CHAPTER 25 Weighted Graphs and Applications Objectives • To ...

(a) Before moving u to T
(b) After moving u to T
Let us illustrate Dijkstra’s algorithm using the graph in Figure 25.10a. Suppose the source vertex is 1.
Therefore, cost[1] = 0 and parent[1] = -1, and the costs for all other vertices are initially , as
shown in Figure 25.10b.
Figure 25.10
The algorithm will find all shortest paths from source vertex 1.
2
5
8
1
9
10
5
6
8
3
8
4
cost
0
0 1 2 3 4 5 6
parent
1
2
7
5
-1
0
4
5
0 1 2 3 4 5 6
(a)
(b)
Now T contains {1}. Vertex 1 is the one in V-T with the smallest cost, so add 1 to T, as shown in
Figure 25.12 and update the cost and parent for vertices in V-T and adjacent to 1 if applicable. The cost
and parent for vertices 0, 2, 3, and 6 are now updated, as shown in Figure 25.12b.
Figure 25.12
Now vertex 1 is in set T.
2
5
8
T
1
9
10
5
6
8
3
8
4
cost
8 0 5 10 9
0 1 2 3 4 5 6
parent
1
2
7
5
1 -1 1 1 1
0
4
5
0 1 2 3 4 5 6
(a)
(b)
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