Linked Questions

1 vote
1 answer

Complexity of an algorithm with multiple inputs [duplicate]

I've just started reading about the complexity of algorithms, but everywhere I look, it is only defined for one input $n$. For example an algorithm is cubic if its complexity is $O(n^3)$. But what ...
MattBurrows's user avatar
101 votes
3 answers

How does one know which notation of time complexity analysis to use?

In most introductory algorithm classes, notations like $O$ (Big O) and $\Theta$ are introduced, and a student would typically learn to use one of these to find the time complexity. However, there are ...
Miles's user avatar
  • 1,323
53 votes
4 answers

What is the meaning of $O(m+n)$?

This is a basic question, but I'm thinking that $O(m+n)$ is the same as $O(\max(m,n))$, since the larger term should dominate as we go to infinity? Also, that would be different from $O(\min(m,n))$. ...
Frank's user avatar
  • 1,642
20 votes
1 answer

Can a Big-Oh time complexity contain more than one variable?

Let us say for instance I am doing string processing that requires some analysis of two strings. I have no given information about what their lengths might end up being, so they come from two distinct ...
corsiKa's user avatar
  • 423
2 votes
3 answers

Can we test whether two vertices are connected in time linear in the number of nodes?

Consider the problem: Given an undirected graph and two of its vertices, is there a path between them? I often read that this problem can be solved in linear time in the number of vertices! I am ...
Luke's user avatar
  • 43
4 votes
1 answer

Time complexity based on two variables

Suppose we have a function based on two inputs of length $m,n$. Therefore the time complexity of the function is calculated by $T(m,n)$. Suppose that we have: $T(m,c)\in O(m^2)$ for any constant $c$. ...
Naji's user avatar
  • 143
2 votes
1 answer

$O(n+nm) = O(nm) = O(m+nm)$?

I am thinking about the worst-case space complexity of an algorithm. Obviously, if $f \in O(nm)$ then $f \in O(n+nm)$. But is the converse true? $O(m)+O(nm) = O(m+nm) = O(m(1+n)) = O(m)O(1+n) = O(m)...
David's user avatar
  • 33
1 vote
2 answers

Simplifying an upper O-bound in two variables

I have an algorithm that depends on two input sizes n and m. The complexity breaks down to the following equation: $\frac{nm - 1}{n-1} = O(?)$ Is Big-O of the Formula $O(mn)$ or $O(m)$ because $n$ ...
user4758246's user avatar
3 votes
2 answers

Compare Complexity of Graph Algorithm

Assume I know that there is an algorithm of complexity $ \mathcal{O}( log ( \vert V \vert^2 \vert E \vert ) ) $ for a Graph $G(E,V)$. How do I compare this for example to the complexity of $ \mathcal{...
N8_Coder's user avatar
  • 133
2 votes
2 answers

What does it mean to add up O-terms with different variables? [duplicate]

Is this true? O(n) + O(k) =O(n+k).I have searched for it ,the answers were quite ambiguous and I couldn't find a good explanation.
Prithvi Raj's user avatar
1 vote
2 answers

What kind of growth is $O(0.24\cdot K\cdot 2^w)$

I've calculated the running time of an algorithm I'm interested in to be $$O(0.24\cdot K\cdot 2^{w})\,,$$ where $K$ and $w$ are both variables. ($K$ is the number of elements in some set, ...
Jesus Salas's user avatar
2 votes
1 answer

Does this program have a runtime of O(N) or O(n*m)

This question is similar to, but distinct from this one, in that I am considering a specific case that demonstrates an apparent inconsistency in how I see Big-O notation used. I would like to be sure ...
Brian C's user avatar
  • 121
1 vote
1 answer

Can the following O(...) expression be simplified?

I have an algorithm with three variables affecting the time complexity: $k$, $L$, and $n$. I have come up with the following that expresses the complexity: $O(kn + k^2L + k^2nL + knL)$ I think I ...
xdhmoore's user avatar
  • 113
2 votes
1 answer

Interpretation of an asymptotic notation

Assume that we measure the complexity of an algorithm (for some problem) by two parameters $n$ and $m$ (where $m \le n$). What is the formal interpretation of the following claim: there is no ...
user91015's user avatar
  • 151