Data Structures and Algorithms for Information Processing Lecture

Stacks • What is a Stack? – A stack is a data structure of

Stacks • What can we do with a stack? – push - place an

Stacks • A stack is a LIFO (Last-In/First-Out) data structure • A stack is

Stacks • Problem: – What happens if we try to pop an item off

Implementing a Stack • There are two ways we can implement a stack: –

Implementing a Stack • Implementing a stack using an array is fairly easy. –

Implementing a Stack • Implementing a stack using a linked list isn’t that bad

Reversing a Word • We can use a stack to reverse the letters in

Reversing a Word • Read each letter in the word and push it onto

The N-Queens Problem • Main slides 90 -723: Data Structures and Algorithms for Information

Queues • What is a queue? – A data structure of ordered items such

Queues • What can we do with a queue? – Enqueue - Add an

Queues • A queue is called a FIFO (First in-First out) data structure. •

Implementing a Queue • Just like a stack, we can implementing a queue in

Implementing a Queue • Using an array to implement a queue is significantly harder

Implementing a Queue • There are two options for implementing a queue using an

Implementing a Queue • Option 2 – Enqueue at data[rear+1] – Dequeue at data[front]

Implementing a Queue // option 2 sketch of insert(Object item) { if(many. Items ==

Implementing a Queue // option 2 sketch of get. Front Object get. Front() {

Implementing a Queue • Which approach is better? • Assume that the queue has

Implementing a Queue • Implementing a queue using a linked list is still easy:

Palindromes • We can determine whether or not a word is a palindrome using

Palindromes • Read each letter in the phrase. Enqueue the letter into the queue,

Priority Queues • Sometimes we may want certain things to get to go to

Priority Queues • In a priority queue, each item stored in the queue has

Implementing a PQ • There are several ways in which we might implement a

Thinking Exercise • Where might a computer’s operating system use queues? 90 -723: Data

Review • A stack is a LIFO data structure • A queue is a

Slides: 29

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Data Structures and Algorithms for Information Processing Lecture 5: Stacks & Queues 90 -723: Data Structures and Algorithms for Information Processing Lecture 5: Stacks and Queues Copyright © 1999, Carnegie Mellon. All Rights Reserved. 1

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 90 -723: Data Structures and Algorithms for Information Processing Lecture 5: Stacks and Queues Copyright © 1999, Carnegie Mellon. All Rights Reserved. 2

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 90 -723: Data Structures and Algorithms for Information Processing Lecture 5: Stacks and Queues Copyright © 1999, Carnegie Mellon. All Rights Reserved. 3

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 90 -723: Data Structures and Algorithms for Information Processing Lecture 5: Stacks and Queues Copyright © 1999, Carnegie Mellon. All Rights Reserved. 4

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 happened. In java we use the java. util. Empty. Stack. Exception 90 -723: Data Structures and Algorithms for Information Processing Lecture 5: Stacks and Queues Copyright © 1999, Carnegie Mellon. All Rights Reserved. 5

Implementing a Stack • There are two ways we can implement a stack: – Using an array – Using a linked list 90 -723: Data Structures and Algorithms for Information Processing Lecture 5: Stacks and Queues Copyright © 1999, Carnegie Mellon. All Rights Reserved. 6

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[num. Items-1] – push onto the stack at data[num. Items] – pop off of the stack at data[num. Items -1] 90 -723: Data Structures and Algorithms for Information Processing Lecture 5: Stacks and Queues Copyright © 1999, Carnegie Mellon. All Rights Reserved. 7

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 90 -723: Data Structures and Algorithms for Information Processing Lecture 5: Stacks and Queues Copyright © 1999, Carnegie Mellon. All Rights Reserved. 8

Reversing a Word • We can use a stack to reverse the letters in a word. • How? 90 -723: Data Structures and Algorithms for Information Processing Lecture 5: Stacks and Queues Copyright © 1999, Carnegie Mellon. All Rights Reserved. 9

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. 90 -723: Data Structures and Algorithms for Information Processing Lecture 5: Stacks and Queues Copyright © 1999, Carnegie Mellon. All Rights Reserved. 10

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 90 -723: Data Structures and Algorithms for Information Processing Lecture 5: Stacks and Queues Copyright © 1999, Carnegie Mellon. All Rights Reserved. 12

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 get. Front in order to simplify things. 90 -723: Data Structures and Algorithms for Information Processing Lecture 5: Stacks and Queues Copyright © 1999, Carnegie Mellon. All Rights Reserved. 13

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 90 -723: Data Structures and Algorithms for Information Processing Lecture 5: Stacks and Queues Copyright © 1999, Carnegie Mellon. All Rights Reserved. 14

Implementing a Queue • Just like a stack, we can implementing a queue in two ways: – Using an array – Using a linked list 90 -723: Data Structures and Algorithms for Information Processing Lecture 5: Stacks and Queues Copyright © 1999, Carnegie Mellon. All Rights Reserved. 15

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. 90 -723: Data Structures and Algorithms for Information Processing Lecture 5: Stacks and Queues Copyright © 1999, Carnegie Mellon. All Rights Reserved. 16

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[num. Items-1] 90 -723: Data Structures and Algorithms for Information Processing Lecture 5: Stacks and Queues Copyright © 1999, Carnegie Mellon. All Rights Reserved. 17

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. 90 -723: Data Structures and Algorithms for Information Processing Lecture 5: Stacks and Queues Copyright © 1999, Carnegie Mellon. All Rights Reserved. 18

Implementing a Queue // option 2 sketch of insert(Object item) { if(many. Items == 0) front = rear = 0; else rear = (rear + 1) mod size; data[rear] = item; many. Items++; } 90 -723: Data Structures and Algorithms for Information Processing Lecture 5: Stacks and Queues Copyright © 1999, Carnegie Mellon. All Rights Reserved. 19

Implementing a Queue // option 2 sketch of get. Front Object get. Front() { answer = data[front]; front = (front + 1) mod size; many. Items--; return answer } 90 -723: Data Structures and Algorithms for Information Processing Lecture 5: Stacks and Queues Copyright © 1999, Carnegie Mellon. All Rights Reserved. 20

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”? 90 -723: Data Structures and Algorithms for Information Processing Lecture 5: Stacks and Queues Copyright © 1999, Carnegie Mellon. All Rights Reserved. 21

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. 90 -723: Data Structures and Algorithms for Information Processing Lecture 5: Stacks and Queues Copyright © 1999, Carnegie Mellon. All Rights Reserved. 22

Palindromes • We can determine whether or not a word is a palindrome using a stack and a queue. • How? 90 -723: Data Structures and Algorithms for Information Processing Lecture 5: Stacks and Queues Copyright © 1999, Carnegie Mellon. All Rights Reserved. 23

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 90 -723: Data Structures and Algorithms for Information Processing Lecture 5: Stacks and Queues Copyright © 1999, Carnegie Mellon. All Rights Reserved. 24

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 90 -723: Data Structures and Algorithms for Information Processing Lecture 5: Stacks and Queues Copyright © 1999, Carnegie Mellon. All Rights Reserved. 25

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. 90 -723: Data Structures and Algorithms for Information Processing Lecture 5: Stacks and Queues Copyright © 1999, Carnegie Mellon. All Rights Reserved. 26

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 priorities of the items contained • Which approach is better? 90 -723: Data Structures and Algorithms for Information Processing Lecture 5: Stacks and Queues Copyright © 1999, Carnegie Mellon. All Rights Reserved. 27

Thinking Exercise • Where might a computer’s operating system use queues? 90 -723: Data Structures and Algorithms for Information Processing Lecture 5: Stacks and Queues Copyright © 1999, Carnegie Mellon. All Rights Reserved. 28

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. 90 -723: Data Structures and Algorithms for Information Processing Lecture 5: Stacks and Queues Copyright © 1999, Carnegie Mellon. All Rights Reserved. 29