How do you choose the best algorithm for a given problem?

Just as mathematics is based on philosophy and logic, so creating an algorithm is largely based on the same. The numbers and metrics you’re using need to make sense to get the answers you are searching for.

An algorithm is a plan or an outline detailing what needs to be done to accomplish a certain result. A step by step procedure, detailed enough to be followed exactly, yet flexible enough to be applicable in multiple different scenarios in computer science.

Algorithm design allows you to throughly and rigorously examine a real business problem. They force you to strip out the noise and focus on the relationship of inputs and outputs—fundamental drivers of results. A good algorithm is an abstraction but it’s invaluable in identifying and eliminating biases. It provides for scalability and repeatability, and thus can drive efficiency gains much more readily than ad hoc or qualitative approaches to business analysis.

Algorithm design is important for creating a consistent, reliable, and efficient implementation of a solution to a coding problem. It's good to understand what is it that you're trying to do, and how you will do it, before creating an implementation to solve a problem. Rather than jumping straight in and trying to hack it away, go back to see the big picture, identifying the problem, and breaking it down into manageable pieces. Use a whiteboard to outline what happens to the data, at a high level, before attempting an implementation. This is what algorithm design is all about. Without designing an algorithm in advance, one finds that the final implementation maybe unreliable, inefficient, buggy, or hard to trouble shoot and maintain.

There is no one "best" algorithm design principle, as different principles may be more important depending on the specific problem being solved and the context in which the algorithm will be used. However, it's generally a good practice to strive for a balance between different principles, such as simplicity, efficiency, and maintainability. A well-designed algorithm should not only produce the correct output in a timely manner, but also be easy to understand, modify, and reuse. It's also important to consider scalability, robustness, and flexibility to ensure that the algorithm can handle unexpected scenarios and adapt to changing requirements.

Understand the problem first. This is very critical. Do not jump to conclusions. Survey various algorithms that fit the problem. Evaluate the pros and cons while keeping in mind the system constraints.

This requires having knowledge of the common algorithms. What are the tools at your disposal? What are the properties, positives, and drawbacks of common algorithms and data structures? What kinds of problems are each of these algos and DS best suited for? Once you are familiar with various algos, DS, and their implementations and solutions, then it becomes easier to see applications for them. Then when you see a problem, you can identify a fitting algorithm for it.

I agree, another watch out to look for in algorithms design problems will be potential bias from the data sets inputted, training bias, and programming bias during the set up phase. These limitations are important to consider when evaluating the results of the output from a neutral perspective.