Question

This is about analysis of algorithms:
Say, the running time of a problem is:

T(n) = { 1, for n == 1 | T(n/3) + THETA(1), for n > 1}

Now, this is THETA(log base3 n)

But, if I use Master Method, I evaluate to THETA(log base2 n), using Case II

How am I supposed to get the correct answer from master method?

Answer 1

They’re the same. For any two bases a and b, Θ(loga n) = Θ(logb n), so we usually don’t mention the base at all and just say Θ(log n).

This is because loga n = (1 / logb a) * logb n, so they differ by a factor of 1 / logb a which is constant with respect to n.