1. Queues
Lecture 30
Fri, Apr 2, 2004
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2. Topics
Queues
Queue ADT
Queue implementation
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3. Queues
A queue is a List that operates under the principle “first in, first out” (FIFO).
New elements are enqueued into the queue.
Old elements are dequeued from the queue.
To enforce the FIFO principle, we enqueue and dequeue at opposite ends.
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4. Implementation of Queues
Implement a Queue as a subclass of a List class.
Use PushFront() and PopBack(), or
Use PushBack() and PopFront().
Choose a List class for which enqueuing and dequeuing will be efficient.
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5. Private Inheritance
Private inheritance prevents violations of the FIFO principle.
The Queue class has access to all public and protected List functions.
The Queue class user has access only to the queue functions.
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6. Queue Constructors Construct an empty queue.
Construct a copy of the specified queue.
Queue(const Queue& q);
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7. Inspectors Get a copy of the element at the head of the queue.
T Head() const;
Get the number of elements in the queue.
int Size() const;
Determine whether the queue is empty.
bool Empty() const;
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8. Mutators Enqueue the specified value at the tail of the queue.
void Enqueue(const T& value);
Dequeue and return the element at the head of the queue.
T Dequeue();
Make the queue empty.
void MakeEmpty();
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9. Facilitators Read a queue from the specified input stream.
void Input(istream& in);
Write a queue to the specified output stream.
void Output(ostream& out) const;
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10. Other Member Functions
Determine whether the queue has a valid structure.
void Validate() const;
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11. Non-Member Functions Read a queue from the specified input stream.
istream& operator>>(istream& in, Queue& q);
Write a queue to the specified output stream.
ostream& operator<<(ostream& out, const Queue& q);
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12. Queue Implementation Choose an appropriate List class as a base class.
Good choices
CircArrayList
LinkedListwTail
DoublyLinkedList
CircLinkedList
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13. Queue Implementation
Bad choices
ArrayList
LinkedList
Use private inheritance to enforce the Queue structure on the List.
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14. Implementation of Queue Member Functions
Example
arrayqueue.h
linkedqueue.h
QueueTest.cpp
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15. Queue Applications
Lecture 31
Mon, Apr 5, 2004
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16. Topics Evaluating infix expressions Simulating waiting lines 5/3/2019
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17. Queue Application: Infix Expression Evaluation
An infix expression with one (binary) operator is written in the order: left-operand, operator, right-operand.
Example:
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18. Disadvantages of Infix Notation
Parentheses are often needed to indicate order of operation.
Example: (3 + 4) * (5 + 6)
Operators follow a precedence hierarchy.
Example: * 5 – 6 / 7
Operators have left or right associativity.
Example: 100 – 50 – 10 – 5 – 1
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19. Queue Application: Infix Expression Evaluation
Begin with an empty stack and an empty queue.
Process the tokens from left to right according to the following rules.
If the token is a number,
Enqueue the token.
If the token is a left parenthesis,
Push the token onto the stack.
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20. Queue Application: Infix Expression Evaluation
If the token is a right parenthesis,
Pop tokens off the stack and enqueue them until
A left parenthesis is popped.
Discard the right and left parentheses.
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21. Queue Application: Infix Expression Evaluation
If the token is an operator,
Pop tokens off the stack and enqueue them until
An operator of lower precedence is on top of the stack, or
A left parenthesis is on top of the stack, or
The stack is empty.
Push the operator onto the stack.
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22. Queue Application: Infix Expression Evaluation
After processing the last token
Pop all tokens off the stack and enqueue them.
The queue now contains the expression in post-fix notation.
Process the queue as a post-fix expression.
Sample program - InfixEvaluator.exe
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23. Queue Application: Waiting Lines
Specify the arrival rate (average time between arrivals).
Specify the departure rate (average time between departures).
New arrivals are enqueued.
Departures leave the service window.
If the queue is not empty, a customer is dequeued and steps up to the service window.
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24. Queue Application: Waiting Lines
Maintain statistics on
Number of arrivals.
Number of departures.
Average time between arrivals.
Average time between departures.
Average time spent in the queue.
Average queue size.
Fraction of the time that the window is idle.
Explore the relationship between these statistics and the arrival and departure rates.
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