Chapter 3 Stacks

Chapter Objectives To learn about the stack data type and how to use it To understand how Java implements a stack To learn how to implement a stack using an underlying array or 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

Stack Abstract Data Type Section 3.1

The Stack ADT (§4.2) A stack is one of the most commonly used data types. The Stack ADT stores arbitrary objects Insertions and deletions follow the last-in first-out scheme (LIFO) Think of a spring-loaded pez dispenser Main stack operations: push(object): inserts an element object pop(): removes and returns the last inserted element Auxiliary stack operations: object peek(): returns the last inserted element without removing it integer size(): returns the number of elements stored boolean empty(): indicates whether no elements are stored

Stack Applications Section 3.2

( a + b * ( c / ( d – e ) ) ) + ( d / e ) Balanced Parentheses 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 ) The problem is further complicated if braces or brackets are used in conjunction with parentheses The solution is to use stacks!

Parentheses Matching Each “(”, “{”, or “[” must be paired with a matching “)”, “}”, or “[” correct: ( )(( )){([( )])} correct: ((( )(( )){([( )])} incorrect: )(( )){([( )])} incorrect: ({[ ])} incorrect: (

Figure 6.2 Traces of the algorithm that checks for balanced braces

Implementing a Stack Section 3.3

Figure 6.4 An array-based implementation

Figure 6.5 A reference-based implementation

Additional Stack Applications Section 3.4

Figure 6.7 The action of a postfix calculator when evaluating the expression 2 * (3 + 4)

Figure 6.8 A trace of the algorithm that converts the infix expression a - (b + c * d)/e to postfix form