The "Master" Theorem/Method, Derivation

Here we give a proof of the "master" theorem, which is a derivation of the runtime for all recursive algorithms obeying a recurrence of the form T(n) = aT(n/b) + f(n) (i.e., a subproblems of size n/b, and f(n) time to combine the solutions). We see that there are 3 different cases, mainly based on how big f(n) is compared to a, b, and n. We look at a "computation tree" to show what the runtime across all nodes will be.

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