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Computer Science

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  • $\begingroup$ So am I wrong is saying that the time complexities of both average case and worst case are both θ(n)? $\endgroup$ Commented Mar 2, 2016 at 8:56
  • $\begingroup$ Yes, that's incorrect in general. Your professor was right when she suggested you find out yourself why. I tried to give you a hint in my answer. $\endgroup$ Commented Mar 2, 2016 at 8:57
  • $\begingroup$ Here n is the input size and m is a constant. If generally θ(kn) = θ(n) where k is a constant, then why is θ(1/m * n) ≠ θ(n) where 1/m is a constant. $\endgroup$ Commented Mar 2, 2016 at 9:04
  • $\begingroup$ We don't think of $m$ as constant, since it's not really constant. Different instances of the data structure can have widely different $m$. It's as if you would say that the space is $O(1)$ rather than $\Theta(m)$. $\endgroup$ Commented Mar 2, 2016 at 9:42
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    $\begingroup$ Whenever you run an algorithm on a particular input, all the parameters are fixed. That doesn't mean that when we compute the asymptotic performance of an algorithm we assume that they are constant. In other words, $m$ and $n$ are both values of the same "type". You can call them parameters, but that's not a particularly good term. $\endgroup$ Commented Mar 2, 2016 at 12:02