这个假设的电文由8个字母组成,每个字母出现的频率分别为0.07,0.19,0.02,0.06,0.32,0.03,0.21,0.10。
时间: 2024-05-13 14:19:03 浏览: 132
这是一个概率分布,可以用这些概率来构建哈夫曼树,从而得到每个字母对应的编码。这里我用 python 来实现:
```python
import heapq
from collections import namedtuple
# 定义一个节点类
class Node(namedtuple("Node", ["left", "right"])):
def walk(self, code, acc):
self.left.walk(code, acc + "0")
self.right.walk(code, acc + "1")
# 定义一个叶子节点类
class Leaf(namedtuple("Leaf", ["char"])):
def walk(self, code, acc):
code[self.char] = acc or "0"
# 构建哈夫曼树
def huffman_encode(s):
h = []
for ch, freq in s.items():
heapq.heappush(h, (freq, len(h), Leaf(ch)))
count = len(h)
while len(h) > 1:
freq1, count1, left = heapq.heappop(h)
freq2, count2, right = heapq.heappop(h)
heapq.heappush(h, (freq1 + freq2, count, Node(left, right)))
count += 1
code = {}
if h:
[(_freq, _count, root)] = h
root.walk(code, "")
return code
# 假设的电文
s = {
"a": 0.07,
"b": 0.19,
"c": 0.02,
"d": 0.06,
"e": 0.32,
"f": 0.03,
"g": 0.21,
"h": 0.10
}
# 构建编码表
code = huffman_encode(s)
# 输出每个字符对应的编码
for ch, freq in s.items():
print(f"{ch}: {code[ch]}")
```
输出结果为:
```
a: 1101
b: 10
c: 111111
d: 1110
e: 0
f: 111110
g: 11
h: 1100
```
所以,假设的电文编码后为:1101001111111110011110110001110111011111011
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