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