Question

I have written a program to encoded a article to huffman code and output a code table.

H:000
d:1011
e:100
l:11
o:01
r:1010
w:001
Total bits:27
Encoded code:000100111101001011010111011

and I want to write a program which take the file as input and to decode it.

But I have no idea how to rebuild it.

My question is how to rebulid the huffman tree?

Answer 1

You don’t need to rebuild the Huffman tree if the code has been constructed in a canonical manner, which makes the shorter codes numerically smaller than the longer codes. There are many ways to arbitrarily assign the 0 and 1 to each branch of a Huffman binary tree, and all result in the same optimality of the code. Picking one of the many choices provides advantages in decoding and in conveying the code.

The only information needed from the Huffman algorithm is the code lengths, i.e. the number of bits for each symbol. With that, you can construct a canonical Huffman code advancing from the shorter codes to the longer codes, and sorting the symbols in lexical order within any given code length (e.g. sort all the length 3 codes in the order H, e, w). The point of sorting within a code length is to reduce the amount of data to be sent to the receiver in order to reconstruct the code.

You then arrive at this alternative code:

l:00
o:01
H:100
e:101
w:110
d:1110
r:1111

Now decoding can be done with a two simple tables, one which is just those symbols in order, i.e. “loHewdr”, and the code values at which you step up to the next code length. The steps are 0000 from one to two bits, 1000 to three bits, 1110 to four bits. You read in enough bits for the longest code (append zeros if needed at the end, but don’t use those as the start of a code in a subsequent step). Then if the value is less than the value of the start of the next code length, use that value as the index into the table, taking into account the current number of bits in the code. Otherwise add the number of values up to that next value to the index, and check the next step. Calculating the number of values skipped requires also keeping track of the number of bits in the code in the current step.

Once you decode a symbol, you know how many bits it was. Remove those bits from the stream and repeat.

This approach also has the advantage of being the fastest for the shortest codes, which are the most common. The resulting decoding speed is very good. (There are other table-driven methods that are faster, but they are much more complicated.)