[dict, avglen] = huffman(probabilities, symbols)写出在matlab能够运行的配套.m文件

在MATLAB中，Huffman编码是一种用于数据压缩的无损编码算法，它基于频率来构建哈夫曼树并生成对应的二进制码字。`[dict, avglen] = huffman(probabilities, symbols)`这段描述看起来像是函数调用，其中`probabilities`是一个包含字符概率分布的向量，`symbols`是一组需要编码的字符，`dict`将返回一个哈夫曼字典（映射每个字符到其编码），`avglen`则计算平均编码长度。

为了编写一个可以在MATLAB中运行的`huffman.m`文件，你可以参考以下结构：

function [dict, avgLen] = huffman(probabilities, symbols)
% HUFFMAN Huffman coding algorithm in MATLAB
% probabilities: Vector of character frequencies
% symbols: Characters to be encoded

% Ensure input types
if ~isnumeric(probabilities) || ~isscalar(probabilities) || length(probabilities) ~= length(symbols)
    error('Invalid input: probabilities must be a scalar numeric vector of same length as symbols.');
end

% Create a priority queue for the Huffman tree construction
pq = PriorityQueue;
for i = 1:length(probabilities)
    pq.insert([probabilities(i), i], symbols{i});
end

% Build the Huffman Tree and generate codes
while pq.size > 1
    % Pop two smallest nodes from the queue
    node1 = pq.removeMin();
    node2 = pq.removeMin();
    
    % Combine them into a new node with combined probability
    newNode = Node(node1.probability + node2.probability, [node1, node2]);
    pq.insert(newNode.probability, newNode);
end

% Convert the root node's path to a dictionary (mapping characters to codes)
root = pq.root;
dict = containers.Map();
traverse(root, '', dict);

% Calculate average code length
avgCodeLengths = cellfun(@(x) -x.probability * log2(x.probability), pq.nodes, 'UniformOutput', false);
avgLen = mean(avgCodeLengths);

% Helper function for traversing the Huffman tree
function traverse(node, prefix, dict)
    if isLeaf(node)
        dict(node.symbol) = prefix;
    else
        traverse(node.leftChild, prefix + '0', dict);
        traverse(node.rightChild, prefix + '1', dict);
    end
end

% Check if we have reached a leaf node
function isLeaf(node)
    return isa(node, 'PriorityQueue.Node') && isequal(node.leftChild, []);
end

% Define a simple Node class (you may already have one in your toolbox)
classdef Node < handle
    properties
        probability
        leftChild
        rightChild
        symbol
    end
    methods
        % ... constructor and other methods here
    end
end

end

这个`huffman.m`文件首先检查输入的有效性，然后构建哈夫曼树、生成编码字典，并计算平均编码长度。请注意，这里假设你已经有了`PriorityQueue`和`Node`类，如果没有，你需要自己实现它们。运行这个函数后，可以用`[dict, avgLen] = huffman(probabilities, symbols)`的形式来获取结果。