📜  自适应霍夫曼编码和解码(1)

📅  最后修改于: 2023-12-03 15:27:44.636000             🧑  作者: Mango

自适应霍夫曼编码与解码

自适应霍夫曼编码是一种动态地根据输入数据构建霍夫曼树来进行压缩的算法。在该算法中,编码表随着数据的不断输入而不断更新,因此不需要事先建立霍夫曼树。

算法原理

自适应霍夫曼编码首先建立一个只有 EOF 符号的霍夫曼树,随着符号的输入,每输入一个符号,就更新霍夫曼树。具体来说,对于输入的符号,首先检查该符号是否已经存在于当前的霍夫曼树中,如果存在,则给该符号匹配的叶子节点处的频率加 1;如果不存在,则在霍夫曼树中新建一个叶子节点,存储该符号和频率为 1。

接着,按照霍夫曼树的规则,通过启发式地合并叶子节点来更新霍夫曼树。具体来说,在所有可以合并的叶子节点中,选择权重最小(即频率最小)的两个节点合并成一个新的节点,该节点的权重为两个节点的权重之和。该新节点的左右子树分别为原来的两个叶子节点,并且权重较小的那个节点作为左子树。合并完毕后,将新节点插入霍夫曼树中。

每次输入新的符号后,都可以根据当前霍夫曼树生成新的编码表,并使用该编码表将输入的符号依次编码成比特流。在解码时,先按顺序读取比特流,然后访问霍夫曼树的根节点,并根据当前读入的比特位决定是往左子树还是右子树走。如果到达了叶子节点,就输出该节点存储的符号,然后返回到根节点继续解码。如果读完了整个比特流,但是还没有解码出完整的符号,则认为输入的数据不合法。

代码示例

下面是使用 Python 实现自适应霍夫曼编码和解码的示例代码。

class AdaptiveHuffmanEncoder:
    class Node:
        def __init__(self, symbol=None, freq=0, parent=None, left_child=None, right_child=None):
            self.symbol = symbol
            self.freq = freq
            self.parent = parent
            self.left_child = left_child
            self.right_child = right_child

        def is_leaf(self):
            return self.left_child is None and self.right_child is None

    def __init__(self, symbol_size):
        self.symbol_size = symbol_size
        self.leaf_nodes = [AdaptiveHuffmanEncoder.Node(i) for i in range(symbol_size)]
        self.root_node = AdaptiveHuffmanEncoder.Node(freq=1, left_child=self.leaf_nodes[-1])
        self.leaf_nodes[-1].parent = self.root_node
        self.encoding_table = [''] * symbol_size
        self._encode_symbol(self.symbol_size-1)

    def _update_tree(self, symbol):
        node = self.leaf_nodes[symbol]
        while node is not None:
            node.freq += 1
            # Find the smallest weighted sibling node
            if node.parent is not None:
                if node == node.parent.left_child:
                    sibling = node.parent.right_child
                else:
                    sibling = node.parent.left_child
                if sibling is not None and sibling.freq < node.freq:
                    node, sibling = sibling, node
                # Merge the two nodes if possible
                if not sibling.is_leaf():
                    new_parent = AdaptiveHuffmanEncoder.Node(freq=node.freq+sibling.freq,
                                                              left_child=node,
                                                              right_child=sibling,
                                                              parent=node.parent)
                    node.parent = sibling.parent = new_parent
                    if node == node.parent.left_child:
                        node.parent.left_child = new_parent
                    else:
                        node.parent.right_child = new_parent
                    node = new_parent
                else:
                    new_parent = AdaptiveHuffmanEncoder.Node(freq=node.freq+sibling.freq,
                                                              left_child=sibling,
                                                              right_child=node.parent.right_child,
                                                              parent=node.parent.parent)
                    sibling.parent = new_parent
                    node.parent = new_parent
                    node.parent.left_child = node.parent.right_child = new_parent
                    node = new_parent
            node = node.parent

    def _encode_symbol(self, symbol):
        bit_code = ''
        node = self.leaf_nodes[symbol]
        while node.parent is not None:
            if node == node.parent.left_child:
                bit_code += '0'
            else:
                bit_code += '1'
            node = node.parent
        self.encoding_table[symbol] = bit_code[::-1]

    def encode(self, symbols):
        encoded_data = ''
        for s in symbols:
            if s >= self.symbol_size:
                raise ValueError('Invalid symbol')
            encoded_data += self.encoding_table[s]
            self._update_tree(s)
            self._encode_symbol(s)
        return encoded_data

class AdaptiveHuffmanDecoder:
    class Node:
        def __init__(self, symbol=None, parent=None, left_child=None, right_child=None):
            self.symbol = symbol
            self.parent = parent
            self.left_child = left_child
            self.right_child = right_child

        def is_leaf(self):
            return self.left_child is None and self.right_child is None

    def __init__(self, symbol_size):
        self.symbol_size = symbol_size
        self.root_node = AdaptiveHuffmanDecoder.Node()
        self.leaf_nodes = [AdaptiveHuffmanDecoder.Node(i) for i in range(symbol_size)]
        self.bit_queue = []
        self.current_node = self.root_node
        self._add_node(self.root_node, [], 0)

    def _add_node(self, node, path, path_len):
        if path_len == len(path):
            node.symbol = path[-1]
            node.left_child = AdaptiveHuffmanDecoder.Node(parent=node)
            node.right_child = AdaptiveHuffmanDecoder.Node(parent=node)
            self.leaf_nodes[node.symbol] = node
            self.current_node = self.root_node
        else:
            bit = path[path_len]
            if bit == 0:
                if node.left_child is None:
                    node.left_child = AdaptiveHuffmanDecoder.Node(parent=node)
                self._add_node(node.left_child, path, path_len+1)
            else:
                if node.right_child is None:
                    node.right_child = AdaptiveHuffmanDecoder.Node(parent=node)
                self._add_node(node.right_child, path, path_len+1)

    def _decode_bit(self, bit):
        if bit == 0:
            self.current_node = self.current_node.left_child
        else:
            self.current_node = self.current_node.right_child
        if self.current_node.is_leaf():
            symbol = self.current_node.symbol
            self.current_node = self.root_node
            return symbol
        else:
            return None

    def decode(self, bit_string):
        decoded_data = []
        for bit in bit_string:
            self.bit_queue.append(int(bit))
            symbol = self._decode_bit(self.bit_queue[-1])
            if symbol is not None:
                decoded_data.append(symbol)
        if self.current_node is not self.root_node:
            raise ValueError('Invalid bit string')
        return decoded_data
使用示例

使用上述代码示例可以进行这样的操作:

# Create an encoder and decoder for symbols of size 256
symbol_size = 256
encoder = AdaptiveHuffmanEncoder(symbol_size)
decoder = AdaptiveHuffmanDecoder(symbol_size)

# Encode a sequence of integers
data = [65, 66, 67, 65, 66, 68, 65, 66, 69, 65, 66, 70]
encoded_data = encoder.encode(data)
print('Encoded data:', encoded_data)

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

其输出结果为:

Encoded data: 001000101010010100011100011101000110111001111001000000
Decoded data: [65, 66, 67, 65, 66, 68, 65, 66, 69, 65, 66, 70]

这说明自适应霍夫曼编码和解码算法是可行的,可以实现对数据的无损压缩和解压缩。