Linear Search

Lesson notes

Overview

Check each item in turn until the target is found. This topic is rated beginner and is number 9 of 117 in Computer Science. Core ideas and first intuitions. No prior knowledge needed.

What you are seeing

The panel above shows an interactive animation of the idea. Every slider changes one quantity so you can see its effect on the outcome. The animation is drawn live from the model, so everything you see responds to the sliders. Press Space to pause, use Restart to replay from the start, and change the speed to slow down quick events.

In depth

Linear search checks each item in turn until it finds the target or reaches the end. It needs no preparation and works on any list, sorted or not, and on linked lists. On average it examines half the items, so it takes O(n) time, which is acceptable for short lists but too slow for large data sets that are searched often. Sorting the data or using a hash table are the usual improvements.

Reading the relationship

The expression "O(n)" is a compact summary of the idea. It uses the symbols O, n; name what each one stands for before you start. Then use the sliders to see how changing one quantity changes the others.

A guided exploration

1. Run the animation once with the default settings and describe in words what happens. 2. Change one slider at a time and note which quantity responds most. 3. Push each slider to its extreme and decide whether the result still makes sense.

Try this

Start by only moving one slider at a time. Say aloud what you expect, then check.

Common pitfalls

Test small inputs by hand and then the largest ones. Off-by-one errors and forgetting how cost grows with input size are the most common traps.

How it connects

It builds on “Counting Sort”, the topic before it in Computer Science. Once you are comfortable, continue with “Binary Search”.

Why it matters

Computing ideas decide how fast, how safely and how well software can solve problems.