> For the complete documentation index, see [llms.txt](https://cs61b-2.gitbook.io/cs61b-textbook-fall-2026/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://cs61b-2.gitbook.io/cs61b-textbook-fall-2026/25.-hashing-i/25.4-handling-collisions-linear-probing-and-external-chaining.md).

# 25.4 Handling Collisions: Linear Probing and External Chaining

In hashing, a collision occurs when we have multiple elements that have the same index in our array.

There are two common methods to deal with collisions in hash tables:

1. **Linear Probing:** Store the colliding keys elsewhere in the array, potentially in the next open array space. This method can be seen with distributed hash tables, which you will see in later computer science courses that you may take.
2. **External Chaining:** A simpler solution is to store all the keys with the same hash value together in a collection of their own, such as a `LinkedList`. This collection of entries sharing a single index is called a **bucket**.


---

# 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 by asking a question.

Perform an HTTP GET request on the following URL with the `ask` and `goal` query parameters:

```
GET https://cs61b-2.gitbook.io/cs61b-textbook-fall-2026/25.-hashing-i/25.4-handling-collisions-linear-probing-and-external-chaining.md?ask=<question>&goal=<user_goal>
```

`ask` is the immediate question: it should be specific, self-contained, and written in natural language.
`goal` is what the user is ultimately trying to achieve, the reason they need the answer. Sharing it helps GitBook give you a better, more relevant answer. A goal is most helpful when it describes the outcome the user wants rather than restating the question. For example, with `ask=how do I create an API token`, a goal like `automate deployments from our CI pipeline` lets GitBook tailor the answer to that use case.

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.