Prelude

Algorithms, while mostly associated with computer science, compose fundamental parts of other fields as well. Jon Kleinberg and Eva Tardos cite economics and biology as fields outside of computer science that rely on algorithms. The authors also point out that algorithms very rarely appear as “cleanly packaged, mathematically precise questions.” Most of the time, algorithms are created for one specific application; such algorithms usually have unnecessary or inefficient sections, especially when trying to conform the algorithm to solve a different problem.
Due to this, the study of algorithms holds two distinct components. First, algorithms attempt to solve the problem cleanly. Second, an algorithm must seek to solve the problem in the most efficient way possible by strategically structuring itself around the problem itself. Algorithms that do this effectively do not only solve the problem at hand, but also “form the language that lets you cleanly express the underlying questions.”