1. Prim’s algorithm for minimum spanning trees

2. 1 9 2 8 1 4 6 4 3 4 5 5 1 9 7 11 2 6 3 7 8

3. 1 9 2 8 1 4 6 4 3 4 5 5 1 9 7 11 2 6 3 7 8

4. 1 9 2 8 1 4 6 4 3 4 5 5 1 9 7 11 2 6 3 7 8

5. 1 9 2 8 1 4 6 4 3 4 5 5 1 9 7 11 2 6 3 7 8

6. 1 9 2 8 1 4 6 4 3 4 5 5 1 9 7 11 2 6 3 7 8

7. 1 9 2 8 1 4 6 4 3 4 5 5 1 9 7 11 2 6 3 7 8

8. 1 9 2 8 1 4 6 4 3 4 5 5 1 9 7 11 2 6 3 7 8

9. 1 9 2 8 1 4 6 4 3 4 5 5 1 9 7 11 2 6 3 7 8

10. Kruskal’s algorithm for minimum spanning trees

11. 1 9 2 8 1 4 6 4 3 4 5 5 1 9 7 11 2 6 3 7 8

12. 1 9 2 8 4 6 1 4 3 4 5 5 1 9 7 11 2 6 3 5 7 8 2

13. 1 9 2 8 4 6 1 4 3 4 5 5 1 9 7 11 2 6 3 5 7 8 6 2

14. 1 9 2 8 4 6 1 4 3 4 5 5 1 9 7 11 2 6 3 5 7 8 8 6 2

15. 1 9 2 8 1 4 6 4 3 4 5 5 1 9 7 11 2 6 7 3 5 7 8 1 8 6 2

16. 4 1 9 2 8 4 6 1 4 3 4 3 5 5 1 9 7 11 2 6 7 3 5 7 8 1 8 6 2

17. 4 1 9 2 8 4 6 1 4 3 4 3 5 5 1 9 7 11 2 6 7 3 5 7 8 1 8 6 2

18. 4 1 9 2 8 4 6 1 4 3 4 3 5 5 1 9 7 11 2 6 7 3 5 7 8 1 8 6 2

19. Dijkstra’s algorithm for single-source shortest paths

20. x 4 s 5 6 1 k z 1 3 b 5 c u 4 1 5 2 4 d 2 y 3
V’ = { s}
Choose node b

21. V’ = { s, b} x s k b c u d Choose node c z y 4 5 6 1 1 3 5 4 1 5 2 4 2

22. V’ = { s, b, c} x s k b c u d Choose node d z y 4 5 6 1 1 3 5 4 1 5 2

23. V’ = { s, b, c, d} x s k b c u d Choose node y z y 4 5 6 1 1 3 5 4 1 52 4 d 2 y 3
V’ = { s, b, c, d}
Choose node y

24. x 4 s 5 6 1 k z 1 3 b 5 c u 4 1 5 2 4 d 2 y 3
V’ = { s, b, c, d, y}
Whenever a new node is added to V’, we need to update nearest(x) for all x not in V’.