Data Structures Using C++1 Chapter 7 Stacks. Data Structures Using C++2 Chapter Objectives Learn...

Data Structures Using C++ 1

Chapter 7

Stacks

Data Structures Using C++ 2

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• Become aware of the STL class stack

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Stacks

• Definition: list of homogeneous elements, wherein the addition and deletion of elements occur only at one end, called the top of the stack

• Last In First Out (LIFO) data structure• Used to implement function calls• Used to convert recursive algorithms

(especially not tail recursive) into nonrecursive algorithms

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Various Types of Stacks

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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

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Empty Stack

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Stack Operations

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Basic Operations on a Stack

• initializeStack: Initializes the stack to an empty state

• destroyStack: Removes all the elements from the stack, leaving the stack empty

• isEmptyStack: Checks whether the stack is empty. If empty, it returns true; otherwise, it returns false

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Basic Operations on a Stack

• isFullStack: Checks whether the stack is full. If full, it returns true; otherwise, it returns false

• 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

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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.

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Example of a Stack

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Empty Stack

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initializeStack and destroyStack

template<class Type>void stackType<Type>::initializeStack(){ stackTop = 0;}//end initializeStack

template<class Type>

void stackType<Type>::destroyStack()

{

stackTop = 0;

}//end destroyStack

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emptyStack and fullStack

template<class Type>bool stackType<Type>::isEmptyStack(){ return(stackTop == 0);}//end isEmptyStack

template<class Type>

bool stackType<Type>::isFullStack()

{

return(stackTop == maxStackSize);

}//end isFullStack

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Push

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Pushtemplate<class Type>void stackType<Type>::push(const Type& newItem){ if(!isFullStack()) { list[stackTop] = newItem; //add newItem at the top //of the stack stackTop++; //increment stackTop } else cerr<<"Cannot add to a full stack."<<endl;}//end push

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Return Top Element

template<class Type>Type stackType<Type>::top(){ assert(stackTop != 0); //if the stack is empty, //terminate the program return list[stackTop - 1]; //return the element of the //stack indicated by //stackTop - 1}//end top

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Pop

template<class Type>void stackType<Type>::pop(){ if(!isEmptyStack()) stackTop--; //decrement stackTop else cerr<<"Cannot remove from an empty stack."<<endl;}//end pop

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Pop

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copyStacktemplate<class Type>void stackType<Type>::copyStack(const stackType<Type>& otherStack){ delete [] list; maxStackSize = otherStack.maxStackSize; stackTop = otherStack.stackTop; list = new Type[maxStackSize]; assert(list != NULL);

//copy otherStack into this stack for(int j = 0; j < stackTop; j++) list[j] = otherStack.list[j];}//end copyStack

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Copy Constructor

template<class Type>stackType<Type>::stackType(const stackType<Type>& otherStack){ list = NULL; copyStack(otherStack);}//end copy constructor

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Overloading the Assignment Operator (=)

template<class Type>const stackType<Type>& stackType<Type>::operator= (const stackType<Type>& otherStack){ if(this != &otherStack) //avoid self-copy copyStack(otherStack); return *this;}//end operator=

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Time-Complexity of Operations of class stackType

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Stack Header File//Header file: myStack.h

#ifndef H_StackType#define H_StackType

#include <iostream>#include <cassert>

using namespace std;

//Place the definition of the class template stackType, as given//previously in this chapter, here.

//Place the definitions of the member functions, as discussed in//this chapter, here.#endif

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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 Lisa3.6 John3.9 Susan3.7 Kathy3.4 Jason3.9 David3.4 Jack

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Programming Example: Highest GPA (Algorithm)

1. Declare the variables.2. Open the input file.3. If the input file does not exist, exit the program.4. Set the output of the floating-point numbers to a

fixed decimal format with a decimal point and trailing zeroes. Also, set the precision to two decimal places.

5. Read the GPA and student name.6. highestGPA = GPA;7. Initialize the stack.

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Programming Example: Highest GPA (Algorithm)

8. while (not end of file) { 8.1 if (GPA > highestGPA) { 8.1.1 destroyStack(stack); 8.1.2 push(stack, student name); 8.1.3 highestGPA = GPA; } 8.2 else if(GPA is equal to highestGPA) push(stack, student name); 8.3 Read the GPA and student name;}

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Programming Example: Highest GPA (Algorithm)

9. Output the highest GPA.

10. Output the names of the students having the highest GPA.

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Programming Example: Highest GPA (Sample Run)

Input File (Ch7_HighestGPAData.txt)3.4 Holt3.2 Bolt2.5 Colt3.4 Tom3.8 Ron3.8 Mickey3.6 Pluto3.5 Donald3.8 Cindy3.7 Dome3.9 Andy3.8 Fox3.9 Minnie2.7 Goofy3.9 Doc3.4 Danny

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Programming Example: Highest GPA (Sample Run)

Output

Highest GPA = 3.90

The students holding the highest GPA are:

Doc

Minnie

Andy

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Empty and Nonempty Linked Stack

Empty linked stack Nonempty linked stack

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Default Constructor

template<class Type> //default constructor

linkedStackType<Type>::linkedStackType()

{

stackTop = NULL;

}

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Destroy Stacktemplate<class Type>void linkedStackType<Type>::destroyStack(){ nodeType<Type> *temp; //pointer to delete the node while(stackTop != NULL) //while there are elements //in the stack { temp = stackTop; //set temp to point to //the current node stackTop = stackTop->link; //advance stackTop //to the next node delete temp; //deallocate the memory //occupied by temp }}//end destroyStack

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initializeStack and isStackEmptytemplate<class Type>void linkedStackType<Type>:: initializeStack(){ destroyStack();}

template<class Type>

bool linkedStackType<Type>::isEmptyStack()

{

return(stackTop == NULL);

}

template<class Type>

bool linkedStackType<Type>::isFullStack()

{

return false;

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Push

Stack before the push operation

Stack and newNode

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Push

Stack after the statement newNode->link = stackTop; executes

Stack after the statement stackTop = newNode; executes

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Return Top Element

template<class Type>Type linkedStackType<Type>::top(){ assert(stackTop != NULL); //if the stack is empty, //terminate the program return stackTop->info; //return the top element}//end top

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Pop

Stack before the pop operation

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Pop

Stack after the statements temp = stackTop; and stackTop = stackTop->link; execute

Stack after the statement delete temp; executes

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Application of Stacks:Postfix Expression Calculator

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Application of Stacks:Postfix Expression Calculator

Stack after pushing 6

Stack after pushing 3

Stack after retrieving the top two elements and popping twice

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

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Application of Stacks:Postfix Expression Calculator

Stack after pushing 2

Stack after retrieving the top two elements and popping twice

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

Stack after popping the element

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Postfix Expression Calculator (Main Algorithm)

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Nonrecursive Algorithm to reverse linked list

current = first; while(current != NULL){ stack.push(current); current = current->link; }llistType, *newfirst = stack.pop();current = newfirst;while (!stack.empty()) current->link = stack.pop();current->link = NULL;

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List After Execution of Statementcurrent = first;

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Repeated Execution of:stack.push(current);current = current->link;

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STL class stack (Stack Container Adapter)

• Standard Template Library (STL) provides a class to implement a stack in a program

• Name of the class defining a stack is “stack”

• Name of the header file containing the definition of the class stack is “stack”

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Operations on a stack Object