A problem about Huffman codeword Under Huffman Encoding, what circumstances codeword length  of each character
be equal?(suppose number of character is power of 2)

I think if all frequency of characters is same then codeword length of all characters be the same.
Surprisingly, if there are two characters that differences between frequency of two characters be $2$, and frequency of other be equal then codeword length of all characters be the same.
Main problem is, can i say, for each constant $c$, if there are two character that difference of  frequency be $c$, and all remaining of characters  have equal frequency then codeword length  of each character be equal?
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.