CS502 – Design and Analysis of Algorithms
Assignment No. 02
Spring 2026
Due Date: 29-06-2026

Question

Given the message string “aaddbbeess”, use the Huffman Encoding algorithm to:

1. Calculate the frequency of each character.
2. Determine the probability of each character.
3. Construct the Huffman codes (codewords) for each character.

Solution

Step 1: Calculate Frequency

Message String = aaddbbeess

Total Characters = 10

Character	Frequency
a	2
b	2
d	2
e	2
s	2

Step 2: Calculate Probability

Probability = Frequency / Total Characters

Character	Probability
a	2/10 = 0.20
b	2/10 = 0.20
d	2/10 = 0.20
e	2/10 = 0.20
s	2/10 = 0.20

Step 3: Assign Huffman Codewords

Character	Codeword
a	00
b	01
d	100
e	101
s	11

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Final Answer

Character	a	b	d	e	s
Frequency	2	2	2	2	2
Probability	0.20	0.20	0.20	0.20	0.20
Codeword	00	01	100	101	11

Submitted By: zaniklawnak
Student ID: bc100201010