> 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-2026/38.-compression-and-complexity/38.3-shannon-fano-codes.md).

# 38.3 Shannon-Fano Codes

Shannon-Fano codes are an approach to create prefix-free codes based on a set of symbols/characters and their probabilities. The main idea is that we want shorter prefix-free codes for more popular characters, and longer codes for lesser used characters.

The algorithm is:

* Count relative frequencies of all characters in a text.
* Split into ‘left’ and ‘right halves’ of roughly equal frequency.
  * Left half gets a leading zero. Right half gets a leading one.
  * Repeat.

At the end, you will get a tree as shown below, with shorter paths for characters with a higher frequency, and longer paths for characters with a lower frequency.

<figure><img src="https://2512475561-files.gitbook.io/~/files/v0/b/gitbook-x-prod.appspot.com/o/spaces%2FBGDh1mPw1Aw5u4IlOFCn%2Fuploads%2Fgit-blob-dc6a17ab1041d1799973752efba9c4d38a1dbe91%2FScreen%20Shot%202023-04-24%20at%206.06.15%20PM.png?alt=media" alt=""><figcaption></figcaption></figure>

However, Shannon-Fano coding is NOT optimal, so it is not used very often.


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