huffman algorithm
TRANSCRIPT
7/24/2019 Huffman Algorithm
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Huffman Coding:
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Trees and Priority Queues
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Encoding and
Compression of Data
• Fax Machines
• ASCII
• Variations on ASCII
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– min number of bits needed – cost of savings
– patterns
– modifications
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Purpose of Huffman
Coding
•Proposed by Dr. David A.Huffman in 1952
– “A Method for the Construction
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of Minimum Redundancy Codes”
• Applicable to many forms of
data transmission
– Our example: text files
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The Basic Algorithm
• Huffman coding is a form of
statistical coding
• Not all characters occur with the
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same requency• Yet all characters are allocated
the same amount of space
– 1 char = 1 byte, be it e or x
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The Basic Algorithm
•
Any savings in tailoring codesto frequency of character?
• Code word lengths are no longer
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fixed like ASCII.
• Code word lengths vary and will
be shorter for the morefrequently used characters.
7/24/2019 Huffman Algorithm
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The (Real) Basic
Algorithm 1. Scan text to be compressed and tally
occurrence of all characters.
2. Sort or prioritize characters based on
number of occurrences in text.
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3. Build Huffman code tree based on prioritized list.
4. Perform a traversal of tree to determine
all code words.
5. Scan text again and create new file
using the Huffman codes.
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Building a Tree
Scan the original text
•Consider the following shorttext:
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Eerie eyes seen near lake.
• Count up the occurrences of all
characters in the text
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Building a Tree
Scan the original text
Eerie eyes seen near lake.• What characters are present?
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E e r i space
y s n a r l k .
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Building a Tree
Scan the original text
Eerie eyes seen near lake.
• What is the frequency of each
character in the text?
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Char Freq. Char Freq. Char Freq.E 1 y 1 k 1e 8 s 2 . 1r 2 n 2i 1 a 2space 4 l 1
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Building a Tree
Prioritize characters
• Create binary tree nodes with
character and frequency of
each character
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•Place nodes in a priorityqueue
– The lower the occurrence, the
higher the priority in the queue
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Building a Tree
Prioritize characters
• Uses binary tree nodes
public class HuffNode{
ublic char m Char
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public int myFrequency; public HuffNode myLeft, myRight;}
priorityQueue myQueue;
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Building a Tree
• The queue after inserting all nodes
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• Null Pointers are not shown
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Building a Tree
• While priority queue contains two
or more nodes– Create new node
–
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– Dequeue next node and make it right
subtree
– Frequency of new node equals sum of
frequency of left and right children
– Enqueue new node back into queue
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Building a Tree
E i y l k . r s n a sp e
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Building a Tree
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Building a Tree
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Building a Tree
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Building a Tree
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Building a Tree
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Building a Tree
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Building a Tree
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Building a Tree
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Building a Tree
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Building a Tree
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Building a Tree
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Building a Tree
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Building a Tree
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Building a Tree
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What is happening to the characters
with a low number of occurrences?
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Building a Tree
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Building a Tree
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Building a Tree
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Building a Tree
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Building a Tree
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Building a Tree
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Building a Tree
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Building a Tree
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• After
enqueueingthis node
there is only
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8
10 one node left
in priority
queue.
7/24/2019 Huffman Algorithm
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Building a Tree
Dequeue the single node
left in the queue.
This tree contains the 1016
26
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character.
Frequency of root node
should equal number ofcharacters in text.
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Eerie eyes seen near lake. 26 characters
E di th Fil
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Encoding the File
Traverse Tree for Codes
• Perform a traversal
of the tree to
obtain new code
words
26
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• Going left is a 0going right is a 1
• code word is only
completed when a
leaf node is
reached
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E di th Fil
7/24/2019 Huffman Algorithm
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Encoding the File
Traverse Tree for Codes
Char CodeE 0000i 0001y 0010l 0011
26
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k 0100. 0101space 011e 10
r 1100s 1101n 1110a 1111
E1
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sp
4
e8
2
y1
l1
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k1
.1
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r2
s2
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n2
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8
10
7/24/2019 Huffman Algorithm
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Encoding the File
• Rescan text and
encode file using
new code words
Eerie eyes seen near lake.
Char Code
E 0000i 0001y 0010l 0011
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k 0100. 0101space 011e 10
r 1100s 1101n 1110a 1111
1000101011011010011
1110101111110001100
1111110100100101
• Why is there no need
for a separator
character?
.
Encoding the File
7/24/2019 Huffman Algorithm
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Encoding the File
Results
• Have we made
things any better?
• 73 bits to encode
0000101100000110011
1000101011011010011
1110101111110001100
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the text• ASCII would take
8 * 26 = 208 bits
hIf modified code used 4 bits percharacter are needed. Total bits
4 * 26 = 104. Savings not as great.
7/24/2019 Huffman Algorithm
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Decoding the File
• How does receiver know what the codes are?
• Tree constructed for each text file.
– Considers frequency for each file
–
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,
files
• Tree predetermined
– based on statistical analysis of text files or
file types
• Data transmission is bit based versus byte
based
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Decoding the File
• Once receiver has
tree it scans
incoming bit stream
• 0 ⇒⇒⇒⇒ go left10
16
26
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• 1 ⇒⇒⇒⇒ go right
E1
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y1
l1
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k1
.1
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r2
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101000110111101111
01111110000110101
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Summary
• Huffman coding is a technique used
to compress files for transmission
• Uses statistical coding
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–
more frequently used symbols haveshorter code words
• Works well for text and fax
transmissions
• An application that uses several
data structures