When talking about theory, I have two points:
- First: O(N) < O(N log N), so your example isn't good
- Second: Your description of Radix sort is actually O(N), and the standard sorting algorithms are O(N log N), so it again isn't a surprise, theoretically speaking...
The thing that Big-O knowingly hides is the constant factor. For example, some algorithms are 2N and some are 1000N. For large enough N, this may not matter, but for any reasonably sized N, it does.
In practice, of course that Big-O is not sufficient to describe absolute algorithm performance, as it depends on so many factors such as implementation, computer architecture, relative size of data, etc. But, when looking at an algorithm and knowing its Big-O complexity can often be a useful input to your decision on whether to use it. So I disagree with this Big-O bashing...
The thing that Big-O knowingly hides is the constant factor. For example, some algorithms are 2N and some are 1000N. For large enough N, this may not matter, but for any reasonably sized N, it does.
In practice, of course that Big-O is not sufficient to describe absolute algorithm performance, as it depends on so many factors such as implementation, computer architecture, relative size of data, etc. But, when looking at an algorithm and knowing its Big-O complexity can often be a useful input to your decision on whether to use it. So I disagree with this Big-O bashing...