Lecture 7

John did the standard lower bound for comparison based sorting. We argued that all comparison-based sorting algs could be represented by a decision tree (a subtle proposition, actually) and then noted that all n! permutations must appear at the leaves. This gave us a lower bound of ceiling(lg n!) comparisons for ANY sorting algorithm.

Next we used an argument from Baase's text to show that at least 3/2n-3/2 comparisons were required to find the median of n elements, no matter what algorithm was used.