As for the language of choice - congratulations - you'll find C++ is very rich in making you think of mathematical shortcuts and millions of ways to make your code perform even better (or to implement fancy patterns).
To the question: When I was beggining to program I would always try to break down one real life problem into several steps and then as I see similarity between tasks or data they transform I would always try to find a lazier, easier, meanier way to implement it.
Elegance came after when learning patterns and real algorithms.
