I'm trying to solve a recurrence problem using substitution method:
Given the following recurrence equation:
$ T(n) = \begin{cases} 3 &n = 0 \\ 3T(\frac{n}{5}) + T(\frac{n}{6}) + n&n > 0 \end{cases} $
provide a tight asymptotic bound for the solution
I've been trying to understand how the recursion tree is made, but I'm not sure that's the smartest way to get the hypothesis to apply the substitution method.
In fact, I looked at the solution provided with the exercise and the first statement is just $T(n) = \Theta(n)$ (the demonstration of this is made right after)
I just don't understand how to get the proper hypothesis, because in my mind, this should have been something like $T(n) = \Theta(n\log n)$.