I have always wondered what is the philosophy behind those ICPC problems that don't specify the number of test cases. What are the problem setters trying to evaluate, and how should I respond? Obviously, enough test cases will TLE out my solution.

One of the great things about programming contests is choosing the right algo for the right job, say, I wouldn't go full Fast Fourier Transform if simple convolution gets the job done. So, should I respond to those problems with the best algo I can think of? Should I respond with a provably optimal algo? Or, should I reverse engineer the problem-setter expectations and choose something along those lines?

This is blog intended for discussion, please don't understand this as a rant :)