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  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  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  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”  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)

 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!  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)

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  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  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  Can use either the ArrayList, Vector, or the LinkedList classes as all implement the List interface  Name of class illustrated in text is ListStack  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  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  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  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)

 Advantage of postfix form is that there is no need to group subexpressions in parentheses  No need to consider operator precedence  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)

Converting from Infix to Postfix

Additional Stack Applications (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  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  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