On implicit means of algorithmic problem solving

Students of challenging algorithmics learn and utilize a variety of problem solving tools. The primary tools are data structures, generic algorithms, and algorithm design techniques. However, for solving challenging problems, one needs more than that. Many creative solutions involve implicit notions, whose creative employments yield elegant, concise, and efficient solutions. We elaborate on such notions and advocate their relevance as valuable means in one’s problem solving toolbox. We display our experience with students who lacked awareness of these notions, and illustrate the relevant role of three such notions – the notions of “candidate”, “complement”, and “invariance”.