algo>queues
DESCRIPTION
QueuesTRANSCRIPT
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Queues
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Queues
“A Queue is a special kind of list, where items are inserted at one end (the rear) And deleted at the other end (the front)”
Other Name: First In First Out (FIFO)
Difference from Stack:
Insertion go at the end of the list, rather than the beginning of the list.
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Common Operations on Queues(Queue ADT)
1. MAKENULL(Q): Makes Queue Q be an empty list.
2. FRONT(Q): Returns the first element on Queue Q.
3. ENQUEUE(x,Q): Inserts element x at the end of Queue Q.
4. DEQUEUE(Q): Deletes the first element of Q.
5. EMPTY(Q): Returns true if and only if Q is an empty queue.
Example:Line of customers in a bank
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Applications of Queues
Operating systemmulti-user/multitasking environments, where
several users or task may be requesting the same resource simultaneously.
Communication Softwarequeues to hold information received over
networks and dial up connections. (Information can be transmitted faster than it can be processed, so is placed in a queue waiting to be processed)
Some other?
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Implementation
StaticQueue is implemented by an array, and size of
queue remains fix
DynamicA queue can be implemented as a linked list,
and expand or shrink with each enqueue or dequeue operation.
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A pointer Implementation of Queues
Keep two pointers: FRONT: A pointer to the first element of the
queue. REAR: A pointer to the last element of the queue.
x y .zFront
Rear
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A pointer Implementation of Queues
Q.front
Q.Rear
MAKENULL(Q)
Q.front
Q.Rear
ENQUEUE(x,Q)
.x
NULL
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Q.front
Q.Rear
ENQUEUE(y,Q)
x .y
Q.front
Q.Rear
DEQUEUE(Q)
.y
A pointer Implementation of Queues
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A class for Dynamic Queue implementationclass DynIntQueue{private:
struct QueueNode{
int value;QueueNode *next;
};
QueueNode *front;QueueNode *rear;int numItems;
public:DynIntQueue(void);
~DynIntQueue(void);void enqueue(int);
int dequeue(void); bool isEmpty(void); void makeNull(void);};
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Implemenaton
//************************// Constructor *//************************
DynIntQueue::DynIntQueue(void){
front = NULL;rear = NULL;numItems = 0;
}
//************************// Destructor *//************************
DynIntQueue::~DynIntQueue(void){
makeNull();}
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//********************************************// Function enqueue inserts the value in num *// at the rear of the queue. *//********************************************
void DynIntQueue::enqueue(int num){
QueueNode *newNode;
newNode = new QueueNode;newNode->value = num;newNode->next = NULL;if (isEmpty()){
front = newNode;rear = newNode;
}else{
rear->next = newNode;rear = newNode;
}numItems++;
}
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//**********************************************// Function dequeue removes the value at the *// front of the queue, and copies it into num. *//**********************************************
int DynIntQueue::dequeue(void){
QueueNode *temp;int num;if (isEmpty())
cout << "The queue is empty.\n";else{
num = front->value;temp = front->next;delete front;front = temp;numItems--;
}return num;
}
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//*********************************************// Function isEmpty returns true if the queue *// is empty, and false otherwise. *//*********************************************
bool DynIntQueue::isEmpty(void){
if (numItems)return false;
elsereturn true;
}
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//********************************************// Function makeNull dequeues all the elements *// in the queue. *//********************************************
void DynIntQueue::makeNull(void){
while(!isEmpty())dequeue();
}
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Program
// This program demonstrates the DynIntQeue classvoid main(void){
DynIntQueue iQueue;
cout << "Enqueuing 5 items...\n";// Enqueue 5 items.for (int x = 0; x < 5; x++)
iQueue.enqueue(x);
// Deqeue and retrieve all items in the queuecout << "The values in the queue were:\n";while (!iQueue.isEmpty()){
int value; value =iQueue.dequeue();cout << value << endl;
}}
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Program Ouput
Enqueuing 5 items...The values in the queue were:01234
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Array Implementation
First Element
Last Element
maxlength
Front
Second Element.
.
Rear
When queue is empty both front and rear are set to -1
While enqueueing increment rear by 1, and while dequeueing increment front by 1
When there is only one value in the Queue, both rear and front have same index
Can we implement Queue by using only one index variable Front or Rear??
YES, by moving elements of array to neighboring locations like we did in STACK but this is in-efficient
Why it is inefficient?
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Array Implementation
5 4 6 7 8 7 6
0 1 2 3 4 5 6 7 8
Front=0Rear=6
8 7 6
0 1 2 3 4 5 6 7 8
Front=4Rear=6
7 6 12 67
0 1 2 3 4 5 6 7 8
Front=5Rear=8
How can we insert more elements? Rear index can not move beyond the last element….
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Solution: Using circular queue
Allow rear to wrap around the array.
if(rear == queueSize-1)
rear = 0;
else
rear++;Or use module arithmetic
rear = (rear + 1) % queueSize;
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7 6 12 67
0 1 2 3 4 5 6 7 8
Front=5Rear=8
Enqueue 39 Rear=(Rear+1) mod Queue Size = (8+1) mod 9 = 0
39 7 6 12 67
0 1 2 3 4 5 6 7 8
Front=5Rear=0
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How to determine empty and full Queues?
It is some trickyNumber of approaches
A counter indicating number of values in the queue can be used (We will use this approach)
We will see another approach as well at the end
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Implementationclass IntQueue{private:
int *queueArray;int queueSize;int front;int rear;int numItems;
public:IntQueue(int);
~IntQueue(void); void enqueue(int); int dequeue(void); bool isEmpty(void); bool isFull(void); void clear(void);};Note, the member function clear, which clears the queue by resetting the front and rear indices, and setting the numItems to 0.
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IntQueue::IntQueue(int s) //constructor{
queueArray = new int[s];queueSize = s;front = -1;rear = -1;numItems = 0;
}
IntQueue::~IntQueue(void) //destructor
{ delete [] queueArray;
}
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//********************************************// Function enqueue inserts the value in num *// at the rear of the queue. *//********************************************
void IntQueue::enqueue(int num){
if (isFull())cout << "The queue is full.\n";
else{
// Calculate the new rear positionrear = (rear + 1) % queueSize;// Insert new itemqueueArray[rear] = num;// Update item countnumItems++;
}}
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//*********************************************// Function dequeue removes the value at the *// front of the queue, and copies t into num. *//*********************************************
int IntQueue::dequeue(void){
if (isEmpty())cout << "The queue is empty.\n";
else{
// Move frontfront = (front + 1) % queueSize;// Retrieve the front itemint num = queueArray[front];// Update item countnumItems--;
}return num;
}
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//*********************************************// Function isEmpty returns true if the queue *// is empty, and false otherwise. *//*********************************************
bool IntQueue::isEmpty(void){
if (numItems)return false;
elsereturn true;
}
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//********************************************// Function isFull returns true if the queue *// is full, and false otherwise. *//********************************************
bool IntQueue::isFull(void){
if (numItems < queueSize)return false;
elsereturn true;
}
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//*******************************************// Function clear resets the front and rear *// indices, and sets numItems to 0. *//*******************************************
void IntQueue::clear(void){
front = - 1;rear = - 1;numItems = 0;
}
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//Program demonstrating the IntQueue class
void main(void){
IntQueue iQueue(5);
cout << "Enqueuing 5 items...\n";// Enqueue 5 items.for (int x = 0; x < 5; x++)
iQueue.enqueue(x);
// Attempt to enqueue a 6th item.cout << "Now attempting to enqueue again...\n";iQueue.enqueue(5);
// Deqeue and retrieve all items in the queuecout << "The values in the queue were:\n";while (!iQueue.isEmpty()){
int value;iQueue.dequeue(value);cout << value << endl;
}}
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Program Output
Enqueuing 5 items...Now attempting to enqueue again...The queue is full.The values in the queue were:0
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Another implementation of Queues using Arraysclass CQueue{
int Data*,QueueSize,Front,Rear;public:
CQueue(int size);~CQueue(int size);bool IsFull();bool IsEmpty();void Enqueue(int num);int Dequeue();void MakeNull;
};
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CQueue::CQueue(int size){
Front=Rear=-1;Data=new int[size];
}void CQueue ::Enqueue(int num);{
if (IsFull()) { cout<<“Overflow” return; }if (IsEmpty() Rear=Front=0;else Rear=(Rear+1) % QueueSize;Data[Rear]=num;
}
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int CQueue ::Dequeue(int num);
{
if (IsEmpty()) { cout<<“Underflow”; return; }
int ReturnValue=Data[Front];
if (Front==Rear) //only one element in the queue
Front=Rear=-1;
else
Front=(Front+1) % QueueSize;
return ReturnValue;
}
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bool CQueue::IsEmpty()
{
if (Front==-1) return true;
else return false;
}
bool CQueue::IsFull()
{
If (((Rear+1)%QueueSize)==Front)
return true;
else return false;
}