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Beginner Topic 7 of 51 Algorithms

Binary Search

Halving a sorted range repeatedly to locate a target.

How it works

Binary search finds a target in a sorted array by repeatedly comparing it with the middle element and discarding the half that cannot contain it. Each step halves the search range, so it takes O(log n) comparisons, about 20 for a million items. It works on any monotonic predicate, not just arrays, which enables searching on answers.

Where it is used

Dictionary lookups, finding insertion points, searching sorted database indexes, version bisection in debugging such as git bisect, and solving optimization problems by binary searching on the answer all use it.

Common pitfall

Off-by-one errors in the bounds and infinite loops from wrong midpoint updates are famous. Computing mid as (lo + hi) / 2 can overflow in fixed-width integers; use lo + (hi - lo) / 2. The data must be sorted, and duplicates require care about which index you return.

Where it fits in the course

Binary Search is topic 7 of 51 in Algorithms, rated Beginner. It follows Linear Search. The next topic is Bubble Sort.

Practice and explore

How to study this topic

  1. Read the explanation above and restate the definition in your own words.
  2. Open the interactive lesson and answer its mini quiz.
  3. Read the common pitfall, then write a short example that avoids it.
  4. Check your understanding in the Algorithms quiz, and revisit the topic if you miss a question.

Frequently asked questions

What is Binary Search?
Halving a sorted range repeatedly to locate a target. It belongs to Algorithms and is a beginner-level topic.
Where do people use Binary Search?
Dictionary lookups, finding insertion points, searching sorted database indexes, version bisection in debugging such as git bisect, and solving optimization problems by binary searching on the answer all use it.
What is the most common mistake with Binary Search?
Off-by-one errors in the bounds and infinite loops from wrong midpoint updates are famous.
What should I learn before this topic?
Start with Linear Search, the topic just before it in Algorithms.
How can I practice it?
Answer the mini quiz in the interactive lesson, then take the Algorithms quiz. You can also explore Linear vs Binary Search in the Visual Lab.
Is Binary Search hard to learn?
It is a Beginner topic, so it works as an entry point. If the terms are new, read the explanation twice and try the visualizer before the quiz.
How long does it take to learn Binary Search?
Most learners can read the explanation and finish the interactive lesson in under an hour. Fluency comes from applying the idea, so plan a few short practice sessions with the quiz.
Which topics are related to Binary Search?
Linear Search, Bubble Sort, Big-O Notation are closely connected. The full list is in the related topics section of this page.
What should I study after Binary Search?
Continue with Bubble Sort, the next topic in Algorithms.

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