The key takeaway for me is that, we can do worst-, best- case analysis on anything of the asymptotic bounded functions. To me, that shows the independence of Big O vs. worst case analysis. Thanks!
I occasionally see these terms used and I'm not really sure what is meant by all of them. Is it possible for an asymptotic bound that is not Big $\\Theta$ bound to be "tight"? What does it mean for ...
What does it mean that the bound $2n^2 = O(n^2)$ is asymptotically tight while $2n = O(n^2)$ is not? We use the o-notation to denote an upper bound that is not asymptotically tight. The definitions...
The last times i was searching a lot to understanding Big O notation or in general asymptotic notations concepts because i didnt hear about it or them before starting studying in computer science....
In short asymptotic complexity is a relatively easy to compute approximation of actual complexity of algorithms for simple basic tasks (problems in a algorithms textbook). As we build more complicated programs the performance requirements change and become more complicated and asymptotic analysis may not be as useful.
The asymptotic growth of $4 \log n$ is referred to as $\Theta (\log n)$. You will have to look at the definition of asymptotic growth to see why that is the case, but intuitively, it is the growth of a function when we discard constant factors and only look at the function "in the limit".
From what I have learned asymptotically tight bound means that it is bound from above and below as in theta notation. But what does asymptotically tight upper bound mean for Big-O notation?
The pattern in general is that loop count = lg (n)+1, where "lg" is read "log base 2", which means that the asymptotic time complexity is O (lg (n)) See for yourself with the following python code snippet:
In asymptotic notation the transivity holds, however what happens when we have small o such as if f (n)= o (h (n)) does that means that also g (n)=o (h (n)) holds?
