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

Now T contains {1, 2, 0}. Vertex 6 is the one in V-T with the smallest cost, so add 6 to T, as shown in
Figure 25.15 and update the cost and parent for vertices in V-T and adjacent to 6 if applicable.
Figure 25.15
Now vertices {1, 2, 0, 6} are in set T.
2
T
5
8
1
9
10
5
6
8
3
8
4
cost
6 0 5 10 10 8
0 1 2 3 4 5 6
parent
1
2
7
5
2 -1 1 1 0 1
0
4
5
0 1 2 3 4 5 6
(a)
(b)
Now T contains {1, 2, 0, 6}. Vertex 3 or 5 is is the one in V-T with the smallest cost. You may add
either 3 or 5 into T. Let us add 3 to T, as shown in Figure 25.16 and update the cost and parent for vertices
in V-T and adjacent to 3 if applicable. cost[4] is now updated to 18 and its parent is set to 3.
2
5
T
8
1
9
10
5
6
8
3
8
4
cost
6 0 5 10 18 10 8
0 1 2 3 4 5 6
parent
1
2
7
5
2 -1 1 1 3 0 0
0
4
5
0 1 2 3 4 5 6
(a)
(b)
Figure 25.16
Now vertices {1, 2, 0, 6, 3} are in set T.
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