3.5. Constructing the Minimum Cost Spanning Tree

Try these first

1. 1.

   What is a spanning tree?

   Hint

   Think about the definition of a tree in general.

2. 2.

   What does Prim's algorithm aim to achieve?

   Hint

   Consider the words 'minimum cost' and 'spanning tree'.

3. 3.

   What is Prim's algorithm primarily used for?

   • Finding shortest paths
   • Constructing minimum cost spanning trees
   • Sorting data

   Hint

   Think about what it means to connect every vertex at the lowest cost.

4. 4.

   True or False: In Prim's algorithm, you can revisit edges once they have been added to the spanning tree.

   • True
   • False

   Hint

   Consider the definition of a tree.

5. 5.

   Given a weighted graph with eight vertices and various edge weights, describe how Prim's algorithm progresses step-by-step starting at any chosen vertex.

   Hint

   Keep track of the edges and their cumulative total weight.

6. 6.

   How would the minimum spanning tree change if some of the edges had the same weight? Discuss the implications on Prim's algorithm.

   Hint

   Reflect on what it means for edges to have equal weights.