1. Shortest Path Solutions
ENGM 631
Shortest Path Solutions

2. Shortest Path 2 7 5 [1] 1 10 [-1] 3 8 6 4 9 (Cost) [External Flow]
(10) 2 7
(6)
(4)
(40)
(1) 5
(4)
(0)
(20)
(2)
(8)
(20)
[1] 1 3
(2) 10
[-1] 8
(2)
(4)
(2)
(12) 6
(10)
(10)
(1)
(3)
(6) 4 9

3. Dijkstra’s Algorithm Initial : let S={s}, s=0
Find an arc k(i,j) that passes from an unsolved node to a solved node such that
Add node j and arc k(i,j) to tree
Add j to solved set S. Let j=I + ck
Go to step 2, repeat until S = set of all nodes

4. Shortest Path 2 7 5 1 10 3 8 6 4 9 [0] [8] (Cost) [s] (10) (6) (4)
(40)
(1) 5
(4)
(0)
(20)
(2)
[0]
[8]
(8)
(20) 1 3
(2) 10 8
(2)
(4)
(2)
(12) 6
(10)
(10)
(1)
(3)
(6) 4 9

5. solved closest length to node length of
Iter nodes unsolved unsolved added shortest path

6. Shortest Path 2 7 5 1 10 3 8 6 4 9 [0] [8] (Cost) [s] (10) (6) (4)
(40)
(1) 5
(4)
(0)
(20)
(2)
[0]
[8]
(8)
(20) 1 3
(2) 10 8
(2)
(4)
(2)
(12) 6
(10)
(10)
(1)
(3)
(6) 4 9

7. Shortest Path 2 7 5 1 10 3 8 6 4 9 [0] [8] [10] [10] (Cost) [s] (10)
(6)
(4)
(40)
(1) 5
(4)
(0)
(20)
(2)
[0]
[8]
(8)
(20) 1 3
(2) 10 8
(2)
(4)
[10]
(2)
(12) 6
(10)
(10)
(1)
(3)
(6) 4 9
[10]

8. Shortest Path 2 7 5 1 10 3 8 6 4 9 [0] [8] [10] (Cost) [s] (10) (6)
(4)
(40)
(1) 5
(4)
(0)
(20)
(2)
[0]
[8]
(8)
(20) 1 3
(2) 10 8
(2)
(4)
(2)
(12) 6
(10)
(10)
(1)
(3)
(6) 4 9
[10]

9. solved closest length to node length of
Iter nodes unsolved unsolved added shortest path

10. Shortest Path 2 7 5 1 10 3 8 6 4 9 [0] [8] [10] [10] (Cost) [s] (10)
(6)
(4)
(40)
(1) 5
(4)
(0)
(20)
(2)
[0]
[8]
(8)
(20) 1 3
(2) 10 8
(2)
(4)
[10]
(2)
(12) 6
(10)
(10)
(1)
(3)
(6) 4 9
[10]

11. solved closest length to node length of
Iter nodes unsolved unsolved added shortest path

12. Shortest Path 2 7 5 1 10 3 8 6 4 9 [12] [0] [8] [10] [10] (Cost) [s]
(10) 2 7
(6)
(4)
(40)
(1) 5
(4)
(0)
(20)
(2)
[0]
[8]
(8)
(20) 1 3
(2) 10 8
(2)
(4)
[10]
(2)
(12) 6
(10)
(10)
(1)
(3)
(6) 4 9
[10]

13. Shortest Path 2 7 5 1 10 3 8 6 4 9 [12] [0] [8] [10] [10] (Cost) [s]
(10) 2 7
(6)
(4)
(1) 5
(4)
(0)
(20)
[0]
[8]
(8)
(20) 1 3 10 8
(2)
(4)
[10]
(2) 6
(10)
(10)
(3) 4 9
[10]

14. solved closest length to node length of
Iter nodes unsolved unsolved added shortest path

15. Shortest Path 2 7 5 1 10 3 8 6 4 9 [12] [0] [8] [10] [10] (Cost) [s]
(10) 2 7
(6)
(4)
(1) 5
(4)
(0)
(20)
[0]
[8]
(8)
(20) 1 3 10 8
(2)
(4)
[10]
(2) 6
(10)
(10)
(3) 4 9
[10]

16. Shortest Path 2 7 5 1 10 3 8 6 4 9 [12] [0] [8] [10] [10] [13] (Cost)
(10) 2 7
(6)
(4)
(1) 5
(4)
(0)
(20)
[0]
[8]
(8)
(20) 1 3 10 8
(2)
(4)
[10]
(2) 6
(10)
(10)
(3) 4 9
[10]
[13]

17. solved closest length to node length of
Iter nodes unsolved unsolved added shortest path

18. Shortest Path 2 7 5 1 10 3 8 6 4 9 [12] [0] [8] [10] [10] [13] (Cost)
(10) 2 7
(6)
(4)
(1) 5
(4)
(0)
(20)
[0]
[8]
(8)
(20) 1 3 10 8
(2)
(4)
[10]
(2) 6
(10)
(10)
(3) 4 9
[10]
[13]

19. Shortest Path 2 7 5 1 10 3 8 6 4 9 [12] [0] [8] [14] [10] [10] [13]
(Cost)
[s]
(10) 2 7
(6)
(4)
(1) 5
(4)
(0)
(20)
[0]
[8]
[14]
(8)
(20) 1 3 10 8
(2)
(4)
[10]
(2) 6
(10)
(10)
(3) 4 9
[10]
[13]

20. Shortest Path 2 7 5 1 10 3 8 6 4 9 [12] [0] [8] [14] [10] [10] [13]
(Cost)
[s]
(10) 2 7
(6)
(4)
(1) 5
(4)
(0)
[0]
[8]
[14]
(8)
(20) 1 3 10 8
(2)
(4)
[10]
(2) 6
(10)
(3) 4 9
[10]
[13]

21. solved closest length to node length of
Iter nodes unsolved unsolved added shortest path

22. Shortest Path 2 7 5 1 10 3 8 6 4 9 [12] [0] [8] [14] [10] [10] [13]
(Cost)
[s]
(10) 2 7
(6)
(4)
(1) 5
(4)
(0)
[0]
[8]
[14]
(8)
(20) 1 3 10 8
(2)
(4)
[10]
(2) 6
(10)
(3) 4 9
[10]
[13]

23. Shortest Path 2 7 5 1 10 3 8 6 4 9 [12] [14] [0] [8] [14] [10] [10]
(Cost)
[s]
(10) 2 7
(6)
[14]
(4)
(1) 5
(4)
(0)
[0]
[8]
[14]
(8)
(20) 1 3 10 8
(2)
(4)
[10]
(2) 6
(10)
(3) 4 9
[10]
[13]

24. Shortest Path 2 7 5 1 10 3 8 6 4 9 [12] [14] [0] [8] [14] [10] [10]
(Cost)
[s]
(10) 2 7
[14]
(4)
(1) 5
(4)
(0)
[0]
[8]
[14]
(8)
(20) 1 3 10 8
(2)
(4)
[10]
(2) 6
(10)
(3) 4 9
[10]
[13]

25. solved closest length to node length of
Iter nodes unsolved unsolved added shortest path

26. Shortest Path 2 7 5 1 10 3 8 6 4 9 [12] [14] [0] [8] [14] [10] [10]
(Cost)
[s]
(10) 2 7
[14]
(4)
(1) 5
(4)
(0)
[0]
[8]
[14]
(8)
(20) 1 3 10 8
(2)
(4)
[10]
(2) 6
(10)
(3) 4 9
[10]
[13]

27. Shortest Path 2 7 5 1 10 3 8 6 4 9 [12] [14] [0] [8] [14] [15] [10]
(Cost)
[s]
(10) 2 7
[14]
(4)
(1) 5
(4)
(0)
[0]
[8]
[14]
(8)
(20) 1 3 10 8
[15]
(2)
(4)
[10]
(2) 6
(10)
(3) 4 9
[10]
[13]

28. Shortest Path 2 7 5 1 10 3 8 6 4 9 [12] [14] [0] [8] [14] [15] [10]
(Cost)
[s]
(10) 2 7
[14]
(4) 5
(4)
(0)
[0]
[8]
[14]
(8) 1 3 10 8
[15]
(2)
(4)
[10]
(2) 6
(10)
(3) 4 9
[10]
[13]

29. solved closest length to node length of
Iter nodes unsolved unsolved added shortest path

30. Shortest Path 2 7 5 1 10 3 8 6 4 9 [12] [18] [14] [0] [8] [14] [15]
(Cost)
[s]
(10)
[18] 2 7
[14]
(4) 5
(4)
(0)
[0]
[8]
[14]
(8) 1 3 10 8
[15]
(2)
(4)
[10]
(2) 6
(10)
(3) 4 9
[10]
[13]

31. Shortest Path 2 7 5 1 10 3 8 6 4 9 [12] [18] [14] [0] [8] [14] [15]
(Cost)
[s]
[18] 2 7
[14]
(4) 5
(4)
(0)
[0]
[8]
[14]
(8) 1 3 10 8
[15]
(2)
(4)
[10]
(2) 6
(10)
(3) 4 9
[10]
[13]

32. solved closest length to node length of
Iter nodes unsolved unsolved added shortest path