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[Solved]: How long would it take a computer with twice the processing power to solve a polynomial time problem?

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Problem Detail: 

Say I have some problem of $O\left(n^k\right)$ complexity.

If I were to solve the problem on a computer $x$, it would take time $t$.

Now I have a new computer $x'$, which has double the computing power of $x$.

How long would it take $x'$ to solve the same problem in terms of $t$?

Asked By : JibbyJames

Answered By : Yves Daoust

It will take half the time of course, $t'=t/2$, and the asymptotic complexity remains $O(n^k)$ !

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Question Source : http://cs.stackexchange.com/questions/40558

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