Brute force solution for number of ways to make a change in C++

num_ways_to_make_change.cpp

#include <vector>
#include <set>

//Just a brute force recursive solution, to be used as a first step in finding the optimal solution, i.e. by adding memoization
//and then possibly flipping into a table-based bottom-up solution
namespace with_multiset
{
    void make_change (int amount, std::vector<int> const &coins, std::set<std::multiset<int>> &changes, std::multiset<int> partial = {})
    {
        if (amount == 0)
        {
            changes.insert(partial);
            return;
        }

        int res = 0;
        for (auto c : coins)
        {
            if (c <= amount)
            {
                auto where = partial.insert(c);
                make_change(amount - c, coins, changes, partial);
                partial.erase(where);
            }
        }
    }
    std::set<std::multiset<int>> make_change (int amount, std::vector<int> const &coins)
    {
        std::set<std::multiset<int>> changes;
        make_change(amount, coins, changes);
        return changes;

    }
}//namespace with_multiset