Time complexity of euclidean distance

Question

How can I calculate the time compelxity of euclidean distance, which is calculated with this formula:

Answer 1

Well, let's see. How many operations do we have?

• n subtractions (xi - yi)
• n squares of the previous
• n-1 further additions to add them up
• one square root at the end.

So each of these is (at most) linear in n, and hence so is the whole algorithm. (Assuming that determining the xi and yi are also no worse than O(1).)