Definition of an algorithm

Definition of an Algorithm

  • An algorithm can be defined as a well-defined, self-contained series of steps or instructions for resolving a specific problem or achieving a particular goal.
  • Step-by-step, unambiguous commands characterise an algorithm. Each step must be rigorously defined and clear, with no ambiguity.
  • An algorithm’s finiteness is a critical component. It states that after a finite number of steps, an algorithm must halt.
  • It’s crucial that an algorithm be effective. This implies that every instruction should be simple enough that it can be carried out, in principle, by a person using only pencil and paper. It should not require any inherent “cleverness.”
  • The algorithm requires being generally applicable, meaning it can handle all cases relevant to the problem at hand. Even under different scenarios, it should give correct outcomes.

Properties of Algorithms

  • Determinism: For the same input, an algorithm will always produce the same output. This predictability is crucial for the algorithm’s reliability.
  • Definiteness: Each step in an algorithm must be precisely defined; there can be no vagueness or ambiguity in an algorithm.
  • Input and output: An algorithm should have specified inputs and produce specified outputs related to those inputs.
  • Finiteness: An algorithm should always terminate following a finite number of steps.
  • Generality: The algorithm must be able to solve all instances of the problem it is meant to address.

Functions of an Algorithm

  • Solvability: An algorithm must solve the problem for which it was created. While an algorithm may not solve every problem, it should solve a well-defined class of problems.
  • Efficiency: An algorithm must execute its task as efficiently as possible, using the least amount of computing resources like time and memory.
  • Maintainability: A well-crafted algorithm is easy to maintain and modify, making it adaptable to changing needs or systems.
  • Readability: A well-designed algorithm is simple to understand, facilitating developers in maintaining and modifying it, and making it easier for others to learn and use.

Writing and Testing Algorithms

  • When writing an algorithm, be sure to keep the objective clear, eliminate redundancies, consider edge cases, and anticipate potential issues.
  • To verify an algorithm, consider both its efficiency and correctness. Test it with various inputs, including typical cases, boundary cases, and invalid inputs.
  • When considering the efficiency of an algorithm, consider both time and space complexity. These considerations will inform decisions about when and where certain algorithms are suitable.
  • Keep in mind that a simpler, less efficient algorithm may be more suitable for smaller inputs or less critical tasks, while a more complex, efficient algorithm may be necessary for larger inputs or more demanding tasks.