TY - JOUR
T1 - Effective Binary Perspectives in Algorithmic Problem Solving
AU - Ginat, David
PY - 2002/6/1
Y1 - 2002/6/1
N2 - 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. Categories and Subject Descriptors: K.3.2 [Computers and Education]: Computer and Information Science Education; G.2.1 [Discrete Mathematics]: Combinatorics-Combinatorial algorithms; F.3.1 [Logics and Meanings of Programs]: Specifying and Verifying and Reasoning about Programs-Assertions; invariants.
AB - 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. Categories and Subject Descriptors: K.3.2 [Computers and Education]: Computer and Information Science Education; G.2.1 [Discrete Mathematics]: Combinatorics-Combinatorial algorithms; F.3.1 [Logics and Meanings of Programs]: Specifying and Verifying and Reasoning about Programs-Assertions; invariants.
KW - Algorithmic problem solving
KW - Algorithms
KW - Design
KW - binary representation
KW - education
KW - games
KW - invariant properties
UR - http://www.scopus.com/inward/record.url?scp=85024256291&partnerID=8YFLogxK
U2 - 10.1145/772938.772942
DO - 10.1145/772938.772942
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AN - SCOPUS:85024256291
VL - 2
SP - 4
JO - ACM Journal on Educational Resources in Computing
JF - ACM Journal on Educational Resources in Computing
SN - 1531-4278
IS - 2
ER -