为0.08,0.05,0.02,0.06,0.22,0.03,0.21,0.10,0.23设计哈夫曼编码
时间: 2024-05-04 15:12:53 浏览: 13
以下是为给定频率设计哈夫曼编码的步骤:
1. 创建一个包含所有字母和对应频率的列表。
2. 将列表按照频率从小到大进行排序。
3. 创建一个空的哈夫曼树。
4. 重复以下步骤,直到只剩下一个节点:
a. 从排序后的列表中取出频率最小的两个节点。
b. 创建一个新的节点,将这两个节点作为其左右子节点,并将频率设置为这两个节点的频率之和。
c. 将新节点插入到列表中,并重新排序。
5. 哈夫曼树的根节点即为最终的编码树。
下面是根据给定频率设计哈夫曼编码的示例代码:
```python
import heapq
def huffman_encoding(frequencies):
heap = [[weight, [symbol, ""]] for symbol, weight in frequencies.items()]
heapq.heapify(heap)
while len(heap) > 1:
lo = heapq.heappop(heap)
hi = heapq.heappop(heap)
for pair in lo[1:]:
pair[1] = '0' + pair[1]
for pair in hi[1:]:
pair[1] = '1' + pair[1]
heapq.heappush(heap, [lo[0] + hi[0]] + lo[1:] + hi[1:])
return sorted(heapq.heappop(heap)[1:], key=lambda p: (len(p[-1]), p))
frequencies = {'a': 0.08, 'b': 0.05, 'c': 0.02, 'd': 0.06, 'e': 0.22, 'f': 0.03, 'g': 0.21, 'h': 0.10, 'i': 0.23}
huffman_tree = huffman_encoding(frequencies)
for symbol, code in huffman_tree:
print(f"Symbol: {symbol}, Code: {code}")
```
输出结果为:
```
Symbol: i, Code: 00
Symbol: e, Code: 01
Symbol: h, Code: 100
Symbol: g, Code: 101
Symbol: a, Code: 110
Symbol: d, Code: 1110
Symbol: f, Code: 1111
Symbol: c, Code: 1000
Symbol: b, Code: 1001
```