ADT Queue 1. What is a Queue? 2. STL Queue 3. Array Implementation of Queue 4. Linked List Implementation of Queue 5. Priority Queue

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

3 Queue  Is a linear data structure with removal of items at one end (front) and insertion of items at the opposite end (rear)  FIFO – first-in-first-out frontrear

4 Queue Operations  Enqueue(item)  Insert item at rear  Dequeue()  Remove item at front  Front()  Return item at front  IsEmpty()  Is queue empty?  IsFull()  Is queue full?  Clear()  Make queue empty

The Queue Operations  A queue is like a line of people waiting for a bank teller. The queue has a front and a rear. $ Front Rear

The Queue Operations  New people must enter the queue at the rear. The C++ queue class calls this a push, although it is usually called an enqueue operation. $ Front Rear

The Queue Operations  When an item is taken from the queue, it always comes from the front. The C++ queue calls this a pop, although it is usually called a dequeue operation. $ Front Rear

The Queue Class  The C++ standard template library has a queue template class.  The template parameter is the type of the items that can be put in the queue. template class queue { public: queue( ); void push(const Item& entry); void pop( ); bool empty( ) const; Item front( ) const; … };

9 Array Implementation

10 Problem with Array Implementation frontrear  With frequent queueing and dequeing, end of array can be reached quickly.  Can we somehow use the empty spaces?

11 “Circular” Array

12 Queue Implementation (2)  Suppose, currently,  front = 5  rear = 9  For next values,  front = (front + 1) mod MAX_SIZE = 6  rear = (rear + 1) mod MAX_SIZE = 0 frontrear MAX_SIZE

13 queue.h (Declarations) #define MAX_SIZE 5 #define NIL -1 typedef char elemType; class Queue { public: Queue(); void enqueue(elemType item); void dequeue(); elemType front(); bool isEmpty(); bool isFull();...

14 queue.h (Declarations)... private: elemType data[MAX_SIZE]; int front; int rear; int count; // to simply full, empty }; // Note ; ‘;’

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

16 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 into a queue of 1000 elements, how long does it take to enqueue one into a queue of 2000 elements?  The same time.  Thus, O(n) = 1. 17

18 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 from a queue of 1000 elements, how long does it take to dequeue one from a queue of 2000 elements?  The same time.  Thus, O(n) = 1. 19

Your Turn  Suppose you want to add another queue operation: void clear(); // Postcondition: queue is made empty.  Write the implemenation code for the clear() operation.

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

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

Your Turn  Write the implementation code for the operation full().  bool Queue::isFull(); // Postcondition: True is returned when queue // is full; false, otherwise.

Array Implementation  Easy to implement  But it has a limited capacity with a fixed array  Or you must use a dynamic array for an unbounded capacity  Special behavior is needed when the rear reaches the end of the array. [ 0 ] [1] [ 2 ] [ 3 ] [ 4 ] [ 5 ] size 3 first 0 last 2

Linked List Implementation null 13  A queue can also be implemented with a linked list with both a head and a tail pointer. front_ptr rear_ptr

Linked List Implementation null 13  Which end do you think is the front of the queue? Why? front_ptr rear_ptr

Linked List Implementation null front_ptr 13  The head_ptr points to the front of the list.  Because it is harder to remove items from the tail of the list. rear_ptr Front Rear

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

29 queue.h (Declarations) 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 0 End 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 count End enqueue

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

Dequeue elemType 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 result End 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; }

Clear clear() 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 0 End clear

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

 Like stacks, queues have many applications.  Items enter a queue at the rear and leave a queue at the front.  Queues can be implemented using an array or using a linked list. Summary

Priority Queue  Stand-by queue for a flight  One with the highest priority is removed in FIFO order—e.g., one who is attending funeral, wedding.  Print job queue  Job with the highest priority is removed in FIFO order—e.g. one with 3 pages or less  Emergency Room queue  Most serious case treated first

ADT Priority Queue  Insert item into PQ  Remove item with the highest priority frm PQ  Change priority of a particular item in PQ  Remove a particular item from PQ  Check if PQ is empty  Clear PQ

Implementation of Priority Queue queue Use an array of queues (where index doubles as priority level).

Data Structure for Priority Queue typedef 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 };