Question

I know what the O(lg n) and the T(n) mean, and in algorithm analysis I don’t know how to calculate the T(n) = 3T(n/3) + O(lg n). Should I expand it?

Just like:

T(n) = 3^2 *T(n/3^2) + O(lg n/3) + O(lg n) and so on...

then I get

T(n) = 3^(log b^n) * T(1)+ 3^[log b ^ (n-1)]* lg (n/(3^[log b ^(n-1)])) ...+ O(lg n/3) +O(lg n)

But how can I get the right answer, and can I get an easy way to find it out?

Answer 1

I think you can use Masters Theorem.

T(n)=aT(n/b) + f(n)
Here a=3, b=3 and f(n)=O(log n)
f(n) = O(log n) = O(n)

which implies the answer as BigTheta(n)

For Masters theorem formula plz see Wikipedia. There are three rules and are quite simple