What is an algorithm in computer science?

Definition

In computer science, an algorithm is a finite, well-defined sequence of steps or instructions designed to solve a specific problem or perform a computation. Algorithms take input, process it through a series of operations, and produce output.

An algorithm must have the following properties:

• Finiteness: It must terminate after a finite number of steps.
• Definiteness: Each step must be precisely defined.
• Input: It has zero or more inputs.
• Output: It produces at least one output.
• Effectiveness: All operations must be basic enough to be performed exactly and in a finite amount of time.

Worked Example: Finding the Maximum of Two Numbers

Problem: Given two numbers, $a$ and $b$, find the maximum.

Algorithm Steps:

1. Compare $a$ and $b$.
2. If $a > b$, then $a$ is the maximum.
3. Otherwise, $b$ is the maximum.

Step-by-step math:

Let $a = 7$, $b = 5$.

• Step 1: Compare $a$ and $b$.
• $7 > 5$ is true. - Step 2: Since $a > b$, the maximum is $a$. **Mathematical representation:** %%MATH_DISPLAY_0%% For $a = 7$, $b = 5$:

$$ \text{max}(7, 5) = 7 $$

Takeaways

• An algorithm is a precise, step-by-step procedure for solving a problem.
• Algorithms must be finite, unambiguous, and effective.
• They are fundamental to all areas of computer science and programming.