Common categories of problems
Before we start, we need to have some understanding of the different categories of problems. This is important because it forms part of the context in which we formulate our abstractions and thus guides our choices of how to implement solutions. All problems can be broken down into a set of basic problems via a sequence of reductions. These basic problems are those that you probably already know how to solve – for instance, using classic data structures and algorithms. As you gain experience, fewer reductions will be needed in most cases, and you will recognize problems that are of increasing complexity and know how to solve these. Very broadly, basic problems fall into one of four domains, at least for the purposes of this discussion, each with numerous subcategories and some overlapping concepts:
- Combinatorial problems, including sorting and searching
- Input-output (IO) problems, and interacting with the host system
- Numerical...
