Asymptotic vs real-world complexity Let's say an algorithm has an asymptotic time complexity of $\Theta(N)$. However in practice, $N$ is bound by a small upper limit (e.g. the size of a character set). Can we then say the complexity is $\Theta(1)$? Or is there a better way of describing the performance of an algorithm in a particular real-life situation?
If $N$ is bounded by a small upper limit, asymptotics cease to be useful. At that point you want either exact operation counts, or even better just measure actual speed.