Find K nearest Points to Point P in 2-dimensional plane

Question

Source: AMAZON INTERVIEW QUESTION

Given a point P and other N points in two dimensional space, find K points

Answer 1

// point_type pt, length_sq(p) { return pt[0] * pt[0] + pt[1] * pt[1]}
// std::vector points to search.
// The algorithm should recursion depth to 
//       O(k * log(points.size())), and
// running time to O(points.size()).

std::nth_element(
               points.begin(),
               points.begin() + k,
               points.end(),
               [&pt](point_type const & a)
               {
                    return length_squared(a - pt);
               });

// points[0], ... , points[k - 1] are the closest points to pt