python实现算数编码与译码

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：

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：

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。