GATE | GATE-CS-2007 | Question 77
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
Quiz of this Question
Last Updated :
28 Jun, 2021
Like Article
Save Article
Share your thoughts in the comments
Please Login to comment...