Question

g Suppose we want to compress a text consisting of 6 characters,a, b, c, d, e, fusingthe Huffman Algorithm. Give an example for which the algorithm produces at least onecodeword of length 5. In other words, you are being asked to give a set of the characterfrequencies that results in the deepest tree.

Answer 1

e(a) = 0

e(b) = 10

e(c) = 110

e(d) = 1110

Step-by-step explanation:

The Worst case will happen when f(a) > 2*f(b) ; f(b) > 2*f(c) ; f(c) > 2*f(d) ; f(d) > 2*f(e) and f(e) > 2*f(f).

Where f(x) is frequency of character x.

Lets consider the scenario when

f(a) = 0.555, f(b) = 0.25, f(c) = 0.12, f(d) = 0.05, f(e) = 0.02 and f(f) = 0.005

Please see attachment for image showing the steps of construction of Huffman tree:- see attachment

From the Huffman tree created, we can see that endcoding e() of each character are as follows:-

e(a) = 0

e(b) = 10

e(c) = 110

e(d) = 1110

e(e) = 11110

e(f) = 11111

So we can see that maximum length of encoding is 5 in this case.