How can I make min_element catch ALL points with the lowest value?

Question

I'm writing a program to calculate the perimeter of a convex hull using the graham scan and need to find the lowest y coordinate in a set of data points. I'm using std::min_element(vector.begin(), vector.end()) with an overloaded < operator in my struct point. The problem is that some points may share the same lowest y coordinate, and in that case I need to compare them using their x values. Is there any quick cheat to check if any other points are sharing the same y as the min_element without having to loop through everything?

struct:

struct cord{
        cord():x(0),y(0){}
        int x,y;
        bool operator<(const cord &p) const { return y < p.y; }
};

typedef std::vector<cord>::iterator vecIter;

function call:

vecIter lowestPoint =
                std::min_element(points.begin(), points.end());

std::cout << "the lowest point of the data set is: " << "(" <<
                lowestPoint->x << "," << lowestPoint->y << ")"  << std::endl;

Answer 1

So, just something like this? (to replace your existing operator< function)

bool operator<(const cord &p) const
{
   if (y != p.y)
     return y < p.y;
   else
     return x < p.x;
}