Algorithms

An algorithm is a finite sequence of steps that gives the desired output in a finite amount of time. It has a definite beginning and a definite end. The word comes from the name of the Persian mathematician Al-Khwarizmi.

An example: find the GCD (greatest common divisor) of 24 and 36.

• Step 1: list the divisors of 24: 1, 2, 3, 4, 6, 8, 12, 24.
• Step 2: list the divisors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36.
• Step 3: find the divisors common to both: 1, 2, 3, 4, 6, 12.
• Step 4: the largest of these is the GCD: 12.

An algorithm is the roadmap of a program, its building block. Search engines, messaging apps, taxi booking apps and banking systems all run on algorithms. A clear algorithm makes a solution reliable, accurate and efficient.

A good algorithm has these characteristics:

• Precision: every step is clearly stated.
• Uniqueness: the result of each step depends only on the input and the earlier steps.
• Finiteness: it always stops after a finite number of steps.
• Input: it receives some input.
• Output: it produces some output.

While writing an algorithm, identify three things: the input, the processing to be done, and the output expected.