1. Chapter 3
Stacks

2. 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

3. Stack Abstract Data Type
Section 3.1

4. 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

5. Stack Applications
Section 3.2

6. ( 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!

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

8. Figure 6.2
Traces of the algorithm that checks for balanced braces

9. Implementing a Stack
Section 3.3

10. Figure 6.4
An array-based implementation

11. Figure 6.5
A reference-based
implementation

12. Additional Stack Applications
Section 3.4

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

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