A problem about Huffman codeword
Assume there are 2^n symbols, n &gt;= 2, and the frequencies of the most common and the two least common symbols are f, g, and h. We could use a code of n-1 bits for the most common and n+1 bits for the two least common symbols. This will reduce the average code length if f &gt; g+h.
You were specifically asking for the frequencies 2^-n + c/2, 2^-n, and 2^-n - c/2, so that’s the case for c &gt; 2^-n / 2.