I am writing a simple Python program. My program seems to suffer from linear access to dictionaries, its run-time grows exponentially even though the algorithm is quadratic. I use a dictionary to memoize values. That seems to be a bottleneck. The values I’m hashing are tuples of points. Each point is: (x,y), 0 <= x,y … Read more
Okay so I have this project I have to do, but I just don’t understand it. The thing is, I have 2 algorithms. O(n^2) and O(n*log2n). Anyway, I find out in the project info that if n<100, then O(n^2) is more efficient, but if n>=100, then O(n*log2n) is more efficient. I’m suppose to demonstrate with … Read more
Brief: When academic (computer science) papers say “O(polylog(n))”, what do they mean? I’m not confused by the “Big-Oh” notation, which I’m very familiar with, but rather by the function polylog(n). They’re not talking about the complex analysis function Lis(Z) I think. Or are they? Something totally different maybe? More detail: Mostly for personal interest, I’ve … Read more
Lets say I have an array as: int a[]={4,5,7,10,2,3,6} when I access an element, such as a[3], what does actually happen behind the scenes? Why do many algorithm books (such as the Cormen book…) say that it takes a constant time? (I’m just a noob in low-level programming so I would like to learn more … Read more
Is anybody able to give a ‘plain english’ intuitive, yet formal, explanation of what makes QuickSort n log n? From my understanding it has to make a pass over n items, and it does this log n times…Im not sure how to put it into words why it does this log n times. Answer Complexity … Read more
Assume I have two algorithms: for (int i = 0; i < n; i++) { for (int j = 0; j < n; j++) { //do something in constant time } } This is naturally O(n^2). Suppose I also have: for (int i = 0; i < 100; i++) { for (int j = 0; … Read more
It just occurred to me, if you know something about the distribution (in the statistical sense) of the data to sort, the performance of a sorting algorithm might benefit if you take that information into account. So my question is, are there any sorting algorithms that take into account that kind of information? How good … Read more
I’m not new to using regular expressions, and I understand the basic theory they’re based on–finite state machines. I’m not so good at algorithmic analysis though and don’t understand how a regex compares to say, a basic linear search. I’m asking because on the surface it seems like a linear array search. (If the regex … Read more
Recently, I noticed some people mentioning that std::list::size() has a linear complexity. According to some sources, this is in fact implementation dependent as the standard doesn’t say what the complexity has to be. The comment in this blog entry says: Actually, it depends on which STL you are using. Microsoft Visual Studio V6 implements size() … Read more
Is it a fair assumption that in v8 implementation retrieval / lookup is O(1)? (I know that the standard doesn’t guarantee that) Answer Is it a fair assumption that in v8 implementation retrieval / lookup is O(1)? Yes. V8 uses a variant of hash tables that generally have O(1) complexity for these operations. For details, … Read more
