(a) Consider extending the Huffman procedure to codes with ternary symbols {0,1, 2 }. Think in terms of code words as leaves of ternary trees. Assume an alphabet with M = 4 symbols. Note that you cannot draw a full ternary tree with four leaves. By starting with a tree of three leaves and extending the tree by converting leaves into intermediate nodes, show for what values of M it is possible to have a complete ternary tree.
(b) Explain how to generalize the Huffman procedure to ternary symbols, bearing in mind your result in part (a).
(c) Use your algorithm for the set of probabilities {0.30.20.20.10.10.1}.