哈夫曼编码和译码数据结构

哈夫曼编码是一种可变长度编码，它将出现频率较高的字符用较短的编码表示，出现频率较低的字符用较长的编码表示，从而达到压缩数据的目的。哈夫曼编码的核心思想是构建哈夫曼树，将出现频率较高的字符放在离根节点较近的位置，出现频率较低的字符放在离根节点较远的位置。哈夫曼编码的译码过程就是根据哈夫曼树和编码表，将编码还原成原始数据的过程。

哈夫曼编码的数据结构包括哈夫曼树和编码表。哈夫曼树是一种二叉树，它的每个叶子节点都代表一个字符，而每个非叶子节点都代表一个字符集合。哈夫曼树的构建过程是将字符集合中出现频率最低的两个字符合并成一个节点，直到最后只剩下一个根节点为止。编码表是一个字典，它将每个字符映射到对应的哈夫曼编码。

以下是Python实现哈夫曼编码和译码的示例代码：

import heapq
from collections import defaultdict

class HuffmanCoding:
    def __init__(self):
        self.heap = []
        self.codes = {}
        self.reverse_codes = {}

    class HeapNode:
        def __init__(self, char, freq):
            self.char = char
            self.freq = freq
            self.left = None
            self.right = None

        def __lt__(self, other):
            return self.freq < other.freq
    def make_frequency_dict(self, text):
        frequency = defaultdict(int)
        for char in text:
            frequency[char] += 1
        return frequency

    def make_heap(self, frequency):
        for char, freq in frequency.items():
            node = self.HeapNode(char, freq)
            heapq.heappush(self.heap, node)

    def merge_nodes(self):
        while len(self.heap) > 1:
            node1 = heapq.heappop(self.heap)
            node2 = heapq.heappop(self.heap)
            merged = self.HeapNode(None, node1.freq + node2.freq)
            merged.left = node1
            merged.right = node2
            heapq.heappush(self.heap, merged)

    def make_codes_helper(self, root, current_code):
        if root is None:
            return
        if root.char is not None:
            self.codes[root.char] = current_code
            self.reverse_codes[current_code] = root.char
            return
        self.make_codes_helper(root.left, current_code + "0")
        self.make_codes_helper(root.right, current_code + "1")

    def make_codes(self):
        root = heapq.heappop(self.heap)
        current_code = ""
        self.make_codes_helper(root, current_code)

    def get_encoded_text(self, text):
        encoded_text = ""
        for char in text:
            encoded_text += self.codes[char]
        return encoded_text

    def pad_encoded_text(self, encoded_text):
        padding = 8 - len(encoded_text) % 8
        for i in range(padding):
            encoded_text += "0"
        padded_info = "{0:08b}".format(padding)
        return padded_info + encoded_text

    def get_byte_array(self, padded_encoded_text):
        if len(padded_encoded_text) % 8 != 0:
            print("Encoded text not padded properly")
            exit(0)
        b = bytearray()
        for i in range(0, len(padded_encoded_text), 8):
            byte = padded_encoded_text[i:i+8]
            b.append(int(byte, 2))
        return b

    def compress(self, text):
        frequency = self.make_frequency_dict(text)
        self.make_heap(frequency)
        self.merge_nodes()
        self.make_codes()
        encoded_text = self.get_encoded_text(text)
        padded_encoded_text = self.pad_encoded_text(encoded_text)
        byte_array = self.get_byte_array(padded_encoded_text)
        return byte_array

    def remove_padding(self, padded_encoded_text):
        padded_info = padded_encoded_text[:8]
        padding = int(padded_info, 2)
        padded_encoded_text = padded_encoded_text[8:]
        encoded_text = padded_encoded_text[:-1*padding]
        return encoded_text

    def decode_text(self, encoded_text):
        current_code = ""
        decoded_text = ""
        for bit in encoded_text:
            current_code += bit
            if current_code in self.reverse_codes:
                char = self.reverse_codes[current_code]
                decoded_text += char
                current_code = ""
        return decoded_text

    def decompress(self, byte_array):
        bit_string = ""
        for byte in byte_array:
            bits = bin(byte)[2:].rjust(8, '0')
            bit_string += bits
        encoded_text = self.remove_padding(bit_string)
        decompressed_text = self.decode_text(encoded_text)
        return decompressed_text

# 示例
text = "ABBCCEEE"
huffman = HuffmanCoding()
compressed_data = huffman.compress(text)
decompressed_data = huffman.decompress(compressed_data)
print("Compressed data:", compressed_data)
print("Decompressed data:", decompressed_data)