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Shortest Path from G to C Using Dijkstra’s Algorithm

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. 1. 5. 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.

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Shortest Path from G to C Using Dijkstra’s Algorithm

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  1. Shortest Path from G to C Using Dijkstra’s Algorithm HamidBehravan 2 B C 1 3 2 6 3 4 4 D E F A 1 5 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 Algorithm 2 B C 1 3 2 6 3 4 4 D E F A 1 5 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 Algorithm 2 B C 1 3 2 6 3 4 4 D E F A 1 5 2 5 G H 5 0 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 Algorithm 2 B C 1 3 2 6 3 4 4 D E F A 1 5 2 5 G H 5 0 Unsolved Node Solved Node Identify all unsolved node connected to any solved node.

  5. Shortest Path from G to C Using Dijkstra’s Algorithm 2 B C 1 3 2 6 3 4 4 D E F A 1 5 2 5 G H 5 0 Unsolved Node Solved Node Identify all unsolved node connected to any solved node.

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

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

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

  13. Shortest Path from G to C Using Dijkstra’s Algorithm 3 2 B C 3 1 2 6 4 4 D E F A 2 3 5 1 5 2 5 G H 0 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 Algorithm 3 2 B C 3 1 2 6 4 4 D E F A 2 3 5 1 5 2 5 G H 0 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 Algorithm 3 2 B C 3 1 2 6 4 4 D E F A 2 3 5 1 5 2 5 G H 0 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 Algorithm 3 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 1 5 0+5=5 2 5 G H 5 0+5=5 0 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 Algorithm 3 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 1 5 0+5=5 2 5 G H 5 0+5=5 0 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 Algorithm 3 5 2 B C 3 1 2 6 4 4 D E F A 2 3 5 1 5 2 5 G H 0 Unsolved Node Solved Node The Shortest Root to C is:

  19. Shortest Path from G to C Using Dijkstra’s Algorithm 3 5 2 B C 3 1 2 6 4 4 D E F A 2 3 5 1 5 2 5 G H 0 Unsolved Node Solved Node The Shortest Root to C is: G – A – B - C

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