Master Method

Compared with the iteration method, the master method is much easier to use once you understand how to use it. The hardest part about the master method is understanding the language of the master theorem.

The Master Theorem:

Let and be constants, let be a function, and let be defined on the nonnegative integers by the recurrence:

where we interpret to mean either or . Then can be bounded asymptotically as follows:
1. If for some constant , then .
2. If , then .
3. If for some constant , and if for some constant and all sufficiently large , then .

Basically all you have to do to solve a recurrence relation is figure out which of the three cases your recurrence falls into and apply the given formula to get the answer!