上限和下限是什么意思？

Question

I am confused with upper and lower bound in algorithm complexity. For example, if 𝑇(𝑛)=𝑂(2𝑛), 𝑇(𝑛)=Ω(𝑛^-1). Can I say that there always exists n^-1≤T(n)≤2n ?

Answer 1

No, you cannot draw this conclusion. The correct statement is that there exist constants C1, C2 > 0 such that for large enough n (n > some constant n0)

C1 * (n^-1) ≤ T(n) ≤ C2 * n