dequeue method:

answer = data[0];

for (int x=0; x<rear; x++)

data[x]=data[x+1];

• Increases complexity of algorithm considerably -- we’ve gone from O(1) operation in original function to O(N)

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Better solution: circular arrayBetter solution: circular array

• Let front continue to float, but add ability for rear to float as well

• When rear reaches index capacity-1, if queue isn’t full, rear=0

• In effect, the successor of the last array index is the first array index -- array can be thought of as circular

• Can also grow array as necessary

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Circular queue implementationCircular queue implementation

• Add helper function nextIndex as private method of queue class: private int nextIndex(int i) {

if (++i == data.length) return 0; else return i;

}

• Call method from enqueue and dequeue

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New enqueue methodNew enqueue method public void add(E item) {

if (manyItems == data.length) ensureCapacity(manyItems*2 + 1); if (manyItems == 0) { front = 0; rear = 0; } else rear = nextIndex(rear); data[rear] = item; manyItems++; }

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New dequeue methodNew dequeue method

public E remove( ) { E answer; if (manyItems == 0) throw new NoSuchElementException("Queue underflow"); answer = data[front]; front = nextIndex(front); manyItems--; return answer; }

Other methodsOther methods

• Besides the queue-specific methods (and clone()), the ArrayQueue implementation includes a few other methods:– ensureCapacity– trimToSize– getCapacity

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Invariant for revised queueInvariant for revised queue

• Number of items on queue stored in variable manyItems

• Items are stored in circular array from data[front] to data[rear]

• If queue is empty, manyItems == 0 and the values of front and rear are undefined

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Queue as linked listQueue as linked list

• Implementation using linked list is actually easier• Ironically, the Java API’s LinkedList class

implements the Queue interface, and will be our preferred implementation when we look at queue applications

• Need to decide which end of list is which; easiest implementation is to have the head pointer point to the front of the list, and maintain another pointer to keep track of the back

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Code for linked list queueCode for linked list queue

public class LinkedQueue<E> implements Cloneable{

private int manyNodes; private Node<E> front; private Node<E> rear;

public LinkedQueue( ) { front = null; rear = null; }

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Code for linked list queueCode for linked list queuepublic void add(E item) {

if (isEmpty( )) { front = new Node<E>(item, null); rear = front; } else { rear.addNodeAfter(item); rear = rear.getLink( ); } manyNodes++;

}

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Code for linked list queueCode for linked list queue

public LinkedQueue<E> clone( ) { LinkedQueue<E> answer; Node<E>[ ] cloneInfo; try { answer = (LinkedQueue<E>) super.clone( ); } catch (CloneNotSupportedException e) { throw new RuntimeException ("This class does not implement Cloneable"); }

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Clone method continuedClone method continued

cloneInfo = Node.listCopyWithTail(front); answer.front = cloneInfo[0]; answer.rear = cloneInfo[1]; return answer; }

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Code for linked list queueCode for linked list queue

public boolean isEmpty( ) { return (manyNodes == 0);

}

public int size( ) { return manyNodes;

}

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Code for linked list queueCode for linked list queue

public E remove( ) { E answer; if (manyNodes == 0) throw new NoSuchElementException("Queue underflow"); answer = front.getData( ); front = front.getLink( ); manyNodes--; if (manyNodes == 0) rear = null; return answer;

}

Invariant for linked list Invariant for linked list implementationimplementation

• The number of items in the queue is stored in the instance variable manyNodes.

• The items in the queue are stored in a linked list, with the front of the queue stored at the head node, and the rear of the queue at the final node.

• For a non-empty queue, the instance variable front is the head reference of the linked list and the instance variable rear is the tail reference. For an empty queue, both front and rear are the null reference.

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Priority QueuesPriority Queues

• Variation on an ordinary queue -- stores entries and a priority value for each entry

• Elements are dequeued according to priority, highest first

• In case of a tie, priority queue reverts to FIFO behavior

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PQ implementationPQ implementation

• One strategy is to create an array of ordinary queues – each element in the array would be a queue of

items– all items in any given queue have equal priority

• Array index indicates priority level

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PQ ImplementationPQ Implementationpublic class PQ<E>{

private ArrayQueue<E>[] queues;public int highest;public int total;public int highCurrent;

public PQ<E> (int h){highest = h;queues = ArrayQueue<E>[] new Object[h+1];total = 0;highCurrent = 0;

}

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PQ implementationPQ implementation

public int size () {

return total;

}

public boolean is_empty() {

return (total == 0);

}

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Enqueue functionEnqueue function

template <class Item>void PQ<Item>::PQenqueue(const Item& entry, int priority){

assert (priority <= HIGHEST);// if this is highest priority entry so far, so note:if (priority > highest_current)

highest_current = priority;// place entry in queue:queues[priority].enqueue(entry);// increment count of total entries:count++;

}

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Dequeue functionDequeue function

template <class Item>

Item PQ<Item>::PQdequeue()

{

assert (PQsize() > 0);

int p = highest_current;

count--;

for(p; p>=0; p--)

if (!queues[p].is_empty())

return queues[p].dequeue();

}