For each of the following problems, write a program or a program segment that performs the specified action.Each problem refers to class Polygon (Fig. L 11.15). This class contains a dynamically allocated array of x-coordinates and a dynamically allocated array of y-coordinates. These coordinates store the polygon's vertices. The Polygon constructor takes the initial vertex for the Polygon.

1 // Coding Exercises: Polygon.cpp
2 // class Polygon definition
3 #include
4 using std::ostream;
5 using std::endl;
6
7class Polygon
8 {
9 public:
10 Polygon( int = 0, int = 0 );
11 ~Polygon();
12
13 void addVertex( int, int );
14 int getNumVertices() const;
15 private:
16 int *xPts;
17 int *yPts;
18 int numVertices;
19 }; // end class Polygon
20
21 // default constructor
22 Polygon::Polygon( int x, int y )
23 {
24 xPts = new int[ 1 ];
25 yPts = new int[ 1 ];
26
27 xPts[ 0 ] = x;
28 yPts[ 0 ] = y;
29 numVertices = 1;
30 } // end class Polygon constructor
31
32 // destructor
33 Polygon::~Polygon()
34 {
35 delete [] xPts;
36 delete [] yPts;
37 } // end class Polygon destructor
38
39 // function addVertex definition
40 void Polygon::addVertex( int x, int y )
41 {
42 int *copyX = new int[ numVertices + 1 ];
43 int *copyY = new int[ numVertices + 1 ];
44
45 for ( int i = 0; i < numVertices; i++ )
46 {
47 copyX[ i ] = xPts[ i ];
48 copyY[ i ] = yPts[ i ];
49 } // end for
50
51 copyX[ numVertices ] = x;
52 copyY[ numVertices ] = y;
53
54 delete [] xPts;
55 delete [] yPts;
56
57 xPts = copyX;
58 yPts = copyY;
59 ++numVertices;
60 } // end function addVertex
61
62 // function getNumVertices
63 int Polygon::getNumVertices() const
64 {
65 return numVertices;
66 } // end function getNumVertices
1. Overload the stream-insertion operator << to output a Polygon object. The prototype for the << operator is
as follows:
ostream &operator<<( ostream &, const Polygon & );
2. Create a copy constructor for class Polygon. The prototype for the copy constructor is as follows:
Polygon( Polygon * );
3. Overload the == operator to compare two Polygons for equality. This member function should return a
boolean value. The prototype for the == operator is as follows:
bool operator==( Polygon & );
4. Overload the = operator to assign one Polygon object to another. This member function should return a const reference to the Polygon object invoking the member function. This member function also should test for self assignment. The prototype for the = operator is as follows:
const Polygon &operator=( const Polygon & );
5. Write a test program that does the follows: 
a. Get user input to create a polygon called polygon1. You can do this by first asking the user for the number of vertices in the polygon and then asking for the (x,y) pairs for each vertex. 
b. Output the polygon1 using your overloaded << operator function
c. Use the copy constructor to create another polygon called polygon2. 
d. Output polygon2
e. Ask the user to input another polygon called polygon3. 
f. Use your equality operator to compare polygon1 and polygon3. Output the result. 
g. Create a new polygon called polygon4 using the default constructor
h. Assign polygon3 to polygon4 using your overloaded assignment operator function. 
i. Output polygon4.