Question

I’m trying to implement the following in Java.

Given a list of circles of different sizes (possibly) and positions, determine a large circle (position and size) which just exactly encloses all the circles.

public class Circle {
    public int x, y, radius;
}

Any ideas?

Answer 1

I’d try to find the topmost western point, then the southern downmost point, then make a circle with those points as diameter.
In order to find those points, I’d cycle through the center of the circles and their radius.

So it ends up in:

 initiate max object and min object to average center of circle and zero radius
 For every circle object
     calculate topmost western point of the circle
     check if further away than current point
     if further, calculate position of topmost western point required to pass over this new point and set as new min object
     calculate down most eastern point of the circle
     do the same as previous step, only for max object
 make a circle with center equals to middle of min-max line and radius equals to half min-max line length

If you are the bookworm type, good university libraries stock this: E.Welzl, Smallest Enclosing Disks (Balls and Ellipsoids), in H. Maurer (Ed.), New Results and New Trends in Computer Science, Lecture Notes in Computer Science, Vol. 555, Springer-Verlag, 359–37 (1991)

And if you want to read C++ code and adapt it to Java, http://miniball.sourceforge.net/.
With circles, d=2, of course.