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

3
4 #include "Tree.h" // Defined in Listing 24.4
5
6 class MST : public Tree
7 {
8 public:
9 // Create an empty MST
10 MST()
11 {
12 }
13
14 // Construct a tree with root, parent, searchOrders,
15 // and total weight
16 MST(int root, vector& parent, vector& searchOrders,
17 double totalWeight) : Tree(root, parent, searchOrders)
18 {
19 this->totalWeight = totalWeight;
20 }
21
22 // Return the total weight of the tree
23 double getTotalWeight()
24 {
25 return totalWeight;
26 }
27
28 private:
29 double totalWeight;
30 };
31 #endif
The getMinimumSpanningTree function was implemented in lines 127–185 in Listing 25.2. The
getMinimumSpanningTree() function picks vertex 0 as the starting vertex and invokes the
getMinimumSpanningTree(0) function to return the MST starting from 0 (line 130).
The getMinimumSpanningTree(startingVertex) function sets cost[startingVertex] to 0 (line
150) and cost[v] to infinity for all other vertices (lines 146-149). It then repeatedly finds the vertex with the
smallest cost in V-T (lines 156-166) and adds it to T (lines 168. After a vertex u is added to T, the cost and
parent for each vertex v in V-T adjacent to u may be adjusted (lines 171-182).
After a new vertex is added to T (line 193), totalWeight is updated (line 169). Once all vertices are
added to T, an instance of MST is created (line 184).
22