The Art of Approximation

A fine line divides "not bad and useful" from "wildly wrong" when it comes to easy approximations for hard-to-compute problems. Monte Carlo methods sometimes play a role slightly similar to the old-time tricks of estimation. However, instead of merely checking a result's plausibility, researchers also use Monte Carlo to estimate things that are impossible to compute exactly. A standard way to introduce several fundamental techniques of algorithm design using the notion of topological sorting. Wikipedia gives pseudo code for two ways of generating a topological sort.