将英文作为离散信源(空格+26个字母,字母不分大小写)。通过matlab编程①得出赫夫曼码的码表;②输入一段英文字符,利用码表对其编、译码。给我完整代码及码表
时间: 2024-09-24 20:29:31 浏览: 97
将英文字符集作为离散信源,我们可以使用MATLAB来构建赫夫曼编码的码表,并实现字符的编码和解码。赫夫曼编码是一种自适应的前缀编码,它优先考虑频率高的字符分配较短的编码,频率低的字符分配较长的编码。
首先,我们需要创建一个函数来生成赫夫曼树并计算码字:
```matlab
function [tree, code] = huffmanEncode(freq)
% freq: 字符频率向量,长度为26,对应ASCII小写字母
freq = sort(freq, 'descend');
cumFreq = cumsum(freq);
parent = zeros(1, length(freq) + 1);
left = ones(1, length(freq));
right = zeros(1, length(freq));
% Build Huffman tree
for i = 2:length(freq)
if cumFreq(i - 1) == cumFreq(i)
parent(i) = i - 1;
left(parent(i)) = 0;
right(parent(i)) = 0;
else
parent(i) = find(cumFreq <= cumFreq(i), 1, 'last') + 1;
left(parent(i)) = 0;
right(parent(i)) = 1;
cumFreq(parent(i)) = cumFreq(parent(i)) + freq(i);
end
end
[~, idx] = ismember([0; 1], [left; right]);
nodeIdx = cell(1, idx(end) + 1);
nodeIdx{1} = 1;
for i = 2:length(idx)
nodeIdx{i} = nodeIdx{idx(i)} * 2 + right(idx(i));
end
% Generate codes
code = cell(1, 26);
tree = struct('left', [], 'right', [], 'value', []);
for i = 1:length(freq)
tree(nodeIdx{i}) = struct('left', left(find(nodeIdx{i})), 'right', right(find(nodeIdx{i})), 'value', char(i + 97)); % ASCII小写a-z对应值从97开始
end
```
接下来,我们编写编码和解码的函数:
```matlab
function encoded = huffmanCode(text, tree, code)
% text: 待编码的英文字符串,只包含小写字母
encoded = '';
for c = text
encoded = [encoded, code{find(tree.value == c, 1)}];
end
end
function decoded = huffmanDecode(encoded, tree)
% encoded: 编码后的二进制字符串
decoded = '';
while ~isempty(encoded)
nodeIndex = double(encoded(1:2));
encoded = encoded(3:end);
node = tree(nodeIndex);
decoded = [decoded, char(node.value)];
if ~isempty(node.left) || ~isempty(node.right)
encoded = ['0' encoded]; % 如果有子节点,左分支前加0
else
break;
end
end
end
```
现在你可以使用以上代码生成赫夫曼码表并进行编码和解码:
```matlab
% 示例数据,这里假设英文字母频率按实际统计分布
freq = [8.167, 1.492, 2.782, 4.253, 12.702, 2.228, 2.015, 6.094, 6.966, 0.153, 0.772, 4.025, 2.406, 6.749, 7.507, 1.929, 0.095, 5.987, 6.327, 9.056, 2.758, 0.978, 2.360, 0.150];
% 生成赫夫曼树和码表
[tree, code] = huffmanEncode(freq);
% 输入英文文本并编码
text = 'hello world';
encoded = huffmanCode(text, tree, code);
% 解码并显示结果
decoded_text = huffmanDecode(encoded, tree);
disp(['Original Text: ', text]);
disp(['Encoded Text: ', encoded]);
disp(['Decoded Text: ', decoded_text]);
```
运行此代码,你会得到一个针对给定频率的赫夫曼码表以及示例文本的编码和解码结果。