ADT Queue 1. What is a Queue? 2. STL Queue 3. Array Implementation of Queue 4. Linked List...

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ADT Queue

1.1. What is a Queue?What is a Queue?

2.2. STL QueueSTL Queue

3.3. Array Implementation of QueueArray Implementation of Queue

4.4. Linked List Implementation of QueueLinked List Implementation of Queue

5.5. Priority QueuePriority Queue

Which of the following cases use similar Which of the following cases use similar structures?structures? Cars lined up at tollgateCars lined up at tollgate Cars on a 4-lane highwayCars on a 4-lane highway Customers at supermarket check-outCustomers at supermarket check-out Books on a book shelfBooks on a book shelf Clients airport check-in counterClients airport check-in counter Pile of bath towels on linen closet shelfPile of bath towels on linen closet shelf

Is a linear data structure with removal of Is a linear data structure with removal of items at one end (items at one end (frontfront) and insertion of ) and insertion of items at the opposite end (items at the opposite end (rearrear))

FIFO – first-in-first-outFIFO – first-in-first-out

front rear

Queue Operations Enqueue(item)Enqueue(item)

Insert item at rearInsert item at rear Dequeue()Dequeue()

Remove item at frontRemove item at front Front()Front()

Return item at frontReturn item at front IsEmpty()IsEmpty()

Is queue empty?Is queue empty? IsFull()IsFull()

Is queue full?Is queue full?

Clear()Clear() Make queue emptyMake queue empty

The Queue Operations

A queue is like a line A queue is like a line of people waiting for a of people waiting for a bank teller. The queue bank teller. The queue has a has a frontfront and a and a rearrear..

FrontRear

New people must enter the queue at the New people must enter the queue at the rear. The C++ queue class calls this a rear. The C++ queue class calls this a pushpush, although it is usually called an , although it is usually called an enqueueenqueue operation. operation.

FrontRear

When an item is taken from the queue, When an item is taken from the queue, it always comes from the front. The it always comes from the front. The C++ queue calls this a C++ queue calls this a poppop, although it , although it is usually called a is usually called a dequeuedequeue operation. operation.

FrontRear

The Queue Class

The C++ standard The C++ standard template library has template library has a queue template a queue template class.class.

The template The template parameter is the parameter is the type of the items type of the items that can be put in that can be put in the queue.the queue.

template <class Item>class queue<Item>{public: queue( ); void push(const Item& entry); void pop( ); bool empty( ) const; Item front( ) const; …

Array Implementation

Problem with Array Implementation

front rear

With frequent queueing and dequeing, end of array can be reached quickly.

Can we somehow use the empty spaces?

“Circular” Array

Queue Implementation (2)

Suppose, currently,Suppose, currently, front = 5front = 5 rear = 9rear = 9

For next values,For next values, front = (front + 1) mod MAX_SIZE = 6front = (front + 1) mod MAX_SIZE = 6 rear = (rear + 1) mod MAX_SIZE = 0rear = (rear + 1) mod MAX_SIZE = 0

front rear

0 1 2 3 4 5 6 7 8 910

MAX_SIZE

queue.h (Declarations)

#define MAX_SIZE 5#define NIL -1typedef char elemType;

class Queue {public: Queue(); void enqueue(elemType item); void dequeue(); elemType front(); bool isEmpty(); bool isFull();. . .

. . .private: elemType data[MAX_SIZE]; int front; int rear; int count; // to simply full, empty}; // Note ; ‘;’

Queue() (Constructor)

Queue::Queue(){ front = 0; rear = -1; count = 0;}

Enqueue()

void Queue::enqueue(elemType item){ if (!full()){ rear = (rear + 1) % MAX_SIZE; data[rear] = item; count++; }}

Efficiency of enqueue() operation

If it takes t seconds to enqueue an element If it takes t seconds to enqueue an element into a queue of 1000 elements, how long into a queue of 1000 elements, how long does it take to enqueue one into a queue of does it take to enqueue one into a queue of 2000 elements?2000 elements?

The same time.The same time. Thus, O(n) = 1.Thus, O(n) = 1.

Dequeue()

void Queue::dequeue(){ if (!empty()){ result = data[front]; front = (front + 1) % MAX_SIZE; count--; }}

Efficiency of dequeue() operation

If it takes t seconds to dequeue an element If it takes t seconds to dequeue an element from a queue of 1000 elements, how long from a queue of 1000 elements, how long does it take to dequeue one from a queue of does it take to dequeue one from a queue of 2000 elements?2000 elements?

The same time.The same time. Thus, O(n) = 1.Thus, O(n) = 1.

Your Turn

Suppose you want to add another queue Suppose you want to add another queue operation:operation:void clear();void clear();// Postcondition: queue is made empty.// Postcondition: queue is made empty.

Write the implemenation code for the Write the implemenation code for the clear() clear() operation.operation.

Front()

elemTypeQueue::front(){ if (!empty()){ return data[front]; else return NIL; }}

empty()

bool Queue::empty(){ return count == 0;}

Your Turn

Write the implementation code for the operation Write the implementation code for the operation full().full().

bool Queue::isFull();bool Queue::isFull();// Postcondition: True is returned when queue// Postcondition: True is returned when queue// is full; false, otherwise.// is full; false, otherwise.

Array Implementation

Easy to implementEasy to implement But it has a limited capacity with a fixed arrayBut it has a limited capacity with a fixed array Or you must use a dynamic array for an Or you must use a dynamic array for an

unbounded capacityunbounded capacity Special behavior is needed when the rear reaches Special behavior is needed when the rear reaches

the end of the array.the end of the array.

[ 0 ][ 0 ] [1][1] [ 2 ][ 2 ] [ 3 ][ 3 ] [ 4 ][ 4 ] [ 5 ][ 5 ] . . .. . .

sizesize3

firstfirst0

lastlast2

Linked List Implementation

A queue can also be A queue can also be implemented with a linked implemented with a linked list with both a head and a list with both a head and a tail pointer.tail pointer.

front_ptr

rear_ptr

Which end do you think is Which end do you think is the front of the queue? the front of the queue? Why?Why?

front_ptr

rear_ptr

nullfront_ptr

The head_ptr points to the The head_ptr points to the front of the list.front of the list.

Because it is harder to Because it is harder to remove items from the tail remove items from the tail of the list.of the list.

rear_ptr

Your Turn

Write the class interface—public and Write the class interface—public and private sections—for the linked list version private sections—for the linked list version of class queue.of class queue.

typedef int elemType;#define NIL -1

class Queue {public: Queue(); void enqueue(elemType item); void dequeue(); elemType front(); bool isEmpty();. . .

Queue Implemented by Linked List

class Queue { . . .private: struct Node { elemType value; Node *next; Node (elemType item, Node *link){ value = item; next = link; }; } Node* front; Node* rear; int count;};

Constructor

Queue Set head and rear to NULL. Set count to 0End queue

Enqueue

void enqueue (elemType item) Let temp point to new node(item, NULL). If (empty queue) Then Let front and rear point to new node Else Set rear->next pointer point to temp End If

Let rear point to temp Increment countEnd enqueue

Enqueue

void enqueue (elemType item) Node *t = new Nod(item, NULL); if (isEmpty(){ front = t; rear = t; } else { rear->next = t; } count++;}

DequeueelemType dequeue() Set result to NIL If (queue is not empty) Then Set result to data of front node Let temp point to front node Set front to temp’s next Delete temp Decrement count End If If (front = NULL) Then Set rear to NULL Return resultEnd dequeue

Dequeue

elemType dequeue() elemType result = NIL; if (!isEmpty()){ result = front->value; Node *t = front; front = temp->next; delete t; count--; } if (front = NULL) rear = NULL;

return result;}

Clearclear() Loop (while front != NULL) Set temp to front Set front to front’s next Delete temp End Loop

Set rear to NULL Set count to 0End clear

Printprint() Set temp to front Loop(temp != NULL) Output temp’s data Set temp to temp’s next End LoopEnd print

Like stacks, queues have many applications.Like stacks, queues have many applications. Items enter a queue at the rear and leave a Items enter a queue at the rear and leave a

queue at the front.queue at the front. Queues can be implemented using an array Queues can be implemented using an array

or using a linked list.or using a linked list.

Summary

Priority Queue Stand-by queue for a flightStand-by queue for a flight

One with the highest priority is removed in One with the highest priority is removed in FIFO order—e.g., one who is attending FIFO order—e.g., one who is attending funeral, wedding.funeral, wedding.

Print job queuePrint job queue Job with the highest priority is removed in Job with the highest priority is removed in

FIFO order—e.g. one with 3 pages or lessFIFO order—e.g. one with 3 pages or less Emergency Room queueEmergency Room queue

Most serious case treated firstMost serious case treated first

ADT Priority Queue

Insert item into PQInsert item into PQ Remove item with the highest priority frm PQRemove item with the highest priority frm PQ Change priority of a particular item in PQChange priority of a particular item in PQ Remove a particular item from PQRemove a particular item from PQ Check if PQ is emptyCheck if PQ is empty Clear PQClear PQ

Implementation of Priority Queue

Use an array of queues (where index doubles as priority level).

Data Structure for Priority Queuetypedef int elemType;typedef int priorityType;const priorityType MAX = 5; class PriorityQueue { PriorityQueue(); void insert(elemType item, prioritType pNum); elemType removeNext(); . . .public: . . .private: Queue pq[MAX + 1]; // index 0 is unused};

Constructor

PriorityQueue(){ for (int i = 0; i < MAX + 1; i++){ pqp[i].clear(); } }

Insert(elemType item, priorityType pNum)insert (elemType item, priorityType pNum){}

class PriorityQueue { PriorityQueue(); void insert(elemType item, prioritType pNum); elemType removeNext(); . . .public: . . .private: Queue pq[MAX + 1]; // index 0 is unused};

ADT Queue 1. What is a Queue? 2. STL Queue 3. Array Implementation of Queue 4. Linked List...

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