Linked Questions

1
vote
1answer
65 views

Big O and constants [duplicate]

I've already asked this question on stack overflow, but guys have suggested me to ask my question here. Let's consider classic big O notation definition (proof link): The $O(f(n))$ is the set of all ...
40
votes
7answers
3k views

Explaining the relevance of asymptotic complexity of algorithms to practice of designing algorithms

In algorithms and complexity we focus on the asymptotic complexity of algorithms, i.e. the amount of resources an algorithm uses as the size of the input goes to infinity. In practice, what is ...
5
votes
4answers
2k views

How can a quadratic algorithm be faster than a linearithmic one?

I have to solve the following problem: Al and Bob are arguing about their algorithms. Al claims his $O(n\log n)$ time method is always faster than Bob’s $O(n^2)$ time method. To settle the issue, ...
4
votes
2answers
9k views

What is the complexity of this matrix transposition?

I'm working on some exercises regarding graph theory and complexity. Now I'm asked to give an algorithm that computes a transposed graph of $G$, $G^T$ given the adjacency matrix of $G$. So basically ...
2
votes
2answers
271 views

Why do compute time complexity for algorithms? [closed]

I read about Big-O notation with modular arithmetic. So, Time complexity is commonly estimated by counting the number of elementary operations performed by the algorithm, where an elementary operation ...
1
vote
2answers
264 views

What is the significance of a Θ-bound on the running time of Mergesort?

While studying algorithm analysis I found that there is something called tight bound and there is some mathematical formula to support it. Given: Mergesort takes $\Theta(n \log n)$ compares to sort ...
1
vote
2answers
163 views

Reasoning on Efficiency (2)

Two algorithms to solve a particular problem can have theur efficiency compared using the $O$ and $o$ notation. However, this is very crude method, and tells us no information on how more effective ...
0
votes
1answer
261 views

What is the importance of C in big-Oh notation?

From the definition of Big Oh, it states that there should be a function $g(x)$ such that it is always greater than or equal to $f(x)$. Or $f(x) \le cg(n)$ for all values of $n > n_0$. What I'm not ...
8
votes
1answer
333 views

What is the running time of this recursive algorithm?

I made the following (ungolfed) Haskell program for the code golf challenge of computing the first $n$ values of A229037. This is my proposed solution to compute the $n$th value: ...
2
votes
3answers
131 views

Are hardware specs relevant in software performance comparisons?

I notice occasionally in blogs or articles comparing different languages, algorithms, etc. that the author will divulge info about the processor used in the testing. Is this meaningful? Shouldn't ...
1
vote
1answer
69 views

Master theorem recurrence relation

Consider I have the following recurrence $$T(n) = 10T(n/3) + \Theta(n^2\log^5 n)\,.$$ Now, by the master theorem, if we evaluate $n^{\log_{b}{a}}$, we get $n^{\log_{b}{a}} = n^{\log_{3}{10}} = n^{2....
2
votes
0answers
95 views

Why do we focus on asymptotics when analyzing algorithms? [duplicate]

Maybe a newbie question, but why when we analyze algorithms do we focus on asymptotics? It seems to me the performance of algorithms on finite input sizes (after all, problems are rarely infinitely ...