Question

Apply Dijkstra's algorithm to find the shortest distance from vertex 0 to every other vertex in the graph shown in Figure 1 below. You must show supporting. You need to list the paths and the minimum distances. 

Answer 1

Vertex 0 is selected as the source.

• Relaxing all the outgoing edges from the vertex 0.
  
• Relaxing all the outgoing edges from the vertex 4.
  
  
• Relaxing all the outgoing edges from the vertex 1.
  
  
• Relaxing all the outgoing edges from the vertex 5.
  
  
• Relaxing all the outgoing edges from the vertex 7.
  
  
• Relaxing all the outgoing edges from the vertex 2.
  
  
• Relaxing all the outgoing edges from the vertex 3.
  
  
• Relaxing all the outgoing edges from the vertex 9.
  
  
• Relaxing all the outgoing edges from the vertex 6.
  
  
• Relaxing all the outgoing edges from the vertex 8.
  
  
• Relaxing all the outgoing edges from the vertex 10.
  
  
• All the outgoing edges from vertex 10 has been relaxed. This is the final Single source shortest path(SSSP) tree.
  
  All the edges in orange are part of the SSSP tree.

VERTEX	DISTANCE FROM SOURCE VERTEX 0	SHORTEST PATH FROM THE SOURCE
0	0	0
1	4	0 - 4 - 1
2	5	0 - 4 - 5 - 2
3	7	0 - 4 - 5 - 2 - 3
4	1	0 - 4
5	4	0 - 4 - 5
6	8	0 - 4 - 5 - 9 - 6
7	4	0 - 7
8	8	0 - 7 - 8
9	7	0 - 4 - 5 - 7
10	10	0 - 4 - 5 - 2 - 3 - 10