> 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/25.6-summary.md). # 25.6 Summary In this chapter, we learned about hashing, a powerful technique for turning a more complex object like a `String` into a numerically representable value like an `int`. The *hash table* is a data structure that combines the *hash function* with the fact that arrays can be indexed in constant time. Using the hash table and the map abstract data type, we can build a `HashMap` which allows for amortized constant time access to any key-value pair so long as we know which bucket the key falls into. However, we quickly demonstrated that this naive implementation has several drawbacks: the ability to represent all different kinds of objects, memory efficiency, and collisions. We investigated the importance of the `hashCode()` function to gain an understanding of how it affects the runtime of the hash table. To allow for smaller `size()` in the array, we used the modulo operator to shrink hash values down to a specified range of numbers. We then added external chaining to solve collisions by allowing multiple entries to live in a single bucket in the form of a LinkedList, and explored resizing functionality based on the load factor! --- # 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://cs61b-2.gitbook.io/cs61b-textbook-fall-2026/25.-hashing-i/25.6-summary.md?ask=&goal= ``` `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.