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Computer notes - Analysis of Union

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Union is clearly a constant time operation. Running time of find(i) is proportional to the height of the tree containing node i.If unions are done by weight (size), the depth of any element is never greater than log2n.

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Class No.30 Data Structures http://ecomputernotes.com
Running Time Analysis ,[object Object],[object Object],[object Object],[object Object],http://ecomputernotes.com
Union by Size ,[object Object],[object Object],[object Object],[object Object],http://ecomputernotes.com
Union by Size ,[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],[object Object],http://ecomputernotes.com
Union by Size ,[object Object],http://ecomputernotes.com 1 2 3 4 5 6 7 8 -1 -1 -1 -1 -1 -1 -1 -1 1 2 3 4 5 6 7 8
Union by Size ,[object Object],http://ecomputernotes.com 1 2 3 4 5 6 7 8 -1 -1 -1 -2 -1 4 -1 -1 1 2 3 4 5 6 7 8
Union by Size ,[object Object],http://ecomputernotes.com 1 2 3 4 5 6 7 8 -1 -2 2 -2 -1 4 -1 -1 1 2 3 4 5 6 7 8
Union by Size ,[object Object],http://ecomputernotes.com 1 2 3 4 5 6 7 8 4 -2 2 -3 -1 4 -1 -1 1 2 3 4 5 6 7 8
Union by Size ,[object Object],http://ecomputernotes.com 1 2 3 4 5 6 7 8 4 4 2 -5 -1 4 -1 -1 1 2 3 4 5 6 7 8
Union by Size ,[object Object],http://ecomputernotes.com 1 2 3 4 5 6 7 8 4 4 2 -6 4 4 -1 -1 1 2 3 4 5 6 7 8
Analysis of Union by Size ,[object Object],http://ecomputernotes.com
Analysis of Union by Size ,[object Object],[object Object],[object Object],[object Object],http://ecomputernotes.com
Union by Height ,[object Object],[object Object],[object Object],http://ecomputernotes.com
Sprucing up Find ,[object Object],[object Object],[object Object],http://ecomputernotes.com
Sprucing up Find ,[object Object],[object Object],[object Object],[object Object],http://ecomputernotes.com
Sprucing up Find ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],http://ecomputernotes.com
Path Compression ,[object Object],12 14 20 10 22 7 3 6 16 4 2 9 30 5 13 11 1 http://ecomputernotes.com 8 31 32 35 13 19 18 17
Path Compression ,[object Object],12 14 20 10 22 7 3 6 16 4 2 9 30 5 13 11 1 http://ecomputernotes.com 8 31 32 35 13 19 18 17
Path Compression ,[object Object],12 14 20 10 22 7 3 6 16 4 2 9 30 5 13 11 1 http://ecomputernotes.com 8 31 32 35 13 19 18 17
Path Compression ,[object Object],12 14 20 10 22 7 3 6 16 4 2 9 30 5 13 11 1 http://ecomputernotes.com 8 31 32 35 13 19 18 17
Path Compression ,[object Object],12 14 20 10 22 7 3 6 16 4 2 9 30 5 13 11 1 http://ecomputernotes.com 8 31 32 35 13 19 18 17
Path Compression ,[object Object],http://ecomputernotes.com a b f c d e
Path Compression ,[object Object],http://ecomputernotes.com a b f c d e
Timing with Optimization ,[object Object],[object Object],[object Object],http://ecomputernotes.com

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Computer notes - Analysis of Union

  • 1. Class No.30 Data Structures http://ecomputernotes.com
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Editor's Notes

  1. End of lecture 35, start of lecture 36
  2. End of lecture 36