How I Studied Algorithms
In Spring 2013, I took Purdue CS’s required graduate level Algorithms course. It was a lot of work, but I did pretty well, especially considering my background is in the less theoretical field of Computer Engineering.
At first when I was trying to understand a new algorithm, I’d code it up in my favorite language (Python). This works OK for the simpler algorithms like sorting, but for some of the esoteric topics (ahem Fibonacci Heaps ahem) I’d end up spending more time coding than answering homework problems.
Another technique I used was working out an example on paper. That only works for a very specific subset of algorithms. The obstacle is representing the state of the algorithm in writing in a concise way. It’s easy to write a whole lot and not get through a small example. But there were some problems for which a small example or diagram sparked an idea that eventually led me to a solution.
Studying some algorithms forces the student to run the algorithm through in their head. This is great practice for my “brain debugger” – finding a bug by mentally stepping through the code. It’s a skill that is invaluable for any programmer, and a good reason to study algorithms even if you have no interest in theory.
The most important trait when studying algorithms is the ability to work on a problem without finding the solution for a long period of time without getting frustrated. For example, say I’m working through an exam and I turn the page and read the next problem, but I have no idea how to do it. The worst thing I could do is panic or get frustrated, but that comes naturally to a student who is used to getting the correct answer easily. Sometimes the only thing to do is brainstorm: make diagrams, do a small example, etc, and be prepared to throw away ideas that aren’t going to work out. That’s research in a nutshell. The answers to hard, interesting problems aren’t obvious or someone would have already found it.