Linked Questions

2
votes
2answers
97 views

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.
0
votes
1answer
30 views

Why is max{n,k}= Ө(n+k) [duplicate]

I saw this relationship in my exercise. max{n,k}= Ө(n+k) Could somebody prove it?
90
votes
3answers
24k views

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 ...
23
votes
5answers
10k views

Is O(mn) considered “linear” or “quadratic” growth?

If I have some function whose time complexity is O(mn), where m and n are the sizes of its two inputs, would we call its time complexity "linear" (since it's linear in both m and n) or "quadratic" (...
10
votes
1answer
5k views

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 ...
11
votes
1answer
1k views

Asymptotic Analysis for two variables?

How is asymptotic analysis (big o, little o, big theta, big theta etc.) defined for functions with multiple variables? I know that the Wikipedia article has a section on it, but it uses a lot of ...
4
votes
1answer
2k views

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 $c$. ...
1
vote
2answers
154 views

Is $O(N+M)$ exponential or polynomial?

So In a review section, our professor asked: Given integers $N$ and $M$ Is $O(N+M)$ exponential or polynomial. It's exponential, but I just don't see how that is. I would have thought it's linear.
1
vote
2answers
94 views

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 $n$ ...
0
votes
1answer
431 views

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 ...
2
votes
1answer
423 views

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

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)...
4
votes
1answer
162 views

What's the formal definition of Big-O notation for functions of more than one variable?

For functions of a single totally ordered variable, I already know that $f(n)$ is $O(g(n))$ if and only if $\exists m. \exists c. \forall n. (n \ge m) \rightarrow [ f(n) \le c \cdot g(n) ]$. What I ...
1
vote
2answers
118 views

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, ...
3
votes
1answer
89 views

O(f) vs O(f(n))

I first learned about the Big O notation in an intro to Algorithms class. He showed us that function $g \in O(f(n))$ Afterwords in Discrete Math another Professor, without knowing of the first, told ...
3
votes
2answers
99 views

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{...

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