Exercises - Lecture 20

20A

For the following several questions, use the following coding tree; note that the space character is written as ' ' for clarity:

1. How many characters were in the input?
2. How many distinct characters were in the input?
3. Decode the binary code 1001111011010111110011
4. Encode the string bead; for clarity, separate the codes for each distinct character with spaces.

20B

5. Let’s build a coding tree for the input string: kakakakangarrooo

   1. Write down the table of character frequencies.

   2. Build a Huffman Coding Tree that minimizes the encoded length of the message.

      Ties may arise when deciding which of two equal-priority trees to pull out of the forest. Break these ties using the following rules:

      • Take the tree with fewer leaves first
      • If tied, take the tree with the earliest alphabetical leaf

      We also get to choose which tree goes to the left and right of its parent. Decide this as follows:

      • The lower-frequency tree is the left child of the parent
      • If tied, the tree with fewer leaves is the left child
      • If still tied, the tree with the earliest alphabetical leaf.

   3. Give the message’s bitstring encoding; for clarity, separate the codes for each distinct character with spaces.