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.
Shortest Path from G to C Using Dijkstra’s Algorithm 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 Initialize by displaying the origin as solved node. We labeled it as 0, since it has 0 units from the origin.
Shortest Path from G to C Using Dijkstra’s Algorithm 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 Initialize by displaying the origin as solved node. We labeled it as 0, since it has 0 units from the origin.
Shortest Path from G to C Using Dijkstra’s Algorithm 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 Identify all unsolved node connected to any solved node.
Shortest Path from G to C Using Dijkstra’s Algorithm 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 Identify all unsolved node connected to any solved node.
Shortest Path from G to C Using Dijkstra’s Algorithm 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 For each node connecting a solved and unsolved nodes, calculate the candidate distance. Candidate Distance = Distance to the solved node + Length of arc
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 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
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 5 0+5 1 0+2 5 G H 0+5 5 Unsolved Node Solved Node Choose the smallest Node Distance
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 5 1 5 G H Unsolved Node Solved Node Change Node A to solved and labeled it with the candidate distance.
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 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
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 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.
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 5 1 2 5 G H Unsolved Node Solved Node Choose the smallest Node Distance
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 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.
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 5 1 2 5 G H 5 Unsolved Node Solved Node We have not reached our destination node, so we will continue.
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 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.
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 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.
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 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.
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 5 1 2 5 G H Unsolved Node Solved Node The Shortest Root to C is:
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 5 1 2 5 G H Unsolved Node Solved Node The Shortest Root to C is: G – A – B - C