Transcript document

Stacks
Chapter 5
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
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
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
Specification of the Stack
Abstract Data Type (continued)
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”
Stack Applications (continued)
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!
Stack Applications (continued)
Stack Applications (continued)
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
Implementing a Stack as an
Extension to Vector (continued)
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
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
Implementing a Stack Using an
Array (continued)
Implementing a Stack as a Linked
Data Structure
 We can implement a stack using a linked list of nodes
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
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
Additional Stack Applications
(continued)
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
Evaluating Postfix Expressions
Evaluating Postfix Expressions
(continued)
Evaluating Postfix Expressions
(continued)
Evaluating Postfix Expressions
(continued)
Converting from Infix to Postfix
Additional Stack Applications
(continued)
Evaluating Postfix Expressions
(continued)
Evaluating Postfix Expressions
(continued)
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 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