GATE | GATE-CS-2007 | Question 76

Suppose the letters a, b, c, d, e, f have probabilities 1/2, 1/4, 1/8, 1/16, 1/32, 1/32 respectively. Which of the following is the Huffman code for the letter a, b, c, d, e, f?
(A) 0, 10, 110, 1110, 11110, 11111
(B) 11, 10, 011, 010, 001, 000
(C) 11, 10, 01, 001, 0001, 0000
(D) 110, 100, 010, 000, 001, 111


Answer: (A)

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


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