Smallest Enclosing Circle : 2-Dimension Problem (Written in Korean. Output is the smallest enclosing circle's position on the first line and the radius on the second line.)
Smallest Enclosing Sphere : 3-Dimension Problem
Let P(X, Y, Z) = (Average(x(i)), Average(y(i)), Average(z(i)))
Average(x(i)) = Sum(x(i)) / N
Average(y(i)) = Sum(y(i)) / N
Average(z(i)) = Sum(z(i)) / N
P is inside of the points' convex hull.
Now find the farthest point(M) to P.
Move P toward M a little bit and the ratio should be small and decreasing.
If there is no such a movement, that is the answer.
Total Time Complexity is O(N * constant number)
(We can reduce 'N' by getting convex hull.)