1. Data Structures and Algorithms for Information Processing
Lecture: Stacks & Queues
Lecture: Stacks and Queues

2. Lecture: Stacks and Queues
What is a Stack?
A stack is a data structure of ordered items such that items can be inserted and removed only at one end.
Examples of Stacks:
Pez Dispenser
Cafeteria Trays
Lecture: Stacks and Queues

3. Lecture: Stacks and Queues
What can we do with a stack?
push - place an item on the stack
peek - Look at the item on top of the stack, but do not remove it
pop - Look at the item on top of the stack and remove it
Lecture: Stacks and Queues

4. Lecture: Stacks and Queues
A stack is a LIFO (Last-In/First-Out) data structure
A stack is sometimes also called a pushdown store.
What are some applications of stacks?
Program execution
Converting infix to postfix
Evaluating postfix expressions
Lecture: Stacks and Queues

5. Lecture: Stacks and Queues
Problem:
What happens if we try to pop an item off the stack when the stack is empty?
This is called a stack underflow. The pop method needs some way of telling us that this has happened. In java we use the java.util.EmptyStackException
Lecture: Stacks and Queues

6. Lecture: Stacks and Queues
Implementing a Stack
There are two ways we can implement a stack:
Using an array
Using a linked list
Lecture: Stacks and Queues

7. Lecture: Stacks and Queues
Implementing a Stack
Implementing a stack using an array is fairly easy.
The bottom of the stack is at data[0]
The top of the stack is at data[numItems-1]
push onto the stack at data[numItems]
pop off of the stack at data[numItems-1]
Lecture: Stacks and Queues

8. Lecture: Stacks and Queues
Implementing a Stack
Implementing a stack using a linked list isn’t that bad either…
Store the items in the stack in a linked list
The top of the stack is the head node, the bottom of the stack is the end of the list
push by adding to the front of the list
pop by removing from the front of the list
Lecture: Stacks and Queues

9. Lecture: Stacks and Queues
Reversing a Word
We can use a stack to reverse the letters in a word.
How?
Lecture: Stacks and Queues

10. Lecture: Stacks and Queues
Reversing a Word
Read each letter in the word and push it onto the stack
When you reach the end of the word, pop the letters off the stack and print them out.
Lecture: Stacks and Queues

11. Lecture: Stacks and Queues
The N-Queens Problem
Main slides
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12. Lecture: Stacks and Queues
What is a queue?
A data structure of ordered items such that items can be inserted only at one end and removed at the other end.
Example
A line at the supermarket
Lecture: Stacks and Queues

13. Lecture: Stacks and Queues
What can we do with a queue?
Enqueue - Add an item to the queue
Dequeue - Remove an item from the queue
The book calls these insert and getFront in order to simplify things.
Lecture: Stacks and Queues

14. Lecture: Stacks and Queues
A queue is called a FIFO (First in-First out) data structure.
What are some applications of queues?
Round-robin scheduling in processors
Input/Output processing
Queueing of packets for delivery in networks
Lecture: Stacks and Queues

15. Lecture: Stacks and Queues
Implementing a Queue
Just like a stack, we can implementing a queue in two ways:
Using an array
Using a linked list
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16. Lecture: Stacks and Queues
Implementing a Queue
Using an array to implement a queue is significantly harder than using an array to implement a stack. Why?
Unlike a stack, where we add and remove at the same end, in a queue we add to one end and remove from the other.
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Implementing a Queue
There are two options for implementing a queue using an array:
Option 1:
Enqueue at data[0] and shift all of the rest of the items in the array down to make room.
Dequeue from data[numItems-1]
Lecture: Stacks and Queues

18. Lecture: Stacks and Queues
Implementing a Queue
Option 2
Enqueue at data[rear+1]
Dequeue at data[front]
The rear variable always contains the index of the last item in the queue.
The front variable always contains the index of the first item in the queue.
When we reach the end of the array, wrap around to the front again.
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Implementing a Queue
// option 2 sketch of insert
insert(Object item) {
if(manyItems == 0) front = rear = 0;
else rear = (rear + 1) mod size;
data[rear] = item;
manyItems++; }
Lecture: Stacks and Queues

20. Lecture: Stacks and Queues
Implementing a Queue
// option 2 sketch of getFront
Object getFront() {
answer = data[front];
front = (front + 1) mod size;
manyItems--;
return answer }
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21. Lecture: Stacks and Queues
Implementing a Queue
Which approach is better?
Assume that the queue has a large number of entries.
In best case, for both queues, what is Big Theta?
In the worst case, for both queues, what is Big Theta?
Does it make sense to talk about “cases”?
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22. Lecture: Stacks and Queues
Implementing a Queue
Implementing a queue using a linked list is still easy:
Front of the queue is stored as the head node of the linked list, rear of the queue is stored as the tail node.
Enqueue by adding to the end of the list
Dequeue by removing from the front of the list.
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23. Lecture: Stacks and Queues
Palindromes
We can determine whether or not a word is a palindrome using a stack and a queue.
How?
Lecture: Stacks and Queues

24. Lecture: Stacks and Queues
Palindromes
Read each letter in the phrase. Enqueue the letter into the queue, and push the letter onto the stack.
After we have read all of the letters in the phrase:
Until the stack is empty, dequeue a letter from the queue and pop a letter from the stack.
If the letters are not the same, the phrase is not a palindrome
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25. Lecture: Stacks and Queues
Priority Queues
Sometimes we may want certain things to get to go to the front of the line.
Examples:
Frequent fliers on airlines
Real-time video and audio packets in networks
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26. Lecture: Stacks and Queues
Priority Queues
In a priority queue, each item stored in the queue has a priority associated with it.
When we call enqueue, we pass the item to be enqueued and the priority associated with that item.
Lecture: Stacks and Queues

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Implementing a PQ
There are several ways in which we might implement a priority queue:
Use an array of ordinary queues, one for each priority.
Queues[0] is the queue for priority 0, queues[1] is the queue for priority 1
Use a sorted linked list
The list should be sorted according the the priorities of the items contained
Which approach is better?
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28. Lecture: Stacks and Queues
Thinking Exercise
Where might a computer’s operating system use queues?
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29. Lecture: Stacks and Queues
Review
A stack is a LIFO data structure
A queue is a FIFO data structure
Both queues and stacks can be implemented using either linked lists or arrays
A priority queue is a queue in which the ordering of the items is determined by the priorities assigned to them.
Lecture: Stacks and Queues