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Suppose the letters a, b, c, d, e, f have probabilities 1/2, 1/4, 1/8, 1/16, 1/32, 1/32 respectively. What is the average length of Huffman codes?Group of answer choices2.18752.251.93753

Question

Suppose the letters a, b, c, d, e, f have probabilities 1/2, 1/4, 1/8, 1/16, 1/32, 1/32 respectively. What is the average length of Huffman codes?Group of answer choices2.18752.251.93753

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Solution

To calculate the average length of Huffman codes, we need to multiply the probability of each letter by the length of its Huffman code, and then sum these products.

The Huffman codes for the given probabilities are:

  • a: 0 (1 bit)
  • b: 10 (2 bits)
  • c: 110 (3 bits)
  • d: 1110 (4 bits)
  • e: 11110 (5 bits)
  • f: 11111 (5 bits)

So, the average length is:

(1/2 * 1) + (1/4 * 2) + (1/8 * 3) + (1/16 * 4) + (1/32 * 5) + (1/32 * 5) = 0.5 + 0.5 + 0.375 + 0.25 + 0.15625 + 0.15625 = 1.9375

So, the average length of Huffman codes is 1.9375.

This problem has been solved

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