1. Shortest Path from G to C Using Dijkstra’s Algorithm
Hamid Behravan 2 B C 1 3 2 6 3 4 4 D E F A 5 1 2 5 G H 5
Unsolved Node
Solved Node
We will be finding the shortest path from origin, G, to the destination, C, using Dijkstra’s Algorithm.

2. Shortest Path from G to C Using Dijkstra’s Algorithm2 B C 1 3 2 6 3 4 4 D E F A 5 1 2 5 G H 5
Unsolved Node
Solved Node
Initialize by displaying the origin as solved node. We labeled it as 0, since it has 0 units from the origin.

3. Shortest Path from G to C Using Dijkstra’s Algorithm2 B C 1 3 2 6 3 4 4 D E F A 5 1 2 5 G H 5
Unsolved Node
Solved Node
Initialize by displaying the origin as solved node. We labeled it as 0, since it has 0 units from the origin.

4. Shortest Path from G to C Using Dijkstra’s Algorithm2 B C 1 3 2 6 3 4 4 D E F A 5 1 2 5 G H 5
Unsolved Node
Solved Node
Identify all unsolved node connected to any solved node.

5. Shortest Path from G to C Using Dijkstra’s Algorithm2 B C 1 3 2 6 3 4 4 D E F A 5 1 2 5 G H 5
Unsolved Node
Solved Node
Identify all unsolved node connected to any solved node.

6. Shortest Path from G to C Using Dijkstra’s Algorithm2 B C 1 3 2 6 3 4 4 D E F A 5 1 2 5 G H 5
Unsolved Node
Solved Node
For each node connecting a solved and unsolved nodes, calculate the candidate distance.
Candidate Distance = Distance to the solved node + Length of arc

7. Shortest Path from G to C Using Dijkstra’s Algorithm2 B C 1 3 2 6 3 5 4 4 D E F A 2 2 5 5
0+5 1
0+2 5 G H
0+5 5
Unsolved Node
Solved Node
For each node connecting a solved and unsolved nodes, calculate the candidate distance.
Candidate Distance = Distance to the solved node + Length of arc

8. Shortest Path from G to C Using Dijkstra’s Algorithm2 B C 1 3 2 6 3 5 4 4 D E F A 2 2 5 5
0+5 1
0+2 5 G H
0+5 5
Unsolved Node
Solved Node
Choose the smallest Node Distance

9. Shortest Path from G to C Using Dijkstra’s Algorithm2 B C 1 3 2 6 3 5 4 4 D E F A 2 2 5 5 1 5 G H
Unsolved Node
Solved Node
Change Node A to solved and labeled it with the candidate distance.

10. Shortest Path from G to C Using Dijkstra’s Algorithm2 B C 1 3 2 6 3 4 4 D E F A 2 5 5 1 2 G H 5
Unsolved Node
Solved Node
Add the arc to arc set
Repeat all these steps until we get to destination node

11. Shortest Path from G to C Using Dijkstra’s Algorithm3 2 B C
1+2=3 3 1 2 6 5 5
3+2=5 4 4 D E F A 2 3 5 5
0+5=5 1 2 5 G H
0+5=5 5
Unsolved Node
Solved Node
Calculate the candidate distance of each connecting arc.

12. Shortest Path from G to C Using Dijkstra’s Algorithm3 2 B C
1+2=3 3 1 2 6 4 4 D E F A 2 3 5 5 1 2 5 G H
Unsolved Node
Solved Node
Choose the smallest Node Distance

13. Shortest Path from G to C Using Dijkstra’s Algorithm3 2 B C 3 1 2 6 4 4 D E F A 2 3 5 5 1 2 5 G H 5
Unsolved Node
Solved Node
Change Node B to solved and labeled it with the candidate distance. Add the arc to the arc set.

14. Shortest Path from G to C Using Dijkstra’s Algorithm3 2 B C 3 1 2 6 4 4 D E F A 2 3 5 5 1 2 5 G H 5
Unsolved Node
Solved Node
We have not reached our destination node, so we will continue.

15. Shortest Path from G to C Using Dijkstra’s Algorithm3 2 B C 3 1 2 6 4 4 D E F A 2 3 5 5 1 2 5 G H 5
Unsolved Node
Solved Node
Identify all unsolved node connected to any solved node. Calculate the candidate distance of each connecting arc.

16. Shortest Path from G to C Using Dijkstra’s Algorithm3 5
3+2=5 B C 2 3 1 2 6
3+2=5
0+5=5 5 4 4 D E F A 2 3 5 5
0+5=5 1 2 5 G H 5
0+5=5 5
Unsolved Node
Solved Node
Identify all unsolved node connected to any solved node. Calculate the candidate distance of each connecting arc.

17. Shortest Path from G to C Using Dijkstra’s Algorithm3 5
3+2=5 B C 2 3 1 2 6
3+2=5
0+5=5 5 4 4 D E F A 2 3 5 5
0+5=5 1 2 5 G H 5
0+5=5 5
Unsolved Node
Solved Node
We have a tie for the smallest candidate distance. If we choose C, then we get to our destination.

18. Shortest Path from G to C Using Dijkstra’s Algorithm3 5 2 B C 3 1 2 6 4 4 D E F A 2 3 5 5 1 2 5 G H
Unsolved Node
Solved Node
The Shortest Root to C is:

19. Shortest Path from G to C Using Dijkstra’s Algorithm3 5 2 B C 3 1 2 6 4 4 D E F A 2 3 5 5 1 2 5 G H
Unsolved Node
Solved Node
The Shortest Root to C is:
G – A – B - C