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Huffman Coding:  An Application of Binary Trees and Priority Queues CS 102
Encoding and Compression of Data ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],CS 102
Purpose of Huffman Coding ,[object Object],[object Object],[object Object],[object Object],CS 102
The Basic Algorithm ,[object Object],[object Object],[object Object],[object Object],CS 102
The Basic Algorithm ,[object Object],[object Object],[object Object],CS 102
The (Real) Basic Algorithm CS 102 ,[object Object],[object Object],[object Object],[object Object],[object Object]
Building a Tree Scan the original text ,[object Object],[object Object],[object Object],CS 102
Building a Tree Scan the original text ,[object Object],[object Object],CS 102 E  e  r  i space  y s n a r l k .
Building a Tree Scan the original text ,[object Object],[object Object],CS 102 Char Freq.  Char Freq.  Char Freq. E  1   y 1   k 1 e  8   s  2   . 1 r  2   n  2   i  1   a 2 space  4   l 1
Building a Tree Prioritize characters ,[object Object],[object Object],[object Object],CS 102
Building a Tree Prioritize characters ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],CS 102
Building a Tree ,[object Object],[object Object],CS 102 E 1 i 1 y 1 l 1 k 1 . 1 r 2 s 2 n 2 a 2 sp 4 e 8
Building a Tree ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],CS 102
Building a Tree CS 102 E 1 i 1 y 1 l 1 k 1 . 1 r 2 s 2 n 2 a 2 sp 4 e 8
Building a Tree CS 102 E 1 i 1 y 1 l 1 k 1 . 1 r 2 s 2 n 2 a 2 sp 4 e 8 2
Building a Tree CS 102 E 1 i 1 y 1 l 1 k 1 . 1 r 2 s 2 n 2 a 2 sp 4 e 8 2
Building a Tree CS 102 E 1 i 1 k 1 . 1 r 2 s 2 n 2 a 2 sp 4 e 8 2 y 1 l 1 2
Building a Tree CS 102 E 1 i 1 k 1 . 1 r 2 s 2 n 2 a 2 sp 4 e 8 2 y 1 l 1 2
Building a Tree CS 102 E 1 i 1 r 2 s 2 n 2 a 2 sp 4 e 8 2 y 1 l 1 2 k 1 . 1 2
Building a Tree CS 102 E 1 i 1 r 2 s 2 n 2 a 2 sp 4 e 8 2 y 1 l 1 2 k 1 . 1 2
Building a Tree CS 102 E 1 i 1 n 2 a 2 sp 4 e 8 2 y 1 l 1 2 k 1 . 1 2 r 2 s 2 4
Building a Tree CS 102 E 1 i 1 n 2 a 2 sp 4 e 8 2 y 1 l 1 2 k 1 . 1 2 r 2 s 2 4
Building a Tree CS 102 E 1 i 1 sp 4 e 8 2 y 1 l 1 2 k 1 . 1 2 r 2 s 2 4 n 2 a 2 4
Building a Tree CS 102 E 1 i 1 sp 4 e 8 2 y 1 l 1 2 k 1 . 1 2 r 2 s 2 4 n 2 a 2 4
Building a Tree CS 102 E 1 i 1 sp 4 e 8 2 y 1 l 1 2 k 1 . 1 2 r 2 s 2 4 n 2 a 2 4 4
Building a Tree CS 102 E 1 i 1 sp 4 e 8 2 y 1 l 1 2 k 1 . 1 2 r 2 s 2 4 n 2 a 2 4 4
Building a Tree CS 102 E 1 i 1 sp 4 e 8 2 y 1 l 1 2 k 1 . 1 2 r 2 s 2 4 n 2 a 2 4 4 6
Building a Tree CS 102 E 1 i 1 sp 4 e 8 2 y 1 l 1 2 k 1 . 1 2 r 2 s 2 4 n 2 a 2 4 4 6 What is happening to the characters with a low number of occurrences?
Building a Tree CS 102 E 1 i 1 sp 4 e 8 2 y 1 l 1 2 k 1 . 1 2 r 2 s 2 4 n 2 a 2 4 4 6 8
Building a Tree CS 102 E 1 i 1 sp 4 e 8 2 y 1 l 1 2 k 1 . 1 2 r 2 s 2 4 n 2 a 2 4 4 6 8
Building a Tree CS 102 E 1 i 1 sp 4 e 8 2 y 1 l 1 2 k 1 . 1 2 r 2 s 2 4 n 2 a 2 4 4 6 8 10
Building a Tree CS 102 E 1 i 1 sp 4 e 8 2 y 1 l 1 2 k 1 . 1 2 r 2 s 2 4 n 2 a 2 4 4 6 8 10
Building a Tree CS 102 E 1 i 1 sp 4 e 8 2 y 1 l 1 2 k 1 . 1 2 r 2 s 2 4 n 2 a 2 4 4 6 8 10 16
Building a Tree CS 102 E 1 i 1 sp 4 e 8 2 y 1 l 1 2 k 1 . 1 2 r 2 s 2 4 n 2 a 2 4 4 6 8 10 16
Building a Tree CS 102 E 1 i 1 sp 4 e 8 2 y 1 l 1 2 k 1 . 1 2 r 2 s 2 4 n 2 a 2 4 4 6 8 10 16 26
Building a Tree CS 102 E 1 i 1 sp 4 e 8 2 y 1 l 1 2 k 1 . 1 2 r 2 s 2 4 n 2 a 2 4 4 6 8 10 16 26 ,[object Object]
Building a Tree CS 102 Dequeue the single node left in the queue. This tree contains the new code words for each character. Frequency of root node should equal number of characters in text. Eerie eyes seen near lake.    26 characters E 1 i 1 sp 4 e 8 2 y 1 l 1 2 k 1 . 1 2 r 2 s 2 4 n 2 a 2 4 4 6 8 10 16 26
Encoding the File Traverse Tree for Codes ,[object Object],[object Object],[object Object],CS 102 E 1 i 1 sp 4 e 8 2 y 1 l 1 2 k 1 . 1 2 r 2 s 2 4 n 2 a 2 4 4 6 8 10 16 26
Encoding the File Traverse Tree for Codes ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],CS 102 E 1 i 1 sp 4 e 8 2 y 1 l 1 2 k 1 . 1 2 r 2 s 2 4 n 2 a 2 4 4 6 8 10 16 26
Encoding the File ,[object Object],[object Object],CS 102 Char Code E 0000 i 0001 y 0010 l 0011 k 0100 . 0101 space 011 e 10 r 1100 s 1101 n 1110 a 1111 0000101100000110011100010101101101001111101011111100011001111110100100101 ,[object Object],[object Object]
Encoding the File Results ,[object Object],[object Object],[object Object],CS 102 0000101100000110011100010101101101001111101011111100011001111110100100101 ,[object Object],[object Object],[object Object]
Decoding the File ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],CS 102
Decoding the File ,[object Object],[object Object],[object Object],CS 102 10100011011110111101111110000110101 E 1 i 1 sp 4 e 8 2 y 1 l 1 2 k 1 . 1 2 r 2 s 2 4 n 2 a 2 4 4 6 8 10 16 26
Summary ,[object Object],[object Object],[object Object],[object Object],[object Object],CS 102

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Huffman 2

  • 1. Huffman Coding: An Application of Binary Trees and Priority Queues CS 102
  • 2.
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  • 14. Building a Tree CS 102 E 1 i 1 y 1 l 1 k 1 . 1 r 2 s 2 n 2 a 2 sp 4 e 8
  • 15. Building a Tree CS 102 E 1 i 1 y 1 l 1 k 1 . 1 r 2 s 2 n 2 a 2 sp 4 e 8 2
  • 16. Building a Tree CS 102 E 1 i 1 y 1 l 1 k 1 . 1 r 2 s 2 n 2 a 2 sp 4 e 8 2
  • 17. Building a Tree CS 102 E 1 i 1 k 1 . 1 r 2 s 2 n 2 a 2 sp 4 e 8 2 y 1 l 1 2
  • 18. Building a Tree CS 102 E 1 i 1 k 1 . 1 r 2 s 2 n 2 a 2 sp 4 e 8 2 y 1 l 1 2
  • 19. Building a Tree CS 102 E 1 i 1 r 2 s 2 n 2 a 2 sp 4 e 8 2 y 1 l 1 2 k 1 . 1 2
  • 20. Building a Tree CS 102 E 1 i 1 r 2 s 2 n 2 a 2 sp 4 e 8 2 y 1 l 1 2 k 1 . 1 2
  • 21. Building a Tree CS 102 E 1 i 1 n 2 a 2 sp 4 e 8 2 y 1 l 1 2 k 1 . 1 2 r 2 s 2 4
  • 22. Building a Tree CS 102 E 1 i 1 n 2 a 2 sp 4 e 8 2 y 1 l 1 2 k 1 . 1 2 r 2 s 2 4
  • 23. Building a Tree CS 102 E 1 i 1 sp 4 e 8 2 y 1 l 1 2 k 1 . 1 2 r 2 s 2 4 n 2 a 2 4
  • 24. Building a Tree CS 102 E 1 i 1 sp 4 e 8 2 y 1 l 1 2 k 1 . 1 2 r 2 s 2 4 n 2 a 2 4
  • 25. Building a Tree CS 102 E 1 i 1 sp 4 e 8 2 y 1 l 1 2 k 1 . 1 2 r 2 s 2 4 n 2 a 2 4 4
  • 26. Building a Tree CS 102 E 1 i 1 sp 4 e 8 2 y 1 l 1 2 k 1 . 1 2 r 2 s 2 4 n 2 a 2 4 4
  • 27. Building a Tree CS 102 E 1 i 1 sp 4 e 8 2 y 1 l 1 2 k 1 . 1 2 r 2 s 2 4 n 2 a 2 4 4 6
  • 28. Building a Tree CS 102 E 1 i 1 sp 4 e 8 2 y 1 l 1 2 k 1 . 1 2 r 2 s 2 4 n 2 a 2 4 4 6 What is happening to the characters with a low number of occurrences?
  • 29. Building a Tree CS 102 E 1 i 1 sp 4 e 8 2 y 1 l 1 2 k 1 . 1 2 r 2 s 2 4 n 2 a 2 4 4 6 8
  • 30. Building a Tree CS 102 E 1 i 1 sp 4 e 8 2 y 1 l 1 2 k 1 . 1 2 r 2 s 2 4 n 2 a 2 4 4 6 8
  • 31. Building a Tree CS 102 E 1 i 1 sp 4 e 8 2 y 1 l 1 2 k 1 . 1 2 r 2 s 2 4 n 2 a 2 4 4 6 8 10
  • 32. Building a Tree CS 102 E 1 i 1 sp 4 e 8 2 y 1 l 1 2 k 1 . 1 2 r 2 s 2 4 n 2 a 2 4 4 6 8 10
  • 33. Building a Tree CS 102 E 1 i 1 sp 4 e 8 2 y 1 l 1 2 k 1 . 1 2 r 2 s 2 4 n 2 a 2 4 4 6 8 10 16
  • 34. Building a Tree CS 102 E 1 i 1 sp 4 e 8 2 y 1 l 1 2 k 1 . 1 2 r 2 s 2 4 n 2 a 2 4 4 6 8 10 16
  • 35. Building a Tree CS 102 E 1 i 1 sp 4 e 8 2 y 1 l 1 2 k 1 . 1 2 r 2 s 2 4 n 2 a 2 4 4 6 8 10 16 26
  • 36.
  • 37. Building a Tree CS 102 Dequeue the single node left in the queue. This tree contains the new code words for each character. Frequency of root node should equal number of characters in text. Eerie eyes seen near lake.  26 characters E 1 i 1 sp 4 e 8 2 y 1 l 1 2 k 1 . 1 2 r 2 s 2 4 n 2 a 2 4 4 6 8 10 16 26
  • 38.
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