4.1.2. Executing Prim's Algorithm

Try these first

1. 1.

   What does a minimum spanning tree do?

   Hint

   Think about the purpose of connecting nodes efficiently.

2. 2.

   Define edge weight in the context of graphs.

   Hint

   What quantity is associated with each edge?

3. 3.

   What is Prim's algorithm used for?

   • Finding shortest path
   • Creating a minimum spanning tree
   • Sorting elements

   Hint

   Think about tree structures in graphs.

4. 4.

   True or False: Prim's algorithm can be executed starting from any vertex in the graph.

   • True
   • False

   Hint

   Consider starting points in a graph.

5. 5.

   Given a graph with vertices and weighted edges, execute Prim's algorithm starting from vertex A and illustrate the tree formed step-by-step.

   Hint

   Keep track of the distances for each vertex through the process.

6. 6.

   Analyze a scenario where edge weights are not unique. Discuss how Prim's would select edges differently if multiple edges had the same weight.

   Hint

   Consider how selections could produce various trees.