Asymptotic Bound

Now, we want to show that $T(n) \le c n \log n$ for some constant c.

True for small n.
Assume true for n' < n.

$\begin{eqnarraystar} T(n) &\le& n + 1/2\; [T(3n/4) + T(n/4)] + 1/2\; T(n-1)\ &\... ...(3/8)(2-\log(3)) -c/4)\ &\le& c n \log n, \mbox{if $c \ge 3$}\end{eqnarraystar}$

So, $T(n) = O(n\log n)$

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