$5.(6$ points$)$ Let F be a text file consisting of $128$ characters, each in the set A $=\{$a; b; c; d; e; f; g; h$\},$ and let T be a Huffman encoding tree for F$.$ The height of T depends on the frequencies the characters of A in F$.$

a$)$ Assign a frequency to each character of A such that the height of T is maximum.

To maximize the height, there should be a large difference between the most frequent and least frequent characters. We can do this by making one character very common and the others rarer, making the tree as unbalanced as possible$$