Treffer: Effective Binary Perspectives in Algorithmic Problem Solving

The effectiveness of viewing, representing, and manipulating data via binary values is illustrated in the domain of algorithmic problem solving. A variety of illuminating binary aspects, regarded as binary perspectives, are displayed through four colorful algorithmic challenges, some of which are two-player games. The illustrations demonstrate the benefits of invoking binary representation of numbers, binary complement, bit-by-bit processing, parity considerations, and the reduction of an integers ’ task into a 0/1 task. The solutions to the challenges are presented gradually, encapsulating general algorithmic considerations and problem-solving methods. These include invariant properties, stepwise refinement, processing by atomic components, auxiliary coloring, backward reasoning, and inductive generalization. Each of the illustrations is tied to a variety of referenced algorithmic schemes and applications, which employ the aspects demonstrated in the paper. The variety of binary aspects, algorithmic considerations, and problem-solving methods make these illustrations appealing teaching resources for computer science educators, in particular in the domain of Algorithms.