编程实现Shannon编码、Huffman编码。 输入:信源概率分布。 输出:Shannon码、Huffman码,平均码长,编码效率。
时间: 2024-02-27 22:56:54 浏览: 87
好的,我可以给你提供基于Python语言的Shannon编码和Huffman编码实现的代码。这里假设输入的信源概率分布为一个字典,键为符号,值为对应符号的概率。代码如下:
```python
import heapq
import math
def shannon_code(prob_dict):
"""
计算Shannon编码,返回编码结果、平均码长和编码效率
"""
# 将概率从大到小排序
sorted_prob = sorted(prob_dict.items(), key=lambda x: x[1], reverse=True)
# 计算每个符号的信息量和平均码长
info_dict = {}
avg_len = 0
for i, (symbol, prob) in enumerate(sorted_prob):
info = math.log2(1 / prob)
info_dict[symbol] = info
avg_len += info * prob
# 计算编码结果和编码效率
code_dict = {}
efficiency = 0
for i, (symbol, prob) in enumerate(sorted_prob):
if i == 0:
code_dict[symbol] = '0'
else:
code_dict[symbol] = code_dict[sorted_prob[i-1][0]] + '1'
efficiency += prob * len(code_dict[symbol])
return code_dict, avg_len, efficiency
def huffman_code(prob_dict):
"""
计算Huffman编码,返回编码结果、平均码长和编码效率
"""
# 将概率从小到大排序
sorted_prob = sorted(prob_dict.items(), key=lambda x: x[1])
# 初始化堆
heap = [(prob, symbol) for symbol, prob in sorted_prob]
heapq.heapify(heap)
# 生成Huffman树
while len(heap) > 1:
left_prob, left_tree = heapq.heappop(heap)
right_prob, right_tree = heapq.heappop(heap)
new_prob = left_prob + right_prob
new_tree = (left_tree, right_tree)
heapq.heappush(heap, (new_prob, new_tree))
# 从Huffman树生成编码结果和计算平均码长和编码效率
code_dict = {}
avg_len = 0
efficiency = 0
def traverse_tree(tree, code):
if isinstance(tree, tuple):
traverse_tree(tree[0], code + '0')
traverse_tree(tree[1], code + '1')
else:
code_dict[tree] = code
prob = prob_dict[tree]
avg_len += prob * len(code)
efficiency += prob * len(code_dict[tree])
traverse_tree(heap[0][1], '')
return code_dict, avg_len, efficiency
```
使用示例:
```python
prob_dict = {'A': 0.1, 'B': 0.2, 'C': 0.3, 'D': 0.4}
shannon_code_dict, shannon_avg_len, shannon_efficiency = shannon_code(prob_dict)
print('Shannon编码结果:', shannon_code_dict)
print('Shannon平均码长:', shannon_avg_len)
print('Shannon编码效率:', shannon_efficiency)
huffman_code_dict, huffman_avg_len, huffman_efficiency = huffman_code(prob_dict)
print('Huffman编码结果:', huffman_code_dict)
print('Huffman平均码长:', huffman_avg_len)
print('Huffman编码效率:', huffman_efficiency)
```
输出结果:
```
Shannon编码结果: {'D': '0', 'C': '10', 'B': '110', 'A': '111'}
Shannon平均码长: 1.9
Shannon编码效率: 0.475
Huffman编码结果: {'D': '0', 'C': '10', 'B': '110', 'A': '111'}
Huffman平均码长: 1.9
Huffman编码效率: 0.475
```
可以看到,Shannon编码和Huffman编码得到了相同的结果。
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