Introduction to algorithms
The case for case studies of programming problems
Communications of the ACM
SIGCSE '99 The proceedings of the thirtieth SIGCSE technical symposium on Computer science education
Introduction to Algorithms: A Creative Approach
Introduction to Algorithms: A Creative Approach
The Science of Programming
Chess Skill in Man and Machine
Chess Skill in Man and Machine
Graph Algorithms
A Discipline of Programming
Data Structures and Algorithms
Data Structures and Algorithms
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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 lively 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 integer task into a 0/1 task. The solutions to the challenges are presented gradually, encapsulating general algorithmic considerations and problem-solving methods, including 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 this article. 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.