霍夫曼编码matlab
时间: 2023-07-13 13:39:47 浏览: 38
以下是一个简单的MATLAB实现霍夫曼编码的例子:
```matlab
function [code, dict] = huffman_encode(symbols, prob)
% symbols: 符号数组
% prob: 符号出现概率
% 构建霍夫曼树
num_symbols = numel(symbols);
nodes = cell(num_symbols, 1);
for i = 1:num_symbols
nodes{i} = struct('symbol', symbols(i), 'prob', prob(i), 'left', [], 'right', []);
end
while numel(nodes) > 1
[prob_sorted, idx_sorted] = sort(prob);
idx1 = idx_sorted(1);
idx2 = idx_sorted(2);
new_node = struct('symbol', [], 'prob', prob_sorted(1)+prob_sorted(2), 'left', nodes{idx1}, 'right', nodes{idx2});
nodes(idx_sorted(1:2)) = [];
nodes{end+1} = new_node;
prob(idx_sorted(1:2)) = [];
prob(end+1) = new_node.prob;
end
% 生成编码
dict = cell(num_symbols, 2);
for i = 1:num_symbols
node = nodes{1};
code = '';
while ~isempty(node.symbol)
if node.left.prob < node.right.prob
code = [code, '0'];
node = node.left;
else
code = [code, '1'];
node = node.right;
end
end
dict{i, 1} = symbols(i);
dict{i, 2} = fliplr(code);
end
% 返回编码和字典
code = cell(num_symbols, 1);
for i = 1:num_symbols
idx = find(cellfun(@(x) strcmp(x, symbols(i)), dict(:, 1)));
code{i} = dict{idx, 2};
end
end
```
使用方式:
```matlab
symbols = {'A', 'B', 'C', 'D', 'E', 'F'};
prob = [0.05, 0.1, 0.15, 0.2, 0.25, 0.25];
[code, dict] = huffman_encode(symbols, prob);
```
其中,`symbols`是符号数组,`prob`是每个符号出现的概率。`code`是编码数组,`dict`是字典数组,每一行是一个符号和它对应的编码。
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