1. Spanning Trees

2. Prims MST Algorithm Algorithm ( this is also greedy) Select an arbitrary vertex to start the tree, while there are fringe vertices: 1)select an edge of minimum weight between a tree vertex and a fringe vertex. 2)add the selected edge and the fringe vertex to the tree. end.

3. Prims Algorithm Minimal Spanning Tree 1 6 24 35 3 2 1 4 4 2 5 3 4 78 1 6 2 5 2 6

4. 1 6 24 35 3 2 1 4 4 2 5 3 4 78 1 6 2 5 2 6 Example: start with 7

5. Prims Algorithm Minimal Spanning Tree 1 6 24 35 3 2 1 4 4 2 5 3 4 78 1 6 2 5 2 6

6. 1 6 24 35 3 2 1 4 4 2 5 3 4 78 1 6 2 5 2 6

7. 1 6 24 35 3 2 1 4 4 2 5 3 4 78 1 6 2 5 2 6

8. 1 6 24 35 3 2 1 4 4 2 5 3 4 78 1 2 5 2 6

9. 1 6 24 35 3 2 1 4 4 2 5 3 4 78 1 2 5 2 6

10. 1 6 24 35 3 2 1 4 4 2 5 3 4 78 1 2 5 6

11. 1 6 24 35 3 2 1 4 4 2 5 3 4 78 1 2 5 6

12. 1 6 24 35 2 1 4 4 2 5 3 4 78 1 2 6

13. 1 6 24 35 2 1 4 4 2 5 3 4 78 1 2 6

14. 1 6 24 35 2 1 4 2 5 3 4 78 1 2 6

15. 1 6 24 35 2 1 4 2 5 3 4 78 1 2 6

16. 1 6 24 35 2 1 2 5 3 4 78 1 2

17. 1 6 24 35 2 1 2 5 3 4 78 1 2

18. 1 6 24 35 2 1 2 3 78 1 2 MST weight = 15 4

19. Topological Sorting Algorithm while (the graph has a node with no successor) do remove one of those nodes from the graph and add it to the end of a list if (the graph is empty) then the list contains the reverse of some topological order else the graph contains a cycle

20. A B C D E F G HI J L K M

21. A B C D E F G HI J L K M D

22. A B C E F G HI J L K M D E

23. A B C F G HI J L K M DE F

24. A B C G HI J L K M DEF C

25. A B G HI J L K M DEFC B

26. A G H I J L K M DEFCB I

27. A G H J L K M DEFCBI H

28. A G J L K M DEFCBIH G

29. A J L K M DEFCBIHG A

30. J L K M DEFCBIHGA K

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