Ordering Points based on their distance to each other ?

Question

I have a vector of 3 Points A, B and C I want to order this vector based on the distance between those points, say the biggest distance is between B and C and than C and A and

Answer 1

If the question is rephrased: Get all Manhattan distances between the points in a sorted vector:

#include 
#include 
#include 

struct Point { int x; int y; };
struct ManhattanDistance {
    std::size_t a;
    std::size_t b;

    int value;

    ManhattanDistance(std::size_t index_a, const Point& a, std::size_t index_b, const Point& b)
    :   a(index_a), b(index_b), value(abs(b.x - a.x) + abs(b.y - a.y))
    {}

    operator int () const { return value; }
};

inline std::ostream& operator << (std::ostream& stream, const ManhattanDistance& x) {
    return stream << x.a << " - " << x.b << ": " << x.value;
}

int main()
{
    typedef std::pair Pair;
    std::vector points = { {0,0}, {2,2}, {3,3}, {4,4}, {5,5} };
    std::vector distances;
    distances.reserve(points.size() * (points.size() - 1) / 2);
    for(std::size_t a = 0; a < points.size() - 1; ++a) {
        for(std::size_t b = a + 1; b < points.size(); ++b) {
            distances.push_back(ManhattanDistance(a, points[a], b, points[b]));
            std::cout << "Add: " << distances.back() << std::endl;
        }
    }
    std::sort(distances.begin(), distances.end(), std::greater());
    for(const auto& d: distances) std::cout << "Sorted: "  << d << '\n';
    std::cout << std::endl;
    return 0;
}