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Shortest Path from G to C Using Dijkstra’s Algorithm

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Shortest Path from G to C Using Dijkstra’s Algorithm

HamidBehravan

2

B

C

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6

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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.

Shortest Path from G to C Using Dijkstra’s Algorithm

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B

C

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A

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5

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G

H

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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

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B

C

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G

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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.

Shortest Path from G to C Using Dijkstra’s Algorithm

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B

C

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A

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G

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Unsolved Node

Solved Node

Identify all unsolved node connected to any solved node.

Shortest Path from G to C Using Dijkstra’s Algorithm

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B

C

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A

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5

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G

H

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Unsolved Node

Solved Node

Identify all unsolved node connected to any solved node.

Shortest Path from G to C Using Dijkstra’s Algorithm

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B

C

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E

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A

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5

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G

H

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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

Shortest Path from G to C Using Dijkstra’s Algorithm

2

B

C

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F

A

2

2

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0+5

1

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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

Shortest Path from G to C Using Dijkstra’s Algorithm

2

B

C

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A

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2

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0+5

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0+2

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G

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0+5

0

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Unsolved Node

Solved Node

Choose the smallest Node Distance

Shortest Path from G to C Using Dijkstra’s Algorithm

2

B

C

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A

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1

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G

H

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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

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A

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5

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G

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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

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2

B

C

1+2=3

3

1

2

6

5

5

3+2=5

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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.

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

Shortest Path from G to C Using Dijkstra’s Algorithm

3

2

B

C

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4

D

E

F

A

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5

1

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G

H

0

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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

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E

F

A

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1

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G

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0

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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

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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.

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.

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.

Shortest Path from G to C Using Dijkstra’s Algorithm

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B

C

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Unsolved Node

Solved Node

The Shortest Root to C is:

Shortest Path from G to C Using Dijkstra’s Algorithm

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B

C

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Unsolved Node

Solved Node

The Shortest Root to C is:

G – A – B - C