next up previous
Next: Now for the boundary Up: l2 Previous: Solution Techniques

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


next up previous
Next: Now for the boundary Up: l2 Previous: Solution Techniques