///
/// vector.h
///
///


#ifndef VECTOR_H
#define VECTOR_H



// A Vector in space
struct Vector
{
public:

    double x;
    double y;
    double z;

    Vector operator- ();
    Vector operator* ( const double d );
    Vector operator/ ( const double d );
    Vector operator+= ( const Vector& v );
    Vector operator-= ( const Vector& v );
    Vector operator*= ( const double d );
    Vector operator/= ( const double d );
    void operator++ ();
    void operator-- ();

    // Get the length of a Vector
    double length();

    // Get the unit Vector with length 1
    Vector unit();

};

Vector operator+ ( const Vector& v1, const Vector& v2 );
Vector operator- ( const Vector& v1, const Vector& v2 );
double operator* ( const Vector& v1, const Vector& v2 );

// Return a Vector
Vector newVector( double x, double y, double z );

// Get the distance between two Vectors
double dist( Vector v1, Vector v2 );

// Create the cross product between a and b
Vector crossproduct( Vector a, Vector b );



# endif // VECTOR_H

///
/// vector.cpp
///
///


#include "vector.h"
#include <cmath>



Vector operator+ ( const Vector& v1, const Vector& v2 )
{
    return newVector( v1.x + v2.x, v1.y + v2.y, v1.z + v2.z );
}

Vector operator- ( const Vector& v1, const Vector& v2 )
{
    return newVector( v1.x - v2.x, v1.y - v2.y, v1.z - v2.z );
}

double operator* ( const Vector& v1, const Vector& v2 )
{
    return v1.x*v2.x + v1.y*v2.y + v1.z*v2.z;
}

Vector Vector::operator- ()
{
    return newVector( -this->x, -this->y, -this->z );
}

Vector Vector::operator* ( const double d )
{
    return newVector( this->x * d, this->y * d, this->z * d );
}

Vector Vector::operator/ ( const double d )
{
    return newVector( this->x / d, this->y / d, this->z / d );
}

Vector Vector::operator+= ( const Vector& v )
{
    *this = *this + v;
    return *this;
}

Vector Vector::operator-= ( const Vector& v )
{
    *this = *this - v;
    return *this;
}

Vector Vector::operator*= ( const double d )
{
    *this = *this * d;
    return *this;
}

Vector Vector::operator/= ( const double d )
{
    *this = *this / d;
    return *this;
}

void Vector::operator++ ()
{
    *this += this->unit();
}

void Vector::operator-- ()
{
    *this -= this->unit();
}



// Return a Vector
Vector newVector( double x, double y, double z )
{
    Vector v;
    v.x = x;
    v.y = y;
    v.z = z;

    return v;
}


// Get the length of a Vector
double Vector::length()
{
    return sqrt( this->x*this->x + this->y*this->y + this->z*this->z );
}

Vector Vector::unit()
{
    return *this / this->length();
}


// Get the distance between two Vectors
double dist( Vector v1, Vector v2 )
{
    return sqrt( (v2.x-v1.x)*(v2.x-v1.x) + (v2.y-v1.y)*(v2.y-v1.y) + (v2.z-v1.z)*(v2.z-v1.z) );
}

// Create the cross product between a and b
Vector crossproduct( Vector a, Vector b )
{
    return newVector( a.y*b.z - a.z*b.y, a.z*b.x - a.x*b.z, a.x*b.y - a.y*b.x );
}



/// End of vector.cpp
///

class Num{	public:		// automatic type conversion		Num(int x) : n(x) {}		int getNum( ) const		{			return n;		}		// member		Num operator+(const Num& rhs) const		{			return n + rhs.n;		}	private:		int n;};int main( ){	Num a(5);	// not allowed	Num sum = 7 + a;	return 0;}$ g++ temp.cpptemp.cpp: In function 'int main()':temp.cpp:28: error: no match for 'operator+' in '7 + a'

class Num{	public:		// automatic type conversion		Num(int x) : n(x) {}		int getNum( ) const		{			return n;		}	private:		int n;};// freeNum operator+(const Num& lhs, const Num& rhs){	return Num(lhs.getNum( ) + rhs.getNum( ));}int main( ){	Num a(5);	// *is* allowed	Num sum = 7 + a;	return 0;}