Lecture Notes on Data Structures and Invariants

What this course studies so far is a pretty comprehensive account of the reasoning principles for algorithms implemented in imperative programs.1 But the point of today’s lecture is that there is more to understanding programs than just understanding their algorithms. Algorithms and data structures courses have two major components: first the algorithms and then the data structures. Indeed, a lot of the more advanced insights come from algorithms that store their data in ways that are particularly well-suited for the task at hand. Just think of how much faster it is to find an entry in an array that is at least sorted compared to naive linear search in an unsorted array. Or remind yourself how important it was that data is stored and shuffled around again in the right way when using various tree data structures such as AVL trees to enable fast searching and insertion. This lecture will, thus, explore how data structures impact our reasoning.