1. Queues

2. What is a queue? First-in first-out data structure (FIFO)
New objects are placed at rear
Removal restricted to front
Examples?

3. Queue ADT Operations enqueue(o): Insert o at rear of queue
Input: Object; Output: None
dequeue(): Remove object at front; error if empty
Input: None; Output: Object removed
size(): Return number of objects in queue
Input: None; Output: Integer
isEmpty(): Return a boolean indicating queue empty
Input: None; Output: Boolean
first(): Return object at front without removing; error if empty
Input: None; Output: Object

4. Example enqueue(5) enqueue(3) dequeue() enqueue(7) front() isEmpty()
size()
enqueue(3)
enqueue(5)
dequeue()

5. Queue Interface int size() const; bool isEmpty() const;
Object& front() throw (QueueEmptyException);
void enqueue(const Object& obj);
Object dequeue() throw(QueueEmptyException);

6. Underlying Representation
Array versus Linked List
Pros and cons?
Running time?
size
isEmpty
enqueue
dequeue
front

7. Array Implementation 1 2 3 4 5 6 … n-1 enqueue(5) enqueue(3) 5 3 1 2 31 2 3 4 5 6 …
n-1
enqueue(5)
enqueue(3) 5 3 1 2 3 4 5 6 …
n-1
dequeue() ?

8. Array Implementation 1 2 3 4 5 6 … n-1 enqueue(5) enqueue(3) 5 3 1 2 31 2 3 4 5 6 …
n-1
enqueue(5)
enqueue(3) 5 3 1 2 3 4 5 6 …
n-1 3
dequeue() ? 1 2 3 4 5 6 …
n-1

9. Circular Array f r 1 2 3 4 5 6 …
n-1
f – stores index of cell which stores first element of queue
r – stores index of next available cell in queue
Initially, f = r = 0
How do you add a new element?
How do you remove an element?

10. Circular Array How do you add a new element?f r 1 2 3 4 5 6 …
n-1
How do you add a new element?
insert at array[r]
increment r
How do you remove an element?
return array[f]
increment f
What happens when r >= n-1?

11. Circular Array Need to be able to wrap around Modulo – %f 1 2 3 4 5 6 …
n-1
Need to be able to wrap around
Modulo – %
increment f using (f+1)%n
increment r using (r+1)%n

12. Circular Array f r f dequeue 1 2 1 2 f r r f r =(2+1)%3= 0 enqueue1 2 1 2 f r r f
r =(2+1)%3= 0
enqueue
enqueue 1 2 1 2 f r
enqueue 1 2

13. Algorithms size isEmpty front dequeue enqueue return (N-f+r) mod N
return (f == r)
front
if isEmpty then throw QueueEmptyException
return array[f]
dequeue
temp = array[f]
f = (f+1)%N
return temp
enqueue
if size == N-1 then throw QueueFullException SIZE MUST BE < N-1
array[r] = object
r = (r+1)%N

14. Linked List Implementation
tail
head Ø
enqueue
dequeue

15. Linked List Implementation
new_node
head
tail
Object
enqueue
if(size == 0) head = new_node
else tail->next_ptr = new_node
tail = new_node
increment size
next_ptr

16. Linked List Implementation
new_node
head
tail
Object1
Object2
enqueue
if(size == 0) head = new_node
else tail->next_ptr = new_node
tail = new_node
increment size
next_ptr
next_ptr

17. Linked List Implementation
dequeue
if (isEmpty) throw QueueEmptyException
head = head->next_ptr
decrement size
if new size is 0 – set tail to NULL

18. Exercises Implement a queue using two stacks
Implement a two-color stack