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Questions about asymptotic notations such as Big-O, Omega, etc.

18 votes

Changing variables in recurrence relations

It's certainly not cheating. Think in calculus how substitution may be used to solve a tricky integral. The substitution makes the equation more manageable for manipulation. Additionally, substitution …
Nicholas Mancuso's user avatar
11 votes
Accepted

Solving $T(n)= 3T(\frac{n}{4}) + n\cdot \lg(n)$ using the master theorem

If our recurrence takes the form $T(n) = aT(n/b) + f(n)$, then to use the "third case" of the Master method we must have the following hold: $f(n) = \Omega(n^{\log_b a + \epsilon})$ for some $\ep …
Nicholas Mancuso's user avatar