LearnViz CompSci
Home / Learn / Data Structures / Binary Search Trees

Beginner Topic 17 of 52 Data Structures

Binary Search Trees

Ordered binary trees with left smaller and right larger keys.

How it works

A binary search tree keeps every key in the left subtree smaller than the node and every key in the right subtree larger. Search, insert and delete follow one root-to-leaf path, so each costs O(h) where h is the height. With random insertions the height is about log n, but sorted insertions produce a chain. Deletion handles three cases: leaf, one child and two children.

Where it is used

Ordered maps and sets, range queries, in-order iteration of sorted data and implementing symbol tables in interpreters use BSTs. They are the base for AVL and red-black trees.

Common pitfall

Without balancing, sorted or nearly sorted input makes the tree degenerate and operations O(n). Duplicate keys need a defined policy. Deleting a node with two children is error-prone: replace it with the inorder successor. Use a self-balancing tree for guaranteed performance.

Where it fits in the course

Binary Search Trees is topic 17 of 52 in Data Structures, rated Beginner. It follows Tree Traversals. The next topic is AVL Trees.

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 Data Structures quiz, and revisit the topic if you miss a question.

Frequently asked questions

What is Binary Search Trees?
Ordered binary trees with left smaller and right larger keys. It belongs to Data Structures and is a beginner-level topic.
Where do people use Binary Search Trees?
Ordered maps and sets, range queries, in-order iteration of sorted data and implementing symbol tables in interpreters use BSTs.
What is the most common mistake with Binary Search Trees?
Without balancing, sorted or nearly sorted input makes the tree degenerate and operations O(n).
What should I learn before this topic?
Start with Tree Traversals, the topic just before it in Data Structures.
How can I practice it?
Answer the mini quiz in the interactive lesson, then take the Data Structures quiz. You can also explore Linear vs Binary Search in the Visual Lab.
Is Binary Search Trees 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 Trees?
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 Trees?
Tree Traversals, AVL Trees, Binary Trees are closely connected. The full list is in the related topics section of this page.
What should I study after Binary Search Trees?
Continue with AVL Trees, the next topic in Data Structures.

Related topics