Huffman coding
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This presentation summarizes Huffman coding. It begins with an outline covering the definition, history, building the tree, implementation, algorithm and examples. It then discusses how Huffman coding encodes data by building a binary tree from character frequencies and assigning codes based on the tree's structure. An example shows how the string "Duke blue devils" is encoded. The time complexity of building the Huffman tree is O(NlogN). Real-life applications of Huffman coding include data compression in fax machines, text files and other forms of data transmission.
![Human Coding
Create New Node m
1. frequencies[m] ←
frequency1 + frequency2 // new
node
2. frequencies[node1] ← m // left link
3. frequencies[node2] ← -m // right link
4. insert in PQueue
(m, frequency1 + frequency2)](https://image.slidesharecdn.com/huffman-coding-170911184817/85/Huffman-coding-5-320.jpg)
Huffman coding
- 1. NAME : NAZMUL HYDER ID : 011 -131-085 WELCOME TO MY PRESENTATION Topic: Huffman Coding
- 2. Outline ✓ Definition of The Problem ✓ History ✓ Building the tree ✓ Implementation ✓Algorithm ✓Example ✓ Run Time Analysis ✓ Applications
- 3. Encoding and Compression of Data ▶ Fax Machines ▶ ASCII ▶ Variations on ASCII ▶ min number of bits needed ▶ cost of savings ▶ patterns ▶ modifications
- 4. Purpose of Huffman Coding ▶ Proposed by Dr. David A. Huffman in 1952 ▶ “A Method for the Construction of Minimum Redundancy Codes” ▶ Applicable to many forms of data transmission ▶ Our example: text files
- 5. Human Coding Create New Node m 1. frequencies[m] ← frequency1 + frequency2 // new node 2. frequencies[node1] ← m // left link 3. frequencies[node2] ← -m // right link 4. insert in PQueue (m, frequency1 + frequency2)
- 6. Huffman Coding ▶ As an example, lets take the string: “Duke blue devils” ▶ We first to a frequency count of the characters: ▶ S:1, i:1, v:1, b:1, k:1, sp:2, l:2, u:2, d:2, e:3. ▶ Next we use a Greedy algorithm to build up a Huffman Tree ▶ We start with nodes for each character e ,3 d ,2 u ,2 l, 2 s p ,2 k, 1 b ,1 v, 1 i, 1 S, 1
- 9. Building a Tree e ,3 d ,2 u ,2 l, 2 s p ,2 k, 1 i, 1 s, 1 2 b ,1 v, 1 2 3 4 4 e ,3 d ,2 u ,2 l, 2 s p ,2 k, 1 i, 1 s, 1 2 b ,1 v, 1 2 3 44 5
- 13. Huffman Coding ▶ Once receiver has tree it scans incoming bit stream ▶ 0 Go left. ▶ 1 Go right. ▶ Note that no code is the prefix of another code
- 14. Huffman Coding e ,3 d ,2 u ,2 l, 2 s p ,2 k, 1 i, 1 s, 1 2 b ,1 v, 1 2 3 44 5 7 9 1 6 e 00 d 010 u 011 l 100 sp 101 i 1100 s 1101 k 1110 b 11110 v 11111 0
- 15. Encoding the String results ▶ These codes are then used to encode the string ▶ Thus, “duke blue devils” turns into 56 bits: 010 011 1110 00 101 11110 100 011 00 101 010 00 11111 1100 100 1101 ▶ ASCII will take 128 bit: 01001111 10001011 11101000 11001010 10001111 11100100 1101xxxx h If modified code used 4 bits per character are needed. Total bits 4 * 16 = 64. Savings not as great ▶ Thus it takes 7 bytes of space compared to 16 characters * 1 byte/char = 16 bytes uncompressed ▶ Total save=128-56=72.
- 16. Running Time 16 Time efficiency of building the Huffman tree The insert and delete operations each take log(N) time, and they are repeated at most 2N times Therefore the run time is O(2NlogN) = O(NlogN)