Algorithm

An algorithm is a sequence of rigorous steps which can be followed to solve a particular type of problem. To fully describe an algorithm, you must specify:

1. The algorithm's name
2. The input to the problem
3. The output to the problem
4. The steps taken to reach the output from the input

Algorithms are often written in programming languages, which have strict rules on syntax to ensure that a computer can compile it. To avoid syntax and focus only on the actual meaning of the code, an in-between language is used: pseudocode. Here's an example of an algorithm (the Euclidean algorithm) written in pseudocode:

algorithm euclid is
    input: two integers, a and b, where a ≤ b
    output: their greatest common divisor (gcd)

    r ← b mod a
    while r ≠ 0
        b ← a
        a ← r
        r ← b mod a
    return a

More advanced algorithms perform work beyond the scope of a simple calculation, using programming constructs such as conditionals to divert code, loops for iteration, and recursion to divide problems into easier sub-problems.

The output of an algorithm is specified by a return command.