How is an "algorithm" defined in problem-solving?

An algorithm is defined as a systematic, step-by-step procedure that guarantees a solution to a given problem when applied correctly. This means that if a person follows the algorithm's instructions precisely, they will achieve the desired result without fail. Algorithms are often used in mathematics and computer science, as they provide a well-structured approach to problem-solving that can be reliably reproduced.

The focus on the reliability and structure of algorithms differentiates them from other methods of problem-solving, such as intuition-based approaches, which can yield inconsistent results depending on the individual's prior experiences or insights. This characteristic of guaranteed solutions positions algorithms as essential tools for logical reasoning and complex problem-solving tasks, ensuring consistent outcomes regardless of subjective interpretations.

In contrast, random approaches or strategies that produce varying outcomes do not have the systematic framework that guarantees a resolution, making them less effective for structured problem-solving scenarios.