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233-234. Sedgewick & Wayne (2004); Chazelle (2005). How to check if adding an edge creates a cycle?. Label i all nodes of i-th tree. 2. 1. 1. 2. 1. 2. 2. How to check if adding an edge creates a cycle?. Label i all nodes of i-th tree. 2. 1. 1. 2. 1. 2. 2.

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233-234

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  1. 233-234 Sedgewick & Wayne (2004); Chazelle (2005)

  2. How to check if adding an edge creates a cycle? Label i all nodes of i-th tree 2 1 1 2 1 2 2

  3. How to check if adding an edge creates a cycle? Label i all nodes of i-th tree 2 1 1 2 1 2 2

  4. How to check if adding an edge creates a cycle? Label i all nodes of i-th tree 2 1 1 2 1 2 2 Relabel smaller tree

  5. How to check if adding an edge creates a cycle? Label i all nodes of i-th tree 2 2 2 2 2 2 2 Relabel smaller tree

  6. How to check if adding an edge creates a cycle? Label i all nodes of i-th tree 2 2 2 2 2 2 2 Each node relabeled at most log V times

  7. edge of the MST correctness 9 3 Bnodes 7 8 Anodes

  8. B 3 A

  9. B 3 A A B A A 8

  10. How much time ? 1. Sorting: 2. Cycle detection:

  11. How much time ? 1. Sorting: 2. Cycle detection: Time proportional to

  12. Advanced MST Algorithms

  13. Ackermann’s function number of particles in the universe If E = 2

  14. The amazing function Tower of height equal to tower of x Two times x Tower of x Two to the x-th

  15. demo time

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