next up previous
Next: Changing Variables Up: CSE 2320: Algorithms and Previous: Example:

Now let's try subtracting a lower-order term:



We know cn - b $\in$ O(n).



Guess:



Show:



Assume:



T(n) = 2T(n/2) + 1
T(n) $\leq$ 2(cn/2 - b) + 1
= cn - 2b + 1 $\leq$ cn - b
True if b - 1 $\geq$ 0, b $\geq$ 1 (okay)



Copyright © 1998 The University of Texas at Arlington