Huffman Coding: Design, Analysis, and Implementation, Lecture notes of Design and Analysis of Algorithms

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BCSE204L Design and

Analysis of Algorithms

Module- 1 Huffman Coding (Greedy Technique) Dr Athira K SCOPE

Data Compression Requirements

• Storage and communication
• Huffman codes compress data very effectively:

savings of 20% to 90% are typical

• Greedy on the frequency of each character in

the data

• Huffman coding is used widely as the basic building block of numerous other compression algorithms
• Fixed length and variable length coding

Prefix Codes

• Codes in which no codeword is also a prefix of some other codeword are called prefix codes
• Advantage:- decoding without ambiguity
• Prefix code can always achieve the optimal data compression among any character coding scheme

Prefix Codes Example

• Encoding:- 𝑎𝑏𝑐 → 0 · 101 · 100 where · is concatenation
• Therefore, instead of 𝑎𝑏𝑐 we send 0101100
• Decoded at the receiving end without ambiguity, provided the receiver must know the coding table

Huffman Tree

• Algorithm builds Huffman tree, 𝑇 in a bottom up manner
• Initially a set of |𝐶| leaves and performs |𝐶| − 1 merge operations
• Uses a min-priority queue 𝑄, keyed on the 𝑓𝑟𝑒𝑞 attribute

Huffman Coding Pseudocode

Exercise

• Draw the Huffman tree and generate the Huffman code
• Answer: a=111, e=10, i=00, o=11001, u=1101, s=01, t= a e i o u s t 10 15 12 3 4 13 1

Thank you..