Stacks Chapter 5

Chapter 5: Stacks2 Chapter Objectives To learn about the stack data type and how to use its four methods: push, pop, peek, and empty To understand how Java implements a stack To learn how to implement a stack using an underlying array or a linked list To see how to use a stack to perform various applications, including finding palindromes, testing for balanced (properly nested) parentheses, and evaluating arithmetic expressions

Chapter 5: Stacks3 Stack Abstract Data Type A stack can be compared to a Pez dispenser Only the top item can be accessed Can only extract one item at a time A stack is a data structure with the property that only the top element of the stack is accessible The stack’s storage policy is Last-In, First-Out

Chapter 5: Stacks4 Specification of the Stack Abstract Data Type Only the top element of a stack is visible, therefore the number of operations performed by a stack are few Need the ability to Inspect the top element Retrieve the top element Push a new element on the stack Test for an empty stack

Chapter 5: Stacks5 Specification of the Stack Abstract Data Type (continued)

Chapter 5: Stacks6 Stack Applications Two client programs using stacks Palindrome finder Parentheses matcher Palindrome: string that reads the same in either direction Example: “Able was I ere I saw Elba”

Chapter 5: Stacks7 Stack Applications (continued)

Chapter 5: Stacks8 Stack Applications (continued) When analyzing arithmetic expressions, it is important to determine whether an expression is balanced with respect to parentheses (a+b*(c/(d-e)))+(d/e) Problem is further complicated if braces or brackets are used in conjunction with parenthesis Solution is to use stacks!

Chapter 5: Stacks9 Stack Applications (continued)

Chapter 5: Stacks10 Stack Applications (continued)

Chapter 5: Stacks11 Implementing a Stack as an Extension of Vector The Java API includes a Stack class as part of the package java.util The vector class implements a growable array of objects Elements of a vector can be accessed using an integer index and the size can grow or shrink as needed to accommodate the adding and removing of elements

Chapter 5: Stacks12 Implementing a Stack as an Extension to Vector (continued)

Chapter 5: Stacks13 Implementing a Stack with a List Component Can use either the ArrayList, Vector, or the LinkedList classes as all implement the List interface Name of class illustrated in text is ListStack ListStack is an adapter class as it adapts the methods available in another class to the interface its clients expect by giving different names to essentially the same operations

Chapter 5: Stacks14 Implementing a Stack Using an Array Need to allocate storage for an array with an initial default capacity when creating a new stack object Need to keep track of the top of the stack No size method

Chapter 5: Stacks15 Implementing a Stack Using an Array (continued)

Chapter 5: Stacks16 Implementing a Stack as a Linked Data Structure We can implement a stack using a linked list of nodes

Chapter 5: Stacks17 Comparison of Stack Implementations Extending a Vector (as is done by Java) is a poor choice for stack implementation as all Vector methods are accessible Easiest implementation would be to use an ArrayList component for storing data All insertions and deletions are constant time regardless of the type of implementation discussed All insertions and deletions occur at one end

Chapter 5: Stacks18 Additional Stack Applications Consider two case studies that relate to evaluating arithmetic expressions Postfix and infix notation Expressions normally written in infix form Binary operators inserted between their operands A computer normally scans an expression string in the order that it is input; easier to evaluate an expression in postfix form

Chapter 5: Stacks19 Additional Stack Applications (continued)

Chapter 5: Stacks20 Additional Stack Applications (continued) Advantage of postfix form is that there is no need to group subexpressions in parentheses No need to consider operator precedence

Chapter 5: Stacks21 Evaluating Postfix Expressions

Chapter 5: Stacks22 Evaluating Postfix Expressions (continued)

Chapter 5: Stacks23 Evaluating Postfix Expressions (continued)

Chapter 5: Stacks24 Evaluating Postfix Expressions (continued)

Chapter 5: Stacks25 Converting from Infix to Postfix

Chapter 5: Stacks26 Additional Stack Applications (continued)

Chapter 5: Stacks27 Evaluating Postfix Expressions (continued)

Chapter 5: Stacks28 Evaluating Postfix Expressions (continued)

Chapter 5: Stacks29 Chapter Review A stack is a last-in, first-out (LIFO) data structure A stack is a simple but powerful data structure; its four operations include empty, peek, pop, and push Stacks are useful to process information in the reverse of the order that it is encountered Java.util.Stack is implemented as an extension of the Vector class

Chapter 5: Stacks30 Chapter Review (continued) Three ways to implement a stack: Using an object of a class that implements the List interface as a container Using an array as a container Using a linked list as a container Stacks can be applied in programs for evaluating arithmetic expressions