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

Output: MST (a minimum spanning tree)
1 MST minimumSpanningTree()
2 {
3 Let T be a set for the vertices in the spanning tree;
4 Initially, add the starting vertex to T;
5
6 while (size of T < n)
7 {
8 Find u in T and v in V – T with the smallest weight
9 on the edge (u, v), as shown in Figure 25.24;
10 Add v to T and set parent[v] = u;
11 }
12 }
Vertices already in
the spanning tree
T
V - T
Vertices not currently in
the spanning tree
v
u
Figure 25.24
Find a vertex u in T that connects a vertex v in V – T with the
smallest weight.
The algorithm starts by adding the starting vertex into T. It then continuously adds a vertex (say v) from V
– T into T. v is the vertex adjacent to a vertex in T with the smallest weight on the edge. For
example, five edges connect vertices in T and V – T, as shown in Figure 25.y, (u, v) is the
one with the smallest weight. This algorithm can be implemented using priority queues to
achieve the O(|E|log|V|) time complexity. Use Listing 25.6 TestMinimumSpanningTree.cpp
to test your new algorithm.
***25.10 (Alternative version of Dijkstra algorithm) An alternative version of the Dijkstra algorithm
can be described as follows:
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