Python实现算术编解码：无损数据压缩算法

算术编码是一种用于无损数据压缩的技术，它通过使用一个区间来表示输入数据的概率范围。下面是一个简单的算术编解码的Python实现示例：

class ArithmeticEncoder:
    def __init__(self):
        self.low = 0.0
        self.high = 1.0
        self.value = 0.0
        self.bits_to_follow = 0
        self.output = []

    def encode(self, data, probabilities):
        for symbol in data:
            low_range = self.low + (self.high - self.low) * probabilities[symbol][0]
            high_range = self.low + (self.high - self.low) * probabilities[symbol][1]
            self.update_range(low_range, high_range)

        # Output the final bits
        if self.low < 0.5:
            self.output.append(0)
            self.bits_to_follow += 1
        else:
            self.output.append(1)
            self.bits_to_follow += 1

        # Output the trailing bits
        for _ in range(self.bits_to_follow):
            if self.low < 0.5:
                self.output.append(1)
            else:
                self.output.append(0)

        return self.output

    def update_range(self, low_range, high_range):
        self.low = low_range
        self.high = high_range

        # Scale the range to avoid underflow or overflow
        while self.low < 0.5 and self.high < 0.5 or self.low >= 0.5 and self.high >= 0.5:
            if self.low < 0.25:
                self.output.append(0)
                self.bits_to_follow += 1
                self.low *= 2
                self.high *= 2
            elif self.low >= 0.75:
                self.output.append(1)
                self.bits_to_follow += 1
                self.low = (self.low - 0.75) * 2
                self.high = (self.high - 0.75) * 2
            else:
                break

        # Renormalize the range
        while self.low >= 0.25 and self.high < 0.75:
            self.low = (self.low - 0.25) * 2
            self.high = (self.high - 0.25) * 2


class ArithmeticDecoder:
    def __init__(self, encoded_data, probabilities):
        self.encoded_data = encoded_data
        self.probabilities = probabilities
        self.low = 0.0
        self.high = 1.0
        self.value = 0.0
        self.output = []

    def decode(self):
        for _ in range(len(self.encoded_data)):
            symbol = self.get_symbol()
            self.output.append(symbol)
            low_range = self.low + (self.high - self.low) * self.probabilities[symbol][0]
            high_range = self.low + (self.high - self.low) * self.probabilities[symbol][1]
            self.update_range(low_range, high_range)

        return self.output

    def get_symbol(self):
        symbol = None
        range_size = self.high - self.low

        for symbol, (low_prob, high_prob) in self.probabilities.items():
            symbol_range = (high_prob - low_prob) * range_size

            if self.low <= low_prob * range_size < self.high <= high_prob * range_size:
                self.low = low_prob * range_size
                self.high = high_prob * range_size
                break

        return symbol

    def update_range(self, low_range, high_range):
        self.low = low_range
        self.high = high_range

        # Scale the range to avoid underflow or overflow
        while self.low < 0.5 and self.high < 0.5 or self.low >= 0.5 and self.high >= 0.5:
            if self.low < 0.25:
                self.low *= 2
                self.high *= 2
            elif self.low >= 0.75:
                self.low = (self.low - 0.75) * 2
                self.high = (self.high - 0.75) * 2
            else:
                break

        # Renormalize the range
        while self.low >= 0.25 and self.high < 0.75:
            self.low = (self.low - 0.25) * 2
            self.high = (self.high - 0.25) * 2


# Example usage

# Define the probabilities for each symbol
probabilities = {
    'A': (0.2, 0.4),
    'B': (0.4, 0.6),
    'C': (0.6, 0.8),
    'D': (0.8, 1.0)
}

# Input data to be encoded
data = ['A', 'B', 'C', 'D']

# Encode the data
encoder = ArithmeticEncoder()
encoded_data = encoder.encode(data, probabilities)
print('Encoded data:', encoded_data)

# Decode the data
decoder = ArithmeticDecoder(encoded_data, probabilities)
decoded_data = decoder.decode()
print('Decoded data:', decoded_data)

这个实现中，ArithmeticEncoder 类用于编码输入数据，ArithmeticDecoder 类用于解码经过编码的数据。在示例中，我们使用了一个简单的概率分布来演示算术编解码的过程。编码过程将输入数据转换为一串二进制编码，解码过程将编码数据转换回原始的输入数据。