1. (10 points) Dr. Sponge claims that in the tree representation of an optimal prefix-free code,
every leaf node must have a sibling. Is the claim true or not? Answer Yes or No, and
explain why.
2. (10 points) Suppose we want to compress a text consisting of 6 characters, a, b, c, d, e, f using
the Huffman Algorithm. Give an example for which the algorithm produces at least one
codeword of length 5. In other words, you are being asked to give a set of the character
frequencies that results in the deepest tree.