An algorithm, according to the American Heritage Dictionary, is defined as follows:

Designing an algorithm is about coming up with this "finite set of unambiguous instructions" in the most efficient way to "achieve a certain goal." For a complex real-world problem, designing an algorithm is a tedious task. To come up with a good design, we first need to fully understand the problem we are trying to solve. We start by figuring out what needs to be done (that is, understanding the requirements) before looking into how it will be done (that is, designing the algorithm). Understanding the problem includes addressing both the functional and non-functional requirements of the problem. Let's look at what these are:

• Functional requirements formally specify the input and output interfaces of the problem that we want to solve and the functions associated with them. Functional requirements help us understand data processing, data manipulation, and the calculations that need to be implemented to generate the result.
• Non-functional requirements set the expectations about the performance and security aspects of the algorithm.

Note that designing an algorithm is about addressing both the functional and non-functional requirements in the best possible way under the given set of circumstances and keeping in mind the set of resources available to run the designed algorithm.

To come up with a good response that can meet the functional and non-functional requirements, our design should respect the following three concerns, as discussed in Chapter 1, Overview of Algorithms:

• Concern 1: Will the designed algorithm produce the result we expect?
• Concern 2: Is this the optimal way to get these results?
• Concern 3: How is the algorithm going to perform on larger datasets?

In this section, let's look at these concerns one by one.