we know these stuff ...

I know that many of you know these stuff, but I think some still do not ;)
This article is intended to give just an overview on the analysis of algorithms, as there are many algorithms out there to give a solution for the same problem I think every programmer should know why they use which algorithm in which particular situation.
I hope you understand my intention and give me more detailled feedback what hightlights you would expect in further articles.

I love how you are treating O-notation as sets. It's unfortunate that you don't do this consistently though. For me this lead to a lot of confusion when I first learned about O-notation. Perhaps you could use T(n) in theta(n^2) instead of T(n) equals theta(n^2)? The former notation leads to paradoxes like n = O(n) = O(2n) = 2n.

I would not have read this blog post but for this comment. @petereigenschink Awesome use of notation! Superlike!

Thanks for your comment, I am glad to hear that you liked my article :)
I know what you mean, but as the use of the equal sign instead of "in" is part of the Landau-Notation (Big O-Notation), it is still required to use it in such cases to be correct.
Many people really do not treat them as sets, but I think the use of the Landau-Symbols as what they are allows to give the runtime in a much more elegant way.

I loved this post Peter. Extremely well explained.

"Before you start reading I would strongly recommend you to get yourself a short introduction into Landau-notation or just the idea behind the use of Big O, \Omega and \Theta notation, as we will make use of the basics here."

Would have been nice if you linked to such a short intro...

Thanks for the note Wes! I have just added a link to a short introduction to "Landau Notation", it should be enough information to understand the essence of the article.

Had you explained bubble sort complexity, without using recursion ( purely iterative approach), it would be easier to grasp for learners. Nice post otherwise.