1 expanded by j. goetz nell dale chapter 6 lists plus slides by sylvia sorkin, community college of...

1expanded by J. Goetz

Nell Dale

Chapter 6

Lists Plus

Slides by Sylvia Sorkin, Community College of Baltimore County - Essex Campus

C++ Plus Data Structures

expanded by J. Goetz

ADT Sorted List OperationsTransformers

– MakeEmpty – InsertItem – DeleteItem

Observers – IsFull– LengthIs

– RetrieveItem

Iterators – ResetList – GetNextItem

change state

observe state

process all

class SortedType<char>

MakeEmpty

~SortedType

DeleteItem . . .

InsertItem

SortedType

RetrieveItem

GetNextItem

‘C’ ‘L’ ‘X’

Private data:

length 3

listData

currentPos

What is a Circular Linked List?A circular linked list is a list in which every node has a successor; the “last” element is succeeded by the “first” element. •In the linear linked list we have to have a pointer to the beginning to access all nodes.

Here we can start at any node in the list and traverse the whole list

‘B’ ‘C’ ‘L’ ‘T’ ‘V’ ‘Y’

listData

Circular Linked List

• listData points to the last item in the list, so we have access to the first and the last node:

listData->info refers to the last node

listData->next->info refers to the first node

• The pointer never becomes NULL. So we never stop when the traversing pointer becomes NULL.

• Are good for applications that require access to both ends of the list. Implementation is not shorter or simpler.

// File: Circle.cpp// This file contains the member functions for the Circular Linked List// list coded in Chapter 6.1 of the text. // There is no need to change any of the declaration in class SortedType#include <cstdlib> template <class ItemType>struct NodeType{ ItemType info; NodeType* next; }; template <class ItemType>class SortedType{public: // constructors // void InsertItem(ItemType item); void DeleteItem(ItemType);…….. // other members go here

private: NodeType<ItemType>* listData; int length;};

template<class ItemType> // similar to RetrieveItem for Linear Linked List SortedTypevoid FindItem(NodeType<ItemType>* listData, ItemType item, NodeType<ItemType>*& location, NodeType<ItemType>*& predLoc, bool& found) //helper function, hidden within implementation p.339// Assumption: ItemType is a type for which the operators ''<'' and "==" are defined as either an appropriate built-in type or a

class that overloads these operations.// Pre: List is not empty.// Post:If there is an element someItem whose key matches item's key, then found = true; otherwise, found = false.// If found, location contains the address of someItem and predLoc contains the address of someItem's predecessor;// otherwise, location contains the address of item's logical successor and predLoc contains the address of item's logical

predecessor.{ // A. Set values bool moreToSearch = true; location = listData->next; // in the Linear Linked List SortedType was: location = listData; predLoc = listData; //(1) in the Linear Linked List SortedType was: predLoc = NULL; found = false;// B. Find the place while (moreToSearch && !found) { if (item < location->info) moreToSearch = false; //exit3: we have passed the location where item belongs (see Post: description), //exit right away if the item SMALLEST than any in the list, then predLoc = listData from (1) else if (item == location->info) found = true; //exit2: item is FOUND, if only ONE element was: predLoc = listData from (1) else { // move running pointers predLoc = location; location = location->next; moreToSearch = (location != listData->next); //exit1: it can be location = listData->next; (it was location != NULL for

//Linear Linked List SortedType ) so the first element again, item is NOT FOUND } }}

template<class ItemType> // concept is similar to InsertItem for Linear Linked List SortedTypevoid SortedType<ItemType>::InsertItem(ItemType item) // Circular Linked List p.340{ NodeType<ItemType>* newNode; NodeType<ItemType>* predLoc; NodeType<ItemType>* location; bool found; // A. Set values: allocate space and store item newNode = new NodeType<ItemType>; newNode->info = item; // B. store item //C. Find the place where the new element belongs if (listData != NULL) { FindItem(listData, item, location, predLoc, found); // D. Put the new element into the list using predLoc received from FindItem() newNode->next = predLoc->next; //(1) // case a: GENERAL – link new node with the next one predLoc->next = newNode; //(2) link new node with the previous one if (listData->info < item) // case d: General+ . If this is the last node (the LARGEST ELEM) in the

list. listData = newNode; //(3) reassign listData } // note: general case covers case c: inserting to front of the list-the SMALLEST one; see exit 1, 2 else // E. // case b: Inserting into an EMPTY list. { listData = newNode; // make listData point to the new node newNode->next = newNode; // make the new node point itself } length++;}

template<class ItemType> //Circular Linked Listvoid SortedType<ItemType>::DeleteItem(ItemType item) // concept is similar to Linear Linked List

SortedType//p.342{ NodeType<ItemType>* location; NodeType<ItemType>* predLoc; bool found; // A. Find FindItem(listData, item, location, predLoc, found); // B. Remove element from the list at location found in FindItem() if (predLoc == location) // check on return from FindItem listData = NULL; //case c: Only ONE node in list else { predLoc->next = location->next; // case a: GENERAL - jump over the node we are deleting // note: general case covers case b: inserting to front of the list-the SMALLEST one; see

exit3 in FindItem if (location == listData) // check on return from FindItem - General+ case listData = predLoc; //case d: Deleting last node in list – the LARGEST item } // C. Deallocate location delete location; length--;}

‘A’ ‘C’ ‘F’ ‘T’ ‘Z’

What is a Doubly Linked List?

listData

A doubly linked list is a list in which each node is linked to both its successor and its predecessor. In a circular linked list we cannot access its predecessors and cannot traverse in reverse, a doubly linked list allows the user to print the list in the ascending and descending order.

Each node contains two pointers template< class ItemType >struct NodeType {

ItemType info; // Data member

NodeType<ItemType>* back; // Pointer to predecessor NodeType<ItemType>* next; // Pointer to successor

. back . info . next

3000 ‘A’ NULL

template<class ItemType> // similar to FindItem for Circular Linked List SortedType – see removal of predLocvoid FindItem(NodeType<ItemType>* listData, ItemType item, NodeType<ItemType>*& location, bool& found) //helper

function, hidden within implementation p.345// Assumption: ItemType is a type for which the operators ''<'' and "==" are defined as either an appropriate built-in

type or a class that overloads these operations.// Pre: List is not empty.// Post:If there is an element someItem whose key matches item's key, then found = true; otherwise, found = false.// If found, location contains the address of someItem;// otherwise, location contains the address of item's logical successor { // A. Set values bool moreToSearch = true; location = listData; // location = listData->next; // in the Linear Linked List SortedType was: location = listData; //predLoc = listData; //(1) in the Linear Linked List SortedType was: predLoc = NULL; found = false;// B. Find the place while (moreToSearch && !found) { if (item < location->info) moreToSearch = false; //exit3: we have passed the location where item belongs (see Post: description), //exit right away if the item SMALLEST than any in the list, then predLoc = listData from (1) else if (item == location->info) found = true; //exit2: item is FOUND, if only ONE element was: predLoc = listData from (1) else { // move a pointer // predLoc = location; location = location->next; moreToSearch = (location != listData->next); //exit1: it can be location = listData->next; (it was location != NULL for

//Linear Linked List SortedType ) so the first element again, item is NOT FOUND

Doubly Linked List

• The algorithms for the insertion and deletion more complicated because there are more pointers to keep track.

Linking the New Node into the List

Deleting from a Doubly Linked List

What are Header and Trailer Nodes?

listData INT_MIN 5 8 13 INT_MAX

• A goal: simplify linked list by making sure that we never have end cases i.e. never insert or delete at the ends of the list

• A Header Node is a node at the beginning of a list that contains a key value smaller than any possible key.

• A Trailer Node is a node at the end of a list that contains a key larger than any possible key.

• Both header and trailer are placeholding nodes used to simplify list processing.

Recall Definition of Stack• Logical (or ADT) level: A stack is an ordered

group of homogeneous items (elements), in which the removal and addition of stack items can take place only at the top of the stack.

• A stack is a LIFO “last in, first out” structure.

Stack ADT Operations• MakeEmpty -- Sets stack to an empty state.

• IsEmpty -- Determines whether the stack is currently empty.

• IsFull -- Determines whether the stack is currently full.

• Push (ItemType newItem) -- Adds newItem to the top of the stack.

• Pop () -- Removes the item at the top of the stack and returns it in item.

• Top (ItemType& item) -- Returns a copy of the top item

class StackType<int>

StackType

MakeEmpty

Pop and Top

IsFull

IsEmpty Private data:

topPtr

~StackType

What happens . . .

• When a function is called that uses pass by value for a class object like our dynamically linked stack?

StackType

MakeEmpty

Pop; Top

IsFull

IsEmpty Private data:

topPtr

~StackType

// FUNCTION CODEtemplate<class ItemType>void MyFunction( StackType<ItemType> SomeStack )

// SomeStack – formal parameter // Uses pass by value{

Passing a class object by value

Shallow Copy vs. Deep Copy

• A shallow copy copies only the class data members, and does not copy any pointed-to data.

• A deep copy copies not only the class data members, but also makes separately stored copies of any pointed-to data.

Pass by value makes a shallow copy

StackType<int> MyStack; // CLIENT CODE . . .

MyFunction( MyStack ); // function call

Private data: 7000 6000

topPtr 7000

Private data:

topPtr 7000

MyStack SomeStack (formal parameter)

shallow copy

What’s the difference?

• A shallow copy shares the pointed to data with the original class object.

• A deep copy stores its own copy of the pointed to data at different locations than the data in the original class object.

Making a deep copy

topPtr 7000SomeStack (formal parameter)

topPtr 5000

MyStack

deep copy

// FUNCTION CODEtemplate<class ItemType>void MyFunction( StackType<ItemType> SomeStack )

// Uses pass by value{

ItemType item;SomeStack.Pop();SomeStack.Top(item);

WHAT HAPPENS IN THE SHALLOW COPY SCENARIO?

Suppose MyFunction Uses Pop

MyStack.topPtr is left dangling

StackType<int> MyStack; // CLIENT CODE . . .

MyFunction( MyStack );

Private data:

topPtr 6000

MyStack SomeStack (formal parameter)

shallow copy

topPtr 7000

MyStack.topPtr is left dangling

Private data:

topPtr 6000

MyStack SomeStack ( formal parameter)

shallow copy

topPtr 7000

NOTICE THAT NOT JUST FOR THE SHALLOW COPY, BUT ALSO FOR ACTUAL PARAMETER MyStack,THE DYNAMIC DATA HAS CHANGED!

As a result . . .

• This default method used for pass by value is not the best way when a data member pointer points to dynamic data.

• Instead, you should write what is called a copy constructor, which makes a deep copy of the dynamic data in a different memory location.

More about copy constructors• When there is a copy constructor provided for a

class, the copy constructor is used to make copies for pass by value.

• You do not call the copy constructor.

• Like other constructors, it has no return type.

• Because the copy constructor properly defines pass by value for your class, it must use pass by reference in its definition.

Copy Constructor

• If a copy constructor is present, the default method of initialization (member by member copying) is inhibited. Instead, the copy-constructor is implicitly invoked whenever one class object is initialized by another

• Copy constructor is a special member function of a class that is implicitly called in these three situations:

1. passing object parameters by value,2. initializing an object variable in a declaration, 3. returning an object as the return value of a function.

// DYNAMICALLY LINKED IMPLEMENTATION OF STACK

template<class ItemType>class StackType {public:

StackType( ); // Default constructor.// POST: Stack is created and empty.

StackType( const StackType<ItemType>& anotherStack );// If a Copy constructor is present, the default method

of initialization (member by member copying) is inhibited. Instead, the copy-constructor is implicitly invoked whenever one class object is initialized by another

// Implicitly called for pass by value.. ..~StackType( );

// DESTRUCTOR is called automatically when the class // instance goes out of scope

// POST: Memory for nodes has been deallocated.private:

NodeType<ItemType>* topPtr ;}; 32

CLASS CONSTRUCTOR

CLASS COPY CONSTRUCTOR

CLASS DESTRUCTOR

DESTRUCTOR is called automatically when the class instance goes out of scope

Classes with Data Member Pointers Need

template<class ItemType> // COPY CONSTRUCTOR p.342

StackType<ItemType>:: // 2 running pointers ptr1 => ptr2

StackType( const StackType<ItemType>& anotherStack ) // copy anotherStack to self

{ NodeType<ItemType>* ptr1 ; //points to the node to be copied from(of anotherStack)

NodeType<ItemType>* ptr2 ; //points to the last node copied to the self stack

if ( anotherStack.topPtr == NULL )

topPtr = NULL ; //so empty self stack; topPtr a private data

else // allocate memory for the first node

{ topPtr = new NodeType<ItemType> ; //(1)allocate memory

topPtr->info = anotherStack.topPtr->info ; //(2)copy info

ptr1 = anotherStack.topPtr->next ; //(3)copy the first link pointer

ptr2 = topPtr ; //(4)ptr2 starts from topPtr

while ( ptr1 != NULL ) // deep copy other nodes

{ ptr2->next = new NodeType<ItemType> ; //(5) create a new next node

ptr2 = ptr2->next ; //(6) move ptr2 to the last of the self

ptr2->info = ptr1->info; //(7) copy info to the corresponding one

ptr1 = ptr1->next ; //(8) move ptr1 to the next one of anotherStack

ptr2->next = NULL ; //(9)while condition gives ptr1 = NULL so the self ends

}gtt534

// DYNAMICALLY LINKED IMPLEMENTATION OF STACK

template<class ItemType>class StackType {public:

StackType( ); // Default constructor.// POST: Stack is created and empty.

StackType( const StackType<ItemType>& anotherStack );// Copy constructor.

friend void copy (StackType<ItemType>, StackType<ItemType>&) //A friend function is not a member of the class, but it has permission to access private class members directly

.~StackType( );

// Destructor.// POST: Memory for nodes has been deallocated.

private:NodeType<ItemType>* topPtr ;

Copy routine is a friend of the class StackType so has access to private variables in the class

template<class ItemType> // COPY FUNCTION - copy anotherStack to mycopy object p.356//StackType<ItemType>:: Copy is no a member function, so 2 stacks should be passed //by parameters //2 running pointers ptr1 => ptr2void Copy (StackType<ItemType> anotherStack, StackType<ItemType>& mycopy)

{ NodeType<ItemType>* ptr1 ; //points to the node to be copied from(of anotherStack)NodeType<ItemType>* ptr2 ; //points to the last node copied to the mycopy stackif ( anotherStack.topPtr == NULL )

mycopy.topPtr = NULL //so empty mycopy stack; topPtr a private dataelse // allocate memory for the first node{ mycopy.topPtr = new NodeType<ItemType> ; //(1)allocate memory

mycopy.topPtr->info = anotherStack.topPtr->info ; //(2)copy infoptr1 = anotherStack.topPtr->next ; //(3)copy the first link pointer ptr2 = mycopy.topPtr ; //(4)ptr2 starts from topPtrwhile ( ptr1 != NULL ) // deep copy other nodes{ ptr2->next = new NodeType<ItemType> ; //(5) create a new next node ptr2 = ptr2->next ; //(6) move ptr2 to the last of the copy object ptr2->info = ptr1->info; //(7) copy info to the corresponding one ptr1 = ptr1->next ; //(8) move ptr1 to the next one of

anotherStack}ptr2->next = NULL ; //(9)while condition gives ptr1 = NULL so the mycopy

ends }

// almost identical to the copy constructor, the difference is marked by mycopy

What about the assignment operator?

• The default method used for assignment operator (=) of class objects makes a shallow copy.

• If your class has a data member pointer to dynamic data, you should write a member function to overload the assignment operator to make a deep copy of the dynamic data.

// DYNAMICALLY LINKED IMPLEMENTATION OF STACK template<class ItemType>class StackType {public:

StackType( ); // Default constructor.

StackType( const StackType<ItemType>& anotherStack );// Copy constructor.

void operator= ( StackType<ItemType> );// Overloads assignment operator.

. . .~StackType( ); // Destructor.

private:NodeType<ItemType>* topPtr ;

};// The function definition looks like thistemplate<class ItemType>void StackType<ItemType>::operator= (StackType<ItemType> anotherStack){//body}

Using Overloaded Binary operator=

When a Member Function was defined

myStack = yourStack

myStack.operator=(yourStack)

When a Friend Function was defined

myStack = yourStack

operator=(myStack, yourStack)

C++ Operator Overloading Guides1 All operators except these :: . sizeof ?: may be

overloaded. 2 At least one operand must be a class instance.3 You cannot change precedence, operator symbols, or

number of operands.4 Overloading ++ and -- requires prefix form use by default,

unless special mechanism is used. 5 To overload these operators = ( ) [ ] member functions

(not friend functions) must be used. 6 An operator can be given multiple meanings if the data

types of operands differ.7 Many meanings for an operator can coexist as long as the

compiler can distinguish among the data types of the operands.

Using Overloaded Binary operator+

When a Member Function was defined

myStack + yourStack

myStack.operator+(yourStack)

When a Friend Function was defined

myStack + yourStack

operator+(myStack, yourStack)

Linked list in an Array of Recordes• Linked structures problems:

– Write a linked list to a file is meaningless on the next run time

– Dynamic allocation of each node is time expensive, specifically for the operating system code

• An array index remains valid on the next run of the program, so we can implement an array of nodes

A Sorted linked list stored in an Array of Nodes

A Sorted linked list Stored in an Array of Nodes

• Each node tells us the array index of the succeeding node

• See the chain of next indexes – following the links in the next member you can get the linked list

• the linked structure uses array indexes as “pointers”

• null is represented by no nodes[-1] exists or by NUL = -1

• no contain value elements in the list constitute free space

An Array with linked list of values and the list of free space

• Write own function to:– allocate nodes from the free

space – GetNode()

– delete nodes and return to the pool of free space – FreeNode()

• list, free are external pointers to the list of values and the list of free space, respectively

An Array with Three Lists (Including the Free List)

// file: ArrayLL.cpp p.366-7// This file contains the code for the array-of-records implementation// in the text. Incomplete definitions of ListType and NodeType and// one stub routine have been included to confirm that the syntax of// this code is correct. The student must write a complete definition// to use this code.typedef int ItemType;struct NodeType;

struct MemoryType{ int free; // index of the first free node NodeType* nodes; // a true pointer to the dynamically // allocated array of nodes

};// An incomplete definition of ListType sufficient to compile the code// in the array linked list implementationclass ListType{public: ListType(); ListType(int); ~ListType(); // Other member function prototypes go here. void MakeEmpty(); bool IsFull() const; int LengthIs() const; void RetrieveItem(ItemType& item, bool& found); void InsertItem(ItemType item); void DeleteItem(ItemType item); void ResetList(); void GetNextItem(ItemType& item);

private: int listData; int currentPos; int length; int maxItems; // new MemoryType storage; // new};

// Prototypes of auxiliary functions.void GetNode(int& nodeIndex, MemoryType& storage);// Returns the index of a free node in nodeIndex.

void FreeNode(int nodeIndex, MemoryType& storage);// Returns nodeIndex to storage.

void InitializeMemory(int maxItems, MemoryType&);// Initializes all memory to the free list.

// Define end-of-list symbol.const int NUL = -1;

struct NodeType{ int info; int next;};

// Definitions of the auxillary functions:void InitializeMemory(int maxItems, MemoryType&

storage){ for (int index = 1; index < maxItems; index++) storage.nodes[index-1].next = index;

storage.nodes[maxItems-1].next = NUL; storage.free = 0;}

void GetNode(int& nodeIndex, MemoryType& storage){ nodeIndex = storage.free; // take first free one

storage.free = storage.nodes[storage.free].next; // update free

void FreeNode(int nodeIndex, MemoryType& storage){ // take the nodeIndex received as a parameter and link it into the list of free nodes

storage.nodes[nodeIndex].next = storage.free; storage.free = nodeIndex; // put as a first one

//The class constructors for class ListType must allocate the storage//for the array of records and call InitializeMemory. For the default//constructor, we arbitrarily choose an array size of 500.

ListType::ListType(int max){ length = 0; maxItems = max; storage.nodes = new NodeType[max]; // pointer to the dynamically allocated array of nodes InitializeMemory(maxItems, storage); listData = NUL; // index of an array}

ListType::ListType(){ length = 0; maxItems = 500; storage.nodes = new NodeType[500]; InitializeMemory(500, storage); listData = NUL;}

ListType::~ListType(){ delete [] storage.nodes;}

void InsertItem(ItemType item){ // STUB: REPLACE WITH USEFUL CODE.}

Composition (containment)• Composition (or containment) means that an

internal data member of one class is defined to be an object of another class type.

A FAMILIAR EXAMPLE . . .

Private data

ComparedTo

Initialize

class ItemType

ItemType Class Interface Diagram

Sorted list contains an array of ItemType

SortedType class

IsFull

LengthIs

ResetList

DeleteItem

InsertItem

MakeEmpty

RetrieveItem

Private data:

length

info [ 0 ] [ 1 ] [ 2 ]

[MAX_ITEMS-1]

currentPos

GetNextItem

Inheritance• Inheritance is a means by which one class

acquires the properties--both data and operations--of another class.

• When this occurs, the class being inherited from is called the Base Class.

• The class that inherits is called the Derived Class.

AN EXAMPLE . . .

Inheritance

A derived class generally is longer but represents a smaller set of more specific objects than its base class (superclass)

• An object of derived class can be treated as an object of its corresponding base class, but the reverse is not true, so

• Derived object “is a” base class object through inheritance

• Reusability can be achieved via inheritance

Recall Definition of Queue• Logical (or ADT) level: A queue is an

ordered group of homogeneous items (elements), in which new elements are added at one end (the rear), and elements are removed from the other end (the front).

• A queue is a FIFO “first in, first out” structure.

Queue ADT Operations• MakeEmpty -- Sets queue to an empty state.

• IsEmpty -- Determines whether the queue is currently empty.

• IsFull -- Determines whether the queue is currently full.

• Enqueue (ItemType newItem) -- Adds newItem to the rear of the queue.

• Dequeue (ItemType& item) -- Removes the item at the front

of the queue and returns it in item.

Class interface diagram for class QueType<char>

QueType

~QueType

Enqueue

Dequeue . . .

Private Data:

‘C’ ‘Z’ ‘T’

// DYNAMICALLY LINKED IMPLEMENTATION OF QUEUE

#include "ItemType.h" // for ItemType

template<class ItemType>class QueType {public:

QueType( ); // CONSTRUCTOR~QueType( ) ; // DESTRUCTORbool IsEmpty( ) const;bool IsFull( ) const;void Enqueue( ItemType item );void Dequeue( ItemType& item );void MakeEmpty( );

private:NodeType<ItemType>* Front;NodeType<ItemType>* Rear;

59expanded by J. Goetz 59

// DERIVED CLASS CountedQue FROM BASE CLASS QueType

template<class ItemType>class CountedQue : public QueType<ItemType> // “:” CountedQue is derived

// from QueType

{public:

CountedQue( ); void Enqueue( ItemType newItem );//redefining the inherited functionvoid Dequeue( ItemType& item ); //redefining the inherited functionint LengthIs( ) const; // new// Returns number of items on the counted queue.

private:int length; // new

SAYS ALL PUBLIC MEMBERS OF QueType CAN BEINVOKED FOR OBJECTS OF TYPE CountedQue

Class interface diagram for class

CountedQue<char>

QueType

~QueType

Enqueue

Dequeue . . .

Private Data:

‘C’ ‘Z’ ‘T’

CountedQue

LengthIs

Enqueue

Dequeue . . .

Private Data:

length 3

61expanded by J. Goetz 61

// Member function definitions for class CountedQue

// Constructor initializertemplate<class ItemType> CountedQue<ItemType>::CountedQue( ) : QueType<ItemType>( )//”:” – it causes the invocation of the base-class constructor{

length = 0 ;}

template<class ItemType>int CountedQue<ItemType>::LengthIs( ) const{

return length ;}

template<class ItemType>void CountedQue<ItemType>::Enqueue( ItemType newItem )

// Adds newItem to the rear of the queue.// Increments length.

{length++;

QueType<ItemType>::Enqueue( newItem );}

template<class ItemType>void CountedQue<ItemType>::Dequeue(ItemType& item )

// Removes item from the rear of the queue.// Decrements length.

{length--;

QueType<ItemType>::Dequeue( item );} 62

// File: VirDemo.cpp// This program demonstrates the use of Polymorhism with virtual functions.#include <iostream>// specificationclass One{public: virtual void Print(); // virtual function !!!}; // end of Oneclass Two : public One{public: void Print(); // virtual because Print is virtual in One – in all derived classes as well}; // end of One // Function definitions:void One::Print(){ using namespace std; cout << "Print member function of class One" << endl;}void Two::Print(){ using namespace std; cout << "Print member function of class Two" << endl;}

void PrintTest(One* ); // prototype

int main(){ using namespace std; One* onePtr; onePtr = new One; // points to the base class cout << "Result of passing an object of class One: " ; PrintTest(onePtr); onePtr = new Two; // points to the derived class using the base class pointer cout << "Result of passing an object of class Two: "; PrintTest(onePtr); return 0;}

void PrintTest(One* ptr) { ptr->Print();} // formal parameter must be a base class type, because// an object of derived class can be treated as an object of its corresponding base class, so it can be passed also.

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