> For the complete documentation index, see [llms.txt](https://interviews.woojiahao.com/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://interviews.woojiahao.com/data-structures/graphs/trees/binary-search-trees.md).

# Binary Search Trees

{% hint style="info" %}
Binary search trees have the core property where `left <= node < right` thus allowing elements to be stored in sorted fashion easily
{% endhint %}

## Runtime analysis

BSTs have the same runtime as [Trees](/data-structures/graphs/trees.md) but if the tree is balanced, it implies that insertions of elements in sorted order can be done in $$O(\log n)$$ which is faster than what inserting into a sorted array can achieve

## Core properties

1. `left <= node < right`
2. In-order traversal produces a sorted array
3. The maximum value exists on the rightmost leaf of the right sub-tree
4. The minimum value exists on the leftmost leaf of the left sub-tree

## Techniques

Most of the techniques of a BST is the same as those [Trees](/data-structures/graphs/trees.md), however, there is a technique that only BSTs can achieve

### Using in-order traversal

The core property of BSTs allow in-order traversal to become a sequential traversal of the elements in sorted order. Once a problem mentions that the tree is a BST, try thinking of how to exploit this property to solve the problem


---

# Agent Instructions
This documentation is published with GitBook. GitBook is the documentation platform designed so that both humans and AI agents can read, navigate, and reason over technical content effectively. Learn more at gitbook.com.

## Querying This Documentation
If you need additional information that is not directly available in this page, you can query the documentation dynamically by asking a question.

Perform an HTTP GET request on the current page URL with the `ask` query parameter, and the optional `goal` query parameter:

```
GET https://interviews.woojiahao.com/data-structures/graphs/trees/binary-search-trees.md?ask=<question>&goal=<endgoal>
```

`ask` is the immediate question: it should be specific, self-contained, and written in natural language.
`goal` is optional and describes the broader end goal you are ultimately trying to accomplish on behalf of the user. GitBook uses it to tailor the answer towards what is most useful for that goal.

The response will contain a direct answer to the question and relevant excerpts and sources from the documentation.

Use this mechanism when the answer is not explicitly present in the current page, you need clarification or additional context, or you want to retrieve related documentation sections.