Is there an algorithm to find the shortest binary representation for every entry within a given rang-CodePudding

I have an encoding scheme, but I don't know the name of it. I know there must be an algorithm to encode/decode integers into this binary scheme. The scheme is as follows:

   1  2  3   4   5    6    7    8    9     etc.

0  -  0  0   00  00   00   00   000  000
1     1  10  01  01   01   010  001  001
2        11  10  10   100  011  010  010
3            11  110  101  100  011  011
4                111  110  101  100  100
5                     111  110  101  101
6                          111  110  110
7                               111  1110
8                                    1111

etc.

Example: When you have a range of 6 integers (0 to 5) you can use column 6. With this you can save a bit on the numbers 0 and 1. When using column 9, you will save a bit on every number except on 7 and 8.

The 'you will save a bit' is opposed to using 2, 3, 4, or N bit words.

I tried to Google this, but I can't find the right search keywords. Could someone point me in the right direction?

Thanks!

CodePudding user response：

This appears to be Huffman Encoding with assumed uniform distribution across all values in any given range.

So for instance, the 5th column is just a huffman encoding for the character set [0-5] (inclusive), which assumes all 6 numbers are of equal probability to occur.