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.

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.

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.

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.