根据文档按照顺序在matlab中编程。（请说出分别在主程序还是脚本编程）

根据文档中的要求，在MATLAB中实现和比较Huffman编码和Shannon-Fano编码的任务可以分为以下几个步骤。每个步骤将在不同的函数或脚本中实现，以保持代码的模块化和可读性。

### 主程序（Main Script）
主程序将调用各个功能函数，并组织整个流程。你可以将其命名为 `FirstnameLastname.mlx`。

#### 主程序结构

% Main Script: FirstnameLastname.mlx

% Step 1: Input Setup
symbols = {'A', 'B', 'C', 'D', 'E', 'F', 'G', 'H'};
probabilities = [0.25, 0.2, 0.15, 0.12, 0.1, 0.08, 0.06, 0.04];
sample_string = 'AABCCDEFGH';

% Step 2: Entropy Calculation
entropy_value = calculate_entropy(probabilities);
fprintf('Entropy of the source: %.4f\n', entropy_value);

% Step 3: Huffman Coding Implementation
[huffman_codes, huffman_tree] = huffman_coding(symbols, probabilities);
encoded_huffman = encode_string(sample_string, huffman_codes);
fprintf('Encoded string using Huffman coding: %s\n', encoded_huffman);

% Step 4: Shannon-Fano Coding Implementation
shannon_fano_codes = shannon_fano_coding(symbols, probabilities);
encoded_shannon_fano = encode_string(sample_string, shannon_fano_codes);
fprintf('Encoded string using Shannon-Fano coding: %s\n', encoded_shannon_fano);

% Step 5: Efficiency Analysis
metrics_huffman = calculate_efficiency_metrics(huffman_codes, probabilities, sample_string, entropy_value);
metrics_shannon_fano = calculate_efficiency_metrics(shannon_fano_codes, probabilities, sample_string, entropy_value);

% Step 6: Mathematical Proof & Justification
compare_methods(metrics_huffman, metrics_shannon_fano);

% Step 7: Output Presentation
display_results(symbols, huffman_codes, shannon_fano_codes, metrics_huffman, metrics_shannon_fano);

### 功能函数（Function Files）

#### 1. 计算熵

function entropy = calculate_entropy(probabilities)
    entropy = -sum(probabilities .* log2(probabilities));
end

#### 2. Huffman 编码实现

function [codes, tree] = huffman_coding(symbols, probabilities)
    % Custom implementation of Huffman Tree and code generation
    % ...
end

#### 3. Shannon-Fano 编码实现

function codes = shannon_fano_coding(symbols, probabilities)
    % Custom implementation of Shannon-Fano coding
    % ...
end

#### 4. 字符串编码

function encoded_string = encode_string(string, codes)
    encoded_string = '';
    for i = 1:length(string)
        encoded_string = [encoded_string codes{strcmp(string(i), symbols)}];
    end
end

#### 5. 效率分析

function metrics = calculate_efficiency_metrics(codes, probabilities, sample_string, entropy)
    % Calculate average code length, compression ratio, redundancy, and coding efficiency
    % ...
end

#### 6. 方法比较

function compare_methods(metrics_huffman, metrics_shannon_fano)
    % Compare the results and provide mathematical justification
    % ...
end

#### 7. 结果展示

function display_results(symbols, huffman_codes, shannon_fano_codes, metrics_huffman, metrics_shannon_fano)
    % Display the generated codes and metrics in a structured manner
    % ...
end

### 提交文件
- **主程序**: `FirstnameLastname.mlx`
- **功能函数**: 可以将上述功能函数保存为单独的 `.m` 文件，例如 `calculate_entropy.m`, `huffman_coding.m`, `shannon_fano_coding.m`, `encode_string.m`, `calculate_efficiency_metrics.m`, `compare_methods.m`, `display_results.m`
- **报告**: 详细的PDF报告，包含所有分析、数学证明和结果。

通过这种方式，你可以确保代码的模块化和清晰度，便于调试和维护。