1. Stacks
Chapter 5

2. 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: Stacks

3. 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: Stacks

4. 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: Stacks

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

6. 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: Stacks

7. Stack Applications (continued)
Chapter 5: Stacks

8. 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: Stacks

9. Stack Applications (continued)
Chapter 5: Stacks

10. Stack Applications (continued)
Chapter 5: Stacks

11. 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: Stacks

12. Implementing a Stack as an Extension to Vector (continued)
Chapter 5: Stacks

13. 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<E>
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: Stacks

14. 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
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15. Implementing a Stack Using an Array (continued)
Chapter 5: Stacks

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

17. 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: Stacks

18. 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: Stacks

19. Additional Stack Applications (continued)
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20. 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
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21. Evaluating Postfix Expressions
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22. Evaluating Postfix Expressions (continued)
Chapter 5: Stacks

23. Evaluating Postfix Expressions (continued)
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24. Evaluating Postfix Expressions (continued)
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25. Converting from Infix to Postfix
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26. Additional Stack Applications (continued)
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27. Evaluating Postfix Expressions (continued)
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28. Evaluating Postfix Expressions (continued)
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29. 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: Stacks

30. 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
Chapter 5: Stacks