[Solved]: Algorithm analysis question in growth of functions

Problem Detail: 

How would I solve the following.

An algorithm that is $O(n^2)$ takes 10 seconds to execute on a particular computer when n=100, how long would you expect to take it when n=500?

Can anyone help me answer dis.

Asked By : Fernando Martinez

Answered By : AJed

Since it is $O(n^2)$, then $t \leq c n^2$. Therefore, since $t = 10$, and $n = 100$, $c \geq t / n^2 = 10 / 100 00$.

Therefore, at $n = 500$. You have $t \leq 10 / 100 00 \times 500^2 = 250$.

But wait, the definition of the $O$-notation claims that the above formula works for large $n$'s only. I assumed that. Although honestly, I dont like this question. It is a bet weird.

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Question Source : http://cs.stackexchange.com/questions/11781