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Using as few resources (e.g. time, space) as possible while solving a problem. Use this tag if your question is specifically about resource usage, not for generic algorithm questions that happen to mention running times.

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Big O Proof , f(n) = 2n + 1 and I have to prove f(n) is O n^2

If I have $f(n) = 2n + 1$ and I have to prove $f(n) \in O(n^2)$, by proving there exists positive constants $c$ and $n_0$ such that $f(n)<cn^2, \forall n\ge n_0$, can I do this all in one step by put …
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2 answers
211 views

How to prove Big-O when $f(n)$ is defined sectionwise

I'm given a function which is defined based on a condition, for example $$ f(n) = \begin{cases} 4n+1, \ \text{n is even}\\ 3n^2+2, \ \text{n is odd} \end{cases}. $$ I have to prove or di …
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