Sum of squares complex numbers in descending order - c++

Question

I would like to calculate the sum of squares complex numbers in descending order by using three source codes(Complex2.h, Complex2.cpp, Vector3)
ex) (5+6i)^2 (3+4i)^2 (1+2i)^2....
I'm trying to add and change some codes in Vector3 to get the result, but stuck in the middle now..
Does anyone give some advice?
//Complex2.h
#ifndef COMPLEX2_H_INCLUDED
#define COMPLEX2_H_INCLUDED
#include <ostream>
using namespace std;
class Complex2 {
double rPart, iPart; // real part and imaginary part
public:
// operator
Complex2(double r = 0, double i = 0) : rPart(r), iPart(i) {}
Complex2 conj() const {
return Complex2(rPart, -iPart);
}
Complex2 operator+(const Complex2 &c) const;
Complex2 operator+(double r) const;
Complex2 operator-(const Complex2 &c) const;
Complex2 operator-(double r) const;
Complex2 operator*(const Complex2 &c) const;
Complex2 operator*(double r) const;
Complex2 operator/(const Complex2 &c) const;
Complex2 operator/(double r) const;
Complex2& operator+=(const Complex2 &c);
Complex2& operator-=(const Complex2 &c);
Complex2& operator*=(const Complex2 &c);
Complex2& operator/=(const Complex2 &c);
bool operator==(const Complex2 &c) const;
bool operator!=(const Complex2 &c) const;
double real() const { return rPart; }
double imag() const { return iPart; }
void display() const; // print complex value
friend Complex2 operator+(double r, const Complex2& c);
friend ostream& operator<<(ostream& os, const Complex2& c);
};
#endif
//Complex2.cpp
#include <iostream>
#include "Complex2.h"
using namespace std;
Complex2 Complex2::operator+(const Complex2 &c) const
{
return Complex2(rPart + c.rPart, iPart + c.iPart);
}
Complex2 Complex2::operator+(double r) const
{
return Complex2(rPart + r, iPart);
}
Complex2 Complex2::operator-(const Complex2 &c) const
{
return Complex2(rPart - c.rPart, iPart - c.iPart);
}
Complex2 Complex2::operator-(double r) const
{
return Complex2(rPart - r, iPart);
}
Complex2 Complex2::operator*(const Complex2 &c) const
{
return Complex2(rPart * c.rPart - iPart * c.iPart, rPart * c.iPart + iPart * c.rPart);
}
Complex2 Complex2::operator*(double r) const
{
return Complex2(rPart * r, iPart * r);
}
Complex2 Complex2::operator/(const Complex2 &c) const
{
double d = c.rPart * c.rPart + c.iPart * c.iPart;
return Complex2((rPart * c.rPart + iPart * c.iPart) / d, (iPart * c.rPart - rPart * c.iPart) / d);
}
Complex2 Complex2::operator/(double r) const
{
return Complex2(rPart / r, iPart / r);
}
Complex2& Complex2::operator+=(const Complex2 &c)
{
rPart += c.rPart; iPart += c.iPart;
return *this;
}
Complex2& Complex2::operator-=(const Complex2 &c)
{
rPart -= c.rPart; iPart -= c.iPart;
return *this;
}
Complex2& Complex2::operator*=(const Complex2 &c)
{
*this = *this * c;
return *this;
}
Complex2& Complex2::operator/=(const Complex2 &c)
{
*this = *this / c;
return *this;
}
bool Complex2::operator==(const Complex2 &c) const
{
return rPart == c.rPart && iPart == c.iPart;
}
bool Complex2::operator!=(const Complex2 &c) const
{
return rPart != c.rPart || iPart != c.iPart;
}
void Complex2::display() const
{
cout << "(" << rPart;
if (iPart > 0)
cout << "+j" << iPart;
else if (iPart < 0)
cout << "-j" << -iPart;
cout << ")";
}
Complex2 operator+(double r, const Complex2& c)
{
return Complex2(r + c.rPart, c.iPart);
}
ostream& operator<<(ostream& os, const Complex2& c)
{
os << "(" << c.rPart; // print real part
if (c.iPart > 0) // print imaginary part
os << "+j" << c.iPart;
else if (c.iPart < 0)
os << "-j" << -c.iPart;
cout << ")";
return os;
}
//Vector3.cpp
#include <iostream>
#include <vector>
#include <cstdlib>
#include <ctime>
#include <algorithm>
#include "Complex2.h";
using namespace std;
template<typename T> struct GREATER {
bool operator()(const T& a, const T& b) const {
return a > b;
}
};
int main()
{
srand((unsigned)time(NULL)); // Initialize random number generation
vector<Complex2> cv1(5);
cout << "vector1 : ";
for (auto &c : cv1) {
c = rand() % 100; // 0~99 random number generation
cout << c << " ";
}
sort(cv1.begin(), cv1.end(), GREATER<int>()); // sort algorithm in descending
cout << endl << "sorted vector1 : ";
for (auto c : cv1)
cout << c << " ";
cout << endl << endl;
vector<Complex2> cv2(5);
cout << "vector2 : ";
for (auto &c : cv2) {
c = rand() % 100; // 0~99 random number generation
cout << c << " ";
}
sort(cv2.begin(), cv2.end(), GREATER<int>()); // sort algorithm in descending
cout << endl << "sorted vector2 : ";
for (auto c : cv2)
cout << c << " ";
cout << endl << endl;
// vector for saving the merged result
vector<Complex2> cv3(cv1.size() + cv2.size());
// Save the result cv1 plus cv2 as cv3
merge(cv1.begin(), cv1.end(),
cv2.begin(), cv2.end(), cv3.begin(), GREATER<int>());
cout << "the result of merged vector1 and vector2 : ";
for (auto c : cv3)
cout << c << " ";
cout << endl << endl;
return 0;
}

Answer 1

To do this, all you actually need is to define operator>:
bool Complex2::operator>(const Complex2 &c) const
{
return rPart * rPart + iPart * iPart > c.rPart * c.rPart + c.iPart * c.iPart;
}
Then you can call std::sort and std::merge with:
std::sort(cv1.begin(), cv1.end(), std::greater<Complex2>());
std::merge(cv1.begin(), cv1.end(), cv2.begin(), cv2.end(),
cv3.begin(), std::greater<Complex2>());
Side note: why not use std::complex?

Answer 2

One thing which is very important here:
It is impossible to order complex numbers!!!
You are talking about ordering them, and you seem to be looking for some ordering function, but you need to know that, whatever the means of ordering complex numbers, the ordering must satisfy following argument:
Order(Number1, Number2) AND Order(Number2, Number3) => Order(Number1, Number3)
This expression can't be true, for any kind of ordering you might be inventing (at least for complex numbers, for real numbers ordering is simple), so your question about "descending order" of complex numbers cannot make sense.
The whole explanation can be found here.