When should auxiliary functions be class members?

[Jazpy]

I have the following question, if there are 2 classes that consist of a private variable of type std::map , and a constructor that reads data from a save file with the help of a function, which of the following 2 examples would be considered correct or "better":

A.h

class A{
private:
    std::map < int, int > the_map;
    void read_from_file();

public:
    A();
}

A.cpp

A::A()
{
    // whatever goes here

    read_from_file():
}

A::read_from_file()
{
    // reads from file into the_map
}

where the auxiliary function is declared as a private member, or example B:

B.h

class B{
private:
    std::map < int, int > the_map;

public:
    B();
}

B.cpp

read_from_file(std::map < int, int >& map);

B::B()
{
    // whatever goes here

    read_from_file(the_map):
}

read_from_file(std::map < int, int >& map)
{
    // reads from file into map
}

where the auxiliary function is not a member function, I find this worrying because with a large class where there are a lot of functions that might need to modify private members, the .h file might get too cluttered, but the little things I know about good coding practices tell me that functions that modify private members should either be members or friends (a third idea that just occurred to me).