38.8 Exercises

Factual

1. 1.
Suppose we build a Shannon Fano or Huffman code for the text of this question including spaces and punctuation characters. Which characters would have the longest code?
2. 2.
What two ways could we represent a Huffman code for characters in Java?
Problem 1
`?` and `.`, since both are only used once in the above sentence.
Problem 2
A `HashMap<Character, BitSequence>` or a `BitSequence[]`. Note that the two are equivalent in Java because a Character is a number.

Procedural

1. 1.
Suppose we have a string `abcdefg` which repeats 1000 times. How many bits would be in the compressed bitstream?
Problem 1
Since all 8 characters are equal in frequency, we get a balanced binary tree as our Huffman encoding, so all codewords are 3 bits long. 1000 * 8 * 3 = 24000 bits.

Metacognitive

1. 1.
Using the idea of self-extracting bits, come up with an encoding for the sequence `abdefg` repeated 1000 times that uses less than 2000 bits.
Problem 1
The idea of self-extracting bits includes writing code or an interpreter that can generate the original uncompressed sequence. This can be done with the following code:
public class Sequence {
public static void main(String[] args) {
for (int i = 0; i < 1000; i++) {
for (int j = 0; j < 8; j++) {
System.out.print(String.format("%c", 'a' + j));
}
}
}
}
This code uses exactly 239 characters, or 1912 bits. This demonstrates the power of the self-extracting bits model: compare this to the 24000 bits required for a Huffman code.