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

Section 3.1

Stack Abstract Data Type

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

Section 3.2

Stack Applications

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!

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Parentheses Matching

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

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Figure 6.2Traces of the algorithm that checks for balanced braces

Section 3.3

Implementing a Stack

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Figure 6.4An array-based implementation

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Figure 6.5A reference-basedimplementation

Section 3.4

Additional Stack Applications

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

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