2.1 The Science of Algorithms
(Algorithmics) – Summary
Nature and Characteristics of Algorithms
Analgorithmis a central concept in mathematics and informatics. Originally referring to
arithmetic procedures, it now designates any exact and finite sequence of instructions that,
when executed, solves a problem. In informatics, an algorithm is defined as a precise and
finite list of instructions for an executor to process data and achieve the expected result.
Algorithms have several essential characteristics:
Discreteness:A finite number of sequential steps, each executed fully before moving
to the next.
Determinacy:Given the same input, the output is always identical.
Understandability:No ambiguous instructions; the executor does not make
independent decisions.
Effectiveness:Execution of all steps guarantees a result within real time.
Mass character:Works correctly for a class of problems, not just one instance.
Algorithms can be described in different forms:
Textual(natural language or algorithmic language),
Graphical(e.g., flowcharts),
Analytical(formulas),
Computer program(in programming languages).
Regardless of form, they can be translated into standard programming structures. Edsger
Dijkstra showed that serial, branched, and cyclic constructs suffice to represent any
algorithm. Algorithmics, as a science, intersects computer science, natural sciences,
economics, and technology. Its key areas are:
1. Algorithm design:Crafting efficient problem-solving procedures.
2. Algorithmic complexity theory:Studying the inherent difficulty of problems.
3. Algorithm analysis:Evaluating algorithm properties and resource requirements.
2.1.1 Algorithm Design
An algorithm represents a problem-solving idea independent of coding syntax or hardware.
Programs are implementations of algorithms, while algorithm creation combines creativity
and engineering. Several design paradigms evolved:
