的渐近运行时间是多少

Question

Can anyone help me check the correctness, and explain why

What is the asymptotic running time of T(n) = 3T(n/3) + O(n) with T(1) = 1   _______ .  

My answer is n ^{log ₃ 3} .

Answer 1

You seem to have misapplied the Master Theorem .

We have T(n) = a T(n/b) + O(n) where a, b = 3 .

Since here the recurence function is O(n) , it takes the form O(n ^c log ^k (n)) with c = 1 and k = 0 .

We are thus in the case where c = log _a (b) = 1 .

Then according to the Master Theorem, the complexity is O(n ^c log ^k+1 (n)) , that is O(n log(n)) .