给定 n 个权重值,按照哈夫曼编码规则,输出该 n 个值对应的哈夫曼编码。
时间: 2023-07-19 17:41:28 浏览: 83
好的,哈夫曼编码的实现需要通过构建哈夫曼树来完成。
具体步骤如下:
1. 将给定的 n 个权重值按从小到大的顺序排列。
2. 选取两个权重值最小的节点,构建成一棵二叉树,该二叉树的根节点的权重值为这两个节点的权重值之和。
3. 将这棵新的二叉树作为一个节点,将其插入到原来的节点列表中,删除原来的两个节点。
4. 重复步骤 2 和 3,直到节点列表中只剩下一个节点,这个节点就是哈夫曼树的根节点。
5. 对哈夫曼树进行遍历,当遇到左子树时添加一个 0,当遇到右子树时添加一个 1,得到该节点的哈夫曼编码。
下面是一个实现哈夫曼编码的 Python 代码示例:
```python
class HuffmanNode:
def __init__(self, weight):
self.weight = weight
self.left = None
self.right = None
def __lt__(self, other):
return self.weight < other.weight
def __eq__(self, other):
if other == None:
return False
if not isinstance(other, HuffmanNode):
return False
return self.weight == other.weight
def build_huffman_tree(weights):
nodes = [HuffmanNode(weight) for weight in weights]
heapq.heapify(nodes)
while len(nodes) > 1:
node1 = heapq.heappop(nodes)
node2 = heapq.heappop(nodes)
parent_node = HuffmanNode(node1.weight + node2.weight)
parent_node.left = node1
parent_node.right = node2
heapq.heappush(nodes, parent_node)
return nodes[0]
def get_huffman_codes(root, current_code, codes):
if root is None:
return
if root.left is None and root.right is None:
codes[root.weight] = current_code
get_huffman_codes(root.left, current_code + "0", codes)
get_huffman_codes(root.right, current_code + "1", codes)
def huffman_encoding(weights):
root = build_huffman_tree(weights)
codes = {}
get_huffman_codes(root, "", codes)
encoded_data = ""
for weight in weights:
encoded_data += codes[weight]
return encoded_data, codes
def huffman_decoding(encoded_data, codes):
decoded_data = ""
current_code = ""
for bit in encoded_data:
current_code += bit
for weight, code in codes.items():
if code == current_code:
decoded_data += str(weight)
current_code = ""
break
return decoded_data
```
其中,build_huffman_tree 函数用于构建哈夫曼树,get_huffman_codes 函数用于遍历哈夫曼树并获取每个节点的编码,huffman_encoding 函数用于对给定的权重值进行哈夫曼编码,huffman_decoding 函数用于将哈夫曼编码解码为原始的权重值。
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