Assignment 6: Huffman Code Generation

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

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ASCII Encoding

• TALLAHASSEE
• ASCII values
• A 0100 0001
• E 0100 0101
• H 0100 1000
• L 0100 1100
• S 0101 0011
• T 0101 0100

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ASCII Encoding

• TALLAHASSEE
• 0101 0100 0100 0001 0100 1100 0100 1100 0100 0001
  0100 1000 0100 0001 0101 0011 0101 0011 0100 0101
  0100 0101
• 811 88 bits

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Huffman Encoding

• TALLAHASSEE
• A 10
• E 00
• H 010
• L 110
• S 111
• T 011

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Huffman Encoding

• TALLAHASSEE
• 011 10 110 110 10 010 10 111 111 00 00
• 28 bits

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Assignment 6

• Generate Huffman Code
• Frequency analysis
• Constructing the code tree
• Printing out the code table

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Frequency Analysis

• TALLAHASSEE
• A 3
• E 2
• H 1
• L 2
• S 2
• T 1

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Constructing the Code Tree

• Create tree nodes

E2
A3
H1
L2
T1
S2
10
Constructing the Code Tree

• Build a modified heap

A3
L2
H1
T1
S2
E2
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Constructing the Code Tree

• Find two nodes with the smallest counter values

A3
L2
T1
S2
E2
H1
12
Constructing the Code Tree

• Find two nodes with the smallest counter values

A3
L2
S2
E2
H1
T1
13
Constructing the Code Tree

• Create a parent node

A3
L2
S2
E2
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Constructing the Code Tree

• Insert the parent node back to the heap

A3
L2
S2
E2
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Constructing the Code Tree

• Find two nodes with the smallest counter values

A3
L2
S2
E2
16
Constructing the Code Tree

• Find two nodes with the smallest counter values

A3
L2
S2
E2
17
Constructing the Code Tree

• Create a parent node

A3
L2
S2
18
Constructing the Code Tree

• Insert the parent node back to the heap

A3
L2
S2
19
Constructing the Code Tree

• Find two nodes with the smallest counter values

A3
S2
L2
20
Constructing the Code Tree

• Find two nodes with the smallest counter values

A3
L2
S2
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Constructing the Code Tree

• Create a parent node

A3
4
E2
2
4
T1
L2
S2
H1
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Constructing the Code Tree

• Insert the parent node back to the heap

A3
4
E2
2
T1
H1
23
Constructing the Code Tree

• Find two nodes with the smallest counter values

4
A3
E2
2
T1
H1
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Constructing the Code Tree

• Find two nodes with the smallest counter values

A3
25
Constructing the Code Tree

• Create a parent node

7
4
A3
E2
2
T1
H1
26
Constructing the Code Tree

• Insert the parent node back to the heap

27
Constructing the Code Tree

• Find two nodes with the smallest counter values

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Constructing the Code Tree

• Find two nodes with the smallest counter values

4
E2
2
T1
H1
29
Constructing the Code Tree

• Create a parent node

11
4
E2
2
T1
H1
30
Constructing the Code Tree

• Insert the parent node back to the heap

11
4
E2
2
T1
H1
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Code Assignment
11
1
0
4
1
0
0
1
E2
2
0
1
1
00
0
10
T1
H1
010
011
110
111
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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