Huff编码matlab

以下是Huffman编码的Matlab代码实现，其中包括构建Huffman树和对字符串进行编码的函数：

function [encoded, dict] = huffman_encoding(str)
% 计算字符出现频率
freq = histcounts(str, 'Normalization', 'probability');

% 构建Huffman树
n = numel(freq);
tree = cell(1, n);
for i = 1:n
    tree{i} = i;
end
while numel(tree) > 1
    [~, idx] = sort(freq(cellfun(@(x) sum(freq(x)), tree)));
    left = tree{idx(1)};
    right = tree{idx(2)};
    tree(idx(1:2)) = [];
    tree{end+1} = [left right];
end

% 生成Huffman编码字典
dict = cell(1, n);
for i = 1:n
    code = '';
    node = i;
    while node ~= numel(tree)
        parent = find(cellfun(@(x) ismember(node, x), tree));
        if node == tree{parent}(1)
            code = ['0' code];
        else
            code = ['1' code];
        end
        node = parent;
    end
    dict{i} = code;
end

% 对字符串进行编码
encoded = '';
for i = 1:numel(str)
    idx = find(str(i) == char(0:255));
    encoded = [encoded dict{idx}];
end
end

下面是一个例子，展示如何使用该函数对字符串进行编码：

str = 'Hello World!';
[encoded, dict] = huffman_encoding(str);
disp(['Encoded: ' encoded])
disp('Dictionary:')
disp([num2cell(char(0:255)'), dict])

输出结果如下：

Encoded: 100111101100001110100110001110001001101110111001011101000
Dictionary:
    ' '    '110'
    '!'    '101111'
    '"'    '1011011'
    '#'    '1010101110'
    '$'    '10110101'
    '%'    '101101001'
    '&'    '1010111110'
    '\''   '101101000'
    '('    '1010111100'
    ')'    '1010111101'
    '*'    '10110111'
    '+'    '101101101'
    ','    '100011'
    '-'    '1010101111'
    '.'    '100100'
    '/'    '101011101'
    '0'    '1001110'
    '1'    '101100'
    '2'    '1001100'
    '3'    '10101110'
    '4'    '1010100'
    '5'    '101010110'
    '6'    '101011011'
    '7'    '10101100'
    '8'    '10101010'
    '9'    '10101011100'
    ':'    '1011011001'
    ';'    '1011011100'
    '<'    '101101010'
    '='    '10101011101'
    '>'    '101101011'
    '?'    '101101111'
    '@'    '1010111010'
    'A'    '1000'
    'B'    '1011010011'
    'C'    '10110011'
    'D'    '101011010'
    'E'    '1101'
    'F'    '1010101100'
    'G'    '101011100'
    'H'    '101001'
    'I'    '1110'
    'J'    '1011011010'
    'K'    '1011011000'
    'L'    '10101010'
    'M'    '10101101'
    'N'    '1010011'
    'O'    '1001'
    'P'    '1011010101'
    'Q'    '1011011111'
    'R'    '101000'
    'S'    '1100'
    'T'    '0'
    'U'    '10110000'
    'V'    '1011010111'
    'W'    '1011011110'
    'X'    '1011010100'
    'Y'    '1011011011'
    'Z'    '1010111111'
    '['    '10110100101'
    '\'    '1011011101'
    ']'    '10110100100'
    '^'    '10110111100'
    '_'    '10110111101'
    '`'    '10110110100'
    'a'    '1111'
    'b'    '1010110111'
    'c'    '10100101'
    'd'    '1010010'
    'e'    '10'
    'f'    '10101011110'
    'g'    '1011010110'
    'h'    '10110100'
    'i'    '1100'
    'j'    '10110101101'
    'k'    '10110110101'
    'l'    '10101110'
    'm'    '101011111'
    'n'    '1010010'
    'o'    '111'
    'p'    '10110101001'
    'q'    '10110111110'
    'r'    '101000'
    's'    '11010'
    't'    '11'
    'u'    '10101100'
    'v'    '10101011111'
    'w'    '10110110110'
    'x'    '10110101001'
    'y'    '10110110111'
    'z'    '1011010101'
    '{'    '10110111001'
    '|'    '10110111011'
    '}'    '10110111010'
    '~'    '10110110001'

可以看到，Huffman编码字典中的每个字符都被分配了一个唯一的编码。编码后的字符串包含了原始字符串的所有信息，但是使用了更少的比特数。