Algorithm Complexity

Basically for running time:
- Count the number of steps
- Constant factors doesn't matter
- And finally, only the highest-order term matters

So basically if an n²  and any other similar polynomials with different constant factors or anything that follows the n² are in the same class of O(n²).

Now O(n2) is an asymptotic notation.
Then, O(f(n)) is an asymptotic upper-bound.
Which means, the set of functions that grows no faster than f(n).

Ω(f(n)) is the asymptotic lower-bound.

θ(f(n)) is the asymptotic tight-bound.

Now, on to the time complexity of a program.
Basically, every line (initialization, giving value to a field, etc) counts as one line. The tricky parts are when a program has loops or recursive functions inside the program. When taking the worst case for loops I was told to always take the last value of an array or something similar to it and therefore most loop's worst case takes n number of steps. Now when there is another loop inside the loop and you take the worst case, you basically assume the same thing which means the inside loop takes n number of steps and therefore the entire loop will take n*n number of steps. Afterwards, you add the other number steps that aren't in a loop and you have your time complexity of a program.