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Stacks Chapter 5

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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

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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

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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

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Specification of the Stack Abstract Data Type (continued)

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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”

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Stack Applications (continued)

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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!

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Stack Applications (continued)

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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

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Implementing a Stack as an Extension to Vector (continued)

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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

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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

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Implementing a Stack Using an Array (continued)

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Implementing a Stack as a Linked Data Structure We can implement a stack using a linked list of nodes

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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

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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

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Additional Stack Applications (continued)

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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

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Evaluating Postfix Expressions

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Evaluating Postfix Expressions (continued)

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Converting from Infix to Postfix

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Additional Stack Applications (continued)

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Evaluating Postfix Expressions (continued)

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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

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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

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