A few days ago, I was trying to split a data set into various files according to their type, but it was terribly slow. I saved an hour by taking a step back and thinking about my algorithms. Because algorithms matter. But not terribly much.

Using the recurrence relation \binom n m = \binom {n - 1} {m - 1} + \binom {n - 1} m, we develop a dynamic programming algorithm to calculate the binomial coefficient. I am aware that better algorithms exist.