Since I haven't discussed how I've been doing with Big-O, Algorithms, and the other things from the past 3 weeks, I felt that by now I've caught up well enough and am ready to discuss how I'm doing.
First off, algorithm analysis. I've done some practice to figure out how many times each loop in an algorithm should run in terms of n. The main issue I've been having is putting it all together. Perhaps this is because I need to better understand Sigma notation and how to use it properly, since I've forgotten some stuff from high-school. I need to brush up on worst-cases, mainly to think about how I can discover what the worst case of an algorithm should be when it may not be too obvious. There are also times where the worst case and best case seem the same (as in, the algorithm only increases running time with increasing size, not anything else such as searching for an item that doesn't exist like in linear search).
As for Big-O and Big-Omega, I understand the notation fairly well. At first the whole over-estimation and under-estimation thing confused me (it was difficult to understand what was going on in the notes, there were a lot of numbers that seemed to come out of nowhere). I was pretty excited when I finally figured it out, and it's actually a fairly easy method to use with polynomials.
As for non-polynomials, while I don't find limits and l'hopital's rule too challenging, the definition of a limit and all those other things were slightly confusing. I didn't really understand fully why you go from existential n' in the limit definition and then back to existential n (when disproving if f(n) exists in O(g(n)).
Finally, for bigger picture general expressions in Big-O, it pretty much varies for me. Some were easier to figure out than others, I really just need more practice with different situations. I do, however, understand the whole picking c and B thing. I should also check up on what the whole max thing is that kept coming up, because while I understand what a maximum is, I don't fully understand its use here other than getting a big number.
I haven't touched on computability because I have little to say about it right now. More on that next week.
First off, algorithm analysis. I've done some practice to figure out how many times each loop in an algorithm should run in terms of n. The main issue I've been having is putting it all together. Perhaps this is because I need to better understand Sigma notation and how to use it properly, since I've forgotten some stuff from high-school. I need to brush up on worst-cases, mainly to think about how I can discover what the worst case of an algorithm should be when it may not be too obvious. There are also times where the worst case and best case seem the same (as in, the algorithm only increases running time with increasing size, not anything else such as searching for an item that doesn't exist like in linear search).
As for Big-O and Big-Omega, I understand the notation fairly well. At first the whole over-estimation and under-estimation thing confused me (it was difficult to understand what was going on in the notes, there were a lot of numbers that seemed to come out of nowhere). I was pretty excited when I finally figured it out, and it's actually a fairly easy method to use with polynomials.
As for non-polynomials, while I don't find limits and l'hopital's rule too challenging, the definition of a limit and all those other things were slightly confusing. I didn't really understand fully why you go from existential n' in the limit definition and then back to existential n (when disproving if f(n) exists in O(g(n)).
Finally, for bigger picture general expressions in Big-O, it pretty much varies for me. Some were easier to figure out than others, I really just need more practice with different situations. I do, however, understand the whole picking c and B thing. I should also check up on what the whole max thing is that kept coming up, because while I understand what a maximum is, I don't fully understand its use here other than getting a big number.
I haven't touched on computability because I have little to say about it right now. More on that next week.
I am also confused about the limit definitions. They are definitely overly complicated.
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