How does an algorithm solve a computational problem?

In computer science, an algorithm is a systematic, step-by-step procedure designed to solve a well-defined computational problem. It functions by transforming input data into a desired output through a finite sequence of logical operations.12

To solve a problem effectively, an algorithm typically relies on the following components:

• Data Structures: Algorithms use specific data structures—such as arrays, linked lists, or graphs—to organize data in memory so that it can be accessed and manipulated efficiently.1
• Computational Logic: The arithmetic-logic unit (ALU) within a computer executes the mathematical and logical steps defined by the algorithm to process data at high speeds.3
• Efficiency and Complexity: Computer scientists analyze computational complexity to predict how much time and memory an algorithm requires. This ensures the solution is not only correct but also practical for real-world applications.41

When a problem is too complex to solve efficiently, researchers may use heuristic algorithms to find near-optimal solutions within a reasonable timeframe. Some problems, however, are proven to be unsolvable, such as the halting problem, meaning no algorithm can be written to solve them.412