Power Set

I need to use a recursive algorithm to find the power set of a given set i.e a set of all the subsets of a given set.
For example, if a set is {a,b,c}, the power set happens to be a set of {a},{b},{c},{a,b}{a,c},{b,c},{a,b,c}.
I know that such a thread existed earlier on this forum but the solutions were not very elaborate. There were a lot of codes. Can someone instead give me the algorithm instaed of the source code. It will be of great help to me . I am just beginning to learn recursive algorithms

Say, original set contains element a. Then all subsets are divided in 2 classes: ones containing a and ones not. Note that set of sets containing a may be obtaining by adding a to each of sets not containing a. And that's the recursion.

Code:

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void comb_rec(string a, string pref="")
{
        if(!a.empty())
        {
                comb_rec(a.substr(1),pref);
                comb_rec(a.substr(1),pref+a[0]);
        }
        else if(!pref.empty())
                cout<<pref<<endl;
}

int main()
{
    comb_rec("abc");
    return 0;
}

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