Prove for two symbols a and b, if p(a) >= p(b), then according to Huffman encoding algorithm, the resultant code length L(a) <= L(b).
I did several examples of this and it is true. But how can I prove this?
2026-04-08 07:26:16.1775633176
Huffman Encoding Symbol Probability
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Assume for the sake of a contradiction that this were not the case. Then you can show that your Huffman code was not chosen correctly --- either that there exists a code with a shorter average code length (but Huffman coding is optimal!) or that the Kraft inequality is not satisfied (but this shouldn't happen either!).