"Gedanken" Experiment

• Scenario:
  • Another strange train station with a monosyllabic information booth attendant.
  • This one has 12 tracks.
  • From experience you know that the train is twice as likely to leave from tracks 1-4 than from tracks 5-12.
  • In other words, the probability that the train leaves from track 1 is $\frac{1}{8}$ (same for tracks 2, 3 , 4).
  • The probability that the train leaves from track 5 is $\frac{1}{16}$ (same for tracks 5-12).
• Question: What is the best (shorstest on average) sequence of questions now?
• Solution:
  • Construct a Huffman tree.
  • To find out that your train leaves on track 3, you would ask the following sequence of questions:
    • Is the track number greater than 4? -- Answer: no
    • Is the track number greater than 2? -- Answer: yes
    • Is the track number equal to 4? -- Answer: no

  

Figure 2.15: Huffman tree for train experiment