Data Structures and Algorithms for Information Processing

1. Data Structures and Algorithms for Information Processing Lecture 5: Stacks & Queues Lecture 5: Stacks and Queues

2. Stacks • 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 5: Stacks and Queues

3. Stacks • 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 5: Stacks and Queues

4. Stacks • 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 • Parsing • Evaluating postfix expressions Lecture 5: Stacks and Queues

5. Stacks • 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 5: Stacks and Queues

6. Implementing a Stack • There are two ways we can implement a stack: • Using an array • Using a linked list Lecture 5: Stacks and Queues

7. 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 5: Stacks and Queues

8. 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 5: Stacks and Queues

9. Reversing a Word • We can use a stack to reverse the letters in a word. • How? Lecture 5: Stacks and Queues

10. 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 5: Stacks and Queues

11. The N-Queens Problem • Main slides Lecture 5: Stacks and Queues

12. 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 5: Stacks and Queues

13. 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 5: Stacks and Queues

14. 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 5: Stacks and Queues

15. Implementing a Queue • Just like a stack, we can implementing a queue in two ways: • Using an array • Using a linked list Lecture 5: Stacks and Queues

16. 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. Lecture 5: Stacks and Queues

17. 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 5: Stacks and Queues

18. 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. Lecture 5: Stacks and Queues

19. 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 5: Stacks and Queues

20. Implementing a Queue // option 2 sketch of getFront Object getFront() { answer = data[front]; front = (front + 1) mod size; manyItems--; return answer } Lecture 5: Stacks and Queues

21. 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”? Lecture 5: Stacks and Queues

22. 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. Lecture 5: Stacks and Queues

23. Palindromes • We can determine whether or not a word is a palindrome using a stack and a queue. • How? Lecture 5: Stacks and Queues

24. 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 Lecture 5: Stacks and Queues

25. 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 Lecture 5: Stacks and Queues

26. 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 5: Stacks and Queues

27. 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? Lecture 5: Stacks and Queues

28. Thinking Exercise • Where might a computer’s operating system use queues? Lecture 5: Stacks and Queues

29. 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 5: Stacks and Queues