Uniform-source Huffman length distribution ($s=\lceil {\log }_{2}m\rceil$)

For $m\ge 2$ equiprobable symbols, the maximum codeword length of a binary Huffman code is $s=\lceil {\log }_{2}m\rceil$. Exactly $2^s-m$ codewords have length $s-1$ and $2m-2^s$ have length $s$. The balancing exchange for a uniform optimal prefix code restricts the depths to these two levels; counting leaves and using equality in the Kraft inequality determine the numbers.

// Target: probability-and-statistics.bigb