Sorting complex numbers by their argument

March 26, 2022

I have a vector of complex numbers and I need to sort them by their argument. Sadly, the numbers have type complex<int>, so function arg(c) returns an integer in range [-3,3] instead of a float and the numbers can’t be sorted properly.

I’ve tried also

typedef complex<int> ci;
typedef complex<double> cd;

vector<ci> a;
sort(a.begin(), a.end(), [](ci v, ci u) { return arg(cd(v)) < arg(cd(u)); });

but it does not work either (compilation error: no matching function for call to ‘std::complex<double>::complex(ci&)).
Can I sort these numbers without changing their type?

>Solution :

You get the error because there is no converting constructor from std::complex<int> to std::complex<double> you have to construct the std::complex<double> by passing real and imaginary parts to the constructor:

#include <vector>
#include <complex>
#include <algorithm>

int main() {

    std::vector<std::complex<int>> a;
    std::sort(a.begin(), a.end(), [](const auto& v,const auto& u) {
        return std::arg(std::complex<double>(v.real(),v.imag())) < std::arg(std::complex<double>(u.real(),u.imag())); 
    });
}

Note that you can also use atan2 directly without constructing the std::complex<double> as mentioned by user17732522.

Last but not least, reconsider if you really need int with std::complex. From cppreference:

T – the type of the real and imaginary components. The behavior is unspecified (and may fail to compile) if T is not float, double, or long double and undefined if T is not NumericType.

Basically this means that you need to check the implementation you are using whether it supports std::complex<int> at all.