Lecture 2

We talked about the Divide-and-Conquer paradigm, drawing a general picture. We discussed "problems" verses "instances." We reviewed the Mergesort algorithm (sorting cards and then writing the algorithm out in pseudocode) and then we wrote a recurrence relation for it, being careful to include the floors and ceilings: S(n)=S(floor(n/2))+S(ceiling(n/2))+n-1. We tablulated the first several values for this. Then we solved this recurrence relation. We proved an exact bound (not an asymptotic one): S(n)<=2n lg 2n.

We reviewed big-O and Theta notaion.