20、Huffman编码与解码的实现与解析

Huffman编码与解码的实现与解析

1. 编码文本输入

1.1 Huffman树与优先队列

Huffman树的数据类型定义如下：

data huffman-tree : Set where
  ht-leaf : string Ñ N Ñ huffman-tree
  ht-node : N Ñ huffman-tree Ñ huffman-tree Ñ huffman-tree
ht-frequency : huffman-tree Ñ N
ht-frequency (ht-leaf _ f) = f
ht-frequency (ht-node f _ _) = f
ht-compare : huffman-tree Ñ huffman-tree Ñ B
ht-compare h1 h2 = (ht-frequency h1) < (ht-frequency h2)

这里定义了Huffman树的两种节点：叶子节点 ht-leaf 和内部节点 ht-node ，并提供了计算频率和比较节点频率的函数。

优先队列使用Braun树实现：

pqueue : N Ñ Set
pqueue = braun-tree
pq-empty : pqueue 0
pq-empty = bt-empty
pq-insert : @ {n : N} Ñ huffman-tree Ñ pqueue n Ñ pqueue (suc n)
pq-insert