Stacks

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 Chapter 5: Stacks

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) Chapter 5: Stacks

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 Chapter 5: Stacks

21. Evaluating Postfix Expressions Chapter 5: Stacks

22. Evaluating Postfix Expressions (continued) Chapter 5: Stacks

23. Evaluating Postfix Expressions (continued) Chapter 5: Stacks

24. Evaluating Postfix Expressions (continued) Chapter 5: Stacks

25. Converting from Infix to Postfix Chapter 5: Stacks

26. Additional Stack Applications (continued) Chapter 5: Stacks

27. Evaluating Postfix Expressions (continued) Chapter 5: Stacks

28. Evaluating Postfix Expressions (continued) Chapter 5: Stacks

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