Tangential question: How can an algorithm end up with a fractional exponent? It's clear to me how nested loops can give O(n^2) or O(n^2), and how a binary search can give O(log n), but how on earth can you get something like O(n^2.371552), or even O(n^2.7)?
The classic example here is Strassen's algorithm. You divide your two input matrices into quarters, and then you need to do 7 matrix multiplies of the smaller (n/2) matrices. When you add up the total work done, this ends up needing to do n^(log base 2 of 7) work, or about n^2.8.
