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QUEUES USINGLINKED LIST

Lecture

7 Dr. Adil Yousif

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Circular Arrays

Neat trick: use a circular arrayto insert and

remove items from a queue in constant time

The idea of a circular array is that the end of the

array wraps around to the start of the array0

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The mod Operator

The modoperator (%) is used to calculateremainders: 1%5 = 1, 2%5 = 2, 5%5 = 0, 8%5 = 3

modcan be used to calculate the front and backpositions in a circular array, therefore avoidingcomparisons to the array size The back of the queue is:

(front + count - 1) % items.length

where countis the number of items currently in thequeue

After removing an item the front of the queue is: (front + 1) % items.length;

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Array Queue Example

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//Java Code

Queue q = newQueue();q.enqueue(6);

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front= 0

insert item at (front + count) % items.length

count= 0

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Array Queue Example

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//Java Code

Queue q = newQueue();q.enqueue(6);

q.enqueue(4);

q.enqueue(7);

q.enqueue(3);

q.enqueue(8);

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front= 0

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count= 1

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Array Queue Example

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//Java Code

Queue q = newQueue();q.enqueue(6);

q.enqueue(4);

q.enqueue(7);

q.enqueue(3);

q.enqueue(8);

q.dequeue();//front = 1

q.dequeue();//front = 2

q.enqueue(9);

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front= 0

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make front = (0 + 1) % 6 = 1

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count= 5

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make front = (1 + 1) % 6 = 2

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Array Queue Example

0 1 2 3 4 5

//Java Code

Queue q = newQueue();q.enqueue(6);

q.enqueue(4);

q.enqueue(7);

q.enqueue(3);

q.enqueue(8);

q.dequeue();//front = 1

q.dequeue();//front = 2

q.enqueue(9);q.enqueue(5);

front= 2

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insert at (front + count) % 6

= (2 + 4) % 6 = 0

count= 45

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Queue: Linked List

Implementation

Removing items from the front of the queue isstraightforward

But we need to insert items at the back of the queue

in constant time So cannot traverse through the list

By using an additional reference (and a little administration)we can keep track of the node at the back of the queue

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List Queue Example

front

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back

//Java Code

Queue q = newQueue();q.enqueue(6);

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List Queue Example

front 4

6

back

//Java Code

Queue q = newQueue();q.enqueue(6);

q.enqueue(4);

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List Queue Example

front 4

6

back

//Java Code

Queue q = newQueue();q.enqueue(6);

q.enqueue(4);

q.enqueue(7);

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List Queue Example

front 4

6

back

//Java Code

Queue q = newQueue();q.enqueue(6);

q.enqueue(4);

q.enqueue(7);

q.enqueue(3);

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List Queue Example

front 4

6

back

//Java Code

Queue q = newQueue();q.enqueue(6);

q.enqueue(4);

q.enqueue(7);

q.enqueue(3);

q.dequeue();7

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Queue: Circular Linked List

Implementation

Possible implementations of a queue

A circular linked list with one external reference

A reference to the back

Figure 8-4b

A reference-based implementation of a queue: b) a circular linear linked list with one

external reference

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Queue: Circular Linked List

Implementation

Figure 8-5

Inserting an item into a nonempty queue

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Queue: Circular Linked List

Implementation

Figure 8-6

Inserting an item into an empty queue: a) before insertion; b) after insertion

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Queue: Circular Linked List

Implementation

Figure 8-7

Deleting an item from a queue of more than one item

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Questions