Thread: Better algorithm for this ? (generating combinations)

The problem is to generate all possible unique selections of n numbers from a given set of size > n.
I've pretty much done it by brute force, as the number of final results should be same whichever way I choose. If a better way is not possible, I'd like suggestions about simple optimizations.

Code:

std::deque<std::set<int>> find_combinations(const std::set<int>& U,unsigned int n)
{
    std::deque<std::set<int>> result;
    if(n<1 || U.size()<n)//Nothing Happens Here !
        {}
    else if(n==1) // The Universal input set is broken up and redistributed.
    {
        for(auto x:U)
            result.push_back(std::set<int>({x}));
    }
    else // Recursion FTW, no comments !!
    {
        std::set<int> temp(U);
        for(auto x:U)
        {
            temp.erase(x);
            auto partial_result = find_combinations(temp,n-1);
            for(auto& y:partial_result)
                y.insert(x);
            result.insert
            (
                std::begin(result),
                std::begin(partial_result),
                std::end(partial_result)
            );
        }
    }
    return result;
}

I noticed that having the return container a deque makes this much faster than if a vector or list is used. Why ?
Also, is it worth the trouble trying to do it iteratively?
Finally, can anyone help me determining the complexity of this function ?
(I think it is something near (log base n U.size() )^ n) but I'm probably very very wrong about that.)

Btw, here is a main you can use to test it.

Code:

int main(int argc,char** argv)
{
    std::set<int> input;
    for(int i=0;i<atoi(argv[1]);i++)
        input.insert(i);
    
    auto foo = find_combinations(input,atoi(argv[2]));
    
//     for(auto x:foo) //displaying results
//     {
//         for(auto y:x)
//             std::cout<<y<<'\t';
//         std::cout<<std::endl;
//     }
}