1 vote
2k 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 ...
• 111
35k 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 ...
• 1,323
7k views

### 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 $O(\min(m,n))$. ...
• 1,642
15k 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 ...
• 423
2k views

### 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 ...
• 43
4k 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 $c$. ...
• 143
3k views

• 133
133 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.
• 157
1 vote
126 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, ...
• 519
82 views

### 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 ...
• 121
1 vote
84 views

### 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 ...
• 113
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 ...
The content of the passage primarily revolves around the concept of time complexity in algorithms, particularly focusing on the Big O notation and its application when dealing with multiple input variables. The passage includes several questions and discussions about how to properly use and interpret Big O notation in the context of algorithms with more than one input variable.
multiple_questions

the passage contains multiple questions and discussions about the time complexity of algorithms with multiple inputs, but it does not provide answers to these questions. the questions are centered around understanding the notation and its implications for different scenarios, such as the complexity of algorithms with two input variables and the relationship between different big o notations.
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
1 vote
2k 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 ...
• 111
35k 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 ...
• 1,323
7k views

### 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 $O(\min(m,n))$. ...
• 1,642
15k 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 ...
• 423
2k views

### 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 ...
• 43
4k 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 $c$. ...
• 143
3k views

• 133
133 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.
• 157
1 vote
126 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, ...
• 519
82 views

### 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 ...
• 121
1 vote
84 views

### 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 ...
• 113
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 ...
user
The content of the passage primarily revolves around the concept of time complexity in algorithms, particularly focusing on the Big O notation and its application when dealing with multiple input variables. The passage includes several questions and discussions about how to properly use and interpret Big O notation in the context of algorithms with more than one input variable.

TYPE: MULTIPLE_QUESTIONS

The passage contains multiple questions and discussions about the time complexity of algorithms with multiple inputs, but it does not provide answers to these questions. The questions are centered around understanding the notation and its implications for different scenarios, such as the complexity of algorithms with two input variables and the relationship between different Big O notations.