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I don't get them, I've been jamming myself full of caffeine for every class, reading the book, and looking up supplemental stuff online and it is still a byzantine mess to me. Unfortunately, there is now an assignment due this week and poking at it for hours has ended with pages and pages of scribbles that don't make a lot of sense. Anyone good at explaining this that can help?
Here's an example: "Solve the following recurrences. If you cannot find an exact answer, give the best upper and lower bounds that you can."
T(n) = 3T(n/2) + n^3
Poking around gets me a big equation with b's, a's, and j's which I can't figure out how to apply because I'm not given T(1).
As far as I can understand it, it seems like n^3 gets smaller with each recursion, and so does 3T(n/2)? So it seems like the lower limit should be something like 3/2 + 1 or 2.5, and the upper limit should be uh...3n?
I've got a list of these to do for the homework and feel like I'm just spinning in circles, can anyone point me in the right direction here? I'm not even sure of what a solution should look like at this point, if I've already gotten there, or if I've totally missed. Argh!
Edit: I am planning on going to the teacher's office hours, but I'd really like to have something vaguely in the right direction instead of stumbling in all bleary eyed and waving my arms helplessly.