霍夫曼编码matlab二叉树

以下是使用Matlab实现霍夫曼编码的二叉树的基本步骤：

1. 创建节点类：首先，我们需要创建一个节点类来表示二叉树的节点。每个节点包含一个字符和其对应的频率。

2. 构建霍夫曼树：根据给定的字符频率，我们可以使用贪心算法构建霍夫曼树。贪心算法的基本思想是每次选择频率最低的两个节点，将它们合并为一个新节点，并将新节点的频率设置为两个节点频率之和。重复此过程，直到只剩下一个节点，即根节点。

3. 生成霍夫曼编码：从根节点开始，遍历霍夫曼树的每个节点。当遍历到左子节点时，添加一个0到编码中；当遍历到右子节点时，添加一个1到编码中。重复此过程，直到遍历到叶子节点。最终，每个字符都有一个唯一的霍夫曼编码。

4. 输出结果：输出每个字符的霍夫曼编码、码长、平均码长、码长方差和编码效率。

以下是一个使用Matlab实现霍夫曼编码的示例代码：

classdef Node
    properties
        character
        frequency
        left
        right
    end
    methods
        function obj = Node(character, frequency)
            obj.character = character;
            obj.frequency = frequency;
            obj.left = [];
            obj.right = [];
        end
    end
end

function huffmanEncoding(inputString)
    % 计算字符频率
    frequencyMap = containers.Map();
    for i = 1:length(inputString)
        character = inputString(i);
        if isKey(frequencyMap, character)
            frequencyMap(character) = frequencyMap(character) + 1;
        else
            frequencyMap(character) = 1;
        end
    end
    
    % 构建霍夫曼树
    nodes = [];
    keys = frequencyMap.keys;
    for i = 1:length(keys)
        character = keys{i};
        frequency = frequencyMap(character);
        node = Node(character, frequency);
        nodes = [nodes, node];
    end
    
    while length(nodes) > 1
        % 找到频率最低的两个节点
        [~, sortedIndices] = sort(arrayfun(@(x) x.frequency, nodes));
        leftNode = nodes(sortedIndices(1));
        rightNode = nodes(sortedIndices(2));
        
        % 合并节点
        newNode = Node('', leftNode.frequency + rightNode.frequency);
        newNode.left = leftNode;
        newNode.right = rightNode;
        
        % 移除已合并的节点
        nodes(sortedIndices(1:2)) = [];
        
        % 添加新节点
        nodes = [nodes, newNode];
    end
    
    huffmanTree = nodes(1);
    
    % 生成霍夫曼编码
    huffmanCodeMap = containers.Map();
    generateHuffmanCode(huffmanTree, '', huffmanCodeMap);
    
    % 输出结果
    disp('Character   Huffman Code   Code Length');
    disp('--');
    keys = huffmanCodeMap.keys;
    totalCodeLength = 0;
    for i = 1:length(keys)
        character = keys{i};
        huffmanCode = huffmanCodeMap(character);
        codeLength = length(huffmanCode);
        totalCodeLength = totalCodeLength + codeLength;
        disp([character, '           ', huffmanCode, '           ', num2str(codeLength)]);
    end
    
    averageCodeLength = totalCodeLength / length(keys);
    disp(['Average Code Length: ', num2str(averageCodeLength)]);
    
    codeLengthVariance = 0;
    for i = 1:length(keys)
        character = keys{i};
        huffmanCode = huffmanCodeMap(character);
        codeLength = length(huffmanCode);
        codeLengthVariance = codeLengthVariance + (codeLength - averageCodeLength)^2;
    end
    codeLengthVariance = codeLengthVariance / length(keys);
    disp(['Code Length Variance: ', num2str(codeLengthVariance)]);
    
    entropy = 0;
    totalFrequency = sum(cell2mat(frequencyMap.values));
    for i = 1:length(keys)
        character = keys{i};
        frequency = frequencyMap(character);
        probability = frequency / totalFrequency;
        entropy = entropy - probability * log2(probability);
    end
    efficiency = entropy / averageCodeLength;
    disp(['Efficiency: ', num2str(efficiency)]);
end

function generateHuffmanCode(node, code, huffmanCodeMap)
    if isempty(node.left) && isempty(node.right)
        huffmanCodeMap(node.character) = code;
    else
        generateHuffmanCode(node.left, [code, '0'], huffmanCodeMap);
        generateHuffmanCode(node.right, [code, '1'], huffmanCodeMap);
    end
end

inputString = 'hello world';
huffmanEncoding(inputString);