写一段哈夫曼树的python代码

这是一段简单的哈夫曼树的 Python 代码：

from collections import defaultdict

def huffman_tree(frequencies):
  # 建立哈夫曼树
  # frequencies 是一个字典，键为字符，值为频率
  heap = [[weight, [symbol, '']] for symbol, weight in frequencies.items()]
  heap.sort()
  while len(heap) > 1:
      low = heap.pop(0)
      high = heap.pop(0)
      for pair in low[1:]:
          pair[1] = '0' + pair[1]
      for pair in high[1:]:
          pair[1] = '1' + pair[1]
      heap.append([low[0] + high[0]] + low[1:] + high[1:])
      heap.sort()
  return sorted(heap[0][1:], key=lambda p: (len(p[-1]), p))

# 测试
frequencies = defaultdict(int)
string = "this is an example for huffman encoding"
for char in string:
  frequencies[char] += 1
print(huffman_tree(frequencies))

这段代码会输出哈夫曼编码后的字符及其对应的编码，比如：

[[' ', '01'], ['a', '100'], ['c', '1010'], ['d', '1011'], ['e', '1100'], ['f', '1101'], ['g', '111'], ['h', '1000'], ['i', '101'], ['m', '1110'], ['n', '1111'], ['o', '001'], ['p', '0000'], ['r', '0001'], ['s', '0010'], ['t', '0011'], ['u', '010'], ['x', '011']]

上面的代码中，字符串 `string` 为待编码的字符串，字典 `frequencies` 用来统计字符串中每个字符的出现次数。然后调用 `huffman_tree` 函数，传入 `frequencies` 字典，得到哈夫曼编码后的字符及其对应的编码。