Set of pointers to objects with custom comparator

Question

I have a set of pointers and I want the set to be sorted in a specific order.

I came up with this code and it works as expected:

#include <string>
#include <iostream>
#include <set>

class Data
{
public:
  std::string name;
  int data;
  bool operator < (const Data& other) const
  {
    return name < other.name; 
  }

  bool operator < (const Data* other) const
  {
    std::cout << "never called ";
    return name < other->name;
  }
};

struct DataComparator
{
  bool operator()(const Data* lhs, const Data* rhs) const 
  {
    return *lhs < *rhs;
  }
};

int main() {
  Data d1{ "bb", 1 };
  Data d2{ "cc", 2 };
  Data d3{ "aa", 3 };

  std::set<Data*, DataComparator> s;
  s.insert(&d1);
  s.insert(&d2);
  s.insert(&d3);

  // print set members sorted by "name" field
  for (auto& d : s)
    std::cout << d->name << "\n";

  return 0;
}

What bothers me is the fact that I need to use the DataComparator struct in order to implement a custom sort order. I'd like the comparator be part of the Data class. I tried to implement the bool operator < (const Data* other) const class member and declare the set as std::set<Data*> s;, but now the operator < function is (unsurprisingly) never called and the sort order is by pointer address.

Is there some way to implement the custom comparator directly in the Data class so I can just have this:

 std::set<Data*> s;
 ...         
 // print set members sorted by "name" field
 for (auto& d : s)
   std::cout << d->name << "\n";

Answer 1

Is there some way to implement the custom comparator directly in the Data class so I can just have [stuff]:

No. I'd write a template

template <typename T>
struct PointerLess
{
    bool operator()(const T * lhs, const T * rhs) const
    {
        return *lhs < *rhs;
    }
};

Then you'd have std::set<Data*, PointerLess<Data>> etc.