编程实现Shannon编码、Huffman编码。
时间: 2024-05-15 22:13:04 浏览: 16
Shannon编码和Huffman编码都是一种压缩算法,用于将数据进行压缩,以减少存储空间和传输带宽的使用。下面分别介绍它们的实现方法:
1. Shannon编码
Shannon编码是一种基于信息熵的编码方法,可以将符号序列压缩成最短的二进制编码。具体实现方法如下:
```
def shannon_encode(symbols, weights):
code_dict = {}
sorted_symbols = sorted(zip(symbols, weights), key=lambda x: x[1], reverse=True)
total_weight = sum(weights)
for i in range(len(sorted_symbols)):
left_weight = sum([w for _, w in sorted_symbols[:i]])
right_weight = total_weight - left_weight - sorted_symbols[i][1]
if left_weight == 0:
code = '0' * (len(sorted_symbols) - 1)
elif right_weight == 0:
code = '1' * (len(sorted_symbols) - 1)
else:
left_prob = left_weight / total_weight
right_prob = right_weight / total_weight
left_code = shannon_encode([sym for sym, _ in sorted_symbols[:i]], [w for _, w in sorted_symbols[:i]])
right_code = shannon_encode([sym for sym, _ in sorted_symbols[i + 1:]],
[w for _, w in sorted_symbols[i + 1:]])
code = ''.join(['0' + left_code[sym] for sym in sorted_symbols[:i]]) + \
''.join(['1' + right_code[sym] for sym in sorted_symbols[i + 1:]])
code_dict[sorted_symbols[i][0]] = code
return code_dict
```
在上面的代码中,symbols和weights分别表示符号序列和其对应的权重。首先将符号按照权重从大到小排序,然后依次对每个符号进行编码。编码过程中,需要计算左子树和右子树的概率,并递归地进行编码。最终返回一个编码字典,其中键为符号,值为对应的二进制编码。
2. Huffman编码
Huffman编码是一种基于贪心算法的编码方法,可以将符号序列压缩成最短的二进制编码。具体实现方法如下:
```
from collections import Counter
import heapq
class Node:
def __init__(self, symbol=None, weight=0, left=None, right=None):
self.symbol = symbol
self.weight = weight
self.left = left
self.right = right
def __lt__(self, other):
return self.weight < other.weight
def __eq__(self, other):
return self.weight == other.weight
def huffman_encode(symbols):
freq_dict = Counter(symbols)
heap = [Node(sym, freq_dict[sym]) for sym in freq_dict]
heapq.heapify(heap)
while len(heap) > 1:
left = heapq.heappop(heap)
right = heapq.heappop(heap)
parent = Node(weight=left.weight + right.weight, left=left, right=right)
heapq.heappush(heap, parent)
root = heap[0]
code_dict = {}
def traverse(node, code):
if node.symbol is not None:
code_dict[node.symbol] = code
else:
traverse(node.left, code + '0')
traverse(node.right, code + '1')
traverse(root, '')
return code_dict
```
在上面的代码中,symbols表示符号序列。首先统计每个符号出现的次数,并将其转化为Node对象,并加入堆中。然后每次从堆中取出两个权重最小的节点进行合并,直到堆中只剩一个节点为止。合并节点的过程中,需要创建一个新的父节点,并将两个子节点作为其左右子树。最终得到的堆中只有一个节点,即为根节点。通过递归遍历树,可以得到每个符号的编码,并将其存储在一个编码字典中返回。
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