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Here is a recursive definition for the runtime of some unspecified function. $a$ and $c$ are positive constants.
$T(n) = a$, if $n = 2$
$T(n) = 2T(n/2) + cn$ if $n > 2$ Use induction to prove that $T(n) = \Theta(n \log n)$
Any idea on how to solve this?