1. Dijkstra Algorithm examples

2. Example 1

3. Walk-Through Initialize array F C A B D H G E K dv pv A F   B C D E2
Initialize array 3 F 5 C K dv pv A F   B C D E G H A 10 7 3 4 8 18 4 B D 9 H 10 9 2 25 3 G E 7

4. Start with G F C A B D H G E K dv pv A B C D E F G T  H 2 3 5 10 7 3 H A 10 7 3 4 8 18 4 B D 9 H 10 9 2 25 3 G E 7

5. Update unselected nodes2
Update unselected nodes 3 F 5 C K dv pv A B C D 2 G E F T  H 3 A 10 7 3 4 8 18 4 B D 9 H 10 9 2 25 3 G E 7

6. Select minimum distance2
Select minimum distance 3 F 5 C K dv pv A B C D T 2 G E F  H 3 A 10 7 3 4 8 18 4 B D 9 H 10 9 2 25 3 G E 7

7. Update unselected nodes2
Update unselected nodes 3 F 5 C K dv pv A B C D T 2 G E 27 F 20  H 3 A 10 7 3 4 8 18 4 B D 9 H 10 9 2 25 3 G E 7

8. Select minimum distance2
Select minimum distance 3 F 5 C K dv pv A B C D T 2 G E 27 F 20  H 3 A 10 7 3 4 8 18 4 B D 9 H 10 9 2 25 3 G E 7

9. Update unselected nodes2
Update unselected nodes 3 F 5 C K dv pv A 7 H B 12 C D T 2 G E 27 F 20  3 A 10 7 3 4 8 18 4 B D 9 H 10 9 2 25 3 G E 7

10. Select minimum distance2
Select minimum distance 3 F 5 C K dv pv A T 7 H B 12 C D 2 G E 27 F 20  3 A 10 7 3 4 8 18 4 B D 9 H 10 9 2 25 3 G E 7

11. Update unselected nodes2
Update unselected nodes 3 F 5 C K dv pv A T 7 H B 12 C D 2 G E 27 F 17  3 A 10 7 3 4 8 18 4 B D 9 H 10 9 2 25 3 G E 7

12. Select minimum distance2
Select minimum distance 3 F 5 C K dv pv A T 7 H B 12 C D 2 G E 27 F 17  3 A 10 7 3 4 8 18 4 B D 9 H 10 9 2 25 3 G E 7

13. Update unselected nodes2
Update unselected nodes 3 F 5 C K dv pv A T 7 H B 12 C 16 D 2 G E 22 F 17  3 A 10 7 3 4 8 18 4 B D 9 H 10 9 2 25 3 G E 7

14. Select minimum distance2
Select minimum distance 3 F 5 C K dv pv A T 7 H B 12 C 16 D 2 G E 22 F 17  3 A 10 7 3 4 8 18 4 B D 9 H 10 9 2 25 3 G E 7

15. Update unselected nodes2
Update unselected nodes 3 F 5 C K dv pv A T 7 H B 12 C 16 D 2 G E 22 F 17  3 A 10 7 3 4 8 18 4 B D 9 H 10 9 2 25 3 G E 7

16. Select minimum distance2
Select minimum distance 3 F 5 C K dv pv A T 7 H B 12 C 16 D 2 G E 22 F 17  3 A 10 7 3 4 8 18 4 B D 9 H 10 9 2 25 3 G E 7

17. Update unselected nodes2
Update unselected nodes 3 F 5 C K dv pv A T 7 H B 12 C 16 D 2 G E 19 F 17  3 A 10 7 4 8 18 4 B D 9 H 10 9 2 25 3 G E 7

18. Select minimum distance2
Select minimum distance 3 F 5 C K dv pv A T 7 H B 12 C 16 D 2 G E 19 F 17  3 A 10 7 4 8 18 4 B D 9 H 10 9 2 25 3 G E 7
Done

19. Example 2

20. Dijkstra's Shortest Path Algorithm
Find shortest path from s to t. 2 24 3 9 s 18 14 2 6 6 4 30 19 11 15 5 5 6 20 16 t 7 44

21. Dijkstra's Shortest Path Algorithm
PQ = { s, 2, 3, 4, 5, 6, 7, t }   2 24 3 9 s 18 14  2 6 6  4 30  19 11 15 5 5 6 20 16 t 7 44 
distance label 

22. Dijkstra's Shortest Path Algorithm
PQ = { s, 2, 3, 4, 5, 6, 7, t }
delmin   2 24 3 9 s 18 14  2 6 6  30  4 19 11 15 5 5 6 20 16 t 7 44 
distance label 

23. Dijkstra's Shortest Path Algorithm
PQ = { 2, 3, 4, 5, 6, 7, t }
decrease key   X 9 2 24 3 9 s 18 14  X 14 2 6 6  4 30  19 11 15 5 5 6 20 16 t 7 44 
distance label  15 X

24. Dijkstra's Shortest Path Algorithm
PQ = { 2, 3, 4, 5, 6, 7, t }
delmin   X 9 2 24 3 9 s 18 14  X 14 2 6 6  4 30  19 11 15 5 5 6 20 16 t 7 44 
distance label  15 X

25. Dijkstra's Shortest Path Algorithm
PQ = { 3, 4, 5, 6, 7, t }   X 9 2 24 3 9 s 18 14  X 14 2 6 6  30  4 19 11 15 5 5 6 20 16 t 7 44   15 X

26. Dijkstra's Shortest Path Algorithm
PQ = { 3, 4, 5, 6, 7, t }
decrease key  X 33  X 9 2 24 3 9 s 18 14  X 14 2 6 6   4 30 19 11 15 5 5 6 20 16 t 7 44   15 X

27. Dijkstra's Shortest Path Algorithm
PQ = { 3, 4, 5, 6, 7, t }  X 33  X 9 2 24 3 9
delmin s 18 14  X 14 2 6 6   4 30 19 11 15 5 5 6 20 16 t 7 44   15 X

28. Dijkstra's Shortest Path Algorithm
PQ = { 3, 4, 5, 7, t } 32  X 33 X  X 9 2 24 3 9 s 18 14  X 14 2 6 6  44 30  X 4 19 11 15 5 5 6 20 16 t 7 44   15 X

29. Dijkstra's Shortest Path Algorithm
PQ = { 3, 4, 5, 7, t } 32  X 33 X  X 9 2 24 3 9 s 18 14  X 14 2 6 6  44 30  X 4 19 11 15 5 5 6 20 16 t 7 44   15
delmin X

30. Dijkstra's Shortest Path Algorithm
PQ = { 3, 4, 5, t } 32  X 33 X  X 9 2 24 3 9 s 18 14  X 14 2 6 6  44 X 35  X 4 30 19 11 15 5 5 6 20 16 t 7 44 59   15 X X

31. Dijkstra's Shortest Path Algorithm
PQ = { 3, 4, 5, t }
delmin 32  X 33 X  X 9 2 24 3 9 s 18 14  X 14 2 6 6  44 X 35 4 30  X 19 11 15 5 5 6 20 16 t 7 44 59   15 X X

32. Dijkstra's Shortest Path Algorithm
PQ = { 4, 5, t } 32  X 33 X  X 9 2 24 3 9 s 18 14  X 14 2 6 6  44 X 35 X 34 4 30  X 19 11 15 5 5 6 20 16 t 7 44 51 59   15 X X X

33. Dijkstra's Shortest Path Algorithm
PQ = { 4, 5, t } 32  X 33 X  X 9 2 24 3 9 s 18 14  X 14 2 6 6  44 X 35 X 34 30  X 4 19 11 15 5 5 6 20
delmin 16 t 7 44 51 59   15 X X X

34. Dijkstra's Shortest Path Algorithm
PQ = { 4, t } 32  X 33 X  X 9 2 24 3 9 s 18 14  X 14 2 6 6 45  44 X 35 X 34 X 30  X 4 19 11 15 5 5 6 20 16 t 7 44 50 51 X 59   15 X X X

35. Dijkstra's Shortest Path Algorithm
PQ = { 4, t } 32  X 33 X  X 9 2 24 3 9 s 18 14  X 14 2 6 6 45  44 X 35 X 34 X 30  X 4 19 11 15 5
delmin 5 6 20 16 t 7 44 50 51 X 59   15 X X X

36. Dijkstra's Shortest Path Algorithm
PQ = { t } 32  X 33 X  X 9 2 24 3 9 s 18 14  X 14 2 6 6 45  44 X 35 X 34 X 30  X 4 19 11 15 5 5 6 20 16 t 7 44 50 51 X 59   15 X X X

37. Dijkstra's Shortest Path Algorithm
PQ = { t } 32  X 33 X  X 9 2 24 3 9 s 18 14  X 14 2 6 6 45  44 X 35 X 34 X 30  X 4 19 11 15 5 5 6 20 16 t 7 44
delmin 50 51 X 59   15 X X X

38. Dijkstra's Shortest Path Algorithm
S = { s, 2, 3, 4, 5, 6, 7, t }
PQ = { } 32  X 33 X  X 9 2 24 3 9 s 18 14  X 14 2 6 6 45  44 X 35 X 34 X  X 4 30 19 11 15 5 5 6 20 16 t 7 44 50 51 X 59   15 X X X

39. Dijkstra's Shortest Path Algorithm
S = { s, 2, 3, 4, 5, 6, 7, t }
PQ = { } 32  X 33 X  X 9 2 24 3 9 s 18 14  X 14 2 6 6 45  44 X 35 X 34 X  X 4 30 19 11 15 5 5 6 20 16 t 7 44 50 51 X 59   15 X X X