1. Assignment 6: Huffman Code Generation
Andy Wang
Data Structures, Algorithms, and Generic Programming

2. Huffman Code Commonly used in compression schemes Idea:
Use variable-length code words
Length of the word inversely proportional to the frequency of its occurrences

3. ASCII Encoding TALLAHASSEE ASCII values A 0100 0001 E 0100 0101

4. ASCII Encoding TALLAHASSEE
8*11 = 88 bits

5. Huffman Encoding
TALLAHASSEE
A 10
E 00
H 010
L 110
S 111
T 011

6. Huffman Encoding TALLAHASSEE 011 10 110 110 10 010 10 111 111 00 00
28 bits

7. Assignment 6 Generate Huffman Code Frequency analysis
Constructing the code tree
Printing out the code table

8. Frequency Analysis
TALLAHASSEE
A 3
E 2
H 1
L 2
S 2
T 1

9. Constructing the Code Tree
Create tree nodes
E:2
A:3
H:1
L:2
T:1
S:2

10. Constructing the Code Tree
Build a modified heap
H:1
L:2
T:1
A:3
E:2
S:2

11. Constructing the Code Tree
Find two nodes with the smallest counter values
T:1
L:2
S:2
A:3
E:2
H:1

12. Constructing the Code Tree
Find two nodes with the smallest counter values
E:2
L:2
S:2
A:3
H:1
T:1

13. Constructing the Code Tree
Create a parent node
E:2
L:2
S:2
A:3
H:1
T:1 :2

14. Constructing the Code Tree
Insert the parent node back to the heap
E:2
L:2
S:2
H:1
T:1 :2
A:3

15. Constructing the Code Tree
Find two nodes with the smallest counter values
H:1
T:1 :2
L:2
S:2
A:3
E:2

16. Constructing the Code Tree
Find two nodes with the smallest counter values
L:2
A:3
S:2
E:2
H:1
T:1 :2

17. Constructing the Code Tree
Create a parent node
L:2
A:3
S:2
E:2
H:1
T:1 :2 :4

18. Constructing the Code Tree
Insert the parent node back to the heap
L:2
A:3
E:2
H:1
T:1 :2 :4
S:2

19. Constructing the Code Tree
Find two nodes with the smallest counter values
S:2
E:2
H:1
T:1 :2 :4
A:3
L:2

20. Constructing the Code Tree
Find two nodes with the smallest counter values
E:2
H:1
T:1 :2 :4
A:3
L:2
S:2

21. Constructing the Code Tree
Create a parent node
A:3 :4
E:2 :2 :4
H:1
T:1
L:2
S:2

22. Constructing the Code Tree
Insert the parent node back to the heap
L:2
S:2 :4
A:3 :4
E:2 :2
H:1
T:1

23. Constructing the Code Tree
Find two nodes with the smallest counter values
L:2
S:2 :4 :4
A:3
E:2 :2
H:1
T:1

24. Constructing the Code Tree
Find two nodes with the smallest counter values
E:2
H:1
T:1 :2 :4
A:3
L:2
S:2 :4

25. Constructing the Code Tree
Create a parent node :7 :4
A:3
L:2
S:2 :4
E:2 :2
H:1
T:1

26. Constructing the Code Tree
Insert the parent node back to the heap
A:3
L:2
S:2 :4 :7
E:2
H:1
T:1 :2 :4

27. Constructing the Code Tree
Find two nodes with the smallest counter values
E:2
H:1
T:1 :2 :4
A:3
L:2
S:2 :4 :7

28. Constructing the Code Tree
Find two nodes with the smallest counter values :4
A:3
L:2
S:2 :4 :7
E:2 :2
H:1
T:1

29. Constructing the Code Tree
Create a parent node
:11 :4
A:3
L:2
S:2 :4 :7
E:2 :2
H:1
T:1

30. Constructing the Code Tree
Insert the parent node back to the heap
:11 :4
A:3
L:2
S:2 :4 :7
E:2 :2
H:1
T:1

31. Code Assignment :11 1 :4 A:3 L:2 S:2 :4 :7 1 1 E:2 :2 00 1 10 1 H:1:4
A:3
L:2
S:2 :4 :7 1 1
E:2 :2 00 1 10 1
H:1
T:1
010
011
110
111

32. Properties of Huffman Code
Higher the frequency, shorter the code
The code for one character is not the prefix for another code
00 is not a prefix for 010
00 is a prefix for 001