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1 Main IndexMain Index ContentsContents1 Main IndexMain Index ContentsContents

Model for a Queue

The Queue

Queue ADT (3 slides) (3 slides)

Radix Sort (2 slides) (2 slides)

miniQueue()

Bounded Queue

Priority Queue

Priority Queue ADT (2 slides) (2 slides)

Chapter 8 Chapter 8 – – Queues and Priority QueuesQueues and Priority Queues

Removing Items from a Heap

Summary Slides (5 slides)


Grocery Store Checkout: A Grocery Store Checkout: A Model for a QueueModel for a Queue


The QueueThe Queue

A Queue is a FIFO (First in First Out) Data Structure. Elements are inserted in the Rear of the queue and are removed at the Front.

C

B C

A B C

A

bac kf ro nt

p u s h A

A Bf ro nt bac k

p u s h B

f ro nt bac kp u s h C

f ro nt bac kp o p A

f ro ntbac k

p o p B


CLASS queue Constructor <queue>

queue();Create an empty queue.

CLASS queue Operations <queue>

bool empty() const;Check whether the queue is empty. Return true if it is empty and false otherwise.

T&l front();Return a reference to the value of the item at the font of the queue.Precondition: The queue is not empty.



const T& front() const;Constant version of front().

void pop();Remove the item from the front of the queue.

Precondition: The queue is not empty.Postcondition: The element at the front of the queue

is the element that was added immediately after the element just popped or the queue is empty.



void push(const T& item);Insert the argument item at the back of the queue.

Postcondition: The queue has a new item at the back

int size() const;Return the number of elements in the queue.


The Radix SortThe Radix SortOrder ten 2 digit numbers in 10 bins from smallest number to largest number. Requires 2 calls to the sort Algorithm.

Initial Sequence: 91 6 85 15 92 35 30 22 39Pass 0: Distribute the cards into bins according

to the 1's digit (100).

9 130

0

39

987

6

6

3 51 58 5

543

2 29 2

21


The Radix SortThe Radix Sort

Final Sequence: 91 6 85 15 92 35 30 22 39Pass 1: Take the new sequence and distribute

the cards into bins determined by the 10's digit (101).

6

0

9 29 1

9

8 5

87654

3 93 53 0

3

2 2

2

1 5

1


m iniQ .pus h(1 0)

m iniQ .pus h(2 5 )

m iniQ .pus h(5 0 )

n = m iniQ .fro nt() // n = 1 0

m iniQ .po p()

Q u e u e S ta te m e n t L is tL is t S ta te m e n tQ u e u e1 0

ba c kfro ntqlis t.pus h_ ba c k (1 0 ) 1 0

ba c kfro nt

1 0 2 5

ba c kfro ntqlis t.pus h_ ba c k (2 5 ) 1 0 2 5

ba c kfro nt

5 01 0 2 5

ba c kfro nt

q list.push _ b a ck (5 0 )1 0 2 5

fro nt

5 0

ba c k

re turn qlis t.fro nt() // re turn 1 0

2 5 5 0

ba c kfro ntqlis t.po p_ fro nt() 2 5 5 0

m in iQ u e u e < in t> m in iQ ; // d e c la re a n e m p ty q u e u e


The Bounded queueThe Bounded queue

A

BC

qf ro ntqbac k

Ins e r t e le m e nts A,B , C

BC qf ro nt

qbac k

R e m o ve e le m e nt A

D

Cqf ro nt

qbac k

Ins e r t e le m e nt D ,

Cqf ro nt

qbac k

R e m o ve e le m e nt B

D

Cqfront

qba c k

Ins e r t e le m e nt D ,

Cqfront qba c k

Ins e r t e le m e nt E

C ircu la r V iewArra y V iew

D E

Ins e r t e le m e nt D , Ins e r t e le m e nt E

C D

qfrontqba c k

E C D

qfrontqba c k

11 Main IndexMain Index ContentsContents

Priority QueuePriority Queue

J o b # 3C lerk

J o b # 4Su p erv is o r

J o b # 2P res id en t

J o b # 1M an ager

A Special form of queue from which items are removed according to their designated priority and not the order in which they entered.

Items entered the queue in sequential order but will be removed in the order #2, #1, #4, #3.


CLASS priority_queue Constructor <queue>

priority_queue();Create an empty priority queue. Type T must

implement the operator <.

CLASS priority_queue Operations <queue>

bool empty() const;Check whether the priority queue is empty. Return true if it is empty, and false otherwise. Create

void pop();Remove the item of highest priority from the queue.

Precondition: The priority queue is not empty.Postcondition: The priority queue has 1 less element


CLASS priority_queue Operations <queue>

void push(const T& item);Insert the argument item into the priority queue.

Postcondition: The priority queue contains a new element.

int size() const;Return the number of items in the priority queue.

T& top();Return a reference to the item having the highest

priority.Precondition: The priority queue is not empty.

const T& top();Constant version of top().


Removing Elements From a Removing Elements From a HeapHeap

45

1511

35102520

4228

H e a p a fte r e ra s ing 5 0

50

101511

35422520

4528

H e a p b e fo re e ra s ing 5 0


Summary Slide 1Summary Slide 1

§- Queue- A first-come-first-served data structure. §- Insertion operations (push()) occur at the back of the

sequence

§- deletion operations (pop()) occur at the front of the sequence.



§- The radix sort algorithm- Orders an integer vector by using queues (bins).

- This sorting technique has running time O(n) but has only specialized applications.

- The more general in-place O(n log2n) sorting algorithms are preferable in most cases.



§- The miniQueue class- Provides a class with STL queue class interface.

- Uses the list class by object composition.



§- Implementing a queue with a fixed-size array

- Indices qfront and qback move circularly around the array.

- Gives O(1) time push() and pop() operations with no wasted space in the array.


s



§- Priority queue- Pop() returns the highest priority item (largest or

smallest).

- Normally implemented by a heap, which is discussed in Chapter 14.

- The push() and pop() operations have running time O(log2n)

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