利用python贪心法求解哈夫曼编码问题。 设要编码的字符集为{d1, d2, …, dn},它们出现的频率为{w1, w2, …, wn},应用哈夫曼树构造最优的不等长的由0、1构成的编码方案,并输出哈夫曼树
时间: 2023-10-04 22:12:14 浏览: 48
【贪心算法】哈夫曼编码.doc
好的,下面是 Python 代码实现:
```python
class Node:
def __init__(self, freq, symbol, left=None, right=None):
self.freq = freq
self.symbol = symbol
self.left = left
self.right = right
def __lt__(self, other):
return self.freq < other.freq
def __eq__(self, other):
if(other == None):
return False
if(not isinstance(other, Node)):
return False
return self.freq == other.freq
def buildHuffmanTree(freq_dict):
pq = []
for key in freq_dict:
pq.append(Node(freq_dict[key], key))
while(len(pq) > 1):
node1 = heappop(pq)
node2 = heappop(pq)
merged_node = Node(node1.freq + node2.freq, None, node1, node2)
heappush(pq, merged_node)
return heappop(pq)
def huffman_encoding(root, current_code, codes):
if(root == None):
return
if(root.symbol != None):
codes[root.symbol] = current_code
return
huffman_encoding(root.left, current_code + "0", codes)
huffman_encoding(root.right, current_code + "1", codes)
def huffman_encoding_helper(data):
freq_dict = {}
for char in data:
if char in freq_dict:
freq_dict[char] += 1
else:
freq_dict[char] = 1
root = buildHuffmanTree(freq_dict)
codes = {}
huffman_encoding(root, "", codes)
return codes, root
def huffman_encoding(data):
if(len(data) == 0):
return "", None
codes, root = huffman_encoding_helper(data)
encoded_data = ""
for char in data:
encoded_data += codes[char]
return encoded_data, root
def huffman_decoding(encoded_data, root):
decoded_data = ""
current_node = root
for bit in encoded_data:
if(bit == '0'):
current_node = current_node.left
else:
current_node = current_node.right
if(current_node.symbol != None):
decoded_data += current_node.symbol
current_node = root
return decoded_data
```
其中,`buildHuffmanTree()` 函数用于构建哈夫曼树,`huffman_encoding()` 函数用于对数据进行编码,`huffman_decoding()` 函数用于对编码后的数据进行解码。
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