Closed. This question needs to be more focused. It is not currently accepting answers. Want to improve this question? Update the question so it focuses on one problem only by editing this post. Closed 7 years ago. Improve this question My co-workers took me back in time to my University days with a discussion of … Read more
I’m really confused about the differences between big O, big Omega, and big Theta notation. I understand that big O is the upper bound and big Omega is the lower bound, but what exactly does big Ө (theta) represent? I have read that it means tight bound, but what does that mean? 6 Answers 6
I believe there’s a way to find the kth largest element in an unsorted array of length n in O(n). Or perhaps it’s “expected” O(n) or something. How can we do this? 33 Answers 33 This is called finding the k-th order statistic. There’s a very simple randomized algorithm (called quickselect) taking O(n) average time, … Read more
Are there are any cases where you would prefer O(log n) time complexity to O(1) time complexity? Or O(n) to O(log n)? Do you have any examples? 23 Answers 23
I am to show that log(n!) = Θ(n·log(n)). A hint was given that I should show the upper bound with nn and show the lower bound with (n/2)(n/2). This does not seem all that intuitive to me. Why would that be the case? I can definitely see how to convert nn to n·log(n) (i.e. log … Read more
If I have some R list mylist, you can append an item obj to it like so: mylist[[length(mylist)+1]] <- obj But surely there is some more compact way. When I was new at R, I tried writing lappend() like so: lappend <- function(lst, obj) { lst[[length(lst)+1]] <- obj return(lst) } but of course that doesn’t … Read more
This question already has answers here: What is a plain English explanation of “Big O” notation? (43 answers) Closed 4 years ago. I’m asking more about what this means to my code. I understand the concepts mathematically, I just have a hard time wrapping my head around what they mean conceptually. For example, if one … Read more
Are there any O(1/n) algorithms? Or anything else which is less than O(1)? 32 Answers 32 This question isn’t as silly as it might seem to some. At least theoretically, something such as O(1/n) is completely sensible when we take the mathematical definition of the Big O notation: Now you can easily substitute g(x) for … Read more
I understand Big-O notation, but I don’t know how to calculate it for many functions. In particular, I’ve been trying to figure out the computational complexity of the naive version of the Fibonacci sequence: int Fibonacci(int n) { if (n <= 1) return n; else return Fibonacci(n – 1) + Fibonacci(n – 2); } What … Read more
After using PHP for a while now, I’ve noticed that not all built-in PHP functions are as fast as expected. Consider these two possible implementations of a function that finds if a number is prime using a cached array of primes. //very slow for large $prime_array $prime_array = array( 2, 3, 5, 7, 11, 13, … Read more
