What is the Big O, Theta O, Omega O for the following code?

Question

for(i = 0; i < n; i++)
{
    j+=i;
} 

Assuming that Big O for the above code is O(2n), what will be Θ ( tight bound ) and Ω (lower bound) for the above code?

Answer 1

1. O(2n) = 2⋅O(n) = O(n)
2. Your algorithm is also in O(n²) or O(nⁿ) or O(n*log(n)) etc. This is because O is an upper bound.
3. It is in Θ(n) - theta (Θ) describes exactly how it works.
4. Your algorithm is in Ω(n), but it is also in Ω(log(n)) or Ω(1), etc. This is because Omega (Ω) is for a lower bound.

Answer 2

Theta O (tight bound) is the actual amount of computation done that will be O(n) and Omega O (lower bound) is also O(n) i.e the minimum computation required