> For the complete documentation index, see [llms.txt](https://docs.1l.lol/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://docs.1l.lol/data-structures/huffman-coding.md).

# 哈夫曼编码

### 什么是哈夫曼编码

一种**前缀编码**（任一编码都不是另一编码的前缀），且平均码长最短，用于数据压缩。

### 构造步骤

1. 统计每个字符的出现频率（作为权值）；
2. 构造哈夫曼树（频率小的在深层）；
3. 左分支标 0，右分支标 1；
4. 从根到叶子的路径 0/1 序列即为该字符的编码。

### 示例

字符频率：A:5，B:2，C:1，D:3。

按哈夫曼构造后可能的编码：A=0，D=11，C=100，B=101。

### 前缀性质

因为字符都对应叶子结点，路径不会互相包含，所以不会出现“一个编码是另一个前缀”的歧义，解码唯一。

### 与哈夫曼树的关系

哈夫曼编码的平均码长 = 哈夫曼树的 WPL ÷ 总频率，因此构造哈夫曼树即得到最优前缀编码。


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