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Chapter 6. Stacks. Chapter Objectives. Learn about stacks Examine various stack operations Learn how to implement a stack as an array Learn how to implement a stack as a linked list Discover stack applications Learn to use a stack to remove recursion. Stacks. Definition:

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Chapter 6

Stacks

Data Structures Using Java

Chapter Objectives
• Examine various stack operations
• Learn how to implement a stack as an array
• Learn how to implement a stack as a linked list
• Discover stack applications
• Learn to use a stack to remove recursion

Data Structures Using Java

Stacks
• Definition:
• list of homogeneous elements
• addition and deletion of elements occurs only at one end, called the top of the stack
• Last In First Out (LIFO) data structure
• Used to implement method calls
• Used to convert recursive algorithms (especially not tail recursive) into nonrecursive algorithms

Data Structures Using Java

Various Types of Stacks

Data Structures Using Java

LIFO
• Last In First Out (LIFO) data structure
• Top element of stack is last element to be added to stack
• Elements added and removed from one end (top)
• Item added last are removed first

Data Structures Using Java

Empty Stack

Data Structures Using Java

Stack Operations

Data Structures Using Java

Basic Operations on a Stack
• initializeStack: Initializes the stack to an empty state
• isEmptyStack: Checks whether the stack is empty. If empty, it returns true; otherwise, it returns false
• isFullStack: Checks whether the stack is full. If full, it returns true; otherwise, it returns false

Data Structures Using Java

Basic Operations on a Stack
• push:
• Add new element to the top of the stack
• The input consists of the stack and the new element
• Prior to this operation, the stack must exist and must not be full

Data Structures Using Java

Basic Operations on a Stack
• top: Returns the top element of the stack. Prior to this operation, the stack must exist and must not be empty
• pop: Removes the top element of the stack. Prior to this operation, the stack must exist and must not be empty

Data Structures Using Java

Example of a Stack

Data Structures Using Java

Empty Stack

Data Structures Using Java

initializeStack

public void initializeStack()

{

for(int i = 0; i < stackTop; i++)

list[i] = null;

stackTop = 0;

}//end initializeStack

Data Structures Using Java

emptyStack and fullStack

public boolean isEmptyStack()

{

return(stackTop == 0);

}//end isEmptyStack

public boolean isFullStack()

{

return(stackTop == maxStackSize);

}//end isFullStack

Data Structures Using Java

Push

Data Structures Using Java

Push

public void push(DataElement newItem) throws StackOverflowException

{

if(isFullStack())

throw new StackOverflowException();

list[stackTop] = newItem.getCopy(); //add newItem at the

//top of the stack

stackTop++; //increment stackTop

}//end push

Data Structures Using Java

public DataElement top() throws StackUnderflowException

{

if(isEmptyStack())

throw new StackUnderflowException();

DataElement temp = list[stackTop - 1].getCopy();

return temp;

}//end top

Data Structures Using Java

Pop

public void pop() throws StackUnderflowException

{

if(isEmptyStack())

throw new StackUnderflowException();

stackTop--; //decrement stackTop

list[stackTop] = null;

}//end pop

Data Structures Using Java

Pop

Data Structures Using Java

copy

private void copy(StackClass otherStack)

{

list = null;

System.gc();

maxStackSize = otherStack.maxStackSize;

stackTop = otherStack.stackTop;

list = new DataElement[maxStackSize];

//copy otherStack into this stack

for(int i = 0; i < stackTop; i++)

list[i] = otherStack.list[i].getCopy();

}//end copy

6

Data Structures Using Java

Constructors

//constructor with a parameter

public StackClass(int stackSize)

{

if(stackSize <= 0)

{

System.err.println(“The size of the array to implement “

+ “the stack must be positive.”);

System.err.println(“Creating an array of size 100.”);

maxStackSize = 100;

}

else

maxStackSize = stackSize; //set the stack size to

//the value specified by

//the parameter stackSize

stackTop = 0; //set stackTop to 0

list = new DataElement[maxStackSize]; //create the array

}//end constructor

Data Structures Using Java

Constructors

//default constructor

public StackClass()

{

maxStackSize = 100;

stackTop = 0; //set stackTop to 0

list = new DataElement[maxStackSize]; //create array

}//end default constructor

Data Structures Using Java

Copy Constructor and copyStack

public StackClass(StackClass otherStack)

{

copy(otherStack);

}//end copy constructor

public void copyStack(StackClass otherStack)

{

if(this != otherStack) //avoid self-copy

copy(otherStack);

}//end copyStack

Data Structures Using Java

Programming Example: Highest GPA

Input The program reads an input file consisting of each student’s GPA, followed by the student’s name. Sample data is:

3.8 Lisa

3.6 John

3.9 Susan

3.7 Kathy

3.4 Jason

3.9 David

3.4 Jack

Data Structures Using Java

Programming Example: Highest GPA (Algorithm)
• Declare the variables
• Create a DecimalFormat object to output a decimal number to two decimal places
• Open the input file
• If the input file does not exist, exit the program
• Read the next input line

Data Structures Using Java

Highest GPA (Algorithm)
• while (not end of file)

{

6.a. Tokenize the input line

6.b. Get the next GPA

6.c. Get the next name

6.d. if (GPA > highestGPA)

{

6.d.i initialize stack

6.d.ii push(stack, student name)

6.d.iii highestGPA = GPA

}

6.e. else

if(GPA is equal to highestGPA)

push(stack, student name)

6.f Read the next input line

}

Data Structures Using Java

Programming Example: Highest GPA (Algorithm)
• Output the highest GPA.
• Output the names of the students having the highest GPA.

Data Structures Using Java

Programming Example: Highest GPA (Sample Run)

3.4 Holt

3.2 Bolt

2.5 Colt

3.4 Tom

3.8 Ron

3.8 Mickey

3.6 Pluto

3.5 Donald

3.8 Cindy

3.7 Dome

3.9 Andy

3.8 Fox

3.9 Minnie

2.7 Goofy

3.9 Doc

3.4 Danny

Data Structures Using Java

Programming Example: Highest GPA (Sample Run)

Output

Highest GPA = 3.90

The students holding the highest GPA are:

Doc

Minnie

Andy

Data Structures Using Java

Data Structures Using Java

Default Constructor

{

stackTop = null;

}

Data Structures Using Java

initializeStack, isStackEmpty, and isStackFull

public void initializeStack()

{

stackTop = null;

}//end initializeStack

public boolean isEmptyStack()

{

return(stackTop == null);

}

public boolean isFullStack()

{

return false;

}

Data Structures Using Java

Push

Stack before the push operation

Stack and newNode

Data Structures Using Java

Push

Stack after the statement newNode.link = stackTop; executes

Stack after the statement stackTop = newNode; executes

Data Structures Using Java

public DataElement top() throws StackUnderflowException

{

if(stackTop == null)

throw new StackUnderflowException();

return stackTop.info.getCopy();

}//end top

Data Structures Using Java

Pop

Stack after the statement

Stack after popping the top element

Stack before the popoperation

Data Structures Using Java

Application of Stacks:Postfix Expression Calculator
• Prefix/Polish Notation
• Suffix/Postfix/Reverse Polish Notation

Data Structures Using Java

Application of Stacks:Postfix Expression Calculator

Stack after pushing 6

Stack after retrieving the top two elements and popping twice

Stack after pushing 3

Stack after pushing the result of op1 + op2, which is 9

Data Structures Using Java

Application of Stacks:Postfix Expression Calculator

Stack after pushing 2

Stack after pushing the result of op1 * op2, which is 18

Stack after retrieving the top two elements and popping twice

Stack after popping the element

Data Structures Using Java

Postfix Expression Calculator (Main Algorithm)

Get the next expression

while more data to process

{

a. initialize the stack

b. process the expression

c. output the result

d. get the next expression

}

Data Structures Using Java

Nonrecursive Algorithm to Print Linked List

current = first; //Line 1

while(current != NULL) //Line 2

{

stack.push(current); //Line 3

}

Data Structures Using Java

Data Structures Using Java

Java class Stack
• Java provides a class to implement a stack in a program
• The name of the Java class defining a stack is Stack
• The class Stack is contained in the package java.util
• Table 6-3 lists the members of the class Stack

Data Structures Using Java

Java class Stack

Data Structures Using Java

Chapter Summary
• Stack Data Structure
• Last In First Out (LIFO)
• Stacks Implemented as Arrays
• Stacks Implemented as Linked Lists
• Postfix Expression Calculator
• Nonrecursive Algorithm to Print Linked List
• Java class Stack

Data Structures Using Java