There are problems (e.g. this one or this other one) that could potentially be solved easily using traditional algorithmic techniques. I think that training a neural network (or any other machine learning model) for such sorts of problems will be more time consuming, resource-intensive, and pointless.

If I want to solve a problem, how to decide whether it is better to solve algorithmically or by using NN/ML techniques? What are the pros and cons? How can this be done in a systematic way? And if I have to answer someone why I chose a particular domain, how should I answer?

Example problems are appreciated.