What would be the most elegant way too fix the following code:

#include <vector>
#include <map>
#include <set>
using namespace std;

typedef map< int, int > row_t;
typedef vector< row_t > board_t;
typedef row_t::iterator area_t;

bool operator< ( area_t const& a, area_t const& b ) {
    return( a->first < b->first );
};

int main( int argc, char* argv[] )
{
    int row_num;
    area_t it;

    set< pair< int, area_t > > queue;
    queue.insert( make_pair( row_num, it ) ); // does not compile
};

One way to fix it is moving the definition of less< to namespace std (I know, you are not supposed to do it.)

namespace std {
    bool operator< ( area_t const& a, area_t const& b ) {
        return( a->first < b->first );
    };
};

Another obvious solution is defining less than< for pair< int, area_t > but I'd like to avoid that and be able to define the operator only for the one element of the pair where it is not defined.