So, even before I get to the what the algorithm does (which is quite interesting on its own, even before you find out how it accomplishes that), the very first intriguing part is its name. It's officially referred to as the Blum-Floyd-Pratt-Rivest-Tarjan Algorithm. Is your mouth watering yet? I thought so.1 However, CLRS refers to it as the Select ( Read more... )

Admittedly, I can't think of an uncontrived use case when I would prefer this to a hash table, union find, or traditional bit field, but I still think this is a pretty cool concept. It's a data structure to hold n items, with constant time initialization (i.e. you can't initialize all n items at the beginning), and constant time random access. ( Read more... )

This year, the Algorithms course at Mudd is using a new book, written by Dasgupta, Papadimitriou (the complexity theorist), and Vazirani (the quantum computing guy). You can view a July 2006 draft of the book, which actually looks pretty nice. It doesn't cover all that I think an algorithms course should (in particular it handles the standard data ( Read more... )

Define a "hub" to be a vertex that shares an edge with every other vertex (such as the middle of a star graph, or any vertex in a complete graph). Suppose we have the adjacency matrix of an undirected, unweighted graph with V vertices (so our input has size V^2). Find an algorithm with running time o(V^2) that can determine whether a hub exists in ( Read more... )

I wrote an integer factorisation program (Java bytecode also available for those without a compiler) using an algorithm I just made up, and it works surprisingly well (significantly better than brute force, not nearly as good as the best-known algorithms out there today). Yes, it still has exponential running time, but I thought it was a neat idea ( Read more... )

\begin{LittleShopOfHorrors ( Read more... )