How to add Big O and Big omega

Question

If an algorithm has two sub algorithm, when it is best case for sub algorithm A1 to the given input, it is the worst case for sub algorithm A2. How could I find the overall algorithm complexity? Simply I mean Ω(N) + O(N)=? I know if the algorithms are in sequential executing order the over all complexity is O(N)+ O(N) and in nested order O(N)* O(N).

Please tell me in both cases, when in sequential and in nested order

Answer 1

Essentially Ω(N) + O(N)= Ω(N). Because O(N) means lower (or at most the same) order of Ω(N). When they are summed, the lower order can be omitted.