python实现算数编码与译码
时间: 2024-01-10 13:02:54 浏览: 128
算数编码是一种无损数据压缩算法,比哈夫曼编码更为高效。下面是Python实现算数编码与译码的示例代码:
算数编码:
```python
from decimal import Decimal
class ArithmeticEncoder:
def __init__(self, alphabet):
self.alphabet = alphabet
self.low = Decimal(0)
self.high = Decimal(1)
self.range = Decimal(1)
self.output = []
def encode(self, sequence):
for symbol in sequence:
symbol_index = self.alphabet.index(symbol)
symbol_range = self.high - self.low
self.high = self.low + symbol_range * self.alphabet.high(symbol_index)
self.low = self.low + symbol_range * self.alphabet.low(symbol_index)
while self.range < Decimal("0.1"):
self.output.append(self.low)
self.range *= Decimal(10)
self.low = Decimal(str(self.low))[2:]
self.high = Decimal(str(self.high))[2:]
self.range = Decimal(str(self.range))[2:]
def finish(self):
midpoint = (self.high + self.low) / 2
if midpoint < Decimal("0.5"):
self.output.append(self.low)
else:
self.output.append(self.high)
while self.range < Decimal("0.1"):
self.output.append(self.low)
self.range *= Decimal(10)
self.low = Decimal(str(self.low))[2:]
self.high = Decimal(str(self.high))[2:]
self.range = Decimal(str(self.range))[2:]
return ''.join(self.output)
class Alphabet:
def __init__(self, symbols, frequencies):
self.symbols = symbols
self.frequencies = frequencies
self.cumulative_frequencies = [sum(frequencies[:i+1]) for i in range(len(frequencies))]
def high(self, symbol_index):
return self.cumulative_frequencies[symbol_index] / sum(self.frequencies)
def low(self, symbol_index):
if symbol_index == 0:
return 0
else:
return self.cumulative_frequencies[symbol_index-1] / sum(self.frequencies)
sequence = "hello world"
symbols = sorted(set(sequence))
frequencies = [sequence.count(symbol) for symbol in symbols]
alphabet = Alphabet(symbols, frequencies)
encoder = ArithmeticEncoder(alphabet)
encoder.encode(sequence)
encoded_sequence = encoder.finish()
print(encoded_sequence)
```
算数译码:
```python
class ArithmeticDecoder:
def __init__(self, alphabet, encoded_sequence):
self.alphabet = alphabet
self.encoded_sequence = encoded_sequence
self.low = Decimal(0)
self.high = Decimal(1)
self.range = Decimal(1)
self.decoded_sequence = []
def decode(self):
while len(self.encoded_sequence) > 0:
midpoint = (self.high + self.low) / 2
symbol_index = self.alphabet.symbol_index(midpoint)
symbol_range = self.high - self.low
self.high = self.low + symbol_range * self.alphabet.high(symbol_index)
self.low = self.low + symbol_range * self.alphabet.low(symbol_index)
while self.encoded_sequence.startswith(self.low):
self.encoded_sequence = self.encoded_sequence[len(str(self.low)):]
self.range *= Decimal(10)
self.low = Decimal(str(self.low))[2:]
self.high = Decimal(str(self.high))[2:]
self.range = Decimal(str(self.range))[2:]
self.decoded_sequence.append(self.alphabet.symbol(symbol_index))
return ''.join(self.decoded_sequence)
class Alphabet:
def __init__(self, symbols, frequencies):
self.symbols = symbols
self.frequencies = frequencies
self.cumulative_frequencies = [sum(frequencies[:i+1]) for i in range(len(frequencies))]
def symbol(self, symbol_index):
return self.symbols[symbol_index]
def symbol_index(self, frequency):
for i in range(len(self.cumulative_frequencies)):
if frequency < self.cumulative_frequencies[i]:
return i
encoded_sequence = "1145141919810"
symbols = [' ', 'd', 'e', 'h', 'l', 'o', 'r', 'w']
frequencies = [1, 1, 1, 1, 3, 2, 1, 1]
alphabet = Alphabet(symbols, frequencies)
decoder = ArithmeticDecoder(alphabet, encoded_sequence)
decoded_sequence = decoder.decode()
print(decoded_sequence)
```
注意,此代码仅适用于Python 3.0及以上版本。
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