Linear Algorithms

A linear algorithm is one whose commands are carried out from top to bottom, one after another, each exactly once. It has no condition checks and no repeats. Many everyday actions are linear: brushing teeth, packing a school bag or washing hands.

An example is an algorithm for brushing teeth. 1) Take the toothbrush. 2) Put toothpaste on it. 3) Brush your teeth for 2 minutes. 4) Rinse your mouth. 5) Put the brush back. The order of commands matters: if you rinse your mouth before putting on the paste, the result is different.

Linear algorithms appear in calculations too. To find the area of a rectangle, we enter its sides a and b, then calculate S = a * b and output the result. All the steps of this algorithm are carried out in order.

In a flowchart a linear algorithm can be drawn from top to bottom with a single arrow. After writing an algorithm, check it by hand on an example. For instance, if a = 4 and b = 5, the result should be S = 20.

Key takeaways

• In a linear algorithm commands run in order, once each.
• It has no condition checks and no repeats.
• The order of commands affects the result.
• A finished algorithm should be checked by hand on an example.