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GATE | GATE-CS-2007 | Question 77
  • Last Updated : 26 Feb, 2014

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?
(A) 3
(B) 2.1875
(C) 2.25
(D) 1.9375


Answer: (D)

Explanation: We get the following Huffman Tree after applying Huffman Coding Algorithm. The idea is to keep the least probable characters as low as possible by picking them first.

The letters a, b, c, d, e, f have probabilities 
1/2, 1/4, 1/8, 1/16, 1/32, 1/32 respectively. 

                 1
               /   \
              /     \
             1/2    a(1/2)
            /  \
           /    \
          1/4  b(1/4) 
         /   \
        /     \
       1/8   c(1/8) 
      /  \
     /    \
   1/16  d(1/16)
  /  \
 e    f
The average length = (1*1/2 + 2*1/4 + 3*1/8 + 4*1/16 + 5*1/32 + 5*1/32)
                   = 1.9375 


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