21.10. Properties of Optimal Trees

Try these first

1. 1.

   What is a prefix code?

   Hint

   Think about how this affects decoding.

2. 2.

   Why is variable-length encoding advantageous?

   Hint

   Consider fixed-length limitations.

3. 3.

   What is a prefix code?

   • A code where one can be a prefix of another
   • No code can be a prefix of another
   • Every code is of fixed length

   Hint

   Think of how this relates to decoding letters.

4. 4.

   True or False: Huffman coding uses fixed-length codes for all characters.

   • True
   • False

   Hint

   Consider how Huffman coding operates.

5. 5.

   Create a Huffman tree for the characters A, B, C with frequencies 0.5, 0.3, and 0.2 respectively. Explain your process.

   Hint

   Draw the tree as you combine the nodes.

6. 6.

   Given a message consisting of the letters {A, B, C} with frequencies {0.6, 0.2, 0.2}, hypothesize how the encoded messages would look like.

   Hint

   Think about how Huffman coding balances to place common letters higher in the tree.