I'm not sure if I should ask this here or over at StackOverflow (sorry if this is not the right place).
I'm constructing a Huffman code for a series of symbols with associated weights. I have a list of the code-lengths corresponding to each symbol, sorted by symbol weight (in non-decreasing order). Does it follow that this list is also sorted by code-length (in non-increasing order)?
I suspect that the answer is yes (since lower-weighted symbols will generally have shorter code lengths), but I'm not sure if this is guaranteed.
I guess what I really want to know is, "if a Huffman tree has two leaves a and b, where a had a higher weight than b, is b's code length always at least that of a's?"