Engagement of students plays a crucial part in education, even if they are gifted children. We know a success story: the extracurricular mathematics camps of Lajos Pósa for talented teenagers in Hungary. The key to that success is the excellently engineered network of problems that guide students through discovering the world of higher level mathematics. It would be a novel approach to teach computer programming and algorithms in a similar way. In this paper we attempt to design a network of problems selected specifically for discovery learning of algorithms and data structures from beginner to advanced level, targeted for secondary and high school talented students. This could serve as the curriculum for extra classes or camps conducted with the problem-based teaching method we describe.