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Solution Techniques

Assume: T(n/2) $\leq$ c n/2 lg n/2

\begin{eqnarray*}T(n) & \leq & 2(c(n/2) \lg n/2) + n \\
& \leq & cn \lg n/2 + ...
...& \leq & cn \lg n - cn \lg 2 + n \\
& \leq & cn \lg n - cn + n
\end{eqnarray*}




Want T(n) $\leq$ cn lg n.
To accomplish this we want (- cn lg 2 + n) to be
$\leq$ 0.
Thus -cn + n
$\leq$ 0, n $\leq$ cn, 1 $\leq$ c.
T(n)
$\leq$ cn lg n, for c $\geq$ 1



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