Binary Search
Lesson notes
Overview
On sorted data, halve the search range each step: a million items need only 20 checks. This topic is rated beginner and is number 10 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
Binary search finds a target in a sorted list by comparing it with the middle item and discarding the half that cannot contain it, repeating until it is found. Each step halves the range, so a million items need only about 20 comparisons and a billion about 30: O(log n). It requires random access and sorted data, and is easy to get wrong, with off-by-one errors in the bounds being a notorious source of bugs.
Reading the relationship
The expression "O(log n)" is a compact summary of the idea. It uses the symbols O, n; name what each one stands for before you start. Notice that it contains a logarithm, which turns multiplication into addition and compresses large values. 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 “Linear Search”, the topic before it in Computer Science. Once you are comfortable, continue with “Interpolation Search”.
Why it matters
Computing ideas decide how fast, how safely and how well software can solve problems.
Where you might use it
- Revising “Binary Search” before a class, exam or certification
- Choosing the right algorithm or data structure when writing software or apps
- Debugging programs and judging how fast or how safely code will run at scale
- Understanding how search engines, games, phones and AI systems make decisions
Frequently asked questions
What is Binary Search?
On sorted data, halve the search range each step: a million items need only 20 checks. It is a beginner topic in Computer Science.
How do I use the Binary Search simulation?
The panel at the top shows an interactive animation of the idea. Every slider changes one quantity so you can see its effect on the outcome. Move the sliders one at a time, then press Space to pause the animation and look closer.
What does the formula mean?
The expression O(log n) packs the idea into symbols. Name each symbol first, then change one quantity with the sliders and see which others respond.
Who is this topic for?
Core ideas and first intuitions. No prior knowledge needed. If the quiz feels hard, reread the lesson notes and try the previous topic first.
What should I learn before this?
Start with “Linear Search”, the previous topic in Computer Science. Each topic in a subject builds on the ones before it.
How do I track my progress?
Press “Mark as learned” on this page. Progress is stored only in this browser and is never sent anywhere. The Browse page can show topics you have learned or still need to learn.
Quick quiz
More in Computer Science
See all →Interpolation Search
Guess where the target should be, like opening a dictionary near the right letter.
Breadth-First Search
Visit nodes level by level using a queue; finds shortest paths in unweighted graphs.
Depth-First Search
Dive down one branch as far as possible before backtracking, using a stack or recursion.