#include

#include

#include

#include

using namespace std;

std::mt$19937$ ranGen;

class Shape $\{$

public:

virtual void Scale$($float scaleFactor$)=0$;

virtual void Display$()$ const $=0$;

virtual ~Shape$()\{\}$

$\}$;

class Shape$2$D : virtual public Shape $\{$

public:

virtual float Area$()$ const $=0$;

void ShowArea$()$ const;

virtual string GetName$2$D$()$ const $=0$;

bool operator$>($const Shape$2$D& rhs$)$ const;

bool operator$<($const Shape$2$D& rhs$)$ const;

bool operator$==($const Shape$2$D& rhs$)$ const;

virtual ~Shape$2$D$()\{\}$

$\}$;

class Shape$3$D : virtual public Shape $\{$

public:

virtual float Volume$()$ const $=0$;

void ShowVolume$()$ const;

virtual string GetName$3$D$()$ const $=0$;

bool operator$>($const Shape$3$D& rhs$)$ const;

bool operator$<($const Shape$3$D& rhs$)$ const;

bool operator$==($const Shape$3$D& rhs$)$ const;

virtual ~Shape$3$D$()\{\}$

$\}$;

const float PI $=3\mathrm{.}14159$f;

$//$ Add 'override' specifier to virtual function implementations

void Shape$2$D::ShowArea$()$ const $\{$

cout $<<$ "The area of the $"<<$ GetName$2$D$()<<"$ is : $"<<$ Area$()<<$ endl;

$\}$

bool Shape$2$D::operator$>($const Shape$2$D& rhs$)$ const $\{$

return $($this$->$Area$()>$ rhs$.$Area$())$;

$\}$

bool Shape$2$D::operator$<($const Shape$2$D& rhs$)$ const $\{$

return $($this$->$Area$()<$ rhs$.$Area$())$;

$\}$

bool Shape$2$D::operator$==($const Shape$2$D& rhs$)$ const $\{$

return $($this$->$Area$()==$ rhs$.$Area$())$;

$\}$

void Shape$3$D::ShowVolume$()$ const $\{$

cout $<<$ "The volume of the $"<<$ GetName$3$D$()<<"$ is : $"<<$ Volume$()<<$ endl;

$\}$

bool Shape$3$D::operator$>($const Shape$3$D& rhs$)$ const $\{$

return $($this$->$Volume$()>$ rhs$.$Volume$())$;

$\}$

bool Shape$3$D::operator$<($const Shape$3$D& rhs$)$ const $\{$

return $($this$->$Volume$()<$ rhs$.$Volume$())$;

$\}$

bool Shape$3$D::operator$==($const Shape$3$D& rhs$)$ const $\{$

return $($this$->$Volume$()==$ rhs$.$Volume$())$;

$\}$

class Square : public Shape$2$D $\{$

private:

float side;

public:

Square$($float $=0\mathrm{.}0)$;

~Square$()\{\}$

float Area$()$ const override;

string GetName$2$D$()$ const override;

void Scale$($float scaleFactor$)$ override;

void Display$()$ const override;

$\}$;

class Triangle : public Shape$2$D $\{$

private:

float base, height;

public:

Triangle$($float $=0\mathrm{.}0,$ float $=0\mathrm{.}0)$;

~Triangle$()\{\}$

float Area$()$ const override;

string GetName$2$D$()$ const override;

void Scale$($float scaleFactor$)$ override;

void Display$()$ const override;

$\}$;

class Circle : public Shape$2$D $\{$

private:

float radius;

public:

Circle$($float $=0\mathrm{.}0)$;

~Circle$()\{\}$

float Area$()$ const override;

string GetName$2$D$()$ const override;

void Scale$($float scaleFactor$)$ override;

void Display$()$ const override;

$\}$;

class TriangularPyramid : public Shape$3$D$,$ private Triangle $\{$

private:

float height;

public:

TriangularPyramid$($float $=0\mathrm{.}0,$ float $=0\mathrm{.}0,$ float $=0\mathrm{.}0)$;

~TriangularPyramid$()\{\}$

float Volume$()$ const override;

string GetName$3$D$()$ const override;

void Scale$($float scaleFactor$)$ override;

void Display$()$ const override;

$\}$;

class Cylinder : public Shape$3$D$,$ private Circle $\{$

private:

float height;

public:

Cylinder$($float $=0\mathrm{.}0,$ float $=0\mathrm{.}0)$;

~Cylinder$()\{\}$

float Volume$()$ const override;

string GetName$3$D$()$ const override;

void Scale$($float scaleFactor$)$ override;

void Display$()$ const override;

$\}$;

class Sphere : public Shape$3$D$,$ private Circle $\{$

private:

float radius;

public:

Sphere$($float $=0\mathrm{.}0)$;

~Sphere$()\{\}$

float Volume$()$ const override;

string GetName$3$D$()$ const override;

void Scale$($float scaleFactor$)$ override;

void Display$()$ const override;

$\}$;

$//$ Implementations of Shape$2$D and Shape$3$D functions

float Square::Area$()$ const $\{$

return side $*$ side;

$\}$

string Square::GetName$2$D$()$ const $\{$

return "Square";

$\}$

void Square::Scale$($float scaleFactor$)\{$

side $=$ side $*$ scaleFactor;

$\}$

void Square::Display$()$ const $\{$

Shape$2$D::ShowArea$()$;

cout $<<$ "Length of a side: $"<<$ side $<<$ endl;

$\}$

float Triangle::Area$()$ const $\{$

return $0\mathrm{.}5*$ base $*$ height;

$\}$

string Triangle::GetName$2$D$()$ const $\{$

return "Triangle";

$\}$

void Triangle::Scale$($float scaleFactor$)\{$

base $=$ base $*$ scaleFactor;

height $=$ height $*$ scaleFactor;

$\}$

void Triangle::Display$()$ const $\{$

Shape$2$D::ShowArea$()$;

cout $<<$ "Base: $"<<$ base $<<$ endl;

cout $<<$ "Height: $"<<$ height $<<$ endl;

$\}$

float Circle::Area$()$ const $\{$

return PI $*$ radius $*$ radius;

$\}$

string Circle::GetName$2$D$()$ const $\{$

return "Circle";

$\}$

void Circle::Scale$($float scaleFactor$)\{$

radius $=$ radius $*$ scaleFactor;

$\}$

voidhe provided C$++$ code defines a hierarchy of classes representing geometric shapes in both $2$D and $3$D$.$ The classes include Shape, Shape$2$D$,$ Shape$3$D$,$ and specific shapes like Square, Triangle, Circle, TriangularPyramid, Cylinder, and Sphere. The code uses virtual functions and operator overloading to handle area, volume, and comparisons between shapes.

Explanation:

The Scale function in the Square, Triangle, Circle, TriangularPyramid, Cylinder, and Sphere classes does not follow the virtual functio