Algorithm

Everyday life is full of activities we complete by following a fixed sequence of steps — getting ready for school, making breakfast, riding a bicycle, wearing a tie, solving a puzzle. Each of these has its own ordered list of actions, and doing the actions in order accomplishes the activity.

Everyday example: riding a bicycle

The activity "riding a bicycle" can be broken down into a sequence like this:

1. Remove the bicycle from the stand.
2. Sit on the seat of the bicycle.
3. Start pedalling.
4. Use brakes whenever needed.
5. Stop on reaching the destination.

Nothing about this is mathematical — it is simply an ordered, finite list of steps that gets a task done.

Worked example: GCD of 45 and 54

The same step-by-step thinking applies to a computational task. The Greatest Common Divisor (GCD) of two numbers is the largest number that divides both of them. To find the GCD of 45 and 54:

Step 1 — list the divisors of each number (the numbers that divide it exactly):

Divisors of 45:  1, 3, 5, 9, 15, 45
Divisors of 54:  1, 2, 3, 6, 9, 18, 27, 54

Step 2 — pick the largest number common to both lists.

The common divisors are 1, 3 and 9; the largest is 9.

GCD(45, 54) = 9

What makes such a sequence an algorithm

Both examples show that accomplishing a task means following a sequence of steps. Such a finite sequence of steps required to get the desired output is called an algorithm. Its defining properties: …