I'm in a data structures class, and am working on an assignment right now that asks me to find the theta complexity of certain loops. I missed class the day we were introduced to the topic, and everything I can find online expects more prior knowledge than I feel I have. Can someone just explain this in beginners terms for me? I don't know what Big-O or theta even refer to in this notation. I think I have a loose idea of what "complexity" refers to (a measure of how efficient code is, depending on how long a function will take in different circumstances?)
The problem in question:
Demonstrate the $\Theta$-complexity of the functions below. In order to demonstrate that $f(n) = \Theta(g(n))$ you must find two constants $C_1$ and $C_2$ such that $$ C_1g(n) ≥ f(n) ≥ C_2g(n). $$
a.) $f(n) = n^3 - 3n^2 + 5$.
b.) $f(n) = 2\log_2 n - 4$.