Huffman coding || Huffman Tree
- 1. Huffman Coding bY P.GuruNadh IIIT SRIKAKULAM
- 2. Huffman Coding ● Huffman coding is proposed by David A. Huffman in 1952 ● It is the one of the application of Binary Search Trees. ● It is Used for compression of Files. ● Compression is Nothing but reducing the size. ● We use this Huffman coding in WinRar,WinZip,7zip Applications etc..,
- 3. Huffman Tree ● It is used for to give unique encoding to a particular code or string ● Properties Of Huffman Tree ○ It should contain root node ○ Internal nodes are indicated with circles( ) and it should contain weights. ○ External nodes are indicated with squares( )and they should contain Frequency & Characters.
- 4. Normal Encoding ● Let we take an example ● Let there are 7 characters in a string and each character is represented in 8 bits(ASCII CODES) ASCII a-97 b-98 c-100 d-101 BINARY(8 bits) a-01100001 b-01100010 c-01100011 d-01100100 For representing abcdaab we need 7*8=56 bits To reduce the bits we go for frequent characters. Binary Encoding Representation a b c d a a b 01100001 01100010 01100011 01100100 01100001 01100001 01100001 01100010
- 5. Frequent Characters Technique ● In frequent characters technique the frequent occur character will take less bits and rarely occur character will take large bits. ⮚ Let’s take the previous example , in this method we first calculate frequency of characters. ⮚ Highest frequency character is represented with less bits and lowest frequency character is represented with large bits. Representation a-0 b-10 c-110 d-111 By this technique for representing abcdaab we need only 13 bits. a b c d a a b 0 10 110 111 0 0 10
- 6. Construction Of Huffman Tree 1.Scan text to be compressed and count occurrence of all characters. 2.Sort characters based on number of occurrences in text. 3.Take 2 characters which are having least frequency as leaf nodes. 4.And sum the data of that nodes and take it as it’s parent node. 5.Take next least occurred node and compare with parent node. 6.If compared node > parent node place at right side of parent node. 7.Else place at left side of parent node and repeat the procedure from step 4. 8.Perform a traversal of tree to determine all code words.
- 7. Huffman Tree Logic HT( ) { N=Priority Queue ; Sort(N); for(i=1 to n-1) { create_Node; //Z Z.left = min(Z); Z.right = Next_min(N); Z.frequency=Z.left + Z.right; push(z.frequency) } }
- 8. Key words of Huffman Tree ● Internal path length ○ The longest path from root node to corresponding internal node. ● External path length ○ The longest path from root node to corresponding external node. ● Let n be the number of internal nodes then, ○ External path length = Internal path length+2*n ● External weighted nodes = External path length * Frequency of External Node ● Sum of External weighted nodes = storage
- 9. Examples ● String = ab ab cba ; Occurrences = a🡪3;b🡪3;c🡪1;space🡪2;eof🡪1; 1 1 c eof 🡪 2 1 1 c eof 🡪 2 1 1 c eof 2 2 1 Space c,eof=1;space=2;a,b=3
- 10. Continue…. Continue….. 1 c eof 2 2 1 Space 4 🡪 1 c eof 2 2 1 Space 4 🡪 1 c eof 2 2 1 Space 4 3 a
- 11. Continue… ● Continue….. 1 c eof 2 2 1 Space 43 1 c eof 2 2 1 Space 43 🡪 7 a a 🡪 1 c eof 2 2 Space 43 7 a 1 b 3
- 12. Continue.. ● Encode with 0’s at left side and 1’s at right side nodes of every parent node to get the representation of characters in bits. 🡪 10 0 1 Representation b-0 a-10 c-1100 Space-111 eof-1101
- 13. Calculations For Example ● For Previous Example Huffman tree ● Internal Length = Sum of Internal Lengths of internal nodes ○ 1(7)+2(4)+3(2)+0(10)=6 ● External length = Sum of External Lengths of External nodes ○ 4(c)+4(eof)+3(space)+2(a)+1(b)=14 ● Storage = sum of weighted external nodes = sum of(external path length*frequency) ○ (4*1)+(4*1)+(3*2)+(2*3)+(1*3) = 23 10,7,4,2 Are Internal Nodes c,eof,space,a,b Are External Nodes 1,1,2,3,3 Are Frequencies Of External Nodes