What is the (worst-case) time analysis for the following loop?

Question

Here is some code for an integer variable n:

while (n > 0)     
    {         
        n = n/10; // Use integer division     
    } 

I am trying to find the worst-case time analysis for this loop. O(n) is new to me and I am having difficulty with it. Wouldn't this just be O(n)?

Answer 1

Actually that algorithm would be O(log(n)). You are dividing by 10 (knocking off a 0 each time through the loop).

Generally an algorithm is O(n) if it scales linearly with the size of n, but for this, if you increase the size of n by a factor of 10, you only have one more iteration, instead of 10x as many iterations through the loop.

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As requested here are a couple of sites with a brief primer. A quick google search will turn up many more:

http://rob-bell.net/2009/06/a-beginners-guide-to-big-o-notation/ http://www.daveperrett.com/articles/2010/12/07/comp-sci-101-big-o-notation/