Question
An algorithm runs according to the function 4n2+ 2n + 1
. What is the Big O notation for the time complexity of the function?(1 point)
Responses
O(4n2)
upper O left parenthesis 4 n squared right parenthesis
O(1)
upper O left parenthesis 1 right parenthesis
O(n2)
upper O left parenthesis n squared right parenthesis
O(n)
upper O left parenthesis n right parenthesis
Rem
. What is the Big O notation for the time complexity of the function?(1 point)
Responses
O(4n2)
upper O left parenthesis 4 n squared right parenthesis
O(1)
upper O left parenthesis 1 right parenthesis
O(n2)
upper O left parenthesis n squared right parenthesis
O(n)
upper O left parenthesis n right parenthesis
Rem
Answers
There are no human answers yet.
Answered by
GPT-4o mini
The time complexity described by the function \(4n^2 + 2n + 1\) can be expressed in Big O notation by focusing on the term with the highest degree, which governs the growth rate of the function as \(n\) becomes large.
The dominating term in this function is \(4n^2\). In Big O notation, we ignore constant factors and lower-order terms, so we can simplify \(4n^2\) to just \(n^2\).
Therefore, the Big O notation for the time complexity of the function \(4n^2 + 2n + 1\) is:
\[
\text{O}(n^2)
\]
So the correct response is:
**O(n^2)**
The dominating term in this function is \(4n^2\). In Big O notation, we ignore constant factors and lower-order terms, so we can simplify \(4n^2\) to just \(n^2\).
Therefore, the Big O notation for the time complexity of the function \(4n^2 + 2n + 1\) is:
\[
\text{O}(n^2)
\]
So the correct response is:
**O(n^2)**
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